SYNTHESIS AND CHARACTERIZATION OF TRANSITION METAL 
DICHALCOGENIDE HETEROSTRUCTURES 
 
 
 
 
 
 
 
 
 
 
 
 
by 
AARON M. MILLER 
 
 
 
 
 
 
 
A DISSERTATION 
 
Presented to the Department of Chemistry and Biochemistry  and the 
Division of Graduate Studies of the University of Oregon 
in partial fulfillment of the requirements for the degree of 
Doctor of Philosophy 
 December 2022 
DISSERTATION APPROVAL PAGE 
 
Student: Aaron M. Miller 
 
Title: Synthesis and Characterization of Transition Metal 
Dichalcogenide Heterostructures  
 
This dissertation has been accepted and approved in partial 
fulfillment of the requirements for the Doctor of Philosophy degree in 
the Department of Chemistry and Biochemistry by: 
 
Prof. Carl Brozek   Chairperson 
Prof. David C. Johnson  Advisor 
Prof. Shannon W. Boettcher Core Member 
Prof. Eric Corwin   Institutional Representative 
 
and  
 
Krista Chronister   Vice Provost for Graduate Studies  
 
 
Original approval signatures are on file with the University of Oregon 
Division of Graduate Studies.  
 
Degree awarded December 2022 
  
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
© 2022 Aaron M. Miller 
 3 
DISSERTATION ABSTRACT 
 
Aaron M. Miller 
 
Doctor of Philosophy 
 
Department of Chemistry & Biochemistry 
 
December 2022 
 
Title: SYNTHESIS AND CHARACTERIZATION OF TRANSITION METAL 
DICHALCOGENIDE HETEROSTRUCTURES 
 
Synthesis of new materials drives technological advances, but the 
ability to consistently predict and synthesize a material with specific 
properties remains unrealized, especially for metastable materials. Using 
the modulated elemental reactants (MER) method provides additional 
experimental parameters that can be used to drive the reaction towards 
formation of the desired product. This work leverages the MER synthetic 
approach to study a variety of transition metal dichalcogenide (TMD) thin 
films and heterostructures based on TMD’s.  
This work begins with an overview of conventional synthetic 
approaches used to grow TMD thin films – highlighting the advantages and 
disadvantages of each technique, along with key reaction steps and 
examples of typical reaction conditions. After this introductory section, a 
method to extract the maximum possible quantity of structural 
information from x-ray diffraction patterns containing Laue oscillations is 
presented. Next, an automated system to measure the temperature-
dependent electrical resistivity and Hall Effect for thin film samples, which 
is utilized in subsequent experimental chapters to characterize electrical 
transport properties, is discussed.  
The latter half of this dissertation contains several experimental 
 4 
synthetic investigations of TMD thin film and TMD heterostructure 
systems leveraging the MER synthetic method – including synthesis and 
characterization of a family of [(PbSe)1+δ]4[TiSe2]4 isomers, a novel 
compound (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) containing metallic 1T-
MoSe2, and a metastable heterostructure based on intergrowths of 
crystalline TiSe2 and amorphous Si layers.  
 
 5 
CURRICULUM VITAE 
 
NAME OF AUTHOR: Aaron M. Miller 
 
GRADUATE AND UNDERGRADUATE SCHOOLS ATTENDED: 
 
University of Oregon, Eugene, OR 
Gustavus Adolphus College, St. Peter, MN 
 
DEGREES AWARDED: 
 
Doctor of Philosophy, Chemistry, 2021, University of Oregon 
Master of Science, Chemistry, 2020, University of Oregon 
Bachelor of Arts, Chemistry, ACS Certified, 2018, Gustavus Adolphus 
College 
 
AREAS OF SPECIAL INTEREST: 
 
Materials Science  
Thin Film Deposition  
Materials Characterization 
Process Control 
 
PROFESSIONAL EXPERIENCE: 
Research Assistant, D. C. Johnson Research Group, University of 
Oregon, 2019 - 2022 
Research Assistant, B. O’Brien Research Group, Gustavus Adolphus 
College, 2016 – 2018 
Statistics and Metrology Intern, PQI Inc., 2017-2017 
 
PUBLICATIONS: 
 
Miller, A.M.; Johnson, D.C. Challenges in synthesis of 
heterostructures. J. Mater. Chem C. 2022. 10, 6546-6562 DOI: 
10.1039/D2TC00324D 
 
Miller, A.M.; Lemon, M.; Choffel, M.A.; Rich, S.R.; Harvel, F.; Johnson, 
D.C. Extracting information from X-ray diffraction patterns containing 
Laue oscillations. Zeitschrift fur̈  Naturforschung B. 2022. 77(4-5)b, 313-
 6 
322. DOI: 10.1515/znb-2022-0020 
 
Choffel, M.A.; Gannon, R.N.; Göhler, F.; Miller, A.M.; Medlin, D.L.; 
Seyller, T.; Johnson, D.C. Synthesis and Electrical Properties of a New 
Compound (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) Containing Metallic 1T-
MoSe2. Chem Mater. 2021, 33, 16, 6403-6411. 
10.1021/acs.chemmater.1c01623 
 
Miller, A.M.; Hamann, D.M.; Hadland, E.C.; Johnson, D.C. 
Investigating the Formation of MoSe2 and TiSe2 Films from Artificially 
Layered Precursors. Inorg. Chem. 2020, 59 (17), 12536-44. 
10.1021/acs.inorgchem.0c01416  
 
Hamann, D.M.; Bauers, S.R, Miller, A.M.; Ditto, J.; Moore, D.B.; 
Johnson, D.C. Synthesis and Characterization of [(PbSe)1+δ]4[TiSe2]4 
Isomers. Inorg. Chem, 2020, 59 (15), 10928-37. 
doi.org/10.1021/acs.inorgchem.0c01416  
 
LeRoy, M.A.; Mroz, A.M.; Mancuso, J.L.; Miller, A.M.; Van Cleve, A.; 
Check, C.; Heinz, H.; Hendon, C.H.; Brozek, C.K. Post-Synthetic 
Modification of Ionic Liquids Using Ligand-Exchange and Redox 
Coordination Chemistry. J. Mater. Chem. A., 2020, 8, 22674-22685. 
doi.org/10.1039/D0TA06195F 
 
 7 
ACKNOWLEDGMENTS 
 
I would like to acknowledge the numerous people who have 
supported me throughout my graduate school journey – you have all been 
an essential part of my success at UO and I will be forever grateful for your 
role in ensuring that I had the energy, willpower, and/or knowledge to 
continue to make progress toward my thesis. I need to begin by expressing 
my gratitude for my wonderful advisor, Dr. David C. Johnson, who let me 
work in his research lab, offered me constant guidance and advice on 
research challenges, and continued to push me to grow as a critical 
thinker, chemist, and materials scientist throughout my time at UO. I also 
need to thank my colleagues, Dr. Danielle Hamann, Dr. Renae Gannon, 
Dr. Marisa Choffel, Mellie Lemon, Hannah Blackwood, Sarah Rich, Fischer 
Harvel, and Celsey Price. My labmates were instrumental in helping me 
succeed, especially during challenging times when equipment issues and 
pandemic-related supply chain problems interfered with research. 
Additionally, I need to acknowledge the efforts of the previous Dave 
Johnson lab members, without which I would’ve never been able to pursue 
the topics discussed in my thesis – we go forwards on the shoulders of 
those who came before us.  
I also need to acknowledge the CAMCOR staff members and UO 
Technical Services Administration (TSA) for your support of our lab. 
Specifically, Steve Weimholt, Jeffrey Garman, John Boosinger, and Cliff 
Dax were crucial in helping to repair broken equipment and fabricate 
custom parts for our lab. Your willingness to share your knowledge and 
perspective and work on the revolving-door array of broken equipment was 
absolutely vital to my success. 
This research would not be possible without the support of my 
collaborators. Specifically, I’ve learned a lot from Yu Wang and Professor 
Stephen B. Cronin about electrical transport measurements. 
I also need to acknowledge funding from the U.S. Department of 
Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award 
#DE-SC0020095. Chapter IX of this work was additionally supported by 
National Science Foundation under grants DMR-1710214 and 1905185. 
Sandia National Laboratories was instrumental for HAADF-STEM images. 
Sandia National Laboratories is a multi-mission laboratory managed and 
operated by National Technology and Engineering Solutions of Sandia, 
LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. 
Department of Energy’s National Nuclear Security Administration under 
contract DE-NA-0003525. This paper describes objective technical results 
and analysis. Any subjective views or opinions that might be expressed in 
the paper do not necessarily represent the views of the U.S. Department 
of Energy or the United States Government.   
 8 
Thank you to all the past professors, teachers, mentors that have 
taught me and helped form me into the scientist and person I’ve become. 
I’m forever indebted to you for indulging my constant questions and 
curiosity.   
Thanks to my committee members, who always pushed me to keep 
deepening and extending my understanding of science. Thanks to the 
Department of Chemistry staff and faculty for support and guidance.  
Last, but certainly not least, I would have been successful without 
the unconditional love and support from my parents, grandparents, 
relatives, and friends. I love you all. 
 9 
TABLE OF CONTENTS 
Chapter          Page 
 
I. INTRODUCTION ............................................................... 22 
1.1 Dissertation Overview .................................................. 22 
1.2 Brief History of Materials Discovery ............................. 24 
1.3 Bridge ......................................................................... 28 
II. CHALLENGES IN SYNTHESIS  
OF HETEROSTRUCTURES ............................................... 32 
2.1 Introduction ................................................................ 32 
2.2 Direct Reaction of Elements and/or Compounds ......... 38 
2.3 Fluid-assisted Synthesis Techniques ........................... 40 
2.4 Chemical vapor transport (CVT) ................................... 42 
2.5 Chemical vapor deposition (CVD) ................................. 44 
2.6 Micromechanical assembly .......................................... 47 
2.7 Molecular beam epitaxy (MBE) .................................... 51 
2.8 Modulated elemental reactants (MER).......................... 53 
2.9 Conclusion .................................................................. 61 
2.10 Bridge ......................................................................... 67 
III. EXPERIMENTAL METHODS ............................................. 79 
3.1 Synthesis of Layered Precursors with Modulated  
Elemental Reactants ................................................... 79 
3.2 X-Ray Fluorescence and Statistical Process Control ..... 80 
3.3 Structural Characterization Techniques ...................... 83 
3.4 Electrical Characterization Techniques  ....................... 84 
3.5 Bridge ......................................................................... 84 
 
 10 
Chapter          Page 
 
IV. EXTRACTING INFORMATION FROM X-RAY  
DIFFRACTION PATTERNS CONTAINING  
LAUE OSCILLATIONS ...................................................... 87 
4.1 Introduction ................................................................ 87 
 
4.2 X-ray reflectivity (XRR) and Kiessig fringes .................. 89 
4.3 Laue oscillations ......................................................... 93 
4.4 Developing structural models from Kiessig  
Fringes and Laue oscillations  ..................................... 100 
4.5 Conclusions ................................................................ 104 
4.6 Experimental ............................................................... 104 
4.7 Bridge ......................................................................... 106 
V. AUTOMATED TEMPERATURE-DEPENDENT  
ELECTRICAL RESISTIVITY AND HALL EFFECT  
MEASUREMENT SYSTEM ................................................ 111 
5.1 Van der Pauw method ................................................. 111 
5.2 System Overview ......................................................... 114 
5.3 Temperature Stabilization ........................................... 117 
5.4 Electrical Resistivity .................................................... 118 
5.5 Hall Effect ................................................................... 119 
5.6 Bridge ......................................................................... 120 
VI. INVESTIGATING THE FORAMTION OF MOSE2  
AND TISE2 FILMS FROM ARTIFICIALLY  
LAYERED PRECURSORS ................................................. 122 
6.1 Introduction ................................................................ 122 
6.2 Materials and Methods ................................................ 124 
6.3 Results and Discussion ............................................... 125 
6.4 Conclusions ................................................................ 140 
 11 
Chapter          Page 
 
6.5 Bridge ......................................................................... 141 
VII. SYNTHESIS AND CHARACTERIZATION OF SI(TISE2)n 
HETEROSTRUCTURES .................................................... 146  
7.1 Introduction ................................................................ 146 
7.2 Results and Discussion ............................................... 150 
7.3 Conclusion .................................................................. 160 
7.4 Bridge ......................................................................... 161 
VIII. SYNTHESIS AND CHARACTERIZATION OF  
[(PBSE)1+δ]4[TISE2]4 ISOMERS ........................................... 165 
8.1 Introduction ................................................................ 165 
8.2 Materials and Methods ................................................ 167 
8.3 Results and Discussion ............................................... 168 
8.4 Conclusion .................................................................. 190 
8.5 Bridge ......................................................................... 191 
IX. SYNTHESIS AND ELECTRICAL PROPERTIES OF A  
NEW COMPOUND (BISE)0.97(BI2SE3)1.26(BISE)0.97(MOSE2)  
CONTAINING METALLIC 1T-MOSE2 ................................. 198 
9.1 Introduction ................................................................ 198 
9.2 Materials and Methods ................................................ 200 
9.3 Results and Discussion ............................................... 202 
9.4 Conclusion .................................................................. 218 
9.5 Bridge ......................................................................... 219 
X. CONCLUSIONS AND SUMMARY ........................................... 227 
APPENDICES 
A. SUPPORTING INFORMATION FOR CHAPTER VI ................ 230 
 12 
Chapter          Page 
 
B. SUPPORTING INFORMATION FOR CHAPTER VIII ............. 232 
C. SUPPORTING INFORMATION FOR CHAPTER IX ............... 234 
 
  
 13 
LIST OF FIGURES 
 
Figure                                                                                              Page 
 
1.1 Change in impurity concentration in metal with  
Blowing time in Bessemer process and Gilchrist-Thomas  
process. ........................................................................... 25 
2.1 Image showing complexity of Cu interconnect structure  
of a 14 nm logic integrated circuit. ................................... 33 
2.2 The ability to prepare heterostructures by stacking 
2D layers in designed sequences enables preparation 
of 2D electronic devices, such as this hypothetical stack 
of alternating p- and n-type semiconducting layers. ......... 34 
2.3 Representative HAADF-STEM images of six of the  
possible “isomer” .............................................................. 35 
2.4 Schematic depiction of the reaction of elements Pb, Ti,  
and Se to form binary intermediates PbSe and TiSe2, 
and ternary product and misfit layered compound,  
(PbSe)1.18(TiSe2)2. .............................................................. 40 
2.5 Schematic depiction of the evolution of the nucleation 
of crystalline phases during the cooling of a fluid- 
assisted synthesis reaction............................................... 44 
2.6 Schematic depiction of the CVT synthesis of MoS2. ........... 43 
2.7 Schematic depictions of two types of CVD reactors. .......... 45 
2.8 Schematic of MBE reactor ................................................ 51 
2.9 Schematic depiction of two different reaction pathways in  
the reaction between ultra-thin layers of Mo and Se ......... 57 
2.10 Schematic depiction of two sample layering sequences for  
deposition of MER precursors. ......................................... 59 
2.11 Schematic free energy surface for the BiSe-NbSe2 system  
showing some of the possible kinetically stable  
heterostructures containing an equal number of BiSe and  
NbSe2 layers and the thermodynamically stable product  
(BiSe)(NbSe2)1 .................................................................. 62 
3.1 Schematic side-view of the high-vacuum chamber used to 
 
 14 
Figure                                                                                               Page  
 
deposit ultrathin elemental layers to form nanostructured  
precursors. ...................................................................... 81 
3.2 Plots of the measured XRF intensity for Ti and Sn  
using samples that display  
Laue oscillations, allowing for the determination of the  
integral number of crystalline unit cells ........................... 82 
4.1 Experimental X-ray reflectivity pattern of a 50.10(5) nm  
TiSe2 film.. ...................................................................... 90 
4.2 Simulated reflectivity patterns from a 30.19 nm TiSe2  
film with different amounts of interfacial roughness.. ...... 92 
4.3 Simulated XRR patterns of TiO2 and TiSe2 films .............. 93 
4.4 Experimental XRR and XRD patterns of a  
79-layer crystalline TiSe2 film. ......................................... 94 
4.5 Comparison of the experimental Laue oscillations  
with that calculated from the Laue interference  
function and a simulation that includes reflectivity using  
the BedeREFS simulation software.................................. 97 
4.6 Experimental diffraction data of a  
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) heterostructure. ....... 98 
4.7 Simulated XRR patterns of a 50-layers TiSe2 film on a  
Si substrate illustrating how the roughness affects the  
symmetry of the satellite reflections around the Bragg  
reflections.. ..................................................................... 99 
4.8 Simulations of diffraction patterns from different  
distributions of coherently diffracting domains. ............... 100 
4.9 Experimental XRR (gray) and XRD (black) patterns of  
a 271.0(2) Å thick crystalline FexV1–xSe2 film and  
simulated XRR pattern (teal) for a 267.9 Å thick  
FexV1–xSe2 film consisting of 44 unit cells. ....................... 102 
4.10 Experimental XRR (grey) and XRD (black) patterns of a 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) heterostructure  
annealed at 350 °C ......................................................... 103 
5.1 Top-down schematic of thin film sample holder with  
soldered In contacts in each of the four corners of the  
sample’s top Hall Cross.  .................................................. 112 
 
 
 15 
Figure                                                                                               Page  
 
5.2 Schematic overview of the structure for the 
automated system’s code. ................................................ 116 
6.1 XRR and XRD patterns from an annealing study of an  
as-deposited Mo|Se precursor. ......................................... 126 
6.2 Grazing incidence in-plane diffraction of a MoSe2 film  
after being annealed at 650 °C for 60 min. ....................... 129 
6.3 MoSe2 crystal quality as determined by specular  
diffraction reflection intensity and peak width graphed  
vs the composition of the Mo|Se precursor. ..................... 129 
6.4 XRR and XRD patterns from an annealing study of an  
as-deposited Ti|Se precursor with a starting composition  
of 1:2.24 (Ti / Se). ............................................................ 132 
6.5 Representative specular and in-plane XRD  
patterns of Ti|Se thin films with various compositions. .... 135 
6.6 Line widths (fwhm) of the 110 reflection in the in-plane  
XRD pattern (top) and 001 reflection in the specular XRD  
pattern (middle) and 001 reflection net area (bottom) as  
a function of precursor composition. ................................ 138 
6.7 Experimental specular XRD patterns (red) for the  
highest quality annealed TiSe2 films overlaid with the  
theoretical Laue oscillations expected for n layers of  
TiSe2 (black). .................................................................... 138 
6.8 Proposed atomic-level pictures for the evolution of  
Mo|Se and Ti|Se precursors as they are annealed  
to form crystalline MoSe2 and TiSe2. ................................. 140 
7.1 Schematic depiction of the reaction of a layered 
(Ti|Se)4|Si precursor to form a  
(TiSe2)4|Si heterostructure ............................................... 149 
7.2 XRR (left) and XRD (right) patterns for the n = 4, 7,  
and 9 Si(TiSe2)n heterostructures collected  
immediately after deposition and prior to annealing. ........ 151 
7.3 XRR and XRD patterns for the n = 4, 7, and 9 Si(TiSe2)n 
heterostructures collected after  
annealing at 350 °C for 30 m. .......................................... 153 
 16 
Figure                                                                                               Page 
 
7.4 Plot of c-axis lattice parameter vs n for the three  
films shown in Figure 7.3 ................................................. 154 
7.5 Representative grazing-incidence in-plane x-ray  
diffraction patterns for as-deposited and annealed  
(TiSe2)nSi heterostructure. ................................................ 154 
7.6 Simulated x-ray reflectivity (XRR) patterns for  
(TiSe2)n|Si heterostructures with  
“perfect” nanoarchitecture ................................................ 155 
7.7 Schematic depiction of a n = 4 heterostructure,  
depicting 3 out of the 7 actual RU’s. ................................. 157 
7.8 Simulated x-ray reflectivity (XRR) patterns for  
(TiSe2)n|Si heterostructures with variance in the  
thickness of each a-Si layer.............................................. 158 
7.9 Schematic depiction of a n = 4 heterostructure,  
depicting 3 out of the 7 actual RU’s. ................................. 159 
7.10 Simulated x-ray reflectivity (XRR) patterns for  
(TiSe2)n|Si heterostructures with variance in the  
number of TiSe2 layers crystallized in each RU. ................ 160 
 
8.1 Representative as-deposited XRR and XRD for a  
211211 isomer demonstrating behavior observed in all  
of the [(PbSe)1+δ]4(TiSe2)4 isomer heterostructures. ............ 169 
8.2 Experimental and simulated XRR patterns for the  
3212 structural isomer. ................................................... 173 
8.3 Schematic representation of the variation of electron  
density through a unit cell for each of the  
[(PbSe)1+δ]4(TiSe2)4 isomers. ............................................... 175 
8.4 X-ray reflectivity patterns (in color) shown against  
simulated patterns created using models of the targeted  
isomers (in black) described in Figure 8.3. ........................ 177 
8.5 Specular and in-plane XRD patterns of the  
[(PbSe)1+δ]4(TiSe2)4 structural isomers. .............................. 179 
8.6 HAADF-STEM image of the 44 [(PbSe)1+δ]4(TiSe2)4  
structural isomer showing the entire film from substrate  
 17 
Figure                                                                                               Page 
 
to surface. ........................................................................ 181 
8.7 HAADF-STEM images of each isomer heterostructure  
highlighting the formation of the targeted  
nanoarchitecture, sharp interfaces between constituents, 
and rotational misregistration between layers. .................. 182 
8.8 Atomistic picture demonstrating the initial  
crystallization in the isomers and a snapshot  
showing the movement of atoms and further crystal  
growth upon annealing. ................................................... 184 
8.9 Temperature-dependent resistivity of six  
[(PbSe)1+δ]4(TiSe2)4 isomer heterostructures, with both  
measured and normalized values. .................................... 186 
8.10 Temperature-dependent carrier concentration and 
mobility) of six [(PbSe)1+δ]4(TiSe2)4 isomer  
heterostructures. ............................................................. 188 
8.11 Room-temperature Seebeck coefficients for each of the 
[(PbSe)1+δ]4(TiSe2)4 isomer heterostructures. ...................... 189 
8.12 Schematic demonstrating charge donation occurring  
in isomers containing different numbers of buried  
interfaces. ........................................................................ 190 
9.1 XRR and specular X-ray diffraction and representative  
in-plane X-ray diffraction patterns of the samples after  
annealing to 350 °C. ........................................................ 205 
9.2 Amounts of Bi and Mo in the samples compared to  
the estimated amounts to form [(Bi2Se3)1+y]2(MoSe2)  
and (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) ............................. 207 
9.3 XRR and specular XRD patterns and in-plane XRD  
patterns of sample 1 as a function of temperature. ........... 209 
9.4 Representative HAADF-STEM image of the 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) heterostructure  
annealed to 350 °C. .......................................................... 210 
9.5 HAADF-STEM image of the  
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) heterostructure with  
zone axes labeled.. ........................................................... 212 
 18 
Figure                                                                                               Page 
 
9.6 HAADF-STEM images, which show a region of  
(a) 1T-MoSe2 and (b) 2H-MoSe2. ....................................... 213 
9.7 XPS analysis of the (a) Mo 3d, (b) Se 3d, and (c) Bi 5d  
core levels. ....................................................................... 215 
9.8 Temperature-dependent resistivity data of 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) samples are plotted  
as a function of temperature for comparison with the  
(BiSe)0.97(MoSe2) heterostructures. ................................... 216 
9.9 Temperature-dependent Hall data plotted as a function 
of temperature for (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2). .... 217 
A.1 XRR of Ti|Se annealing study showing evolution of  
film thickness and roughness as energy is applied  
to the system. .................................................................. 230 
A.2 Specular and in-plane XRD patterns for additional  
Ti|Se precursors annealed at 350°C showing the  
influence of precursor composition on structure. .............. 230 
A.3 XRR patterns for various Ti|Se precursors annealed at  
350 °C showing the variation in roughness and loss of  
layers as a function of stoichiometry. ............................... 231 
A.4 Experimental and simulated XRR patterns  
demonstrating effect of oxide growth. Based on the  
amount of excess material in each film, the  
annealed films developed either a thin (~9 Å) or  
thick (~60 Å) oxide layer. .................................................. 231 
B.1 Representative as-deposited XRR patterns  
demonstrating the initial layering and rearrangement  
occurring in the sample before annealing occurs. ............. 232 
B.2 Representative grazing incidence in-plane diffraction  
of an as-deposited [(PbSe)1+δ]1[TiSe2]1  
heterostructure demonstrating the initial nucleation of  
both PbSe and TiSe2 crystallites before annealing. ............ 233 
B.3 STEM-EDS showing the relative intensity of  
characteristic X-ray signals from Pb and Ti when  
moving down the k=2321 structure. ................................. 233 
 
 19 
Figure                                                                                               Page 
C.1 Electron dispersive x-ray spectroscopy (EDS)  
line profile from substrate to surface of 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2). ................................. 234 
 
  
 20 
LIST OF TABLES 
 
Table                                                                                                 Page 
 
2.1 A Summary of synthetic techniques typically used in the  
synthesis of van der Waal’s heterostructures .................... 64 
 
4.1 Experimental and target atomic areal density for the  
Fe-doped VSe2 and  
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) films as  
determined from XRF measurements ............................... 103 
6.1 Structure and Composition Summary for the  
As-Deposited Ti|Se Precursors ......................................... 132 
6.2 Compositions and Lattice Parameters for Annealed  
Ti|Se Films As Determined from Full Pattern XRD  
Le Bail Fits ...................................................................... 134 
7.1 Structural data extracted from experimental x-ray  
diffraction and x-ray reflectivity patterns for as-deposited  
(Ti|Se)nSi heterostructures............................................... 147 
7.2 Composition data extracted from experimental x-ray  
fluorescence intensities for as-deposited  
(Ti|Se)nSi heterostructures .............................................. 148 
7.3 Structural data extracted from experimental x-ray  
diffraction and x-ray reflectivity patterns for (TiSe2)nSi 
heterostructures annealed at 350 °C ................................ 149 
8.1 Total Atoms/Å2 in Each of the Annealed  
[(PbSe)1+δ]4(TiSe2)4 Isomer Films ........................................ 171 
8.2 Calculated Number of Atoms/Å2 for Each  
Element in the [(PbSe)1+δ]4(TiSe2)4 Isomers  
for Different Film Thicknesses .......................................... 171 
8.3 Parameters Extracted from the XRR Patterns as  
Described in the Text ....................................................... 176 
Table                                                                                                 Page 
 
9.1 Amounts of Material and Repeating Thicknesses  
for Samples Targeting the  
(BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) Nanoarchitecture ......... 203 
B.4 Total Film thickness and repeat layer  
 21 
thickness for representative  
[(PbSe)1+δ]4[TiSe2]4 isomer heterostructures. ...................... 232 
  
 22 
CHAPTER I 
INTRODUCTION 
1.0 Authorship Statement 
This chapter was written for this work alone with no intention of 
publishing it elsewhere. I am the primary author and wrote the following with 
editorial assistance from my advisor, David C. Johnson. 
1.1 Dissertation Overview 
This thesis explores the synthesis and characterization of transition-
metal dichalcogenide (TMD) thin films and TMD heterostructures, created by 
stacking ultrathin layers of 2D materials. The thesis is split into two sections 
– the first presents a comprehensive discussion of each experimental 
technique, along with several chapters that advance existing experimental 
methods. The second half of the work presents experimental studies on 
different TMD material systems, leveraging the advances in experimental 
methods described in the first section to assist in the synthesis and 
characterization of novel TMD heterostructures.  
The opening section, containing Chapters II – V, details the 
experimental methods used to synthesize and characterize thin film samples, 
including a literature review that summarizes current challenges in 
conventional synthetic approaches to 2D heterostructures (Chapter II was 
previously published in the Journal for Materials Chemistry C in 2022).1 The 
following chapter reviews the suite of x-ray characterization techniques that 
are used to elucidate the sample’s structure and composition. Next, Chapter 
IV (previously published in Zeitschrift für Naturforschung B in 2022) contains 
an extensive discussion of the physics involved in x-ray reflectivity diffraction 
experiments and leverages this understanding of the underlying physics to 
show how structural information can be extracted from x-ray diffraction 
patterns containing Laue oscillations.2 The final chapter in the first section of 
this work contains a description of the automated measurement system built 
 23 
and coded by the author, which is used by the Johnson Lab to measure the 
electrical resistivity and Hall effect as a function of temperature for thin film 
samples. 
The final section, Chapters VI – X, presents experimental studies 
exploring various TMD systems, with an emphasis on heterostructures and 
thin films containing titanium and molybdenum diselenide (TiSe2 and MoSe2). 
The opening chapter of this section presents my initial efforts to synthesize 
TMD’s, which could be used as components for more heterostructures with 
more complex nanoarchitecture later. By studying the effect of precursor 
composition on the resulting annealed binary MoSe2 and TiSe2 thin films, we 
were able to conclude that depositing layered precursors with approximately 
15% excess selenium results in high-quality thin films with large crystallite 
sizes and visible Laue oscillations up to the 30th order (Chapter VI was 
previously published in Inorganic Chemistry in 2020).3  
After optimizing the synthesis of binary TMD films, I attempted to grow 
heterostructures using a crystalline and an amorphous component. I 
interleaved few-layer crystalline TiSe2 between layers of amorphous Si of 
varying thickness, resulting in films with a unique combination of a defined 
superlattice, but with the inclusion of a material with a complete lack of 
periodic structure. This chapter describes the initial efforts of the synthetic 
exploration of the TiSe2 + a-Si intergrowth system.  
Next, I studied more complex layering sequences, synthesizing six novel 
isomer heterostructures, making up the six possible combinations of an 
eight-layer-thick unit cell consisting of four PbSe layers and four TiSe2 layers. 
Chapter VIII presents the preparation and characterization of these 
heterostructures. The precursors used in the study were deposited with 
compositions that were far from the desired values, but surprisingly, the 
heterostructures still crystallized with the desired nanoarchitecture. 
Extensive structural modeling was used to understand the complex x-ray 
 24 
reflectivity patterns (previously published in Inorganic Chemistry).4  
The penultimate chapter describes the synthesis and characterization 
of another novel compound (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2). This 
heterostructure was found to contain a significant amount of metallic 1T-
MoSe2 as a result of the increased charge transfer from the two adjacent BiSe 
layers (Chapter IX was previously published in Chemistry of Materials in 
2021).5  
1.2 Brief history of materials discovery 
Materials discovery is a significant factor driving the development of 
new technology. The history of humanity is even discussed through the lens 
of materials discoveries, with eras named after materials that enabled 
significant advances or cultural shifts. Early humans constructed tools and 
weapons from materials they encountered in their environments. 
Archaeological evidence suggests early humans knapped stone into tools and 
sought other materials like bone, feathers, animal skins, and clays for specific 
purposes.6 Copper (Cu) is among the elements that can rarely be found in 
nature in its native state, so it is probable that early humans discovered Cu 
nuggets and began to shape them into basic forms. Shaped Cu artifacts 
dating back to 5000 BCE have been found.7 It is unknown exactly when early 
humans discovered these metals can be heated to make them malleable again 
after work hardening occurs. During re-heating, the metal’s hardness 
increases, and if the Cu-bearing ore or the smelting container contains other 
metals, the resulting alloy can have improved properties. It is likely that alloys 
were initially discovered by accident. Once discovered, it is likely that humans 
enhanced this effect through experimentation. By 3000 BCE, copper-arsenic 
alloys were used for tools and ritual weapons.8,9 It was soon discovered, again 
probably by accident, that alloying Cu with Sn gave a superior alloy, bringing 
about the Bronze Age.10,11 
 Additional advances brought about widespread use of additional 
 25 
metals, ceramics, and cements. At the end of the Middle Ages, advances in 
metalworking resulted in iron alloys with improved properties, bringing about 
the Iron Age. While steel was rarely prepared as an Fe alloy for many years 
prior to the Industrial Revolution, resulting in the “magic” swords known in 
several cultures, there were no known processes that allowed for reproducible 
or industrial-scale production, severely limiting its use.12 The Bessemer 
process, which involves blowing air through molten pig iron to oxidize 
impurities into easily separable slag, was invented in the 1850s. Widespread 
implementation of this process caused the cost of steel production to 
plummet, enabling steel to replace iron as the material of choice in weaponry, 
construction, and manufacturing.13 The development of the basic Bessemer 
(or Thomas-Gilchrist) process in 1879, which used dolomite-based 
((Ca,Mg)CO3) furnace liners, enabled the use of more common phosphorus-
rich iron ores.14 Eventually, both the acidic Bessemer and basic Thomas-
Gilchrist processes were fully understood and optimized, allowing control over 
the concentration of dopants remaining in the alloy, as shown in Figure 1.1. 
Gradual improvements to this process, a variation of which is still universally 
used today, enabled the use of steel and cast iron in complex structures such 
as those in bridges, buildings, ships, trains, and cars.  
Figure 1.1. Change in impurity concentration in hot metal with blowing time 
in the acidic Bessemer process (left) and the basic Gilchrist-Thomas process 
 26 
(right). These processes helped enable industrial-scale manufacturing of 
steels, which marks the beginning of the Industrial Revolution.13,15 
During the nineteenth and twentieth centuries, chemists improved on 
natural polymers, such as gums, horns, or shellac, which had been widely 
utilized in the past, discovering how to prepare man-made polymers. The 
French chemist Henri Braconnot discovered the first semi-synthetic plastic, 
a material he called xyloidine, by treating plant matter with concentrated 
nitric acid. Today, we know that this process converts approximately half of 
the hydroxyl groups (-OH) to nitrate esters (-ONO2) and that xyloidine 
nominally consists of cellulose dinitrate.16,17 Later improvements by German 
chemist Friedrich Schöbein using stronger acidic conditions resulted in more 
conversion of hydroxyl groups, giving a material closer to cellulose trinitrate, 
known as pyroxyline or guncotton.18,19 British inventor Alexander Parkes 
discovered that adding a plasticizer, vegetable oils partially solidified with 
sulfur dichloride, to pyroxyline resulted in a heat-moldable plastic material. 
This became known as Parkesine and was patented in 1865.20,21 Further 
development of these synthetic materials, enabled by chemists thinking about 
materials at the atomic scale and tuning properties by rationally changing the 
atomic or molecular structure of the material, launched the Age of Polymers. 
This brings us to the modern era, the Silicon Age, where electronic 
devices built on Si have become ubiquitous in everyday life. Indeed, it’s nearly 
impossible for individuals to spend a day in a city without interacting with 
this technology. The Silicon Age was launched by the invention of the 
transistor in 1947 by Shockley, Bardeen, and Brattain, who used a 
germanium (Ge) crystal with extremely delicate gold (Au) point contacts to 
build the first working transistor.22 Ge remained the dominant 
semiconducting material until the late 1950s because of its superior 
properties relative to commercially available Si at that time. While Ge was 
constrained in its applications because of its small bandgap - about 0.80 eV 
- it remained the material of choice until the early 1960s due to Si’s higher 
 27 
reactivity.23 Eventually, researchers figured out how to grow Si crystals 
comparable in purity to Ge. Combined with other innovations associated with 
integrated circuit manufacturing, such as the effective and easy to prepare 
SiOx gate dielectrics, the semiconductor industry soon switched their efforts 
to focus their manufacturing efforts on Si-based devices.  
Reducing feature size to increase device density of integrated circuits 
and computational speed has been a major driver for Si technology. Since 
1970, the number of transistors per unit area has doubled approximately 
every two years, a phenomenon known as Moore’s Law.24,25 Maintaining 
Moore’s Law has required overcoming several limiting factors via the inclusion 
of additional materials and elements in the chip design, thereby vastly 
increasing the complexity of these systems. An example is the issue of leakage 
currents through the gate oxide in MOSFET devices. Leakage current due to 
tunnelling becomes a significant factor as the thickness of the gate oxide 
approaches 2 nm.26,27 Since gate capacitance scales inversely with oxide 
thickness and directly with the oxide material’s relative dielectric constant, 
industry developed materials with a larger dielectric constant than SiO2, so-
called “high-κ materials” (first, silicon oxynitride and later, hafnium-based 
gate dielectrics).28–31 Another limiting factor in reducing feature size was the 
integrated circuit’s RC time constant, which increased as device size 
decreased and eventually exceeded the speed of the transistors.32 In 1997, 
IBM shocked the industry when it announced it had successfully replaced the 
industry-standard aluminum interconnects with copper.33,34 The rest of the 
semiconductor industry quickly followed IBM’s lead in using Cu 
interconnects, while also pursuing other “low-κ“ materials, including HF-
treated SiO 352 and lower density materials.  
Current chip designs have feature sizes at the nanometer scale and 
material properties are beginning to no longer scale with dimensions due to 
quantum effects and reduced material dimensionality.36 This thesis focuses 
on approaches to prepare and characterize materials with reduced 
 28 
dimensionality. By advancing our understanding of the fundamental science 
surrounding the preparation, characterization, and structure-property 
relationships of low-dimensional materials, we can better understand how to 
effectively exploit their properties in desired applications.  
1.3 Bridge 
Chapter I contains an unpublished overview of the following 
dissertation. I am the sole author, but had editorial assistance from my 
advisor, David C. Johnson. The following chapter, published in the Journal of 
Materials Chemistry C, continues the discussion above, detailing the 
conventional synthetic methods used to prepare 2D heterostructures and 
thin films, focusing on the advantage and disadvantages to each technique, 
and the advances for each technique that will be required in order to 
synthesize high-quality 2D heterostructures at scale. 
 
 29 
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J. Mater. Chem. C 2022. https://doi.org/10.1039/d2tc00324d. 
(2)  Miller, A. M.; Lemon, M.; Choffel, M. A.; Rich, S. R.; Harvel, F.; Johnson, 
D. C. Extracting Information from X-Ray Diffraction Patterns Containing 
Laue Oscillations. Zeitschrift für Naturforsch. B 2022, 0 (0), 313–322. 
https://doi.org/10.1515/znb-2022-0020. 
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Investigating the Formation of MoSe2and TiSe2 Films from Artificially 
Layered Precursors. Inorg. Chem. 2020, 59 (17), 12536–12544. 
https://doi.org/10.1021/acs.inorgchem.0c01626. 
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Johnson, D. C. Synthesis and Characterization of 
[(PbSe)1+δ]4[TiSe2]4Isomers. Inorg. Chem. 2020, 59 (15), 10928–10937. 
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Seyller, T.; Johnson, D. C. Synthesis and Electrical Properties of a New 
Compound (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) Containing Metallic 
1T-MoSe2. Chem. Mater. 2021, 33 (16), 6403–6411. 
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(8)  Moorey, P. R. S. The Chalcolithic Hoard from Nahal Mishmar, Israel, in 
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Northover, J. P. Tainted Ores and the Rise of Tin Bronzes in Eurasia, c. 
6500 Years Ago. Antiquity 2013, 87 (338), 1030–1045. 
https://doi.org/10.1017/S0003598X0004984X. 
(10)  Stetch, T.; Pigott, V. C. The Metals Trade in Southwest Asia in the Third 
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(11)  Helwing, B. Rethinking the Tin Mountains: Patterns of Usage and 
Circulation of Tin in Greater Iran from the 4th to the 1st Millennium BC. 
T ̈urkiye Bilim. Akad. Arkeol. Derg. 2009, 12, 209–221. 
(12)  Komatsu, M.; Yamaguchi, A.; Ito, M.; Yoneda, S.; Saito, T.; Ohgane, T.; 
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Hayashi, T.; Sakamoto, M.; Mikouchi, T.; Kimura, M. Ryuseito: The 
Japanese Swords Made from Shirahagi Iron Meteorite. In 82nd Annual 
Meeting of The Meteoritical Society; 2019; Vol. 54. 
(13)  Holappa, L. Historical Overview on the Development of Converter 
Steelmaking from Bessemer to Modern Practices and Future Outlook. 
Miner. Process. Extr. Metall. Trans. Inst. Min. Metall. 2019, 128 (1–2), 3–
16. https://doi.org/10.1080/25726641.2018.1539538. 
(14)  Barracglough, R. F. Steelmaking 1850-1900; The Institute of Metals: 
London, 1990. 
(15)  Barth, O. Metallurgian Oppikirja – Osa 2 (Textbook on Metallurgy, Part 2 
Ironmaking and Steelmaking), 1st ed.; Otava: Turku, 1942. 
(16)  Braconnot, H. No Title. Ann. Chim. 1833, 52, 290–294. 
(17)  Seymour, R. B.; Kauffman, G. B. The Rise and Fall of Celluloid. J. Chem. 
Educ. 1992, 69 (4), 311–314. https://doi.org/10.1021/ed069p311. 
(18)  Schöbein, C. F. Improvement in Preparation of Cotton-Woll and Other 
Substances as Substitutes for Gunpowder. 4874, 1846. 
(19)  Gladstone, J. H. Contributions to the Chemical History of Gun-Cotton 
and Xyloidine. Mem. Proc. Chem. Soc. 1845, 3, 412–421. 
(20)  White, J. L. Fourth in a Series: Pioneers of Polymer Processing Alexander 
Parkes. Int. Polym. Process. 1998, 13 (4), 326–326. 
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(21)  Rasmussen, S. C. From Parkesine to Celluloid: The Birth of Organic 
Plastics. Angew. Chemie - Int. Ed. 2021, 60 (15), 8012–8016. 
https://doi.org/10.1002/anie.202015095. 
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Phys. Rev. 1948, 74 (1), 230. 
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History of Semiconductors; Goldstein, A., Aspray, W., Eds.; IEEE Center 
for the History of Electrical Engineering: New Brunswick, 1997; pp 35–74. 
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Electronics 1965, 38 (8), 114. 
(25)  Moore, G. E. Progress in Digital Integrated Electronics. In International 
Electron Devices Meeting; 1975; pp 11–13. 
(26)  Roy, K.; Mukhopadhyay, S.; Mahmoodi-Meimand, H. Leakage Current 
Mechanisms and Leakage Reduction Techniques in Deep-Submicrometer 
CMOS Circuits. Proc. IEEE 2003, 2, 305–327. 
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(27)  Taur, Y. The Incredible Shrinking Transistor. IEEE Spectr. 1996, 36 (7), 
25–29. 
(28)  Lee, D.; Kwong, W.; Blaauw, D.; Sylvester, D. Simultaneous Subthreshold 
and Gate-Oxide Tunneling Leakage Current Analysis in Nanometer CMOS 
Design. Proc. - Int. Symp. Qual. Electron. Des. ISQED 2003, 1, 287. 
https://doi.org/10.1109/ISQED.2003.1194747. 
(29)  Ito, T.; Nakamura, T.; Ishikawa, H. Advantages of Thermal Nitride and 
Nitroxide Gate Films in VLSI Process. IEEE J. Solid-State Circuits 1982, 
17 (2), 128–132. https://doi.org/10.1109/JSSC.1982.1051704. 
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Computing Performance. Intel News Releases. November 11, 2007. 
(31)  Southwick, R. G. I. An Investigation of Carrier Transport in Hafnium 
Oxide/Silicon Dioxide MOS Gate Dielectric Stacks from 5.6-400K, Boise 
State University, 2014. 
(32)  Zhou, D.; Preparata, F. P.; Kang, S. M. Interconnection Delay in Very 
High-Speed VLSI. IEEE Trans. Circuits Syst. 1991, 38 (7), 779–790. 
(33)  Wada, Y.; Sasaoka, K.; Imamura, E.; Odaira, H. A New Circuit Substrate 
for MCM-L. In Proceedings of CARTS EUROPE 95, 9th European Passive 
Components Symposium; Amsterdam, 1995; pp 94–99. 
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Mater. Today 2004, 7 (1), 34. 
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https://doi.org/10.1038/530144a. 
 
  
 32 
CHAPTER II 
CHALLENGES IN SYNTHESIS OF HETEROSTRUCTURES 
2.0 Authorship Statement 
Chapter II was published in the Journal of Materials Chemistry C in 
2022. David C. Johnson and I contributed equally to the text.  
2.1 Introduction 
Materials discovery is a significant factor driving the development of new 
technology. The history of humanity is even discussed through the lens of 
materials discoveries, with eras named after materials that enabled significant 
advances or cultural shifts. As technology has improved, it has done so in part 
by increasing the fundamental understanding of material properties at ever 
decreasing scales and with increasing precision. Indeed, it has only been about 
a century since the mathematical frameworks describing quantum mechanics 
were theorized.1,2 While modern devices based on silicon (Si) exploit our 
understanding of bulk material transport physics, there are still many remaining 
unanswered questions and poorly investigated physical phenomena in the 
quantum regime.  
In today’s era, the Silicon Age, electronic devices built on Si have become 
ubiquitous in everyday life. Reducing feature size to increase device density of 
integrated circuits and computational speed has been a major driver for Si 
technology. Current chip designs have feature sizes at the nanometer scale and 
material properties are beginning to no longer scale with dimensions due to 
quantum effects and reduced material dimensionality.3 The increased complexity 
of today’s chips is evident in the microscope image shown in Figure 2.1, which 
depicts a typical Cu interconnect structure. As feature size continues to 
decrease, more and more elements are also being used to tailor properties. As 
feature size continues to decrease, it will be necessary to develop a more complete 
understanding of the interactions between different materials at interfaces. 
Device properties will no longer predictably scale with size due to quantum 
 33 
effects and emergent properties from the interactions occurring at interfaces. 
Figure 2.1. Image showing the complexity of the Cu interconnect structure of a 14 nm 
logic integrated circuit featuring FinFET’s and air-gapped interconnect. Reprinted, 
with permission, from Natarajan et. al.4 © 2014 IEEE. 
It seems likely that the next era of human materials use will involve 
manipulating materials at ever smaller scales, eventually being limited by the 
size of the constituent material’s unit cells. In 2004, Novoselov and Geim 
observed that the properties of graphite changed significantly when it is a 
monolayer thick.5 Monolayer thick graphite – now called graphene - has a 
gapless Fermi surface due to the removal of interlayer interactions between 
adjacent layers, which results in graphene’s emergent properties.6,7 These 
discoveries were made possible by the ‘scotch tape’ synthesis method and the 
discovery that layer thickness could be observed optically due to an interference 
effect when the resulting flakes were deposited on a thin layer of SiO2.8,9 
Energetic research efforts resulted in subsequent reports of emergent properties 
in other two-dimensional (2D) materials, along with the discovery that the 
emergent properties had a significant dependence on the identity of the substrate 
the 2D material was grown on.10–16 Theorists have been able to predict unusual 
emergent properties for specific arrangements of layers, including new quantum 
states created by the interaction of the properties of different constituent 
layers.17–22 Using exquisite micromechanical manipulation of cleaved flakes, 
assembly of different 2D layers into stacked heterostructures has been 
 34 
successfully used to verify several of these theoretical predictions and construct 
basic electronic devices.23–26 2D layers can be stacked like bricks in different 
sequences, as shown in Figure 2.2, to create desired properties. These 
discoveries launched the field of 2D materials, as researchers explore tuning the 
interactions between 2D layers by stacking them in different orders and 
thickness to form metastable heterostructures.27 
 Figure 2.2. The ability to prepare heterostructures by stacking 2D layers in designed 
sequences enables preparation of 2D electronic devices, such as this hypothetical 
stack of alternating p- and n-type semiconducting layers. 
The rapid growth of research focused on 2D materials results from the 
fundamental differences between heterostructures and composites. While both 
contain regions with distinctly different structures and properties, the properties 
of composite materials typically scale from those found in the bulk phases, 
although interfaces can increasingly impact properties as the size of the 
structural domains decrease to the nanoscale. In heterostructures, properties 
and/or structures distinct from those found in the bulk constituents arise as the 
thickness of constituent layers are reduced to monolayers. The lack of adjacent 
layers changes the band structure of monolayers, causing changes in electronic 
properties. For example, graphene has a gapless Fermi surface,28 monolayers of 
semiconducting dichalcogenides have a direct band gap rather than the indirect 
banc gaps found in the bulk compounds,29–31 and the charge density wave onset 
temperature and structure of VSe2 differ from that found in the bulk.32–35 The 
changes in electronic bonding as thickness is reduced to a single unit cell can 
also result in structural changes. These structural distortions are typically small 
 35 
in layers exfoliated from 2D solids with very anisotropic bonding, as the 
perturbation of removing adjacent layers bound via van der Waals bonding is 
small. The distortions can be much larger if the constituent’s bulk structure is 
less anisotropic. For example, a bilayer of PbSe has a 0.4 Å puckering compared 
to the bulk structure.36 Charge transfer between adjacent layers can also cause 
significant structural changes. For example, a charge donating layer next to 
MoSe2 can cause the 1T polytype to form.37–39 
Since layer properties vary with thickness and identity of adjacent layers, 
the building-block approach of stacking 2D layers in specific sequences to form 
van der Waal’s heterostructures results in an inexhaustible number of different 
target materials/heterostructures.40–43 For example, consider an 8 layer 
heterostructure constructed from 4 layers of 1T-TiSe2 and 4 layers of PbSe (total 
thickness of ~5 nm). One could construct 6 different heterostructures by varying 
the stacking sequences of the 4 PbSe and four TiSe2 layers – all having the same 
size repeating unit and the same overall composition. The simplest case would 
be a 4 layer thick block of TiSe2 stacked sequentially with a 4 layer thick block 
of PbSe. Five other possible heterostructures can be created by varying the order 
in which the TiSe2 and PbSe layers are stacked. Representative HAADF-STEM 
image cross-sections of these isomeric heterostructures are shown in Figure 
2.3.40 An experimental approach needs to be developed where varying 
experimental parameters enables the stacking sequence and the number of 
constituent layers to be freely varied to optimize the properties of the resulting 
devices. 
Figure 2.3. Representative HAADF-STEM images of six of the possible “isomer” 
heterostructures constructed from a unit cell consisting of various layering schemes of 
four layers of 1T-TiSe2 and four layers of PbSe. Because HAADF-STEM intensity 
 36 
increases with atomic number, the PbSe layers are significantly brighter than the 
TiSe2 layers.  
There typically are large differences between the strength of bonding within 
2D layers versus between 2D layers. The prototypical 2D layer – graphene – 
illustrates this case.  The carbon atoms in graphene layers are strongly 
covalently bonded to one another. Monolayers of graphene can be exfoliated from 
graphite because there is only bonding between the layers in graphite. The strong 
in plane bonding found in 2D layers that can be exfoliated from the bulk typically 
make them chemically stable. When on a substrate or adjacent to another 2D 
layer there will be chemical interactions in addition to van der Waals forces 
because the wavefunctions of both will overlap, often to a significant degree. The 
difference in chemical composition and structure between the layers will also 
result in a chemical potential difference. Charge transfer will occur to equalize 
the chemical potential. These additional interactions can be surprisingly strong, 
as evidence by the occurrence of minerals with misfit layer structures that can 
contain interwoven monolayers of two different constituent layers. Like 
artificially stacked monolayers, these minerals and analogous 
thermodynamically stable synthesized compounds consist of two structurally 
distinct layers whose lattices do not structurally match, resulting in an 
incommensurate structural mismatch. An excellent review by Wiegers details the 
structure and properties of misfit layer compounds containing transition metal 
dichalcogenide constituent layers.44,45 Despite the structural misfit, the bonding 
between the constituent layers is strong enough to make them chemically stable 
with respect to mixtures of the constituent compounds. In some of these 
compounds significant charge transfer between constituent layers results in 
strong ionic bonding between layers, for example (LaS)1.2(CrS2), where the 
subscript 1.2 results from the lattice misfit between the in-plane unit cell of the 
distorted rock salt structured LaS layer and the distorted hexagonal CrS2 
dichalcogenide layer. The LaS layer is positively charged while the CrS2 layer is 
negatively charged.46 The origin of the strong interlayer interaction is less 
 37 
obvious in other misfit layer compounds, for example (SnS)1.17(NbS2). As the 
variety of heterostructures that are prepared expands, the range of interlayer 
interactions will expand. 
Historically, many material discoveries have occurred via serendipity.47 
This is largely because traditional synthesis approaches typically make only the 
most thermodynamically stable product, which may or may not be the targeted 
compound. Despite its successes and the discovery of many unpredicted 
structures and phenomena, these approaches are quite inefficient, especially 
when targeting a specific structure. Traditional organic synthesis, with its 
toolbox of well-known reactions and the ability to retrosynthetically design a 
sequence of steps to systematically assemble a complex structure, is perhaps 
the most developed synthetic chemistry field. However, even in organic 
synthesis, the crystal structure of the resulting compound cannot be 
experimentally controlled. In an ideal world, materials scientists would be able 
to predict the existence of new compounds with desired properties, including 
metastable phases, and synthetic approaches would be available to make 
targeted compounds. While this review focuses on approaches to make targeted 
heterostructures, there is a broader need for synthetic advances. In the last 
decade, significant advances have been made in predicting possible new phases 
through targeted programs such as NIST’s Materials Genome Initiative, the 
Materials Project, and other related coordinated efforts.48,49 Of the thousands of 
predicted compounds, only a small percentage have been made experimentally.50 
While this may be partially due to the accuracy of the calculations, synthesis 
limitations also play a significant role.    
The remainder of this review focuses on synthetic approaches to 
heterostructures, briefly describing the reaction pathway(s) typically involved in 
these synthetic approaches. Since most heterostructures are metastable, they 
cannot be prepared as bulk compounds by direct, high temperature reaction of 
the elements and it will be challenging to prepare targeted metastable 
compounds as films on substrates using flux-based synthetic methods. A short 
 38 
summary of various solid-state synthesis techniques used to grow crystals of 
thermodynamically stable heterostructures introduces basic concepts. We then 
discuss vapor phase deposition approaches, which have classically been used to 
prepare thin films and superlattices, showing how the rate limiting steps in 
crystal formation can be controlled by experimental parameters. 
Micromechanical assembly is discussed next, with a focus on more recent 
advances that may enable wafer scale. We discuss molecular beam epitaxy 
(MBE), where substrate structure and reacting fluxes are controlled to define the 
structure and control orientation thickness of constituent layers in metastable 
superlattice structures, traditionally of constituents with 3D structures. The 
final part of this review focuses on a more extensive discussion of the modulated 
elemental reactant growth technique, a newer alternative approach to 
heterostructure synthesis that involves nanostructured precursors.  
2.2 Direct Reaction of Elements and/or Compounds 
The direct reaction of elements and/or binary compounds to form products 
is a classic solid-state synthesis technique. Because of the non-uniform initial 
distribution of each element and the different diffusion rates of elements in the 
different reactants, a variety of local concentration gradients and intermediate 
compounds develop during these reactions. The reaction typically contains one 
or more reaction pathways that may involve multiple intermediate compounds. 
Since diffusion rates in solids are small, it is necessary to increase diffusion rates 
and/or decrease diffusion distances to obtain reasonably fast reaction rates. The 
most common approach uses high temperatures to overcome the small diffusion 
rates and large diffusion distances necessary to form the desired product from 
the initial reaction mixture. While increasing temperature significantly increases 
diffusion rates, the resulting composition gradients at interfaces also result in 
the formation of many of the compounds in the relevant phase diagram as 
reaction intermediates. The final state is typically the thermodynamically stable 
mixture of compounds expected from the appropriate phase diagram. 
For example, consider the synthesis of misfit layer compound (MLC) 
 39 
(PbSe)1.18(TiSe2)2 from the direct reaction of elemental Pb, Ti, and Se, as shown 
in Figure 2.4.51 Typical conditions for traditional synthesis reactions involve 
mixing stoichiometric amounts of each element in an evacuated quartz ampule 
and raising the temperature slowly before heating to high temperatures for a 
week or more. Due to the relatively large differences in melting points of the 
elements, Se melts and reacts with the surfaces of the Pb and Ti while 
temperature is being raised. While intuition might predict the most metal-rich 
phase on the relevant phase diagram would form first, this is not always true. 
However, the compound that forms first will be the phase with the lowest energy 
barrier to nucleation. The literature suggests that in this case, the metal rich 
phase, Ti2Se is the first Ti-Se-containing phase to nucleate and PbSe is first to 
form on the surface of the Pb.52 The amount of each of these compounds will 
increase with time as diffusion of elements through the surface product layers 
occurs. As heat is continually applied to the reaction mixture, the longer 
diffusion paths through the increasingly thick surface layers decrease the 
reaction rates. At some point, the targeted thermodynamically stable ternary 
MLC may nucleate and grow in the composition gradients, but the growth rate 
is slow due to the low diffusion rates of the elements in the intermediates formed, 
PbSe and TiSe2. Grinding the intermediate reaction mixture and pressing a dense 
pellet of the resulting powder decreases the diffusion distances, which speeds 
the formation of the thermodynamically stable MLC.  
While this approach is effective at synthesizing MLC’s and other 
thermodynamically stable heterostructures, it lacks any control over the reaction 
pathway and thermodynamically unstable compounds cannot be prepared using 
this approach. Repeated grinding or ball-milling the reaction charge is one of the 
simplest approaches that can be used to reduce the average particle size by 
breaking up the product forming on the surfaces of each particle. This decreases 
the time it takes to convert the reaction mixture to products. While this can be 
effective at reducing diffusion distances by orders of magnitude (~mm to ~μm or 
smaller), multiple grindings can be required. Researchers often turn to other 
 40 
synthetic techniques that are less diffusion limited, especially when single 
crystals are desired. 
Figure 2.4. Schematic depiction of the reaction of elements Pb, Ti, and Se to form 
binary intermediates PbSe and TiSe2, and ternary product and misfit layered 
compound, (PbSe)1.18(TiSe ) .512 2  The direct reaction of elements results in nucleation 
based on the local composition at that moment in time – here we assume TiSe and 
Ti2Se will be the first to form. Since compositions exist from 0 to 100% of each 
element, there is no control over the reaction pathway.  
2.3 Fluid-assisted Synthesis Techniques 
Another strategy to bypass large diffusion distances is to use a fluid phase 
to significantly increase diffusion rates, which can both lower reaction 
temperatures and decrease reaction times. The large increase in diffusion rates 
relative to those found in solids allows for facile transport and mixing of reactants 
across the fluid portion of the reaction mixture. The choice of fluid is diverse and 
goes by a plethora of different identities and names, including solvent, melt, 
mineralizer, eutectic melt, flux, or reactive flux. When forming a solid crystal 
from a fluid phase, nucleation is typically the rate limiting step.53 The compound 
with the lowest activation energy to nucleate will form, not necessarily the 
compound that is most thermodynamically stable. Having nucleation be the rate 
limiting step in crystal formation has the added advantage of allowing for the 
direct formation of ternary phases without proceeding through binary 
 41 
intermediates, providing the ternary phase is the easiest to nucleate.  
The reaction pathway in a fluid-based synthesis can be quite complex. 
There are basically two strategies used by researchers. Either the initial reaction 
mixture can be heated to a high enough temperature for long enough time that 
all the reactants dissolve in the fluid or researchers will focus their search for 
compounds formed during the initial heating, before all the reactants dissolve. 
In both cases, crystal growth will deplete the fluid of the solvated species 
contained in the compound, potentially causing significant differences in the 
speciation of the fluid phase. In the case of a heterogenous reaction mixture of a 
fluid and undissolved reactants, nucleation and growth impacts the rate that 
reactants dissolve. In-situ studies of melts frequently report nucleation of 
kinetically stable compounds at short times. A sequence of nucleation events as 
the reaction proceeds results in a series of new compounds forming, which can 
cause those previously formed to dissolve.54–58 Figure 2.5 depicts a schematic of 
this sequence of phase formation.  
Figure 2.5. Schematic depiction of the evolution of the nucleation of crystalline 
phases during the cooling of a fluid-assisted synthesis reaction. The first phase to 
nucleate as the reaction is cooled to create supersaturation is simply the easiest to 
nucleate from the liquid (Phase A), given the species in the fluid and their 
concentrations. This phase is not necessarily the most thermodynamically stable 
phase. Growth of the first phase changes the speciation of the flux, potentially 
resulting in nucleation and growth of a subsequent phase (Phase B). As Phase B 
grows, it depletes the flux of species, which may result in Phase A dissolving. 
There is unfortunately little systematic understanding of speciation and 
how speciation varies with time, composition, or temperature in fluid-assisted 
 42 
solid-state synthesis. While recent in-situ total scattering and diffraction 
experiments have provided insights to the evolution of structure in fluids 
during reactions and on the sequence of crystalline phases that form in specific 
systems, it is still not straightforward to predict how reaction parameters can 
be manipulated to achieve a specific product.59 Recent advances in machine 
learning have provided encouraging insights into understanding how varying 
the reaction parameters affect the observed reaction pathway, and this 
approach may be particularly useful for reactions in fluids, which contain 
many coupled parameters (including the amounts of undissolved reactants and 
products, the concentration of different species in solution, the reaction time 
and temperature) that all impact the resulting nucleation and crystal growth 
processes.60 
Relative to the direct reaction of elements, the added experimental 
parameters in fluid-assisted synthesis provide more degrees of freedom to steer 
the reaction towards desired products. Researchers have used chemical insight 
to prepare homologous series of related compounds by tuning reaction 
parameters.61 
2.4 Chemical vapor transport (CVT) 
Chemical vapor transport (CVT) reactions are a common approach used 
by researchers when growing bulk crystals of transition metal dichalcogenides 
(TMD’s) and other layered materials.62 As shown in Figure 2.6, reactants are 
typically sealed in an evacuated quartz ampule with a transport agent (or 
mineralizer) and placed in a temperature gradient. CVT reactions involve three 
basic steps: reaction of the transport agent with the material to be transported 
to form a vapor phase compound, transport of this compound to the other end 
of the ampule, and the decomposition of this compound as the product forms.62 
The transport agent released by the decomposition of the transport compound 
returns to the reactant side of the vessel to react again. To nucleate the desired 
phase, the ampule must become super-saturated with the vapor species needed 
to form the product. Heterogenous nucleation typically occurs at the surface of 
 43 
the substrate or on the ampule walls.63 Once a crystal forms, it is easier to grow 
the crystal than nucleate a second one. The example shown in Figure 2.6 involves 
a reaction to form MoS2, a well-studied 2D TMD.64 In this example, elemental Mo 
reacts with the chosen transport agent, I2, at the hot end of the temperature 
gradient producing a vapor phase mixture of MoIx and Sn intermediate species. 
These intermediate species react at the other end of the temperature gradient, 
known as the deposition zone, forming MoS2 crystals and reforming the I2 
transport agent.  
Figure 2.6. Schematic depiction of the CVT synthesis of MoS2. A stoichiometric 
mixture of Mo + S powders and the chosen transport agent, I2, are sealed inside an 
evacuated quartz ampule. The ampule is placed across a well-defined temperature 
gradient within a multi-zone tube furnace. The temperature gradient is chosen such 
that the reaction and vapor-phase transport of the reactants to the other side of the 
ampule, where they are deposited as products, is thermodynamically favorable.64 
The change in the Gibbs free energy as the transport agent reacts with the 
material to be transported can be used to identify potential transport agents. If 
the reaction of the transport agent with the material to be transported has a very 
large negative ΔG and hence a very large (>104) equilibrium constant, the gas 
phase product will not readily decompose at the other end of the reaction vessel. 
If the reaction of the transport agent with the material to be transported has a 
very small (<10-4) equilibrium constant, then the concentration of the vapor 
phase species will be very small. Either of these thermodynamic conditions make 
transport of the reactant very inefficient and impractical.65 Finding a suitable 
transport agent becomes more difficult when attempting to synthesize 
compounds containing more than one metal constituent, as the above 
constraints must be satisfied for all species that can be formed by reaction of the 
 44 
transport agent with non-volatile elements. Recently it was demonstrated that 
μm2 area MoS2 monolayer crystals and few-layer ReS2, MoSe2, and TiSe2 could 
be grown using CVT by designing reaction vessels with constrictions.64 This is a 
very encouraging breakthrough, showing that with sufficient control over and 
understanding of how experimental parameters affect the chemistry involved, 
the reaction pathway for CVT-based growth can be controlled to obtain 
monolayer crystals. To the best of our knowledge, however, growing a unique 
second material as a monolayer on top of a first monolayer has yet to be 
demonstrated via a closed system CVT reaction. 
2.5 Chemical vapor deposition (CVD) 
Chemical vapor deposition (CVD) reactions are like CVT reactions, but 
epitaxial substrates are typically used to reduce the activation energy for 
heterogeneous nucleation of a targeted structure. The ability to individually vary 
the partial pressure of species by varying the source temperatures allows control 
over the relative concentration of gas phase species in the growth zone to achieve 
conditions for nucleation and growth. By controlling deposition time, one can 
control the thickness of the resulting film.66 Typically, CVD synthesis begins with 
solid or gaseous precursors which are heated to generate a partial pressure of 
each reactant in a carrier gas. The carrier gas containing the precursors is flowed 
through the reaction chamber. When the precursors impinge on the heated 
substrate, they decompose and the resulting species react to form the product, 
as shown in Figure 2.7.  
An important feature of CVD reactions is the significant number of 
experimental parameters available to tune product formation relative to 
traditional solid-state synthesis. Perhaps the most critical parameter to control 
is the residency time of each reactant in the reacting zone. This is done by 
controlling the partial pressures of each reactant in the carrier gas at the 
substrate, which is typically done by setting the temperature of the sources of 
the precursors.67 The flow of a carrier gas controls the residency time of each 
reactant in the reacting zone. The carrier gas is typically an inert gas such as 
 45 
nitrogen or a noble gas but occasionally hydrogen or another reactive gas is  
Figure 2.7. Schematic depictions of two types of CVD reactors. a) Powder-based 
chemical vapor deposition (CVD), in which powdered sources are used to generate the 
vapor, which is transported via carrier gas to the substrate. b) Metal-organic CVD, in 
which the carrier gas is bubbled through a metal-organic-containing solution prior to 
being injected into the reactor. Both experimental setups are open systems, with the 
carrier gas and remaining reactants continually removed from the reaction vessel. 
Adapted from 68. 
mixed in to help decompose precursors at lower temperatures. The carrier gas, 
its temperature, and the partial pressures of the reactants, all affect the number 
of collisions between reactants, the gas phase reaction between them and the 
number of reactant species impacting the substrate surface. The ratio η/η0 
affects the initial incubation time observed prior to regular growth for many CVD 
reaction,69 which is probably related to the initial nucleation of the target 
structure. The substrate temperature controls the decomposition rates of the 
precursors that impact and adsorb, the surface mobility of the resulting species 
and their residency time, and the nucleation rate and growth rate of forming 
solids. 
 46 
The manipulation of the experimental parameters has significant effects 
on the observed growth mechanism of the deposited material. CVD growth 
typically begins with an incubation time prior to a period of regular growth. 
During the incubation period, the concentration of species on the substrate 
surface increases until supersaturation is reached, and nucleation occurs. 
Differences in nucleation energy can result in the formation of metastable 
compounds, which is typically encouraged by choosing substrates with an 
epitaxial relationship with the metastable phase. High temperatures result in 
thermodynamic-controlled processes, while low temperatures result in kinetic-
controlled processes.70 Once nucleation occurs, growth rate is limited either by 
the rate of the chemical reaction or by the rate of material reaching the surface. 
A high concentration of reactants in the vapor phase and low substrate 
temperatures lead to crystal growth being limited by the rate of the chemical 
reaction. A low concentration of reactants in the vapor phase and high substrate 
temperatures result in a mass-transport limited growth mechanism.  
There is often a balancing act between using a sufficiently high substrate 
temperature to promote crystal growth but a low enough temperature to avoid 
desorption of reacting species from the surface. For example, in the growth of 
dichalcogenides reaction rates initially increase with temperature before 
decreasing as concentration of chalcogen on the substrate surface decreases due 
to its significantly higher vapor pressure than the other reactants. Since many 
TMD’s lose chalcogen atoms when heated to high temperatures, the substrate 
temperatures must remain low enough to inhibit the formation of chalcogen 
vacancies. The number of chalcogen vacancies can dominate the properties of 
the resulting film.71 
Three distinct growth modes have been observed in CVD growth, 
depending on reaction conditions: 2D layer-by-layer growth, also known as 
Frank-van der Merwe (FM) growth, 3D island-based growth, known as Volmer-
Weber (VW) growth, and Stanski-Krastanow (SK) growth, which is a combination 
of the first two, involving formation of a few 2D layers followed by 3D island 
 47 
formation.69,72–74 FM growth occurs when the interaction between the incident 
reactants and the substrate is greater than that between the incident reactants 
and itself (η < η0), resulting in preferential growth of each complete layer before 
nucleation of the next layer.75 VW growth occurs when the interaction between 
the incident reactants and the substrate is weaker than the interaction between 
the incident reactants and itself, which causes mostly vertical growth of the 
nucleated islands, typically resulting in films with very rough surfaces.76 SK 
growth is a mixed growth mode that occurs when the interaction between the 
incident reactants and the substrate is about equal to that between the incident 
reactants and itself, resulting in competition between island nucleation and layer 
growth.77 None of these growth mode models account for the initial incubation 
time.74 While strides have been made to modify the growth models to account for 
these other involved processes, a complete understanding of CVD reactions has 
remained elusive.69 
There are still significant challenges to using CVD reactions to synthesize 
metastable 2D films and heterostructures. One challenge is exactly 
determining when a layer’s growth is complete, because incubation times vary 
and are sensitive to experimental conditions. When growing multiple 
constituents, one must determine exactly when layer growth is completed, 
such that growth of the first material can be halted prior to switching sources 
and growth of the second material. This requires reproducibly controlling two 
different incubation periods that may require different reaction conditions. In 
an encouraging breakthrough, Zheng et. al. used a sequential two-step CVD 
method to grow a monolayer PbI  on monolayer WS  and WSe .782 2 2  This was 
enabled by the much lower growth temperature of PbI2 relative to WSe2 and 
WS2 (400 °C vs. 1050 °C). These different growth temperatures, however, 
prevents the growth of WSe2 or WS2 on PbI2.  
2.6 Micromechanical assembly  
The mechanical assembly processes for synthesis of heterostructures is 
conceptually straightforward, involving the sequential stacking of 2D layers in 
 48 
the same way that one might stack bricks or Lego blocks, as depicted earlier in 
Figure 2.2. The steps involved in mechanical assembly consist of the initial 
growth of films or crystals that provide the source of the 2D layers, the exfoliation 
of the 2D layer of desired thickness from the crystal or substrate, the transfer of 
the layer to the growing assembly, and the removal of the substrate used to 
transfer the layer. One of the first reports of high-quality micromechanically 
assembly utilized small flakes of mechanically exfoliated mono- and bilayer 
graphene to make simple devices on single-crystal h-BN substrates.79 The ability 
to prepare targeted structures with designed architectures in such a 
straightforward manner has resulted in literally thousands of papers published 
further optimizing each of the steps involved or using an assembly process to 
make targeted heterostructures. We will not attempt to comprehensibly review 
all this literature, as excellent reviews on targeted aspects already exist,80–82 but 
will highlight what we believe were key synthesis advances as the size of the 
assembled structures increase towards wafer scale. 
Major advances and remaining challenges in growing 2D materials over 
large areas were discussed earlier in this article. It is now possible to prepare 
large area, monolayer thick films of many 2D materials with near complete 
coverage of the substrate.83,84 Since this technique allows one to individually 
prepare each layer, ensuring it is the correct thickness and composition, the 
challenges in finding compatible growth conditions to sequentially deposit 
different materials is avoided altogether. However, one challenge in developing 
growth techniques for a new 2D material is finding a substrate that enables 
crystallographically aligned growth, while also permitting the film to be exfoliated 
as a large area film from the substrate. It is necessary to optimize the CVD growth 
of the 2D layers to generate surface properties that enable the 2D layers to be 
cleanly isolated from substrates they were grown on without the use of any 
etchants or solvents. 
The exfoliation of 2D layers from both crystals and growth substrates has 
undergone significant advances since Frindt first used tape to exfoliate NbSe2 
 49 
crystals to measure the effect of sample thickness on superconductivity.85 Early 
methods typically used an adhesive layer, which needed to have a stronger 
adhesion with the material being cleaved than the interaction of the material 
with either the neighboring layers of itself in a crystal or to the substrate if grown 
as a film. An alternative approach to create large amounts of monolayer material 
is chemical exfoliation, in which ions and/or solvent intercalate between the 2D 
layers resulting in free floating solvated layers in solution.86–88 Like mechanical 
exfoliation, the solvation energy of the solvated layers must be larger than 
bonding between the layers in the 2D crystal for this approach to be successful. 
It is often challenging to completely remove the adhesive or solvent from the 2D 
layer when they are being mechanically stacked via either of these approaches. 
One successful approach to isolate 2D layers of CVD grown films is to spin-coat 
the grown film with an adhesive polymer film, which is then mechanically peeled 
from the growth substrate using a thermal release tape.89 
 To get around organic contamination, gold-assisted exfoliation 
methods were developed.90–92 Ultrasmooth gold layers result in a significant 
degree of charge transfer between the monolayer being transferred and the gold 
layer as the chemical potentials are equalized on contact, resulting in a bond to 
the gold that is stronger than the van der Waals forces between the 2D layers 
themselves. While contamination still can occur when removing gold films with 
chemical solvents in subsequent processing steps, the Au transfer process works 
for a wide variety of 2D materials.25 
Initial micromechanical assembly was done manually on small, cleaved 
layers from crystals to discover emergent properties and to test theoretical 
predictions. Approaches were developed that enabled layers to be stacked with 
control of the rotational angle between the crystal structures of adjacent layers.93 
More recently, automated assembly techniques have been developed to improve 
reproducibility, decrease incorporated material between the 2D layers, and 
increase throughput on large area substrates.89,94 These advances enable 
researchers to consistently synthesize wafer-scale heterostructures, which is an 
 50 
essential step towards being able to manufacture devices made from 
heterostructures. 
2.7 Molecular beam epitaxy (MBE) 
Molecular beam epitaxy (MBE) growth is a well-developed and understood 
technique and is one of the few synthesis techniques able to target and grow 
metastable materials and superlattices. This ability positions MBE as a potential 
source of 2D layers that cannot be prepared as bulk compounds or via CVD. 
MBE is similar to CVD reactions in some respects, but MBE reactions differ by 
taking place in a high or ultra-high vacuum environment. An advantage of 
utilizing high-vacuum and ultra-pure sources is the lower occurrence of impurity 
inclusions from carrier gas molecules or other source impurities, relative to films 
grown via CVD.68 A second advantage is that in-situ characterization tools are 
available to monitor film growth during deposition, including surface-sensitive 
reflection high-energy electron diffraction (RHEED), quartz crystal deposition 
monitors (QCM), auger spectroscopy, and scanning tunnelling microscopy 
(STM).68 These analytical tools have enabled researchers to develop and 
understand the reaction pathways and how and why experimental parameters 
change growth modes.  
MBE involves heating ultra-pure reactant sources with effusion cells 
and/or electron beam guns to generate “beams” of vaporized reactant, which 
are co-incident on an actively heated substrate, as shown in Figure 2.8. The 
heated substrate allows for significant surface diffusion of the reactants after 
they impact the substrate, enabling them to find energetically favorable 
locations such as step edges on the growing surface. Relatively low 
temperatures can be used, which minimizes the formation of vacancy defects 
and limits interlayer diffusion to keep interfaces abrupt.  
 
 
 51 
Figure 2.8. Schematic of MBE reactor, showing effusion cells with a reactant flux 
incident on the heated substrate, along with in-situ RHEED instrument for 
characterization of film growth during deposition. 
MBE exploits the difference in activation energies between surface and 
bulk diffusion, providing enough thermal energy for adatoms to move and react 
with already nucleated layers, but not enough for bulk diffusion. By changing 
the substrate temperature, the observed growth mechanism during deposition 
can be varied. To target a specific structure, an epitaxial match between the 
substrate and the targeted product is used to favor nucleation of the targeted 
structure. When the incident reactants impact the substrate, they interact with 
the dangling bonds present on the substrate’s surface, initially taking on the 
lattice constant of the substrate.95 In practice, the crystal lattices of the chosen 
substrate and the desired material have lattice parameters that are typically 
within 5% of one another. If there is a mismatch between the lattice constants 
of the deposited material and the substrate, increasing strain-induced 
distortions with thickness result in the formation of dislocation defects.96–98 The 
critical thickness where dislocations occur is dependent on the system, dictated 
by the extent of the lattice mismatch and the activation barrier to nucleation of 
the dislocation defect.99 The presence of periodic dislocation defects in the lattice 
of the thin film can degrade the electrical performance of devices fabricated from 
these materials.100 
 52 
The development of so-called “van der Waal’s epitaxy” (VDWE) by Atsushi 
Koma’s group in the late 1980s opened a new regime where epitaxy is no longer 
a strict requirement for ordered growth. Koma utilized typical MBE growth 
conditions but used substrates with a lack of dangling bonds on the surface.101–
104 Koma showed that the materials grown had the lattice parameters of the bulk 
compounds, not those of the substrate.  Large lattice mismatch’s of up to 20% 
or more were possible, because the lattice of the material being grown no longer 
adapted to the substrate’s lattice during the first few layers of growth.105 VDWE 
epitaxy has been used to grow transition metal chalcogenides, TMD’s, and other 
2D materials of interest,106–109 and to grow TMD heterostructures and 
topologically insulating materials, such as Bi Te .110–1122 3  
The growth of large domain size mono- or few-layer transition metal 
dichalcogenide films via MBE, however, has been surprisingly difficult. For MBE-
grown transition metal dichalcogenides (TMD’s), typical growth conditions (<500 
°C, with a ~20:1 chalcogen:metal flux ratio) result in a relatively high nucleation 
rate.113,114 This leads to a dense distribution of small grains in the resulting film, 
with the high density of grain boundaries limiting electrical performance of 
devices fabricated with these materials. As of 2017, the largest reported grain 
sizes for an MBE-grown TMD were relatively small, around 250 nm, observed in 
separate reports of NbSe2 and WSe  films.115,1162  In the WSe2 case, the authors 
report that the grain size significantly increased with the substrate growth 
temperature, although the nucleation density was still so high that the overall 
maximum grain size was restricted due to space considerations on the 
substrate.116 To achieve larger grain sizes, surface diffusion rates must be 
increased while the nucleation rates must be decreased, which is challenging 
given that both diffusion and nucleation rates increase with temperature.95 
When using high substrate temperatures, sticking coefficients are much lower 
relative to those observed at lower temperatures. This results in a lower density 
of surface adsorbed atoms (adatoms) at high temperatures leading to a lower 
probability of the formation of nuclei of critical size.  
 53 
Hinkle’s group recently showed that applying the above concepts result in 
over an order of magnitude increase in the observed grain sizes for MBE-grown 
WSe2 films.113 The challenge in applying these ideas to TMD growth, however, is 
that chalcogen adatoms have a significantly increased likelihood of desorbing, 
due to their much higher vapor pressure relative to metal adatoms. 
Consequently, the disparity in reactant fluxes needed to form stoichiometric 
dichalcogenides is closer to 1000:1 chalcogen:metal. The high substrate growth 
temperatures also result in significantly slower growth rates (around 0.05 
monolayer/hour) due to the increase in adatom desorption. While the much 
slower growth rate observed at high growth temperatures make it unsuitable for 
industrial-scale production of these materials, it does make it easier to terminate 
growth with a completed layer. It was recently shown that using a shutter to 
interrupt the metal beam at regular intervals during MBE growth of TMD’s, 
reduces the probability of metal-metal adatom interactions during deposition 
and allows more time for the chalcogen reactants to react and bond with 
adsorbed metal atoms. This clever way to increase the effective chalcogen:metal 
flux ratio resulted in stoichiometric films and was used to prepare the first 
reported MBE-grown WTe  film.117,1182  
 In summary, the layer-by-layer growth enabled by MBE is an extremely 
powerful tool in the synthesis of metastable materials and heterostructures. 
However, there are still significant challenges to extending these advances to the 
growth of heterostructures using MBE. For example, it can be extremely 
challenging to grow Material A on Material B AND Material B on Material A, due 
to the large differences in growth conditions required. The ability to prepare 2D 
layers not found in equilibrium phase diagrams, however, make MBE potentially 
a key growth technique to supply micromechanical assembly platforms with 2D 
layers that cannot be obtained via other approaches.119–123 
2.8 Modulated elemental reactants (MER) 
MER is the newest of the synthesis approaches outlined in this review, 
hence we will provide a longer description of this technique. MER is based on the 
 54 
idea that a homogenous, amorphous intermediate is a valuable and general 
starting point for the synthesis of metastable compounds, as all crystalline 
compounds will be more thermodynamically stable than the amorphous 
phase.124 Nucleation is the rate limiting step in forming a crystalline solid from 
an amorphous state, which depends on the local concentration and on the prior 
thermal history of the sample. To nucleate a compound with a stoichiometry 
different from the composition of the amorphous phase, diffusion needs to occur. 
Since diffusion rates are low in solids, the nucleation of a compound with 
stoichiometry close to that of the amorphous phase is favored. 
A challenge in using the amorphous state as a reaction intermediate was 
finding a general experimental approach to prepare amorphous alloys of 
controlled composition. One solution to this challenge was discovered in the early 
1980’s, when W. L. Johnson’s group showed that amorphous metals can be 
formed by heating crystalline metal foils at low temperatures. The formation of 
the amorphous alloy is driven by the large enthalpy of mixing.125–127 The D. C. 
Johnson group showed that if the thicknesses of reactant layers are below a 
critical thickness, an amorphous phase forms before any crystalline phases in a 
wide variety of different systems.128–130 This group also showed that the 
composition of the amorphous intermediate controls which compound nucleates 
first.131 Since the activation energy required to nucleate a metastable compound 
from the amorphous alloy with a composition that corresponds to the 
stoichiometry of the metastable compound can be smaller than that required to 
disproportionate and nucleate the more thermodynamically stable mixture of 
binary compounds, this provided a systematic approach to preparing metastable 
binary compounds. New metastable binary (FeSb3, NiSb3 and RuSb )132,1333  and 
ternary (Hf1-xFe4Sb12, and Y1-xFe4Sb12)133 antimonide compounds with the 
skutterudite structure were prepared using this approach, showing the ability to 
make targeted compounds using amorphous intermediates. W. Bensch’s group 
also used designed precursors to prepare amorphous intermediates to synthesize 
a number of new metastable binary compounds. His group used an array of in-
 55 
situ experiments to show that forming these metastable compounds was a result 
of the reaction pathway avoiding more stable compounds.134,135 Jansen’s group 
synthesized amorphous precursors by simultaneously depositing the relevant 
elemental sources onto a liquid-N-cooled substrate  with compositions matching 
the stoichiometries of intended phases.136,137 They synthesized several novel 
alkali nitride phases, including Na3N, and a previously unknown LiBr phase by 
gently heating the amorphous precursors.138,139 
The modulated elemental reactants (MER) approach is an extension of 
these initial findings, based on the  hypothesis that the nanoarchitecture of a 
precursor (elemental layer thicknesses and the layer sequence) can be used to 
control the resulting reaction pathway. One of MER’s advantages is the large 
number of parameters available to manipulate reaction pathways.140,141  
MER precursors are created by depositing sequences of ultra-thin 
elemental layers (~3-30 Å thick) designed to minimize the total diffusion distance 
that the reacting atoms need to travel from their initial positions in the layered 
precursor to their final positions in the targeted crystalline product. Changing 
the absolute layer thicknesses while maintaining a constant ratio of reactants 
per repeated sequence has a significant effect on the observed reaction pathway 
by changing the time required for interdiffusion, which scales as thickness 
squared. If the layer thickness is above some critical thickness, nucleation of the 
binary phase will happen at the layer interfaces prior to the formation of an 
amorphous intermediate. Below the critical thickness, the layers will interdiffuse 
and mix before a nucleation event occurs, forming a homogenous amorphous 
intermediate. The exact value of the critical thickness for each system is defined 
by the energy and time required to diffuse each reactant through the 
surrounding matrix relative to the activation energy and time required to 
nucleate a crystalline phase. As the absolute layer thickness increases, the time 
required for diffusion will increase until it becomes larger than that required for 
nucleation.142  The typical total diffusion distance for reacting atoms is 
nanometers in MER, which is smaller than the ~μm-scale surface diffusion 
 56 
lengths found in CVD and MBE, and much less than the ~mm-scale bulk 
diffusion lengths present in the direct reaction of the elements. The local 
composition is another important parameter, which is controlled by the relative 
layer thicknesses of each element deposited.129,143 The activation barrier for 
nucleating a crystalline compound depends on the local composition. For 
homogenous amorphous alloys, the lowest nucleation energy is observed for 
amorphous intermediate compositions that corresponded to the stoichiometry of 
the compound.144 This gives MER an advantage over other synthetic techniques 
when attempting to synthesize phases that are predicted to be kinetically stable, 
because local compositions are controlled by the design of the precursor. If the 
reactant contains layers or particles thicker than the critical thickness, 
composition gradients formed during interdiffusion provide opportunities for a 
variety of different compounds to nucleate. The goal in designing a MER 
precursor is to have the nucleation and growth of the intended phase be the 
fastest way for the system to reduce its free energy.  
In most systems, the reaction pathway can be controlled by designing 
precursors with specific interdiffusion lengths and layer sequences to avoid 
unwanted intermediate crystalline compounds. Low temperatures are sufficient 
to enable the elements to mix, due to the short diffusion lengths, permitting the 
initial formation of an amorphous intermediate. What forms from the amorphous 
intermediate depends on the relative magnitude of nucleation energies of 
different potential compounds, which is a function of local composition. The 
reaction between ultrathin layers of Mo and Se, depicted schematically in Figure 
2.9, illustrates the importance of both composition and repeat layer thickness. 
When Mo and Se are deposited in a metal rich repeating unit that deviates 
enough from a 1:2 ratio of Mo:Se and has a total thickness of the repeating unit 
less than 27 Å, heating the layered precursor at low temperatures (~125 °C) 
causes the interdiffusion of layers and formation of a homogenous amorphous 
alloy.129 Heating the amorphous alloy at 575 °C results in the formation of MoSe2, 
indicating that it is the easiest compound to nucleate. If the thickness of the 
 57 
repeating unit is larger than 38 Å at this composition, nucleation of MoSe2 occurs 
at the interface between Mo and Se layers during annealing at ~250 °C. 
Depositing bilayers that are Se rich with respect to MoSe2 results in MoSe2 
nucleating at the interfaces during the deposition for all repeat thicknesses that 
were studied, which were smaller than 2 nm.52  Annealing at higher 
temperatures results in the growth of MoSe2 layers perpendicular to the 
substrate and the loss of the excess Se at higher annealing temperatures. 
Figure 2.9. Schematic depiction of two different reaction pathways in the reaction 
between ultra-thin layers of Mo and Se. If the precursor’s composition is Se-rich, small 
grains of MoSe2 nucleate during the precursor’s deposition. If the precursor is Mo-
rich, the thickness of the repeating sequence of layers (Mo|Se) controls the reaction 
pathway. If the thickness of the deposited Mo|Se sequence is less than 27 Å, heating 
the precursor causes interdiffusion of the layers and formation of a homogenous 
amorphous intermediate state. Further heating crystallizes the majority of the 
intermediate into the desired MoSe2 structure, depending on how closely the 
composition of the intermediate matches the compound’s stoichiometry. If the Mo|Se 
thickness is greater than 38 Å, nucleation occurs at the interface between Mo and Se 
 58 
layers, trapping any local composition gradients that might be present in the layers. 
The MoSe2 grains grow until the trapped local composition gradients have come to 
equilibrium. 
In ternary systems, additional experimental parameters can be used to 
avoid the formation of crystalline binary compounds as reaction intermediates. 
Addition of a third element to an amorphous intermediate increases the 
activation barrier to nucleation of possible binary compounds.145 The layer 
sequence can also be used to avoid binary compounds as reaction intermediates 
by controlling the sequence of interdiffusion.146 If layers are deposited in an 
A|B|C sequence, all elements are adjacent to one another. If layers are deposited 
in more complex layer sequences, for example A|B|A|C, one separates the 
elements B and C to avoid the formation of binary B-C compounds. The ability 
to control the sequence of interdiffusion to avoid the formation of binary 
compounds by design of the precursor makes MER an effective approach to use 
when trying to prepare an unknown ternary phase.  
By preparing more complex MER precursors, it is possible to mimic the 
composition profiles of misfit layer compounds, naturally occurring 
heterostructures with lattice mismatched constituents. The planar nature of the 
composition gradients in as deposited MER precursors combined with the low 
nucleation energy of dichalcogenide compounds often leads to their low 
temperature nucleation before the deposited layers can mix.52,147 In the 
Ti|Se|Sn|Se precursor shown in Figure 2.10, monolayers of TiSe2 form during 
the deposition, provided the deposited Ti|Se layers each contain the number of 
atoms required for a single unit cell of TiSe2. The TiSe2 layers are separated by 
amorphous SnSex. If the deposited Sn|Se layers contained enough Sn and Se to 
form one unit cell of SnSe, annealing at higher temperatures results in the 
formation of a (SnSe) 1481.2TiSe2 heterostructure.   Depositing two Sn|Se layers 
and one Ti|Te layer results in the formation of the [(SnSe)1.2]2(TiSe2)1 
heterostructure.149,150 By varying the number of and sequence of deposited 
Sn|Se and Ti|Se layers in the precursor, MER enables the synthesis of a nearly 
 59 
unlimited number of unique heterostructures, including structural isomers.  
Figure 2.10. Schematic depiction of two sample layering sequences for deposition of 
MER precursors used when targeting materials with the distorted NaCl-type structure 
(top), the CdI2-type structure (middle), and a heterostructure combining both layer 
types. 
For example, consider heterostructures containing four layers of 
compound A and four layers of compound B. There are six different layer 
sequences that can be constructed containing four layers of A and B that all have 
the approximately the same c-axis lattice parameter: AAAABBBB, AAABBBAB, 
AAABBABB, AABBBAAB, AABBABAB, AABABBAB. One can prepare these 
structural isomers via MER by simply depositing the correct sequence of 
elemental layers to mimic the composition profiles of these heterostructures. 
However, as an overall synthetic approach, this results in an extremely large 
number of potential heterostructures, since the number of possible 
configurations in the final compound increases rapidly with the number of 
constituents. Even when limiting selections to those with <20 unique layers in 
the unit cell, there are nearly 60,000 possible unique heterostructures 
constructed from only two constituents. With three constituents, this number 
increases to over 130,000,000; with four constituents, the number of possible 
structures is more than 35,000,000,000.151 
MER also enables the synthesis of heterostructures that have no homologs 
 60 
in the systems equilibrium phase diagram. For example, sequentially depositing 
one Bi|Te bilayer (with a 2 to 3 ratio of Bi to Te) and one Ti|Te bilayer (with a 1 
to 2 ratio of Ti to Te) in a MER precursor results in the (Bi2Te3)1(TiTe2)1 
heterostructure.152,153 Heterostructures containing MoSe2 or WSe2 layers with 
SnSe, PbSe or BiSe have also been prepared.43,154–157 Other heterostructures 
incorporating novel constituents and combinations of constituents that do not 
exist on equilibrium phase diagrams have also been reported, based on 
intergrowths of different layered compounds (including Bi2Te3, TiTe2, TiSe2, 
MoSe2, VSe2,) and structural fragments of compounds with 3D structures, 
(including PbSe, SnSe, BiSe, LaSe, and GeSe ).40,142,153,154,158–1612  Key to the 
formation of a specific heterostructure is controlling the deposition parameters 
so that the precursors contain the desired ratio of metal atoms to chalcogen 
atoms (2:3, 1:2, or 1:1) for the Bi2Te3-type, CdI2-type structures and MX layers 
respectively) and the correct number of atoms to form an integer number of 
crystalline layers of the targeted constituents.    
Advances in thin film analytical and characterization techniques have 
been critical to enable the development of the MER synthesis approach. Low 
angle x-ray reflectivity quantifies the thickness of repeating layer sequence and 
infer their compositions.162–164 X-ray fluorescence provides a fast and non-
destructive technique to determine the absolute number of atoms in each 
sample.165 X-ray total scattering techniques and atomic pair distribution 
function (PDF) analysis can used to probe the structure of amorphous 
intermediates.166 High angle annular dark field scanning transmission electron 
microscopy (HAADF-STEM) and energy dispersive spectroscopy (STEM-EDS) 
provide critical atomic scale information about composition, local structure, and 
morphology.167 The relative positions and compositions of atomic planes from 
both HAADF-STEM and STEM-EDS data provide initial structural models for 
Rietveld structural refinement of specular and in plane diffraction data. When 
the resulting refinements match the initial model, it indicates that the STEM 
data is representative of the majority of the sample. 
 61 
2.9 Conclusion 
A free energy landscape, first introduced by Schön and Jansen, provides 
a useful way to discuss the challenges involved in synthesis and the attributes 
of the different synthetic approaches discussed in this review.136,168,169 Consider 
the schematic of a portion of the free energy surface for the BiSe-NbSe2 system, 
shown in Figure 2.11, which shows some of the kinetically stable and the 
thermodynamically stable heterostructure with a 1 : 1 ratio of BiSe to NbSe2 
layers in their unit cell. Like lakes that occupy minima in the local topography, 
each heterostructure is a local free energy minimum in the energy landscape. 
Differences in the minimum value for each lake reflect differences in the bonding 
in and between the constituent layers in each heterostructure. The “lake” at the 
lower left side of the map, labeled 11, has the lowest “altitude” and hence is the 
thermodynamic product, (BiSe)1.10(NbSe2)1. It has a unit cell containing one BiSe 
bilayer and one NbSe2 layer and the strong in interaction between the layers 
make it more stable than heterostructures with thicker layers. The upper right 
hand lake basin of the map contains 6 isomeric heterostructures containing 4 
bilayers of BiSe and 4 layers of NbSe2 in different sequences, analogous to those 
discussed in Figure 2.3, but with different constituents. The lakes in the bottom 
part of the map represent the two heterostructures that can be created with three 
layers of BiSe and NbSe2 layers. Because of the stabilizing electronic interaction 
between BiSe and NbSe2 layers, the relative stability of each compound in this 
system is controlled by the number of interfaces between each constituent layer 
present in the unit cell. The 11 heterostructure realizes the maximum number 
of these interactions by layering alternating BiSe and NbSe2 layers, making it the 
most globally stable compound in the system. The depth of the valleys relative 
to the saddle points leaving them reflects the kinetic stability of each isomer. 
While the 6 isomers in the upper right are relatively close in elevation, their 
relative stability is dictated by the number of interfaces present, 1 for the 44 
isomer, 3 for the 3311, 2321, and 3212 isomers, and 5 for the 221111 and 
 62 
211211 isomers.  
Figure 2.11. Schematic free energy surface for the BiSe-NbSe2 system showing some 
of the possible kinetically stable heterostructures containing an equal number of BiSe 
and NbSe2 layers and the thermodynamically stable product (BiSe)(NbSe2)1 (labeled 
11). By varying the layering sequence or the composition of the MER precursor, one 
can select a starting position on the energy landscape where the steepest slope results 
in the precursor evolving into a specific heterostructure. This is analogous to 
raindrops falling to Earth and flowing down the surrounding topography into a lake.  
To prepare a specific heterostructure, one needs an approach with 
experimental parameters that can be used to avoid both the other metastable 
heterostructures and the thermodynamically stable phase at this composition. 
Traditional high temperature synthesis and vapor transport reactions both yield 
only (BiSe)1.16(NbSe2)1, as they do not have parameters that can be used to 
control the reaction pathway and composition alone will not work, as all of these 
heterostructures have the same composition.170 Synthesis using CVD would 
require shuttling the sample between different experimental conditions to 
prepare BiSe on NbSe2 and NbSe2 on BiSe.  Precise deposition control would be 
 63 
required to stop growth at the correct number of completed layers for each 
constituent. MBE growth would involve the same challenges as CVD, but with 
added difficulties due to the high vapor pressure of Se at the temperatures 
required for Nb to have sufficient surface mobility. It may not be possible to find 
conditions to grow both NbSe2 on BiSe and BiSe on NbSe2 using either CVD or 
MBE growth.  
The challenges in synthesizing a specific heterostructure using the MER 
approach are designing the nanoarchitecture of the precursor (elemental layer 
thicknesses and the layer sequence) and finding annealing conditions that yield 
the desired product. The nanoarchitecture of the precursor determines the initial 
position on the free energy landscape, which needs to be somewhere within the 
local valley of the targeted product. Since solid state diffusion rates are small at 
low temperatures, the initial rearrangements that occur are constrained around 
the structure defined by the as-deposited precursor. Like water flowing downhill, 
the steepest slope of the energy landscape controls the pathway that the reaction 
takes, which is illustrated as dashed lines in Figure 2.11 for potential starting 
points. Therefore, it is essential to find a precursor nanoarchitecture that allows 
the reaction to begin in a spot on the energy landscape where, when annealed, 
it will flow downhill towards the desired lake. For example, if one wanted to 
deposit a MER precursor targeting the 211211 isomer, one would need to deposit 
both the correct number of constituent atoms in each repeating sequence to form 
4 total layers of each constituent and the layer sequence needs to be constructed 
such that the precursor will nucleate and grow the 211211 heterostructure. This 
is achieved by depositing the correct number of constituent atoms in an order 
that mimics the composition profile of the desired heterostructure’s 
nanoarchitecture. The annealing conditions must provide sufficient time and 
thermal energy for the atoms to diffuse and nucleate the targeted structure, but 
not so much that the precursor moves through a saddle point in the energy 
landscape into an adjacent valley. Too much time or too high a temperature will 
cause the precursor to move out of the local minimum, forming a more 
 64 
thermodynamically stable compound. While MER provides access to the desired 
heterostructure, the trade-off is the lack of control of the rotational order of the 
constituent layers.  
While each of the synthesis methods discussed have different 
experimentally adjustable parameters that provide some control over the 
products formed, as summarized in Table 1, further advances are required. 
Ideally, one would be able to combine the strengths of each, for example the 
flexibility of fluid-based synthesis approaches, the ability to control what phase 
nucleates as done in MBE, and ability to prepare single crystals as done using 
chemical vapor transport, and the ability to define starting parameters as in 
MER. While the MER approach can prepare many metastable compounds and 
heterostructures, additional experimental parameters need to be developed to 
control the structure of what nucleates, both as bulk phases and as individual 
layers in heterostructures. Controlling nucleation density in MER would also be 
valuable, as this would provide control of the in-plane grain size of the 
constituent layers in heterostructures. The Age of Heterostructures will be based 
on the exciting developments enabled by emergent properties created by 
controlling structure and composition on the scale of a unit cell.  
Table 2.1 Summary of synthetic techniques typically used in the synthesis of 
van der Waal’s heterostructures 
Synthetic Typical 
Advantages Disadvantages 
Approach Conditions 
Thermodynamics 
open or sealed 
controls which phase 
Direct reaction vessels,  Easy, low-cost, 
forms, low diffusion 
reaction of temperatures direct approach to 
rates in solids lead to 
the >1000 °C, long thermodynamically 
long synthesis times 
elements synthesis times stable compounds 
and/or high reaction 
(days to months) 
temperatures 
 65 
Table 2.1, continued 
Synthetic Typical 
Advantages Disadvantages 
Approach Conditions 
No control over which 
phase nucleates first, 
Increased diffusion 
fluid speciation as a 
in open or sealed in fluids allows for 
function of time is 
reaction vessels,  shorter synthesis 
extremely challenging 
lower times, additional 
Fluid- to determine 
temperatures experimental 
assisted experimentally, 
than direct parameters 
synthesis solubility constants 
reaction, short (composition of 
not known for most 
synthesis times fluid) relative to 
systems, elements 
(seconds to days) direct reaction of 
from fluid can be 
the elements 
incorporated in 
product 
Results in growth of 
single crystals. Can be challenging to 
Evacuated 
Few-layer and find suitable transport 
ampule filled 
Chemical monolayer growth agent for systems with 
with reagents 
vapor of films possible multiple metal 
and placed 
transport with specially constituents, suitable 
across a 
(CVT) designed reaction substrates may be 
temperature 
vessels and difficult to find for film 
gradient 
appropriate growth 
substrates 
Automated 
assembly platforms 
provide consistent 
and repeatable 
In air , inert Extremely sensitive to 
assembly of 
atmosphere or source of constituent 
individual layers 
vacuum, layers, which require 
into 
Micromech assembly takes other synthesis 
heterostructures or 
anical place at room techniques to make, 
devices, recent 
assembly temperature or multiple processing 
advances have 
with low heat to steps increase 
approached wafer-
remove adhesive chances of inter-layer 
scale assembly, 
layers contaminants 
ability to control 
relative rotation 
angle between 
layers. 
 
 66 
Table 2.1, continued 
Synthetic Typical 
Advantages Disadvantages 
Approach Conditions 
Requires epitaxial 
In-situ 
lattice match between 
characterization, 
substrate and desired 
Deposition takes layer-by-layer 
material (VDWE is an 
Molecular place at < 10-8 growth modes 
exception), extremely 
beam Torr, Substrate possible, produces 
challenging to deposit 
epitaxy heated to epitaxial films, 
heterostructures or 
(MBE) increase surface deposition time 
films with multiple 
diffusion rates. controls film 
constituents due to 
thickness, wafer-
the difference in 
scale 
synthesis conditions 
Allows access to 
metastable 
Deposition takes 
compounds and 
place at < 10-7 
Modulated heterostructures Produces films with 
Torr, annealing 
elemental not accessible via turbostratic disorder, 
to self-assembly  
reactants other techniques, high grain boundary 
precursors 
(MER) deposition time density 
typically occurs 
controls film 
at T  < ~650 °C, 
thickness, wafer-
scale 
The development of experimental methods and tools will continue to be an 
important part of research on heterostructures and devices made using them. 
The discovery of optical contrast of thin layers on thin layers of SiO2 
distinguishes between layer thicknesses with single layer resolution8,9 and the 
use of x-ray fluorescence to determine the absolute number of atoms per unit 
area165  are two examples of fast and non-destructive techniques that have 
accelerated discoveries. Advances in focused ion beam171 and electron 
microscopy172–175 enable detailed atomic level structural, compositional, and 
vibrational analysis of chosen analytical volumes. The need for enhanced 
analytical tools will become more important as heterostructure devices enter the 
development stage. Modern manufacturing, especially of complex devices and 
integrated circuits, is facilitated by intensive statistical analysis of process data 
and application of aggressive statistical process control. Analysis tools are the 
foundation of this approach, both defining baseline conditions and identifying 
 67 
deviations from statistical expectations. The importance of obtaining data on 
each manufacturing step will drive the development of new analytical approaches 
and tools.  
 
2.10 Bridge 
This chapter describes the current challenges in the synthesis of metastable 
2D heterostructures, describing the key reaction steps and methods involved in 
various conventional synthetic techniques. The following chapter describes the 
suite of experimental techniques that are utilized extensively in the following 
chapters to synthesize and characterize the compounds discussed 
  
 68 
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 79 
CHAPTER III 
EXPERIMENTAL METHODS 
3.0 Authorship Statement 
This chapter was written for this work alone with no intention of 
publishing it elsewhere. I am the primary author and wrote the following 
with editorial assistance from my advisor, David C. Johnson. 
3.1 Synthesis of Layered Precursors with Modulated Elemental 
Reactants (MER)  
 All of the compounds presented and discussed in the following text 
were synthesized using the modulated elemental reactants (MER) method, 
which was discussed in detail in the introduction and briefly summarized 
again here.1,2  
Conventional solid-state synthesis techniques generally are diffusion-
limited due to the extremely low diffusion rates in solids. While there are 
many creative solutions to increase the diffusion rates, including applying 
higher temperatures, decreasing particle size, or using a liquid phase, MER 
solves this problem using nanostructured layered precursors built from 
ultrathin elemental layers. Using physical vapor deposition, each layer of 
atoms is sequentially deposited in an order that mimics the structure of the 
target compound(s), with the goal of depositing the required number of each 
atom for the target compound(s).) Because the layered precursor very closely 
resembles the target compound(s) in composition and structure on an 
atomic scale, the total diffusion distances required in the reaction are 
significantly decreased relative to traditional solid-state synthesis reactions 
(on the order of Å with MER vs. ~cm - ~μm with conventional solid-state 
methods).  
Because of the six order-of-magnitude reduction of diffusion lengths, 
diffusion is no longer the rate-limiting step in most MER syntheses. Instead, 
heterogenous nucleation is generally limiting. Because the system is no 
 80 
longer diffusion limited, so long as the composition of the layered precursor 
matches that of the target compound, the target compound should be the 
easiest compound to nucleate at that composition and will therefore be the 
first compound to form. This enables the synthesis of many metastable and 
kinetically stable products that are not accessible via other synthetic 
techniques.3–5 Naturally, compounds that include van der Waal’s gaps make 
excellent synthetic targets using the MER method, such as transition meal 
dichalcogenides (TMD’s). MER allows for the preparation of stacked layers of 
2D compounds, termed van der Waal’s heterostructures, in a nearly infinite 
number of different sequences, which represent a huge unexplored 
parameter-space for materials discovery.6,7   
Experimentally, our MER setup utilizes electron-beam guns and a 
Knudsen effusion cell to evaporate elemental sources, each of which are 
placed in their own ports in the bottom of a high-vacuum chamber, as 
shown in Figure 3.1. The resulting plumes of vaporized atoms are all aimed 
at a substrate holder, which spins to average out any mis-aligned or 
asymmetric elemental plumes. During deposition, each source’s flux is 
monitored via quartz crystal microbalances, placed just below the gate valve. 
A deposition controller instructs pneumatic shutters above each element to 
open and close for the appropriate period such that the number of atoms / 
Å2 deposited in each layer is within error of the target value. This allows 
each precursor to be constructed layer-by-layer in a controlled and 
sequential manner, enabling precise control over the nanoarchitecture of the 
resulting compound or heterostructure.  
 81 
Figure 3.1. Schematic side-view of the high-vacuum chamber used to 
deposit ultrathin elemental layers to form nanostructured precursors. 
Elemental sources are placed in electron-beam gun hearths or an effusion 
cell and aimed at a substrate. Computer-controlled shutters placed between 
the substrate and the sources allow for control over the sequence and 
thickness of deposited layers. 
3.2 X-ray Fluorescence and Statistical Process Control 
X-ray fluorescence (XRF) experiments are used to determine the 
amount of atoms / Å2 that were experimentally deposited in each precursor. 
Using a wavelength-dispersive XRF (WD-XRF) instrument (Rigaku Primus 
II), the fluorescence intensity of each element that was deposited in the 
sample is determined. Previous work in the Johnson group has shown that 
there is a linear relationship between the XRF intensity and the number of 
atoms / Å2 , provided the sample is within the thin film regime (i.e. x-ray 
absorption remains negligible). Using calibration curves that relate the XRF 
intensity to the number of atoms / Å2 , the absolute number of atoms / Å2 
in a sample can be determined, with a sub-monolayer accuracy.8  
 82 
While the publication referenced above was critical in establishing the 
accuracy and repeatability of the XRF method, ideally, the calibration 
curves are continually updated as more high-quality thin film samples are 
synthesized by the group. This iterative adjustment of the calibration curves 
as the number of samples included in the curve increases will only serve to 
ensure the maximum accuracy of the method. As shown in Figure 3.2, 
creating sample calibration curves utilizing only samples synthesized by 
this author during his time at UO gives slopes that are within error of those 
published in 2018 by Hamann et. al.  
Figure 3.2. Plots of the measured XRF intensity for Ti (left) and Sn (right) 
using samples made by this author that display Laue oscillations, allowing 
for the determination of the integral number of crystalline unit cells in the 
sample (and therefore, the total number of atoms / Å2). The slopes match 
those published in Hamann et. al. (0.0133(3) kcps*Å2/Ti atoms and 0.211(2) 
kcps*Å2/Sn atoms).8 
The ability to quickly measure the composition and determine the 
absolute number of atoms in each sample via a non-destructive method has 
revolutionized the way that MER is practiced. This method allows for the 
application of statistical process control, which provides iterative 
adjustment of subsequent deposition parameters such that the maximum 
yield of on-target samples may be obtained. Another significant impact of 
being able to determine sample composition quickly and easily is the near 
 83 
order-of-magnitude reduction in the number of samples needed to obtain 
one with the desired composition.  
An index for measuring the consistency of the deposition plume shape 
for each source can be obtained by normalizing the observed XRF signal for 
each element to the number of units of material programmed into the 
deposition controller. After each set of samples is deposited, the background 
corrected total XRF intensity for each element is normalized to the amount 
programmed into the deposition controller. The average normalized value is 
used to iteratively determine the appropriate deposition controller 
parameters for the next samples deposited, such that the number of atoms 
deposited are within error of the target values. 
3.3 Structural Characterization Techniques 
As discussed in detail in Chapter IV and briefly summarized here, x-
ray reflectivity (XRR) and x-ray diffraction (XRD) experiments are used to 
determine the structure of the deposited precursors. Unless otherwise 
specified, all diffraction or reflectivity data presented was collected on a 
Bruker D8-Discover or a Rigaku SmartLab.  
At low angles, the intensity of the reflected beam dominates the signal 
at the detector. The difference in path length between rays that reflect off 
the air-film interface and those that reflect off the film-substrate interface 
creates a phase difference that can be observed as an oscillatory 
interference effect in most low angle reflectivity patterns, known as Kiessig 
fringes. The period of the Kiessig fringes can be used to extract the total film 
thickness, inclusive of any extra material that may not necessarily be 
incorporated into the coherent crystalline domains contributing to the 
diffraction signal. The angle of the last observable Kiessig fringe can be used 
to roughly estimate the interfacial roughness of the top and bottom of the 
film.  
As one moves to higher angles, the reflected intensity falls off as f(θ) = 
 84 
θ-4, but the diffracted intensity remains significant. Bragg’s law predicts the 
angles that planes of atoms will scatter diffracted x-rays constructively. By 
measuring the spacing of observed Bragg maxima in the XRD pattern, 
Bragg’s law can be used to calculate the interplanar spacing of the atoms 
(i.e. the c-axis lattice parameter) in thin film compounds or 
heterostructures. The intensity and width of the reflections can be used to 
estimate the size of the crystallites in the sample. The experimental setup of 
the diffractometer for XRR and XRD experiments is identical, aside from 
some minor differences in the detector optics to avoid saturating the sensor. 
Sequential XRR and XRD experiments of the same film as a function 
of temperature are used to determine the optimal annealing conditions for 
each compound or family of heterostructures and elucidate reaction 
pathways.  
Additionally, high-angle annular dark field scanning transmission 
electron microscopy (HAADF-STEM) is used to image lift-outs of sample 
cross-sections with atomic-level resolution. The lift-outs are prepared via 
standard technique using a focused ion beam (FIB) to mill a small, electron-
transparent section of the annealed film.9 Finally, unless otherwise 
specified, all microscopy images presented were collected with a probe-
corrected Thermo Fisher Scientific Themis Z STEM.  
3.4 Electrical Characterization Techniques 
The van der Pauw method is used to measure the electrical resistivity 
and Hall effect for thin film samples. Further details about the Van der 
Pauw method and these measurements are given in Chapter V.  
3.5 Bridge 
This chapter describes experimental techniques that are utilized 
extensively in the following chapters to synthesize and characterize the 
compounds discussed. The next chapter presents a method for extracting 
structural information from x-ray diffraction patterns that contain Laue 
 85 
oscillations.  
REFERENCES CITED 
(1)  Fister, L.; Li, X.; Mcconnell, J.; Novet, T.; Johnson, D. C. Deposition System for 
the Synthesis of Modulated, Ultrathin-Film Composites. J. Vac. Sci. Technol. A 
1993, 11 (6), 3014. https://doi.org/10.1116/1.578290. 
(2)  Noh, M.; Johnson, C. D.; Hornbostel, M. D.; Thiel, J.; Johnson, D. C. Control of 
Reaction Pathway and the Nanostructure of Final Products through the Design 
of Modulated Elemental Reactants. Chem. Mater. 1996, 8 (8), 1625–1635. 
https://doi.org/10.1021/cm9601087. 
(3)  Hornbostel, M. D.; Hyer, E. J.; Thiel, J.; Johnson, D. C. Rational Synthesis of 
Metastable Skutterudite Compounds Using Multilayer Precursors. J. Am. Chem. 
Soc. 1997, 119 (11), 2665–2668. https://doi.org/10.1021/ja964084g. 
(4)  Bauers, S. R.; Wood, S. R.; Jensen, K. M. Ø.; Blichfeld, A. B.; Iversen, B. B.; 
Billinge, S. J. L.; Johnson, D. C. Structural Evolution of Iron Antimonides from 
Amorphous Precursors to Crystalline Products Studied by Total Scattering 
Techniques. J. Am. Chem. Soc. 2015, 137 (30), 9652–9658. 
https://doi.org/10.1021/jacs.5b04838. 
(5)  Hamann, D. M.; Rudin, S. P.; Asaba, T.; Ronning, F.; Cordova, D. L. M.; Lu, P.; 
Johnson, D. C. Predicting and Synthesizing Interface Stabilized 2D Layers. 
Chem. Mater. 2021, 33 (13), 5076–5084. 
https://doi.org/10.1021/acs.chemmater.1c01064. 
(6)  Merrill, D. R.; Sutherland, D. R.; Moore, D. B.; Falmbigl, M.; Medlin, L.; 
Johnson, D. C. The Synthesis of [(PbSe)1+δ]m(TiSe2)n[(SnSe2)1+γ]m(TiSe2)n 
Heterostructures with Designed Nanoarchitectures by Self Assembly of 
Amorphous Precursors. Nanoscale 2016, 8, 13646–13651. 
https://doi.org/10.1039/c6nr03406c. 
(7)  Miller, A. M.; Johnson, D. C. Challenges in Synthesis of Heterostructures. J. 
Mater. Chem. C 2022. https://doi.org/10.1039/d2tc00324d. 
(8)  Hamann, D. M.; Bardgett, D.; Cordova, D. L. M.; Maynard, L. A.; Hadland, E. C.; 
Lygo, A. C.; Wood, S. R.; Esters, M.; Johnson, D. C. Sub-Monolayer Accuracy in 
 86 
Determining the Number of Atoms per Unit Area in Ultrathin Films Using X-Ray 
Fluorescence. Chem. Mater. 2018, 30, 6209–6216. 
https://doi.org/10.1021/acs.chemmater.8b02591. 
(9)  Schaffer, M.; Schaffer, B.; Ramasse, Q. Sample Preparation for Atomic-
Resolution STEM at Low Voltages by FIB. Ultramicroscopy 2012, 114, 62–71. 
https://doi.org/10.1016/j.ultramic.2012.01.005. 
 
  
 87 
CHAPTER IV 
EXTRACTING INFORMATION FROM X-RAY DIFFRACTION PATTERNS 
CONTAINING LAUE OSCILLATIONS 
4.0 Authorship Statement 
Chapter IV was published in Zeitschrift für Naturforschung B in 2022. I 
am the primary author of the text with David C. Johnson providing extensive 
editorial assistance. Mellie Lemon and Marisa Choffel contributed experimental 
data, while Sarah Rich and Fischer Harvel helped search the literature for all 
references mentioning Laue oscillations.  
4.1 Introduction 
Laue oscillations result from the incomplete destructive interference of a 
finite number of unit cells and occur when a sample consists of domains with 
the same number of unit cells across most of the area being probed. First 
predicted by Max von Laue, the Laue interference function relates the number of 
unit cells in the diffracting crystal to the distribution of diffracted intensity.1 
Generally, the presence of Laue oscillations are taken as confirmation that grown 
films are of high quality, homogenous, contain only the targeted compound, and 
have smooth and planar top and bottom interfaces.2–11 The presence of Laue 
oscillations is frequently used as evidence of “the high crystallinity of samples”12 
, “the uniformity of the film and smoothness of the interfaces”13 or that “the out-
of-plane order is high and coherent over the entire film thickness”14. 
While it is true that Laue oscillations are a qualitative indicator of sample 
quality, the presence of Laue oscillations also provides an opportunity to gain 
significant structural information about films. The most common quantitative 
analysis of Laue oscillations utilizes an equation derived from the Laue 
interference function to extract the total thickness of the crystalline phase.15–25 
The thickness obtained in this manner is often taken to be the total film 
thickness, which assumes that there is no additional thickness from amorphous 
or non-crystallographically-aligned layers present above and/or below the 
 88 
diffracting crystal. There are only a few reports in the literature where both the 
oscillations in the X-ray reflectivity (XRR) at low diffraction angles and the Laue 
oscillations observed in the vicinity of a Bragg reflection are used to detect 
potential excess material. In these reports, differences between the total film 
thickness calculated from Kiessig fringes in the XRR data and the thickness of 
the crystalline layers obtained via the Laue oscillations were found.26,27 
Furthermore, the intensity of experimental Laue oscillations often differs from 
those predicted from the Laue function. The Laue function results in symmetric 
intensities of satellite reflections on either side of the Bragg maxima, but an 
asymmetric distribution of intensities on each side is also frequently 
observed.9,26–28 In addition, the number of Laue oscillations observed on either 
side of the Bragg reflection varies significantly from sample to sample.2–28 The 
extraction of structural information from Laue oscillations has been challenging 
due to the lack of a discussion of all relevant physical phenomena in a single 
reference that relates structural parameters to Laue intensities and provides 
examples illustrating the development of structural models from experimental 
data. 
This paper addresses this challenge by presenting a summary of the 
relevant physical phenomena, showing how structural features in films impact 
the intensity and number of both Kiessig fringes and Laue oscillations that are 
observed, and provides examples of developing a structural model from 
experimental data. The first example illustrates an approach to simultaneously 
model reflectivity and diffraction patterns when these two phenomena are 
relatively uncoupled. The second example involves a more complex example 
where these two phenomena are both important in the same angular regions. 
Further efforts are required to create simulation software that enables the 
development of atom-level structural descriptions of films using the intensities 
of Kiessig fringes and Laue oscillations. 
4.2 Results and Discussion 
We begin this section with a short review of the physical origin of Kiessig 
 89 
fringes and show how increasing the structural complexity of films effects the 
intensity of the fringes with increasing angle using simulations. Examples show 
how to extract structural information from experimental data.  Next, we discuss 
the origin of Laue oscillations and use examples to demonstrate how Laue 
oscillation intensities calculated using the Laue function differ from 
experimental patterns. We illustrate how the interaction between reflectivity and 
diffraction effects cause the asymmetry in Laue intensities around the central 
Bragg reflection and use simulations to show the impact of structural 
imperfections on the intensities of Laue oscillations. We conclude by developing 
structural models from two experimental data sets where the total film thickness 
(calculated from the period of the Kiessig oscillations) is different from the 
thickness derived from the period of the Laue oscillations (defined as the product 
of the number of coherently diffracting unit cells and the c-axis lattice 
parameter). 
4.3 X-ray Reflectivity (XRR) and Kiessig Fringes: 
Figure 4.1. shows XRR patterns for an experimental TiSe2 film, along with 
simulated reflectivity patterns for 5.00 nm (bottom) and 25.00 nm (2nd from 
bottom) TiSe2 films assuming a uniform electron density slab using the 
BedeREFS software.29 The oscillations observed at low angles in these patterns 
are known as Kiessig fringes, first reported in 193130, which result from 
interference between X-rays reflected off the top air/sample interface and those 
reflected off the sample/substrate interface. The position and spacing of the 
maxima (or minima) can be used to quantitatively determine the film thickness 
using a modified version of Bragg’s law that includes a correction for refraction, 
as shown in Eq. 4.1.31 
sin2 (θi) = θ 2 c + (((ni+Δn)2λ2) / (4t2))         Eq. 4.1. 
 90 
In this equation, θi is the angle of the observed Kiessig fringe maxima, θc 
is the critical angle, ni is the index of the observed Kiessig fringe maxima, λ is the 
wavelength of the radiation utilized, and t is the total film thickness. As shown 
in Figure 4.1., the period of the observed Kiessig fringes is inversely related to 
the thickness of the films. The thickness of the experimental TiSe2 film calculated 
using this equation is 50.10(5) nm (top). 
Figure 4.1. Experimental X-ray reflectivity pattern of a 50.10(5) nm (top curve) TiSe2 
film. Simulated reflectivity patterns from 50.1 nm (2nd from top), 25 nm (2nd from bottom), 
and 5 nm (bottom) TiSe2 films are also shown. The period of the Kiessig fringes is 
inversely related to the film’s thickness. 
An important point is that Kiessig fringes result solely from reflectivity 
phenomena - their presence and period do not depend on the crystallinity of the 
sample. Kiessig fringes will be observed in the reflectivity pattern for any thin 
enough sample with sufficiently smooth planar air/sample and 
sample/substrate interfaces, provided there is a difference in the index of 
refraction between the sample and the substrate. The intensity of the Kiessig 
fringes scales with the difference in electron density between the substrate and 
the film, with a larger difference producing more intense oscillations. 
Additionally, because the critical angle for total internal reflection (θc) scales with 
electron density, the angle of each Kiessig fringe shifts depending on the average 
 91 
electron density of the film (Eq. 4.1.). 
The rate of decay in the intensity of Kiessig fringes with increasing angle 
depends on interface roughness. Simulated reflectivity patterns from models 
containing atomically abrupt interfaces have Kiessig fringes that continue 
throughout the angular range, decreasing in intensity as the angle increases. 
The Kiessig fringes in the experimental pattern become unresolvable at an angle 
of ~7° 2θ. Parratt showed that the angle where Kiessig fringes are no longer 
visible depends on the sample’s average top and bottom surface roughness and 
derived the relationship: 
Δt = λ / (4 * (θ 2 m - θ 2 1⁄2c ) ))         Eq. 4.2. 
where θm is the angle of the last observed Kiessig maxima and θc is the critical 
angle.32 The roughness of both the top and bottom interfaces controls the angle 
to which the Kiessig interference pattern will be visible. Figure 4.2. demonstrates 
how different amounts of roughness in the bottom sample/substrate (σsubstrate) 
and the top air/sample (σsample) interfaces reduce the intensity of the Kiessig 
fringes. The slope of the initial decay of the intensity of the Kiessig fringes is 
different for the bottom and top interfaces. The shape of the intensity envelope 
can therefore be used to distinguish between roughness at the top or bottom 
interfaces. Kiessig fringes observed out to 7° 2θ correspond to an interfacial 
roughness of about 5 Å according to the Parratt relationship, eq. (2). 
Further information about a sample’s structure can be extracted from 
deviations in the shape of its XRR pattern from that expected for a single layer.29 
The reflectivity from a film with a single constituent and perfect, planar interfaces 
is described by the Fresnel equations and the intensity decay is smooth, even, 
and continues to the angle at which the average scattered intensity is less than 
the background intensity.33 If there are two layers in the film with different 
electron densities, Kiessig fringes from the two layers will both be apparent in 
the X-ray reflectivity scan. 
 
 92 
Figure 4.2. Simulated reflectivity patterns from a 30.19 nm TiSe2 film with different 
amounts of interfacial roughness. The amount of interfacial roughness determines the 
maximum angle at which the Kiessig interference fringes are visible. The shape of the 
intensity decay differs depending on whether the roughness is at the top or at the bottom 
interface. 
Figure 4.3. illustrates this effect, showing separate simulated reflectivity patterns 
for 2.42 nm TiO2 (bottom) and 50.05 nm TiSe2 (middle) films, along with the 
calculated reflectivity patterns for a film containing a 2.42 nm TiO2 layer on top 
of a 50.05 nm TiSe2 film on a silicon (Si) substrate (top). The presence of 
oscillations with two different frequencies indicates that a second layer of 
material with a unique electron density and thickness is present in a film. 
Although somewhat subtler, the experimental pattern in Figure 4.1. also shows 
this effect, with a weak, low frequency oscillation apparent under the higher 
intensity oscillations from the total film thickness.  The large period of the 
underlying oscillation suggests that the additional layer is much thinner than 
the TiSe2 layer. 
 93 
Figure 4.3. Simulated XRR patterns of 2.42 nm TiO2 (bottom) and 50.05 nm TiSe2 
(middle) films, along with the simulated pattern for a film containing 2.42 nm TiO2 on 
top of 50.05 nm TiSe2 (top). 
4.4 Laue Oscillations  
If the sample consists of a crystallographically aligned film or contains a 
repeating sequence of deposited amorphous layers with different electron 
densities, the interference caused by the periodic changes in electron density 
results in Bragg reflections at angles given by Bragg’s Law: 
    nλ = 2dsin(θ)           Eq. 4.3. 
where n is an integer, and nλ is the difference in distance traveled by a wave 
scattered by repeating planes of equal electron density that are a distance (d) 
apart. The resulting evenly spaced set of reflections can be indexed as a one-
dimensional crystal. Using Bragg’s Law, the thickness of the layers (or the size 
of the unit cell of crystals orientated perpendicular to the substrate) can be 
extracted from the diffraction pattern. Figure 4.4. shows the XRD pattern for a 
79-layer thick TiSe2 film, displaying four evenly spaced Bragg maxima, which 
can be indexed as 00l reflections consistent with those expected for a unit cell 
with a c-axis lattice parameter of 6.036(1) Å. The inset of Figure 4.4. expands the 
 94 
intensity and angular scale about the 001 reflection. The weak subsidiary 
maxima seen on the sides of this Bragg reflections are Laue oscillations. The 
positions and intensities of these satellite reflections are predicted by the Laue 
interference function: 
I(Q) ∝  sin2(0.5*N*Qc) / (sin2(0.5*Qc)         Eq. 4.3. 
where c is the relevant lattice parameter, Q is the scattering vector, and N is the 
integral number of coherently diffracting unit cells.23,33 Because Laue 
oscillations originate from the incomplete destructive interference of a finite 
number of diffracting unit cells between Bragg reflections, their presence 
suggests a low defect density. 
Figure 4.4. Experimental XRR (gray) and XRD (black) patterns of a 79-layer crystalline 
TiSe2 film. The four Bragg reflections can be indexed as 00l reflections yielding a c-axis 
lattice parameter of 6.036(1) Å. The inset highlights the Laue oscillations observed on 
the 001 reflection. 
Kiessig fringes and Laue oscillations provide complementary structural 
information about the sample. The period of the Kiessig fringes determines the 
total film thickness (tsample), inclusive of any impurity layers or amorphous 
material, while the period of the Laue oscillations determines the number of 
coherently diffracting unit cells in the film (N), which can be multiplied by the c-
 95 
axis lattice parameter (c) to obtain the thickness of the coherently diffracting 
crystal. 
Structural defects typically prevent experimental diffraction data from 
exactly matching that expected for a perfect film. For example, the total amount 
of material in a film is difficult to control so the total film thickness is typically 
not equal to the thickness of the coherently diffracting crystal. Thus, the angular 
positions of the Kiessig fringes will differ from those calculated from the 
thickness of the coherently diffraction domain obtained from the Laue 
oscillations. The experimental amplitude of Laue oscillations is also typically 
much smaller than calculated, often asymmetric with respect to the Bragg 
reflection, and the rate of decay of the oscillations as one moves away from the 
main Bragg reflection varies significantly from sample to sample. These 
differences in amplitude are not often discussed when Laue oscillations are 
observed. 
The Laue interference function predicts a symmetric distribution of 
satellite reflections centered on each Bragg maximum, as shown in Figure 4.5a 
(blue trace), but experimentally the intensity of the Laue oscillations is often 
different on either side of the Bragg reflection. Asymmetry of intensities was 
present in slightly more than half of the 27 representative reports we examined 
in a non-exhaustive literature search. This asymmetry occurs whether the Bragg 
reflection is dominated by the substrate, as in epitaxially grown films, or if the 
Bragg reflection is caused only by the film itself. The TiSe2 film in Figure 4.5a 
(black trace) illustrates a typical intensity asymmetry around a Bragg reflection. 
The cause of the asymmetry in the intensity in this sample is the changing phase 
relationship between Kiessig fringes and Laue oscillations as the diffraction angle 
moves through that of a Bragg reflection. Figure 5b illustrates the effect of this 
changing phase relationship in a simulated diffraction pattern of a structurally 
perfect 301.8 nm thick film containing fifty 6.036 Å thick TiSe2 layers. Here we 
use the approach of Zwiebler et. al., approximating the unit cell structure with 
slabs of the appropriate element in the simulation.34 For the TiSe2 layers, equal 
 96 
thickness slabs of Se, Ti, and Se were used totaling the thickness of the c-axis 
of the unit cell. Before the 001 reflection, the Kiessig and Laue effects are 
constructively interfering. Between the 001 and 002 reflections, the two are 
destructively interfering, resulting in the much lower average intensity between 
these reflections. The average intensity between the 2nd and 3rd reflections 
increases because the Kiessig and Laue effects are again constructively 
interfering. The bottom XRR pattern (black trace) in Figure 4.5 shows an 
expanded view of the oscillations around the 001 reflection, which are 
asymmetric. Asymmetry caused by interference of the Kiessig and Laue effects 
is most likely to be observed for Bragg reflections at smaller 2θ values due to the 
decay of Kiessig fringe intensities as 2θ increases.  
Experimentally observing the shift in phase between the Kiessig and Laue 
interference effects through Bragg reflections requires a film with extremely 
smooth interfaces, which is challenging to prepare experimentally. Figure 4.6. 
shows an experimental diffraction pattern where the changing sign relation 
between the two interference effects is clearly visible. This pattern also shows 
how the changing relative intensity of the Kiessig and Laue effects can cause a 
very weak Bragg reflection, resulting from the location of atoms in the unit cell, 
to appear split as the relative phase changes moving through the center of the 
001 reflection. 
The intensities of both Kiessig and Laue oscillations also depend on the 
abruptness and smoothness of the interfaces in the film. The relative magnitude 
of intensities of Kiessig oscillations depends on the smoothness of interfaces and 
the magnitude of the electron density differences between the constituents. The 
intensity of Laue oscillations depends on the percentage of the film that contains 
the dominant thickness of coherently diffracting crystalline domains, the 
distribution of thickness of the crystalline domains (a form of roughness, as the 
entire area measured might contain several thicknesses), and the inherent 
intensity of the Bragg reflections, which depend on the location of atoms within 
the unit cell. Figure 4.7. shows the effects of increasing the substrate and sample  
 97 
 
Figure 4.5. (a) Comparison of the experimental Laue oscillations observed on either side 
of the 001 reflection of a TiSe2 film with that calculated from the Laue interference 
function   and a simulation that includes reflectivity using the BedeREFS simulation 
software. (b) A simulated XRR/XRD pattern of a 50-layer Se|Ti|Se film with a c-axis 
lattice parameter of 6.036 Å. The changing phase relationship between Kiessig fringes 
and Laue oscillations as the scattering angle moves through that of Bragg reflections is 
apparent in the lower average intensity between the 1st and 2nd Bragg reflections.  
 98 
Figure 4.6. Experimental diffraction data of a (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) 
heterostructure. 
Figure 4.7. Simulated XRR patterns of a 50-layers TiSe2 film on a Si substrate 
illustrating how the roughness affects the symmetry of the satellite reflections around 
the Bragg reflections. Increasing roughness of the substrate and/or surface damps the 
intensity of the Kiessig fringes, making the Laue oscillations more symmetric. 
 99 
interfacial roughness on the appearance of the interference pattern around the 
001 reflection in simulated diffraction patterns of TiSe2. The simulations 
approximate roughness by replacing an abrupt change in electron density at 
interfaces with a smooth gradient of width σ. Kiessig interference fringes are 
damped out as the magnitude of the roughness at the interfaces increases. 
Increasing roughness can damp out the Kiessig fringes enough that a 
symmetrical distribution of satellite reflections occurs around the Bragg maxima 
at higher angles. This infers that samples with an asymmetric distribution of the 
intensity of Laue oscillations have smooth interfaces. 
The experimentally observed decrease in the intensities of Laue 
oscillations as one moves further away from the central Bragg maxima is 
typically much faster than predicted by the Laue oscillation function. While some 
of this intensity decrease is caused by substrate and/or surface roughness of 
“extra” material, a distribution in the thickness of the coherently diffracting 
domain also contributes to this accelerated decrease in intensity. Figure 4.8. 
contains several simulations, where the percentage of coherent domains of 
different thicknesses was varied. If there are only two different thicknesses 
present, the interference pattern between the two different Laue oscillation 
functions is evident and the fringes closest to the Bragg maxima yield the average 
value of the coherent diffracting domain thicknesses. The fringes close to the 
Bragg maxima also yield the average value for the thickness for broader 
distributions, but the intensity of the oscillations decreases as one moves away 
from the Bragg maxima. These simulations suggest that the further the angular 
distance that Laue oscillations are observed from the Bragg maxima, the 
narrower the size distribution of coherently diffracting domains. 
 100 
Figure 4.8. Simulations of diffraction patterns from different distributions of coherently 
diffracting domains. The top simulation is from a sample with 44 TiSe2 layers. The 
simulations below this are from different percentages of film area with the indicated 
number of TiSe2 layers in the coherently diffracting domain. 
4.5 Developing Structural Models From Kiessig Fringes and Laue 
Oscillations 
We conclude with two examples demonstrating how to systematically 
construct structural models using extracted structural information from X-ray 
reflectivity and X-ray diffraction data on samples with both Kiessig fringes and 
Laue oscillations. The first example is an Fe-doped VSe2 film whose XRR and 
XRD scans are shown in Figure 4.9. The total thickness of the film can be 
extracted from the Kiessig oscillations using Eq. 4.1, yielding a film thickness of 
271.0(2) Å. The Laue oscillations are used to determine the number of unit cells 
in the coherently diffracting domain from their positions. The Laue oscillations 
are consistent with 44 unit cells in the diffracting domain. The positions of the 
00l Bragg reflections are used to determine the c-axis lattice parameter of 
6.088(3) Å. The product of the number of unit cells (44) and the c-axis lattice 
parameter (6.088(3) Å) yields the thickness of the coherently diffracting domain 
– 267.9(1) Å. The Kiessig derived thickness is 3.1 Å larger, indicating that there 
is a thin layer of excess material. Independent corroborating evidence for a small 
 101 
amount of excess material was obtained from the absolute number of atoms / 
Å2 of each element determined from x-ray fluorescence (XRF) data, which 
indicated that the excess material is vanadium oxide.35 
A structural model of the film to simulate the diffraction data below 20° 2θ 
was created from the data derived from the Kiessig and Laue oscillations. A 
model with a 267.9(1) Å thick FexV1–xSe2 layer and top 3.1 Å thick surface layer 
of vanadium oxide was used to determine the top and bottom roughness of the 
film. Figure 4.9 shows the simulated pattern with interfacial roughness of σVSe2 
= 5.75 Å, σoxide = 5 Å, and σsubstrate = 2.5 Å, which reasonably matches the low 
angle experimental reflectivity pattern. Dividing the 267.9(1) Å thick FexV1–xSe2 
layer into 44 explicit unit cells of FexV1–xSe2 by using elemental slabs as 
discussed earlier provides a good fit to the experimentally observed positions of 
the Laue oscillations around the 001 reflection (see Figure 4.9). The intensities 
of the Laue oscillations, however, are too large, as the actual sample probably 
does not contain exactly 44 unit cells across the entire area probed by the X-ray 
beam, and we need to add the effect of substrate roughness. Including the 
substrate roughness determined from the FexV1–xSe2 slab model does a 
reasonable job of matching the experimental pattern except that the Laue 
intensities are still too intense. The intensities of the Laue oscillations can be 
reduced by assuming that the film consists of regions that contain thinner 
coherently scattering domains, as discussed above. However, this will not yield 
a unique structural model for the film. 
Diffraction patterns and their analysis become increasingly complicated 
as the Kiessig and Laue intensities interact across a large angular range. The 
XRR/XRD patterns collected of a (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) 
heterostructure, displayed in Figure 4.10, illustrates these challenges.36 The 
extracted total film thickness from the Kiessig fringes is 309.6(5) Å. From the 
period of the Laue oscillations at higher angles, it was determined that there are 
10 unit cells in the coherently diffracting domains. The product of 10 unit cells 
times the c-axis lattice parameter (27.97 (10) Å) gives a crystal thickness of  
 102 
Figure 4.9. Experimental XRR (gray) and XRD (black) patterns of a 271.0(2) Å thick 
crystalline FexV1–xSe2 film and simulated XRR pattern (teal) for a 267.9 Å thick FexV1–
xSe2 film consisting of 44 unit cells. The difference in Kiessig fringe period causes a poor 
fit of the simulated film above ~3 °2θ. Including the excess material not incorporated 
into the coherent diffraction domain results in a simulated pattern that provides a 
reasonable fit over the entire range of the scan.  
279.7 Å. The difference between these two values is 29.9 Å. The question is how 
does one divide this thickness between the top and bottom of the crystalline 
domains? Figure 4.10 contains several simulated XRR patterns from models that 
distribute the 30 Å of excess material between the top and/or the bottom of the 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) diffracting domain (Se was used as the 
excess material in these models). The simulated patterns are very sensitive to 
the exact distribution of the excess material between the front and back of the 
film. While we assumed in these simulations that the composition of excess 
material at the bottom and the top were the same, this is not necessarily true, 
which adds another unknown parameter to potential models. This experimental 
pattern does not contain an explicit feature that allows us to estimate or separate 
the roughness of the substrate, the film, or the excess material. The large 
number of potential variables makes it currently impossible to extract additional 
information through simulations. Additional information, for example from 
 103 
HAADF-STEM images of film cross sections, is needed to limit the parameter 
space.  
Figure 4.10: Experimental XRR (grey) and XRD (black) patterns of a 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) heterostructure annealed at 350 °C, along with 
simulated patterns for models that consist of 10 unit cells of the targeted 
heterostructure, plus 30 Å of additional material distributed between either the top 
and/or the bottom of the heterostructure. No interfacial roughness was added to these 
models. 
4.6 Conclusion 
This manuscript shows how to extract quantitative structural information 
from Laue oscillations and Kiessig fringes. The thickness of the coherently 
diffracting domain can be calculated from the product of the c-axis lattice 
parameter and the number of unit cells present determined from the Laue 
oscillations. If there is extra material in the film, there will be a difference 
between total film thickness from the period of the Kiessig fringes and the 
thickness of the coherently diffracting crystal domain. When the Kiessig fringes 
damp out before Laue oscillations are observed, it is possible to extract the 
roughness of the substrate and of the deposited layers. Samples with large 
differences between the total film thickness and crystal thickness are challenging 
 104 
to analyze, because the simulated patterns vary considerably as the extra 
thickness is partitioned above or below the coherently diffracting domain. Also 
challenging are samples with large angular regions where both the Laue and 
Kiessig interference effects contribute significantly. In films where Laue 
oscillations occur around reflections at high angles, however, the approach 
presented provides valuable additional information. Additional simulation tools 
need to be developed to get access to the additional structural information 
present in Laue oscillations obtained from experimental data. 
4.7 Experimental 
Films for this study were prepared using a custom high vacuum physical 
vapor deposition (PVD) chamber. Artificially layered precursors for binary thin 
films were prepared by repeatedly depositing M|Se bilayers, where ideally the 
number of atoms / Å2 deposited in each bilayer is identical to the number 
required to form one unit cell of the targeted compound. Similarly, precursors 
for heterostructures were prepared by repeatedly depositing M|Se|M’|Se layers 
in the same manner. Metal layers were deposited using electron-beam guns, 
while Se was deposited with a Knudsen effusion cell. All precursors were 
deposited onto ⟨100⟩ Si substrates with a native SiO2 layer.  A pressure of less 
than 1 × 10−7 Torr was maintained during the deposition. In-house deposition 
software was used to control and monitor the amount of material deposited in 
each layer using pneumatic-controlled shutters and quartz crystal 
microbalances. After deposition, the precursors were removed from the vacuum 
chamber, briefly exposed to atmosphere, and brought into a dry-box (N2 with 
<0.2 ppm O2) where they were heated for 30 minutes at 500 °C and 350 °C for 
the Fe-doped VSe2 and the (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) films, 
respectively. 
Structural characterization was carried out via x-ray reflectivity (XRR) and 
x-ray diffraction (XRD), while composition was determined using x-ray 
fluorescence (XRF). XRR and specular XRD patterns were collected on a Bruker 
D-8 Discover diffractometer. All diffraction measurements utilized a Cu Kα 
 105 
radiation source. Special care must be taken when aligning each sample to the 
diffractometer, as the positions and intensities of reflectivity/diffraction features 
are extremely sensitive to sample alignment. To confirm the alignment of the 
sample in the goniometer, rocking curve scans were collected at two different 
small 2θ values. The maxima in both rocking curve scans occurring when the 
incident and exit angles are equal are evidence that the sample is correctly 
aligned in the center of the goniometer. 
The absolute amount of each element deposited was determined using 
XRF data collected on a Rigaku ZSX Primus II with a rhodium source. Previously 
published calibration curves were used to relate the background-corrected 
integrated raw intensity to the atoms / Å2 for each element.35 Table 4.1. contains 
the calculated amount of each element required for the crystalline domains that 
contribute to the observed Laue oscillations along with the total number of atoms 
per unit area (areal density) of each element, as determined from the XRF 
measurements of each film. 
Table 4.1. Experimental and target atomic areal density for the Fe-doped VSe2 and 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) films as determined from XRF measurements 
Target 
Exp. V Exp. Fe Exp. Se Target V Target Fe Target Se # of 
Atoms/Å2 Atoms/Å2 Atoms/Å2 Atoms/Å2 Atoms/Å2 Atoms/Å2 Unit 
Cells 
3.43(7) 1.4(1) 10.2(3) 3.43 1.71 10.29 44 
       
Target 
Exp. Bi Exp. Mo Exp. Se Target Bi Target Mo Target Se # of 
Atoms/Å2 Atoms/Å2 Atoms/Å2 Atoms/Å2 Atoms/Å2 Atoms/Å2 Unit 
Cells 
3.88(8) 1.15(2) 6.5(3) 3.37 1.18 6.8 10 
 
Simulated XRR/XRD patterns were created using the BedeREFS software, 
which incorporates both reflectivity and diffraction physics that are required to 
accurately simulate thin film X-ray patterns.29 BedeREFS uses “slabs” of electron 
density that are appropriately scaled to match the thickness and electron density 
of each layer in the film’s structure. Unless otherwise specified, the “slab” models 
 106 
created to simulate the reflectivity patterns, shown in Figures 1, 2, 3, 5, 7, 8, 9, 
and 10, had no added interfacial roughness, and were generated using a Si 
substrate with 10-20 Å of SiO2. 
4.8 Bridge 
 This chapter described a method for extracting the maximum possible 
quantity of structural information from x-ray diffraction patterns that contain Laue 
oscillations, describing best practices to follow in order to avoid potentially misleading 
conclusions about the sample. The next chapter describes the work I did to repair and 
update an automated system used to measure thin film sample’s electrical resistivity 
and Hall effect.  
 
  
 107 
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 111 
CHAPTER V 
AUTOMATED TEMPERATURE-DEPENDENT ELECTRICAL RESISTIVITY 
AND HALL EFFECT MEASUREMENT SYSTEM 
5.0 Authorship Statement 
This chapter was written for this work alone with no intention of 
publishing it elsewhere. I am the primary author and wrote the following with 
editorial assistance from my advisor, David C. Johnson. 
5.1 van der Pauw Method 
The van der Pauw method is commonly used to measure the electrical 
resistivity and Hall effect of thin film samples.1–3 Using four electrodes placed 
around the edges of an arbitrarily shaped sample and making multiple current-
potential measurements, the average resistivity can be determined via the van 
der Pauw equation. However, the van der Pauw method makes several 
assumptions that must be satisfied for the van der Pauw equation to hold: the 
sample must be homogenous (i.e. uniform in thickness and no isolated 
holes/changes in density as a function of position in sample), all four contacts 
must be ohmic, all contacts must be placed at the edge of the sample, and the 
area of each contact must be at least an order of magnitude smaller than the 
sample area.4  
The van der Pauw method for measuring resistivity consists of making 
sequential measurements passing current and measuring potential along the 
vertical and horizontal edges of the sample. Figure 5.1 depicts a thin film sample 
attached to the measurement system in the custom-built sample holder. The 
sample was deposited through an X-shaped Hall cross shadow mask. As shown, 
the electrical contacts made from elemental In are attached to each corner of the 
cross. The contacts are labeled 1 – 4, beginning in the upper left and moving 
counter-clockwise. Measurements made along the vertical edge are obtained by 
passing current between contacts 1 & 2 while measuring the potential between 
contacts 3 & 4 (I12V34), or vice versa. Measurements along the horizontal edge 
 112 
are obtained by passing current between contacts 1 & 4 while measuring the 
potential between contacts 2 & 3 (I14V23), or vice versa. Using Ohm’s Law (V = 
IR), the electrical resistance along the horizontal and vertical edges can be 
calculated. 
Figure 5.1. Top-down schematic of thin film sample holder with soldered In 
contacts in each of the four corners of the sample’s top Hall Cross.  
 As shown in Eq. 5.1, the van der Pauw equation relates the 
measured horizontal and vertical resistances (RH and RV, respectively) to the 
sheet resistance, RS. The average resistivity, ρ, is obtained by multiplying the 
sheet resistivity by the sample’s thickness. 
−𝜋𝑅𝑉 −𝜋𝑅⁄ 𝐻⁄
1 =  𝑒 𝑅𝑠 + 𝑒 𝑅𝑠    Eq. 5.1 
While the average resistivity of a sample can technically be obtained in as 
few as two measurements, to increase accuracy and reduce measurement error 
generally eight total electrode permutations are used, from which the results are 
averaged after correcting for the sign convention. The first two permutations can 
be thought of as resulting from swapping the direction that the current flows (i.e. 
changing the polarity of the current) while maintaining the voltage leads (I21V34 
+ I12V34). The remaining six permutations result from swapping the position of 
the voltmeter and ammeter leads (e.g. if the current was measured between 3 + 
4, it would now be measured between 2 + 1) and again switching the polarity of 
the current (I32V41, I23V41, I34V12, I43V12, I14V23, I41V23). This totals eight possible 
 113 
electrode permutations, which are measured at several different current 
strengths for maximum accuracy. The resulting current-potential data is plotted, 
and the slope is used to extract a resistance. The eight measurements can be 
split into two groups – those taken along the vertical edge (I21V34, I12V34, I34V12, 
I43V12) and those along the horizontal edge (I32V41, I23V41, I14V23, I41V23). By taking 
the absolute value of each of the four horizontal slopes and averaging the result, 
the horizontal resistance, RV,  is obtained. An identical calculation is used to 
determine the horizontal resistance, RH. By adding additional measurements, 
any noise that occurs or offset voltage resulting from thermoelectric potentials 
generated by the difference in temperature across the sample or across the wires 
will be cancelled out. 
To calculate the average resistivity of the sample, an iterative technique 
based on the Newton-Raphson method used in numerical analysis is used to 
repeatedly solve for the next RS until the result converges to the desired precision, 
−𝜋
as shown in Eq 5.2, where 𝑅+𝑆  is the next iteration and 𝑆 =  𝑒
⁄𝑅𝑠 .5 For the 
measurements made in this work, generally less than 50 iterations are required 
before the result converges to the desired accuracy. 
1−𝑆𝑅𝑉−𝑆𝑅𝐻
𝑅+𝑆 =  𝑅
2
𝑆 + 𝑅𝑆 + 𝜋(𝑅 𝑆𝑅     Eq. 5.2 𝑉 𝑉+𝑅 𝑅𝐻𝑆 𝐻)
The van der Pauw method for measuring the Hall effect of a sample is like 
the method described for resistivity, but with only four possible electrode 
permutations. However, in this measurement, current is passed between 
diagonally placed electrodes, while the potential is measured between the other 
pair of diagonal electrodes (e.g. I13V24). The field strength is varied and the 
potential measured again until all the desired field strengths have been 
measured.  
Then, this process is repeated with the remaining three electrode 
permutations. Just as with the resistivity measurement, the first permutation is 
obtained by reversing the polarity of the current while maintaining identical 
 114 
voltage leads (e.g. I31V24). Then the position of the current and voltage leads are 
switched (I24V13) and the current polarity is again flipped (I42V13). Once the 
measurement of each of the four electrode permutations has been completed, 
the module is finished.  
5.2 System Overview 
The automated system consists of many different instruments and devices 
that communicate through a standardized computer-facilitated GPIB interface. 
All code is implemented in Labview. A Keithley 706 Scanner with an installed 
Keithley 7065 Hall Effect card is used to connect the sample electrodes 
(numbered 1 – 4 per the discussion above) with the voltmeter, the ammeter, and 
the current source. By opening and closing the appropriate connections in the 
Hall Card, any of the instruments can be connected to any of the sample 
electrodes. A Keithley 220 Current Source is used to supply current, while a 
Keithley 6485 Picoammeter is used to measure the current passed and a Keithley 
2182A Nanovoltmeter is used to measure potential. For the Hall Effect 
measurement, a LakeShore XEM4 electromagnet with a LakeShore 643 power 
supply is used to provide a variable magnetic field between +9 and -9 kG, while 
a LakeShore InAs Hall Sensor is used to measure the applied magnetic field at 
the sample.  
Temperature control is provided by an Oxford Instruments Intelligent 
Temperature Controller ITC4 which varies the output to a heater anchored to a 
Cu thermal mass. A cold-head driven by a He-compressor is used to cool the 
system as low as 20 K. The cold-head and the heater (driven by the temperature 
controller) work together to vary the sample temperature between 20 K – 298 K.  
Before beginning a temperature-dependent run, it is necessary to make an 
initial resistivity and Hall Effect measurement of the sample at room 
temperature. This measurement will ensure that the sample is properly 
connected to the measurement system and determines the initial value of the 
maximum allowed current for the repeated measurements during the upcoming 
 115 
temperature-dependent run. After replacing the hollow cylindrical Cu thermal 
shield and Al vacuum shield over the sample holder / coldfinger, the pressure of 
the system can be reduced. The system contains two pumps – a roughing and a 
water-cooled turbomolecular pump that provide the vacuum for the system. Two 
valves are placed between the system and the pumps to allow the system to be 
vented to atmospheric pressure. Once the system reaches a sufficiently low 
pressure that there is no risk of atmospheric O2 condensing on the coldhead ( < 
5 × 10−5 Torr), the He compressor is turned on, decreasing the system 
temperature towards its minimum temperature of ~20 K.  
The general structure of the system’s code is shown in Figure 5.2. This 
code is designed to be executed at the beginning of a measurement run – e.g. 
after one has contacted a new sample at room temperature and verified that the 
contacts are ohmic. The code begins with an initial cooldown period in which the 
system is reduced to its minimum temperature, followed by controlled heating of 
the system to the temperatures specified by the text file containing the “List of 
Temperatures”. This begins at the system’s minimum temperature, 20 K, and 
ascends in steps of approximately 10%.  Since the thermal mass of the system 
is very large relative to the thermal mass of a single sample, the heating behavior 
is controlled by the system’s mass. Because of this, a single list of set 
temperatures generally works for all samples.  Before it can be executed, the 
code requires several user-defined initial values to set the parameters of the 
measurements (e.g. name of text file where data output will be saved, # of I-V 
steps in the resistivity measurement, # of B-field steps in Hall Effect 
measurement, Minimum and Maximum B-field strength, etc.). Users also need 
to enter the initial maximum current, which is obtained from the room 
temperature measurement discussed above. At the end of each resistivity 
measurement, the program scales the requested maximum current for the next 
resistivity measurement by the percent difference between the last resistivity 
measurement and the current one. In other words, if there is a 10% increase in 
the resistivity between the current measurement and the previous one, the 
 116 
maximum current for the next measurement will be 10% less. In this manner, 
the maximum current for the measurement is allowed to vary in a manner that 
provides a sufficiently large signal, but a sufficiently small power dissipation that 
the sample is not heated. Immediately after turning on the He compressor, the 
user should plan to press the “Go” button, located on the program’s front panel. 
This will begin the execution of the system’s code, beginning with the Cooldown 
module. After the user enters the initial parameters and begins execution of the 
code, no further human interaction is required until the end of the run is 
reached, when the user is required to turn off the He compressor and vacuum 
pumps.  
Figure 5.2. Schematic overview of the structure for the automated system’s 
code. The system is based around iterative executions of the main Heating 
Loop, which contains three sub-modules: the first stabilizes the system at a 
desired temperature, the next measures the electrical resistivity of the sample, 
and the last measures the Hall effect of the sample. This Heating Loop is 
executed until all the set temperatures from the user-defined list have been 
exhausted.  
The code begins with execution of the Cooldown Loop, which monitors the 
temperature of the system during the initial cooldown period. which continually 
measures the system temperature in two places – at the sample and at the 
heater, monitoring them until the heater temperature nears the first temperature 
on the list of set temperatures. During the cooldown sequence, which typically 
takes approximately ~2.5 hrs for the system to reach minimum temperature of 
~20 K, the electrical resistivity module is repeatedly executed. This provides an 
estimate of the sample’s resistivity before the run has begun, allowing for 
 117 
increased accuracy by checking the cooldown data against the data collected 
during the heating run, along with detection of hysteresis in the sample. Each 
time the Cooldown Loop finishes, it checks whether the temperature of the 
system at the heater is within a certain range of the first set temperature in the 
list (range is modifiable, but currently set at ≤2 K). If the heater temperature is 
outside this range, the loop executes again. If it is, the Cooldown Loop exits and 
execution of the Heating Loop begins.  
The Heating Loop executes once per desired temperature step, which are 
defined in the user-provided “List of Temperatures”. As shown in Figure 5.2, the 
Heating Loop consists of three sub-modules: Temperature Stabilization, 
Resistivity Measurement, and the Hall Effect Measurement. Each time the 
Heating Loop executes, the Temperature Stabilization module begins to heat the 
system until it reaches and is stable at the next set temperature. When the 
stability criteria written into the module are met, the module finishes, writing 
the temperature vs. time data into a file and beginning the Resistivity 
Measurement. After the measurement finishes, the Temperature Stabilization 
module runs again to ensure that the sample temperature remains unchanged. 
After the stability criteria is again met, the Hall Measurement module measures 
the Hall coefficient of the sample at that temperature. The last iteratively scaled 
current used in the final execution of the Cooldown module is used in the initial 
execution of the Heating Loop. After the first execution, the maximum current is 
scaled in the same manner as previously described.  
5.3 Temperature Stabilization 
The Oxford ITC4 temperature controller utilizes a standard proportional-
integral-derivative (PID) control loop mechanism to regulate the potential applied 
to the system’s heater, working to bring the system temperature quickly and 
accurately to each user-defined set temperature. The first iteration of the 
Temperature Stabilization module in each iteration of the Heating Loop serves to 
heat the sample to the next set temperature, working to bring the system to 
stability as efficiently as possible (or it would if the code contained the ideal PID 
 118 
parameters for the system at that temperature). The second iteration of the 
module in each iteration of the Heating Loop serves merely as a compliance 
check, ensuring that the sample temperature did not change during the 
resistivity measurement, correcting it and returning the system to stability if it 
did. The Temperature Stabilization loop measures the sample and heater 
temperatures as a function of time, monitoring the standard deviation of both 
temperatures over the last ~60 sec of measurement (exact value is a user-
definable parameter in the code). The loop contains several criteria that must be 
met before the loop exits: the standard deviation of both the heater and sample 
temperature’s must be less than certain values (currently 2 K and 0.2 K for the 
heater and sample, respectively) AND the difference between the heater 
temperature and the set temperature must be less than a certain value (currently 
2 K).  
A PID loop contains three terms, proportional, integral, and derivative, 
which, when properly tuned, work together to efficiently keep the process 
variable (in this case, temperature) close to the target value.6 The proportional 
term sets the output (in this case, the heater voltage) in proportion to the current 
error between the set point and the current value of the process variable. The 
integral term changes the output by considering the magnitude of the error and 
the time for which the error has occurred, essentially integrating the difference 
between two functions, the step function that describes the set point as function 
of time and the curve that describes the process variable (in this case, heater 
temperature) as a function of time. As the error persists over time, the integral 
term’s contribution to the output will increase to drive any persistent error to 
zero. Finally, the derivative term examines the derivative of the process variable 
as a function of time, attempting to drive this function to zero, which helps 
reduce overshoot as the system approaches the set point. The optimal PID terms 
change with the system temperature, as the total amount of thermal mass in the 
system also changes with temperature.  
5.4 Electrical Resistivity 
 119 
The Electrical Resistivity module communicates with the picoammeter, 
nanovoltmeter, and Hall Card to switch between the eight required electrode 
permutations described above. The module is quite simple, containing only an 
initialization step that ensures the instruments are all set to the correct function, 
a loop that measures each of the eight possible electrode permutations, and a 
final step that writes the measured data to an output file. Based on the user-
defined parameters entered in the Heating Loop, the desired number of current 
strengths are measured for each electrode permutation. As of Summer 2022, 
this value was generally taken as five. The code plots the measured potential as 
a function of the current passed, using the slope of the resulting line as the 
measured resistance for that electrode permutation. After this step is completed 
eight times, the code uses the user-defined sample thickness to iteratively 
calculate the average resistivity of the sample via the Newton-Raphson method. 
After this measurement is completed for a given set temperature, the 
Temperature Stabilization sub-module executes again using the same set 
temperature, ensuring that the sample’s temperature has not changed during 
the resistivity measurement. 
 
5.5 Hall Effect 
After the second execution of the Temperature Stabilization module, the 
Hall Effect module executes. This module communicates with the picoammeter, 
nanovoltmeter, Hall Card, the electromagnet power supply, and a multimeter (to 
measure the magnetic field) to switch between the four required electrode 
permutations described above and control the magnetic field applied to the 
sample. Practically, once the leads are connected, the potential is measured as 
a function of time, until the standard deviation of the last 10 seconds of 
measurements is less than the user defined value (currently ≤2% of the 
measured value). Once the potential is stable, the average potential is measured 
and recorded. After that, the applied magnetic field strength is changed, and the 
potential measured again until all the desired field strengths have been 
 120 
exhausted (currently 5 different field strengths). After the potential has been 
measured at each field strength, the measured potential is plotted versus the 
measured field and the slope is used to extract the Hall coefficient. This process 
is repeated three additional times, until all four of the possible electrode 
permutations have been measured. The results are corrected for sign convention 
and averaged to obtain the Hall coefficient for the sample at that temperature. 
At this point, the iteration of the Heating Loop is complete. As the next 
iteration begins, the next set temperature is pulled from the “List of 
Temperatures” and sent to the first execution of the Temperature Stabilization 
module. 
5.6 Bridge 
 This chapter described the details of the automated system used to 
measure the electrical resistivity and Hall Effect of thin film samples presented 
in the following chapters. The next chapter presents my first synthetic efforts 
using the modulated elemental reactants method – a synthetic exploration of two 
binary transition metal dichalcogenide systems, MoSe2 and TiSe2. 
  
 121 
REFERENCES CITED 
(1)  Ramadan, A. A.; Gould, R. D.; Ashour, A. On the Van Der Pauw Method of 
Resistivity Measurements. Thin Solid Films 1994, 239 (2), 272–275. 
https://doi.org/10.1016/0040-6090(94)90863-X. 
(2)  Hemenger, P. M. Measurement of High Resistivity Semiconductors Using the van 
Der Pauw Method. Rev. Sci. Instrum. 1973, 44 (6), 698–700. 
https://doi.org/10.1063/1.1686224. 
(3)  van der Pauw, L. J. A Method of Measuring Specific Restivity and Hall Effect of 
Discs of Arbitrary Shape. Philips Res. Reports 1958, 13, 1–9. 
(4)  Webster, J. G. The Measurement, Instrumentation, and Sensors Handbook; CRC 
Press in cooperation with IEEE Press: Boca Raton, Fla., 1999. 
(5)  Ypma, T. J. Historical Development of the Newton-Raphson Method. SIAM Rev. 
1995, 37 (4), 531–551. 
(6)  Bennett, S. A Brief History of Automatic Control. IEEE Control Syst. 1996, 16 (3), 
17–25. https://doi.org/10.1109/37.506394. 
 
  
 122 
CHAPTER VI 
INVESTIGATING THE FORMATION OF MOSE2 AND TISE2 FILMS FROM 
ARTIFICIALLY LAYERED PRECURSORS 
6.0 Authorship Statement 
Chapter VI was published in Inorganic Chemistry in 2020. Danielle Hamann, 
David C. Johnson, and I are the main contributors to the text. Eric Hadland 
contributed experimental data.  
6.1 Introduction 
In the 1980s and 1990s, the sequence of solid-state reactions between 
transition metals deposited on silicon substrates was intensely investigated, 
because transition-metal silicides were desired as low-resistance replacements 
for heavily doped polysilicon contacts to transistors in integrated circuits.1–3 A 
focus of this research was understanding the reaction evolution between metals 
on silicon surfaces, as it was crucial to control the first phase formed in 
developing the self-aligned silicide or “salicide” process.4 The first step in the 
reaction was proposed to be the formation of an amorphous layer at the interface 
between the metal and silicon, driven by the enthalpy of mixing of the elements.4 
Since diffusion rates roughly scale with melting temperatures, the amorphous 
phase was suggested to have the composition of the lowest melting eutectic in 
the phase diagram. The compound that is easiest to nucleate from this eutectic 
was suggested to form first, but there was debate over its identity. Walser and 
Bene suggested that the congruently melting compound with the highest melting 
point adjacent to the lowest-melting eutectic would form first. However, a second 
proposal suggested that the compound with the largest effective heat of 
formation at the eutectic composition would initially form.5 Over time, the 
concepts developed for metal−silicon reactions were applied to a broad range of 
systems, from the formation of amorphous metallic alloys6 to the sequence of 
intermetallic phase formation at reacting metal interfaces.7  
Recent interest in preparing monolayers of compounds, either alone or as 
 123 
constituents in heterostructures, has focused attention on understanding the 
formation of ultrathin crystalline layers. Key goals include developing an 
approach that is scalable to wafer-scale synthesis, capable of controlling 
thickness to a precise number of unit cells, and able to control defect levels. 
Thin-film transition-metal dichalcogenides (TMDs) and other layered 
chalcogenides, due to their diverse and exotic physical properties that can be 
manipulated by varying the thickness, substrate, or adjacent layers in 
heterostructures, have attracted significant attention from the two-dimensional 
(2D) research community.8–13 While thickness-dependent properties were 
initially discovered by cleaving bulk samples, subsequent synthesis efforts have 
focused on developing wafer-scale preparation techniques, such as chemical 
vapor deposition (CVD).14–16 More recently, atomic layer deposition,17–19 
metal−organic-CVD,20–22 and direct deposition methods (sputtering, pulsed laser 
deposition, ebeam)23–25 have been used to make high-quality layered TMDs.26 
These approaches use elevated temperatures or light to increase reaction rates, 
and the quality of the product depends on the temperature and the photon 
energy utilized (when applicable). The formation process for 2D materials also 
depends on other process parameters including the structure of the substrate, 
the pressure, and the carrier and reactant gas fluxes. While plausible chemical 
schemes have been proposed for many of these systems, there is little reported 
data of intermediate states and no overarching understanding of how changing 
reaction parameters impact the formation mechanism.  
Here we present X-ray reflectivity (XRR) and X-ray diffraction (XRD) data on 
the reaction between ultrathin layers of two different metals, Mo and Ti, with 
amorphous Se. These systems were investigated due to obvious differences in 
the structure of the as-deposited precursors. The precursors were prepared by 
sequentially depositing metal and selenium layers on nominally room-
temperature substrates. The amount of metal atoms in each of the layers was 
close to the number required to form a single dichalcogenide layer. For Mo|Se 
precursors, nucleation occurs during deposition, but there is little subsequent 
 124 
crystal growth. The as-deposited film, while containing small isolated MoSe2 
crystallites, has a modulated amorphous structure containing alternating Mo-
rich and Mo-poor layers. In contrast, the Ti|Se precursors nucleate both TiSe2 
and Ti2Se during the deposition. There is no evidence for alternating Ti-rich and 
Ti-poor layers due to the repeated deposition of the Ti|Se bilayers. The TiSe2 
grains grow significantly during the deposition of subsequent layers, resulting in 
an as-deposited film dominated by layers of crystalline TiSe2. It was 
experimentally determined that depositing ∼10% excess Se in the precursors 
results in the largest grain sizes for the annealed films for both systems. It is 
likely that the excess Se not only compensates for the loss of Se to the open 
system during annealing but also acts as a flux to help facilitate diffusion of the 
metal atoms during the growth of the crystallites. In summary, these two 
different dichalcogenides have surprisingly different formation pathways. 
Annealing precursors with optimized precursor composition and 
nanoarchitecture at ideal annealing conditions resulted in the formation of 
layered TiSe2 and MoSe2 films with well-defined Laue oscillations, indicating an 
integral number of unit cells across the entire film.  
6.2 MATERIALS AND METHODS  
Precursors were prepared by repeatedly depositing elemental bilayers of 
Ti|Se or Mo|Se to form an artificially layered precursor. Mo and Ti layers were 
deposited using an electron-beam gun, while Se was deposited with a Knudsen 
effusion cell. Precursors were deposited onto silicon substrates with a native 
oxide layer while maintaining a vacuum of less than 1 × 10−7 Torr during the 
deposition. In each precursor, the thickness of the Ti and Mo elemental layers 
was held constant at the thickness required to provide enough metal to form a 
single Se-M-Se dichalcogenide trilayer. However, the thickness of the Se layer 
was varied to probe the influence of composition and excess Se on the nucleation 
and growth of the respective dichalcogenides. Inhouse deposition software was 
used to control and monitor the amount of material deposited in each layer using 
pneumatic-controlled shutters and quartz crystal microbalances.27–30 After 
 125 
deposition, the precursors were removed from the vacuum chamber, briefly 
exposed to air, and pumped into a drybox, where they were heated in an N2 
environment with less than 1 ppm of O2 present to crystallize the deposited 
elemental layers. 
Structure and composition were studied via a suite of X-ray techniques. The 
structures were characterized by X-ray reflectivity (XRR) and X-ray diffraction 
(XRD), while composition was determined using X-ray fluorescence (XRF). XRR 
and specular XRD were collected on a Bruker D-8 Discover diffractometer. In-
plane XRD was collected on a Rigaku SmartLab diffractometer. All diffraction 
measurements utilized a copper Kα radiation source. The absolute amount of 
each element deposited was determined using XRF data collected on a Rigaku 
ZSX Primus II with a rhodium source. Previously published calibration curves 
were used to relate the background-corrected integrated raw intensity to the 
atoms / Å2 for each element.31 
6.3 RESULTS AND DISSCUSION  
The initial structure and evolution of the MoSe2 precursors during annealing 
were investigated using XRR and specular XRD. The as-deposited XRR pattern, 
shown in Figure 6.1, contains Kiessig fringes, reflecting the total thickness of the 
deposited films, and two Bragg reflections. The first narrow reflection at ∼10.9° 
2θ is caused by the artificial layering of the Mo|Se precursor, yielding a Mo|Se 
thickness of 8.1 Å. The total thickness calculated from the Kiessig fringes, 194 
Å, is within error of what is expected for a film composed of 24 8.1 Å layers. The 
disappearance of the Kiessig fringes at 17.8° 2θ indicates that the roughness of 
the deposited film is on the order of 2.5 Å, which we calculated using the 
relationship derived by Parratt.32 The broad reflection at 13.4° 2θ corresponds to 
the first-order Bragg reflection expected for MoSe2 and indicates that the 
nucleation and growth of MoSe2 grains perpendicular to the substrate have 
occurred during deposition. A potential second-order Bragg reflection, related to 
the broad reflection at 13.4° 2θ, may be present at higher angles but is very 
weak, suggesting there is significant variation in the distance between 
 126 
crystallized MoSe2 layers within the grains. Together, the XRR and specular XRD 
indicate that the precursor consists of 24 layers containing Mo-rich and Se-rich 
regions relative to the average composition that are each 8.1 Å thick. Within 
these layers are small regions that consist of several irregularly stacked MoSe2 
layers forming barely coherent grains of MoSe2.  
Figure 6.1. XRR and XRD patterns from an annealing study of an as-deposited Mo|Se 
precursor. The annealing temperatures are presented above the scans. XRR scans are 
from 0−15° 2θ, while XRD scans are from 6−60° 2θ; the patterns are overlaid and 
adjusted vertically. All reflections can be indexed to 00l values corresponding to a 
hexagonal unit cell with lattice parameters consistent with those of MoSe2.  
The specular XRD patterns evolve gradually as the annealing temperature 
is increased, and a very crystalline MoSe2 00l diffraction pattern is obtained after 
being annealed at 650 °C for 60 min. As the annealing temperature is increased, 
the reflection from artificial layering moves to higher angles, indicating that the 
period of the artificial layering is becoming smaller. The initial broad reflection 
at 13.4° 2θ also shifts to higher angles, becoming narrower and more intense as 
annealing temperature is increased, indicating that the spread of interlayer 
distances within each grain is decreasing. This also suggests that there are more 
 127 
MoSe2 layers within each coherent domain and more MoSe2 domains in the film. 
After being annealed at 300 °C, second-, third-, and fourth-order reflections from 
the MoSe2 grains are observed, reflecting the increased order within the 
diffracting domains. These higher order reflections also increase in intensity and 
become narrower as annealing temperature is increased, reflecting the increased 
number and growing size of the MoSe2 domains. The Kiessig fringes become more 
intense and extend out to higher angles as annealing temperature is increased, 
indicating that the film is becoming smoother. Finally, there is considerable 
growth in intensity and narrowing of diffraction line widths between the 500 and 
650 °C annealing steps. The c-axis lattice parameter of the annealed film 
calculated from the position of the Bragg reflections after the 650 °C annealing 
is 6.52 Å, which is slightly larger than that previously reported for MoSe2 
(6.460(1) Å).33 After being annealed at 650 °C, the low-angle reflection from the 
artificial layering is no longer visible, consistent with the transformation of the 
precursor from mostly amorphous layers to well-defined crystalline MoSe2 
layers. The Kiessig fringes observed in the XRR scan after being annealed at 650 
°C are well-resolved and decay in intensity as expected for a film of uniform 
electron density and thickness. The presence of both Kiessig fringes and Laue 
oscillations at higher angles after being annealed at 650 °C indicates that the 
film becomes significantly smoother and that a constant thickness film with an 
integer number of MoSe2 layers occurs across the majority of the substrate. The 
total film thickness calculated from the positions of the Kiessig fringes is 158 Å, 
which is within error of that expected for a 24-layer film of MoSe2 with a c-axis 
lattice parameter of 6.52 Å. Between the first and second Bragg reflections, Laue 
oscillations are present. Laue oscillations result from the incomplete destructive 
interference between Bragg reflections due to a finite number of unit cells. Their 
presence indicates coherent diffraction from domains in the polycrystalline film 
that each consist of the same number of MoSe2 layers. Analysis of the spacing of 
the Laue fringes indicates that the coherent domains contain 24 MoSe2 layers, 
consistent with the number of Mo|Se bilayers deposited in the precursor and 
with the total film thickness.  
 128 
In-plane diffraction data were collected for the Mo|Se film annealed at 650 
°C and are shown in Figure 6.2. All observed reflections can be indexed to a 
hexagonal unit cell with an a-axis lattice parameter of 3.31(1) Å. This is slightly 
larger than what has been previously reported for bulk MoSe2 (3.289(1) Å)33 and 
MoSe2 thin films (3.246 Å).34 The composition and diffraction data provide 
consistent evidence that the crystallized material is MoSe2. Mo|Se precursors 
with different amounts of Se were annealed at 650 °C and characterized by XRD 
to probe the influence of composition on the growth and crystallinity of the final 
product. Figure 6.3 graphs the intensity and peak width of the 001 reflection of 
MoSe2 as a function of the Se content in the precursor prior to being annealed. 
The peak width of the 00l reflections depends on the size and coherence of the 
MoSe2 layers along the c-axis, with a minimum peak width occurring when the 
entire film thickness consists of a single coherent domain. The data in Figure 
6.3. demonstrate that some excess Se is required to obtain the narrowest line 
widths, but too much excess increases the line width. The intensity of the 00l 
reflections is proportional to the number of MoSe2 domains that are aligned 
parallel to the substrate, and the maximum intensity was observed for annealed 
films that began with a 10−15% excess of Se. Rocking curves taken on these 
samples are narrowest for those with the highest intensity of the 001 reflection, 
suggesting that the intensity maximum is due to the percentage of the sample 
that is crystallographically aligned. The variation of crystalline quality with Se 
concentration is likely caused by the excess Se acting as a flux, increasing the 
mobility of the Mo cations during annealing. However, too much Se results in 
the nucleation of grains of MoSe2 that are not aligned with the basal plane 
perpendicular to the substrate, preventing the entire film thickness from 
becoming a single coherent domain.   
 129 
Figure 6.2. Grazing incidence in-plane diffraction of a MoSe2 film after being annealed 
at 650 °C for 60 min. All reflections can be indexed as hk0 reflections (shown above 
each reflection) corresponding to a hexagonal unit cell with lattice parameters consistent 
with those of MoSe2.  
Figure 6.3. MoSe2 crystal quality as determined by specular diffraction reflection 
intensity and peak width graphed vs the composition of the Mo|Se precursor.  
A series of Ti|Se precursors with various Ti/Se ratios were prepared to 
compare their evolution to that found for Mo|Se precursors forming MoSe2. 
Table 6.1. summarizes data obtained from each of the Ti|Se precursors. The XRF 
data show that all precursors were Se rich as-deposited, and the number of Ti 
atoms/Å2 deposited per Ti|Se bilayer ranged from 2% above to 10% below the 
 130 
number required for a single ideal crystalline TiSe2 trilayer, 0.092 Ti atoms / Å2. 
The total thicknesses for the samples were calculated from the Kiessig fringes 
and divided by the number of Ti|Se bilayers that were deposited to obtain the 
average Ti|Se bilayer thickness for each sample (Table 6.1). The thicknesses are 
consistent with the number of atoms deposited calculated from the XRF 
intensities (Table 6.1). The specular diffraction patterns of the as-deposited 
precursors all contain two to four 00l reflections from the crystalline TiSe2 
domains (see Figure 6.5.), indicating that the as-deposited films are much more 
crystalline than the corresponding Mo|Se films. The c-axis lattice parameters 
were all larger than those previously reported for TiSe2, reflecting the high defect 
levels resulting from the low ambient temperature during the deposition. There 
is a systematic increase in the c-axis lattice parameter as the amount of Se 
deposited in the sample increases, suggesting that interstitial Se atoms may be 
trapped between layers due to limited diffusion at these low annealing 
temperatures. The in-plane diffraction patterns (shown in black in Figures 6.5 
and S2) also reflect the more crystalline nature of the as-deposited Ti|Se films, 
containing reflections that can be indexed as hk0 reflections from TiSe2 and 
broad reflections consistent with the presence of Ti2Se deposited, and the 
number of Ti atoms / Å2 deposited per Ti|Se bilayer ranged from 2% above to 
10% below the number required for a single ideal crystalline TiSe2 trilayer, 0.092 
Ti atoms / Å2 . The as-deposited XRR patterns (Figure S1) contained Kiessig 
fringes, reflecting the total thickness of the deposited films and a strong first-
order reflection from crystalline TiSe2. The disappearance of the Kiessig fringes 
at 7.4° 2θ indicates that the roughness of the deposited film is on the order of 6 
Å, which we calculated using the relationship derived by Parratt.32 Unlike the 
Mo|Se precursors, no reflection intensity was observed that could be attributed 
to the artificial layering of the Ti|Se precursors.  
 
 
 
 131 
Table 6.1. Structure and Composition Summary for the As-Deposited Ti|Se Precursors 
Average As-
Average 
Average Se deposited 
# Ti|Se Total film Ti atoms 
bilayer atoms / Composition TiSe2 c-
layers thickness / Å2 per 
thickness Å2 per Ti/Se axis lattice 
deposited (Å, ±0.5) bilayer 
(Å) bilayer parameter 
(±0.07) 
(±0.04) (Å, ±0.01) 
83 478 5.8 0.092 0.185 1:2.01 6.14 
83 487 5.9 0.092 0.188 1:2.05 6.17 
83 507 6.1 0.094 0.198 1:2.11 6.16 
84 509 6.1 0.089 0.192 1:2.14 6.17 
83 524 6.3 0.092 0.198 1:2.16 6.19 
84 527 6.3 0.089 0.197 1:2.22 6.19 
82 482 5.8 0.084 0.188 1:2.24 6.18 
83 532 6.4 0.090 0.204 1:2.26 6.20 
84 564 6.7 0.082 0.210 1:2.57 6.27 
Taken together, the diffraction data indicate that the Ti|Se precursors 
substantially interdiffuse and react during deposition. Since the film’s overall 
compositions are Se-rich, we suspect that the observed Ti2Se is formed during 
the deposition when Se is deposited on top of the initial Ti layer. After the first 
Ti|Se bilayer is deposited, TiSe2 nucleates, either at the surface of the Se layer 
or at the Ti2Se surface below, by diffusing through the amorphous Se layer. When 
subsequent layers are deposited, Ti atoms must diffuse through the Se-rich 
matrix to the growth fronts of existing TiSe2 crystallites. When this diffusion 
length becomes sufficiently large, new crystalline layers of TiSe2 may nucleate 
near the surface of the sample. The reactions during the deposition result in 
large regions of crystalline TiSe2 surrounded by a Se-rich matrix, with Ti2Se 
adjacent to the Si substrate.  
Figure 6.4. contains a series of XRR and XRD patterns collected as a 
function of the annealing temperature for a representative Ti|Se precursor with 
an initial Ti/Se composition of 1:2.24. The 00l reflections of the TiSe2 crystallites 
 132 
move noticeably to a higher angle as the annealing temperature is increased, 
indicating a decrease in the c-axis lattice parameter. Additionally, the reflection 
intensity increases while the line widths (full width at half-maximum (fwhm)) 
decrease as the annealing temperature is increased, suggesting the registration 
between the TiSe2 planes increases excess atoms between layers and at grain 
boundaries are incorporated into the growing crystallites or diffuse to the 
surface. In all but the least Se-rich films, the in-plane reflections of Ti2Se become 
unobservable. However, Ti2Se in-plane reflections remain after being annealed 
in the most Ti-rich film studied. Films annealed at 350 °C have the greatest 
reflection intensity and narrowest peak widths. Annealing above 350 °C results 
in a decrease in intensity and an increase in peak width of the 00l reflections. 
On the basis of the above observations, the optimal annealing temperature for 
the Ti|Se precursors was determined to be 350 °C.  
Figure 6.4. XRR and XRD patterns from an annealing study of an as-deposited Ti|Se 
precursor with a starting composition of 1:2.24 (Ti / Se). The sample was annealed for 
30 min at the temperatures presented above each scan. XRR scans are from 0−11° 2θ, 
while XRD scans are from 3−65° 2θ; the patterns are overlaid and adjusted vertically. 
All reflections can be indexed to 00l values corresponding to a hexagonal unit cell with 
lattice parameters consistent with TiSe2. Reflections marked with an asterisk 
correspond to the substrate.  
 133 
As was done in the Mo|Se system, precursor films were prepared by 
holding the thickness of the Ti layer constant, varying the amount of Se, and 
annealing under identical conditions (350 °C for 30 min) to study the effects of 
precursor composition on film quality. For all the films, the XRF data show that 
Se was lost during annealing (Table 6.2). The XRR patterns, shown in Figures 
A.1 and A.3, all contain Kiessig fringes from the interference of the front and 
back of the film. In contrast to the Mo|Se system, the surface roughness of the 
films does not change significantly during annealing. Because of the loss of Se 
during the annealing, all the annealed films are thinner than the as-deposited 
precursors. Oscillations in the intensity of the Kiessig fringes in all the films 
indicate that a surface layer with a different electron density than the rest of the 
sample has formed, likely a surface layer of amorphous TiO2. This oxide layer 
forms during annealing in an inert atmosphere with less than 1 ppm of O2 
present. This may seem surprising until recognizing that, despite the low oxygen 
concentration present, approximately a monolayer’s worth of O2 molecules 
impacts the film during each second of annealing.  
Table 6.2. Compositions and Lattice Parameters for Annealed Ti|Se Films As 
Determined from Full Pattern XRD Le Bail Fits 
Annealed Annealed Annealed 
AD c-lattice a-lattice Annealed 
total film expt. Ti expt. Se 
composition parameter parameter composition 
thickness atoms / Å2 atoms / Å2 
(Ti/Se) (Å) (Å) (Ti/Se) 
(Å) (±0.08) (±0.02) 
1:2.01 479 6.053(1) 3.551(1) 7.54 15.05 1:2.00 
1:2.05 479 6.051(1) 3.558(1) 7.57 15.21 1:2.01 
1:2.11 503 6.050(1) 3.559(1) 7.86 15.46 1:1.97 
1:2.14 483 6.034(1) 3.558(1) 7.70 14.41 1:1.87 
1:2.16 501 6.037(1) 3.560(1) 7.70 15.49 1:2.01 
1:2.22 503 6.043(1) 3.553(1) 7.70 15.35 1:1.99 
1:2.24 450 6.066(1) 3.549(1) 6.86 12.85 1:1.87 
1:2.26 496 6.058(1) 3.554(1) 7.50 15.10 1:2.01 
1:2.57 505 6.096(1)  6.80 13.80 1:2.03 
The annealed XRR patterns fall into two general categories - those with a thicker 
(∼50 Å) TiO2 layer and those with a thinner (∼10 Å) TiO2 layer on top of the film 
 134 
(Figure A.4). The specular diffraction patterns (Figures 6.5a and A.2a) contain 
00l reflections from crystalline TiSe2. The observed reflections are more intense, 
narrower, and occur at higher 2θ angles than those in the as-deposited 
precursors, indicating there are more 00l planes aligned with the substrate, the 
TiSe2 crystalline domains are thicker, and that the c-axis lattice parameters are 
smaller. The c-axis lattice parameters obtained from full pattern Le Bail fits are 
summarized in Table 6.2. Samples that have a slight excess of Se, in the 
composition range between 1:2.14 and 1:2.22 on deposition, have c-axis lattice 
parameters that best match the reported values for TiSe2. Films with initial 
compositions on either side of this regime have c-axis lattice parameters that are 
slightly larger than the literature value. Representative in-plane XRD patterns 
for the films are shown in Figures 5b and A.2b. The annealed patterns have 
narrower reflections than those found in the as-deposited samples, indicating a 
significant increase in the in-plane domain size. All of the reflections in the 
annealed samples can be indexed to a hexagonal unit cell with lattice parameters 
similar to the reported values for TiSe2 (Table 6.2), except for broad reflections 
in the 1:2.01 sample, which correspond to an impurity phase of Ti2Se.35 This 
phase also appears to be present to some extent in all precursors prior to being 
annealed. The a-axis lattice parameters for all of the Ti|Se films, determined 
from the Le Bail fits of the in-plane diffraction patterns found in Figure 6.5b, are 
very similar to those previously reported for TiSe2 (Table 2).35 Unlike the c-axis 
lattice parameters, which were influenced by the amount of Se present in the 
precursor sample, the a-axis lattice parameter for the annealed TiSe2 films does 
not depend on the precursor composition. The change in the crystallinity of the 
TiSe2 films as a function of precursor composition was estimated by using the 
line widths of the specular and in-plane reflections in the diffraction patterns of 
the annealed precursors. Line widths of the 110 and 001 reflections in the in-
plane and specular XRD patterns, respectively, were determined to help quantify 
the effect of precursor composition on crystal quality (Figure 6.6).  
 
 135 
Figure 6.5. Representative specular (a) and in-plane (b) XRD patterns of Ti|Se thin films 
with various compositions. Black curves show the diffraction pattern of the precursor, 
while red curves show the pattern for the films annealed at 350 °C. All observed 
reflections that correspond to the TiSe2 crystal structure are indexed in black. 
Reflections marked with an asterisk observed in the specular pattern are attributed to 
the Si substrate. Reflections for the observed Ti2Se impurity phase are indexed in blue. 
Additional diffraction patterns can be found in Figure S2. 
 136 
Figure 6.6. Line widths (fwhm) of the 110 reflection in the in-plane XRD pattern (top) 
and 001 reflection in the specular XRD pattern (middle) and 001 reflection net area 
(bottom) as a function of precursor composition. (●) As-deposited parameters. (◆) 
Annealed parameters. The diffraction patterns used to determine these parameters are 
found in Figure 6.4 and Figure A.2.  
In the as-deposited films, both specular and in-plane line widths are 
smallest when the precursors have a Ti/Se ratio of 1:2.15−1:2.2. After being 
annealed, both the in-plane and specular diffraction patterns have the smallest 
line widths (and largest crystallite sizes) at a Se/Ti ratio of ∼2.15−2.2; however, 
there is a much smaller range of in-plane line widths. A Scherrer analysis of the 
line widths for the sample with an as-deposited composition of 1:2.16 yields a c-
axis crystallite size of 443 Å and an in-plane crystallite size of 117 Å. Similar to 
what was observed in the Mo|Se system, it is possible that the slight excess of 
Se acts as a flux to facilitate the transport of Ti atoms to the crystallite growth 
fronts, causing larger crystallite sizes in precursors with the ideal amount of 
excess Se. For the three TiSe2 samples with the optimal amount of excess Se to 
obtain large coherent diffracting domains, Laue oscillations are visible 
surrounding the first Bragg reflection (Figure 6.7). The Laue oscillations occur 
due to the incomplete destructive interference of a finite number of unit cells in 
 137 
a crystal. For a small number of unit cells N, the Laue function, sin(Nx)/ sin(x), 
results in a principle intensity maximum whose position is determined by the 
lattice parameters of the diffracting crystal and a series of evenly spaced maxima 
on either side whose spacing is determined by the number of unit cells in the 
crystal. To observe the Laue oscillations, the majority of the film must consist of 
crystallites with identical numbers of unit cells, because crystallites with 
different numbers of unit cells would contribute Laue intensities at different 
angles, destroying the interference pattern. Figure 6.7 shows the measured 
specular diffraction pattern around the first Bragg reflection for the annealed 
samples with Laue oscillations. The position of the highest intensity maxima is 
consistent with the c-axis lattice parameters given in Table 6.2. The spacing of 
the Laue oscillations is consistent with the diffracting crystallites having a 
specific number of unit cells, as shown by the simulated patterns overlaid on the 
experimental patterns in Figure 6.7. However, the total film thicknesses of these 
annealed samples are larger than the product of the number of unit cells 
calculated from the Laue oscillations multiplied by the appropriate c-axis lattice 
parameter. Since the number of Ti| Se bilayers deposited in the precursors was 
larger than the number of layers formed, there is more Ti in the samples than 
required for the number of TiSe2 layers calculated from the Laue oscillations. 
This suggests that several Ti|Se bilayers were oxidized, formed Ti2Se, and/or 
reacted with the substrate.  
The combination of XRF, XRR, and XRD data allows us to speculate on an 
atomic-level picture of the structure of the as-deposited Mo|Se and Ti|Se 
precursors and how it evolves during annealing. Analysis of the diffraction data 
clearly indicates that the structure of the as-deposited Mo and Ti precursors are 
significantly different, which is illustrated schematically in Figure 6.8. The 
Mo|Se precursor, Figure 6.8a, has a composition modulation from the growth of 
the sequence of as-deposited layers with small crystallites of MoSe2 several layers 
thick distributed throughout the film. Figure 6.8c illustrates how the Ti|Se 
precursor has reacted much more during deposition than the Mo|Se precursor.  
 138 
Figure 6.7. Experimental specular XRD patterns (red) for the highest quality annealed 
TiSe2 films overlaid with the theoretical Laue oscillations expected for n layers of TiSe2 
(black).  
In the Ti|Se precursors, there is no evidence of compositional modulation; Ti2Se 
forms during the deposition of Se on the first layer of Ti deposited, and thick 
domains of poorly stacked TiSe2 layers subsequently grow during the deposition. 
In both the Mo|Se and Ti|Se precursors, there is a gradient in metal 
concentration around the growth front as it is depleted around each crystallite. 
For the Mo|Se precursor, the concentration gradient is not enough to 
induce diffusion during the deposition, likely a result of the high activation 
energies required for diffusion. However, in the Ti|Se precursors, smaller Ti 
atoms diffuse significantly during deposition to form the observed thick TiSe2 
domains. In both systems, annealing at elevated temperatures allows more 
diffusion to occur, leading to the growth of well-organized crystallites. A small 
amount of excess Se (10%) results in the formation of larger coherent domains 
of the dichalcogenide in both systems. The excess Se presumably acts as a flux 
to increase the rate of diffusion of the metal cations. However, too much excess 
Se results in less crystallographically aligned layers and smaller grain sizes. In 
both systems, the optimized precursor structure and annealing temperatures  
 139 
Figure 6.8. Proposed atomic-level pictures for the evolution of Mo|Se (a) and Ti|Se (c) 
precursors as they are annealed to form crystalline MoSe2 (b) and TiSe2 (d). There is 
much more interdiffusion during deposition of the lighter Ti atoms, resulting in larger 
crystalline domains in the as-deposited TiSe2 precursor relative to the Mo|Se precursor.  
resulted in the formation of polycrystalline films that predominantly contained a 
precise and identical number of dichalcogenide planes. For Mo|Se films with the 
correct amount of Mo per Mo|Se bilayer in the precursor, each Mo|Se layer 
evolved into a single MoSe2 trilayer plane in the coherent domain. In analogous 
 140 
Ti|Se films, all of the Ti|Se layers evolved into TiSe2 except for two layers at the 
surface of the film that oxidized, forming a TiO2 surface layer. 
6.4 Conclusions 
 Highly crystalline transition-metal diselenide films can be prepared by 
depositing alternating layers of the metal and selenium. With the correct amount 
of metal and a slight excess of Se deposited per M|Se bilayer, each layer will 
evolve into a dichalcogenide plane upon annealing. This enables the thickness 
of the dichalcogenide film to be controlled to a specified number of unit cells over 
large areas. While a precise number of dichalcogenide planes was obtained in 
both the Ti− Se and Mo−Se systems, the reaction pathways were very different. 
TiSe2 mostly self-assembles during the deposition process, while MoSe2 mostly 
self-assembles during annealing. In both systems, concentration gradients drive 
the diffusion of metals to the crystallite growth fronts, aided by the short 
diffusion distances in the layered precursor during annealing or surface diffusion 
during the deposition. The diffraction data gathered on the as-deposited films 
and during annealing enabled the creation and comparison of atomistic pictures 
describing the self-assembly of MoSe2 and TiSe2 from their respective precursors. 
By understanding the film formation and developing control over the composition 
and morphology of the precursors, we demonstrate that growth of 
dichalcogenides can be controlled to achieve uniform thicknesses over large 
areas. 
6.5 Bridge 
This chapter presents the study of M|Se thin films, where M = Mo, Ti. By 
studying the reaction pathway as a function of the experimental parameters, 
we were able to conclude that synthesis of optimal quality films results from 
precursors deposited with a ~15% excess of Se. The next chapter describes 
the synthetic exploration of a heterostructure containing crystalline and 
amorphous components.  
  
 141 
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 145 
CHAPTER VII 
SYNTHESIS AND CHARACTERIZATION OF SI-TISE2 MULTILAYERS 
7.0 Authorship Statement 
This chapter was written for this work alone with no intention of 
publishing it elsewhere. I am the primary author and wrote the following with 
assistance from my advisor, David C. Johnson. 
7.1 Introduction 
Research into crystalline layered materials over the last 50 years has 
proved extremely exciting and fruitful – yielding the development of lithium-
ion batteries, high-temperature superconductors, and the discovery of 
graphene’s gapless Fermi surface, just to name a few developments.1–3 The 
2019 Nobel Prize in Chemistry went to Goodenough, Whittingham, and 
Yoshino for their work with layered materials, such as TiS2 and LiCoO2, which 
resulted in the development and commercialization of lithium-ion batteries in 
1980. The first known high-temperature superconductor, Ba0.15CuLa1.85O4, 
is a perovskite-type structure, which is a layered material.2 More recently, the 
2001 discovery of Graphene’s gapless Fermi surface spurred pursuit of Lego-
type 2D heterostructures where properties can be tuned by varying the type 
of material used in each layer, the order that the layers are stacked in, the 
thickness of each constituent layer, or even the substrate that the 
heterostructure is grown upon.4–9 These breakthroughs suggest that studying 
layered materials is well worth the time (and funding dollars), but there are 
still many remaining unrealized goals.  
One longstanding goal is rational materials design – in which one could 
go into lab and synthesize a composite material (or heterostructure) that 
exploits the properties of its constituent materials in a predictable manner in 
order to achieve the desired material’s application.10 Novoselov and 
colleagues argue that 2D heterostructures could provide a platform for 
 146 
realizing this goal, by advancing our knowledge of 2D interlayer interactions 
and our methods to prepare 2D layers and assemble them into device-quality 
heterostructures, we could enable the creation of heterostructures with 
properties that are individually tailored to meet the needs of each 
application.11 
Heterostructures constructed from amorphous and crystalline 
materials are not well studied, but existing reports suggest that these 
materials can effectively exploit properties of both their amorphous and 
crystalline components. Perhaps the most widely known example of a device 
that contains and exploits the properties of both crystalline and amorphous 
materials is a Si-based heterojunction solar cell, which utilizes amorphous, 
crystalline, and Si:H for the emitter material, active material, and surface 
passivation, respectively.12  
Other reports include materials with memristive behavior enabled by 
an amorphous-crystalline 2D oxide heterostructure, which was achieved via 
ALD synthesis of few-nm-thick Al2O3 layers onto atomically thin single-crystal 
ZnO nanosheets. In this system, the ZnO provides a 2D host for oxygen 
vacancies, while the a-Al2O3 enables the generation and stabilization of those 
vacancies.13 Because of their modulated electronic structure and abundance 
of catalytically active but chemically stable sites, composite materials or 
heterostructures constructed from crystalline and amorphous constituents 
have shown impressive OER and HER performance.13–15  However, existing 
synthesis techniques for these materials result in either nanocrystals or 
crystalline nanorods coated in an amorphous material – to the best of our 
knowledge there are no reports of a thin film heterostructure containing few-
layer 2D blocks of a crystalline materials intergrown with ultrathin 
amorphous layers.  
Lithium can electrochemically alloy with intermetallic elements to form 
Li4.4M (M = Si, Ge, Sn). While this gives intermetallic anodes for lithium-ion 
batteries a significantly increased theoretical energy density relative to the 
 147 
current standard commercial anode, graphite, which forms LiC6 upon 
lithiation, it also results in a huge volume change (300 – 400 %) during the 
lithiation reaction.16,17 Earlier reports have shown that reducing the 
thickness of Si increases the stability of the layer towards lithium 
intercalation cycling.18–22 Previous work with Si-based multilayers utilized 
amorphous chromium-silicide layered with amorphous Si, resulting in 
strongly enhanced structural stability, as demonstrated by the preservation 
of the heterostructure’s layering during the reversible lithiation reaction.18 
This work describes the synthesis of 2D thin film heterostructures created by 
intergrowing few-layer crystalline TiSe2 blocks with ultra-thin amorphous Si 
layers. 
Ultimately, this experiment may result in the discovery of the optimal 
relative thicknesses of each constituent layer, ideally increasing the stability 
of the Si layer and maintaining/increasing the rate of Li intercalation.  Li-
intercalated TiSe2 is a metal, with empty layers that enable Li cations to 
diffuse quickly even at room temperature.23,24 Si is a semiconductor and the 
movement of both charge and Li cations is much slower than in TiSe2. 
However, Si forms Li4Si upon reversible intercalation, resulting in a large Li 
capacity and a large volume change. As shown in Figure 7.1, by creating a 
heterostructure where the thicknesses of each constituent layer are precisely 
controlled enables the diffusion distance of cations into Si to be tuned and 
the weak interfaces with the TiSe2 platelets provides a mechanism to relieve 
the stress of intercalation. 
These efforts were inspired by previous work done with CrSix-Si 
multilayers - the work presented here involves the synthesis of novel 
multilayers built from alternating ultrathin layers of amorphous Si and 
crystalline TiSe2. Electron-beam evaporation was used to sequentially deposit 
ultrathin titanium, selenium, and silicon layers onto a room temperature 
substrate. A calibration curve is used to relate the number of atoms / Å2 in 
the film to intensity of the measured x-ray fluorescence (XRF) signal. The  
 148 
Figure 7.1. Schematic depiction of the reaction of a layered (Ti|Se)4|Si 
precursor (left) to form a (TiSe2)4|Si heterostructure (right). Diffraction data 
suggests some extent of TiSe2 nucleation and growth during the initial film 
deposition.  
atomic areal density is then compared to that of the target compound(’s).25 
The goal is to deposit the correct amount of atoms in each layer such that 
they will all react to form the desired compound or an integer number of 
layers of the desired layered compound.26 
Previous work on the Ti|Se system has shown that ultrathin titanium 
and selenium layers react to form crystalline TiSe2 when heated at moderate 
temperature in an N  atmosphere.272  When deposited without excess Se, these 
layers react during deposition to form Ti2Se. Optimally, when deposited with 
~19% excess Se, these layers will interdiffuse and react, resulting in the 
nucleating and growth of a crystalline TiSe2 during the film’s deposition. 
Annealing at 350 °C improves the crystallinity of these layers, resulting in 
highly defined large-area (cm2) films that exhibit Laue oscillations in their x-
ray diffraction patterns.28 Previous work studying the reaction between 
ultrathin Ti and Si layers suggests that if heated above 550 °C, TiSi nucleates 
and grows, but below that temperature, the two elements slowly interdiffuse 
at each interface to form an amorphous alloy.29 One interesting challenge of 
this system is the inherent contradiction between the periodic structure of 
the crystalline component and the complete lack of a periodic structure in the 
amorphous component.  
 149 
7.2 Results & Discussion 
The following data was collected on three Si|TiSe2 films that were 
deposited sequentially in a single deposition run. All three samples were 
deposited promptly after each other without breaking vacuum or manually 
adjusting the power of the electron beam guns. Since there is not a calibration 
curve for Si in the XRF method, there is not a direct quantitative measure of 
the amount of Si in each film. However, since the samples were deposited in 
a single instance and the deposition controller was able to maintain a steady 
rate of incident mass on the quartz crystal microbalance used to monitor the 
deposition throughout the entire deposition, it is a reasonable assumption 
that the amount of Si in each layer is relatively constant. We will support this 
assertion with experimental data of our films, drawing on knowledge of what 
the simulated XRR patterns for different possible structures discussed 
earlier. 
Figure 7.2 shows the XRR and XRD patterns for these three samples – 
each of which had a different number of TiSe2 layers deposited in each RU, 
represented by n. As expected, the thickness of the RU increases with the 
number of TiSe2 layers, as demonstrated by the increased frequency and 
lower initial angular position of the Bragg reflections as n increases. Typically 
in a heterostructure, the number of oscillatory minima observed in between 
each Bragg maxima represents the number of layers present – however XRR 
modeling of these structures showed that the number of minima would not 
be expected to be identical. However, this effect is also observed in samples 
that contain a significant impurity phase, which may also be a possibility 
here. The Bragg maxima present in the low angle reflectivity pattern can be 
indexed to 00l reflections that match those expected for the superlattice. The 
total thickness extracted from the position of the Bragg reflections is shown 
in Table 7.1. Additionally, the number of RU deposited matches the total 
thickness divided by the estimated RU thickness for the as-deposited films. 
Interestingly, the higher angle diffraction patterns show two broad Bragg 
 150 
reflections at approximately the locations of those expected for a 6 Å Fourier 
component – approximately the size of a single TiSe2 layer! As one increased 
the amount of TiSe2 in each block, one would expect that the peak width 
would decrease and the intensity of the higher angle reflections around 15 
and 30° would be expected to increase.  
Figure 7.2 XRR (left) and XRD (right) patterns for the n = 4, 7, and 9 
Si(TiSe2)n heterostructures collected immediately after deposition and prior 
to annealing. 
Table 7.1. Structural data extracted from experimental x-ray diffraction and 
x-ray reflectivity patterns for as-deposited (Ti|Se)nSi heterostructures 
n c-axis Total Thickness RU 
lattice thickness / c-axis deposited 
(nm) (nm) 
4 5.81(8) 41.08(6) 7.1 7 
7 7.56(4) 37.0(2) 4.9 5 
9 9.16(6) 36.4(1) 4.0 4 
Table 7.2 shows the number of atoms / Å2 of Ti and Se calculated from 
the XRF data collected on each of the three as-deposited films, along with the 
targeted number of atoms required to form 4, 7, or 9 TiSe2 layers in each RU. 
Coincidentally, the target number of Ti atoms is the same for the n = 7 and 9 
heterostructures – this is because they have different number of RU’s, which 
result in the same number of targeted TiSe2 layers across the entire film. 
 
 
 151 
Table 7.2. Composition data extracted from experimental x-ray fluorescence 
intensities for as-deposited (Ti|Se)nSi heterostructures 
n RU Avg. Ti Avg. Se Target Target 
deposited atoms / atoms / Ti Se 
Å2 Å2 atoms / atoms / 
Å2 Å2 
4 7 3.16 7.80 2.59 6.48 
7 5 3.40 7.63 3.70 7.40 
9 4 3.43 6.63 3.70 7.40 
Figure 7.3 shows the XRR and XRD patterns for the same three films 
after they have been annealed at 350 °C for 30 min in an N2 atmosphere with 
less than 2.0 ppm O2 present. The low angle reflectivity data suggests that 
the layered superlattice structure is preserved after annealing. The presence 
of Kiessig fringes to a higher angle indicates that the film’s surface has 
become smoother. The Bragg reflections also increase in intensity and 
decrease in width, indicating that the crystallites of the heterostructure have 
grown relative to those in the as-deposited film. The higher angle reflections 
become significantly more intense and well-defined relative to those in each 
of the as-deposited patterns. However, this may also be consistent with 
segregation and growth of additional crystalline TiSe2 on the surface of the 
film as the excess material diffuses through the film during annealing. Table 
7.3 shows the c-axis lattice parameter and the total film thickness extracted 
from the Bragg reflections in the reflectivity patterns and the period of the 
Kiessig fringes, respectively. Dividing the total thickness by the c-axis lattice 
parameter serves as a “check” for determining whether any RU’s decomposed 
during the annealing process – in this case, it can be seen that the n = 4 and 
9 films did not lose a significant amount of material during annealing, while 
the n = 7 film lost a partial RU (corresponding to a ~3 nm loss of total 
thickness). By plotting the c-axis lattice parameter against the number of 
TiSe2 layers in each RU, we finally obtain an estimate of the average Si layer 
thicknesses across the three films. As shown in Figure 7.4, the slope of the 
line corresponds to the average c-axis lattice parameter of a single TiSe2 layer 
(0.675 nm), while the y-intercept corresponds to the average Si layer 
 152 
thickness (2.98 nm). The correlation coefficient is very close to 1, which 
supports the earlier assumption made that the Si thickness in each of the 
three samples is relatively constant.  
Representative grazing-incidence in-plane XRD patterns for the as-
deposited and annealed films are shown in Figure 7.5. All of the observed 
reflections can be indexed to a hexagonal unit cell with dimensions matching 
those expected for TiSe .272  There are no other observed reflections, which lead 
us to conclude that the Si layers remain amorphous during the entire 
deposition and annealing process. 
 
Figure 7.3 XRR (left) and XRD (right) patterns for the n = 4, 7, and 9 
Si(TiSe2)n heterostructures collected after annealing at 350 °C for 30 m. The 
Bragg reflections in the low-angle scan can be indexed to 00l reflections 
corresponding to the superlattice structure, while the high angle reflections 
can be indexed to the first two 00l reflections expected for TiSe2.  
Table 7.3. Structural data extracted from experimental x-ray diffraction and 
x-ray reflectivity patterns for (TiSe2)nSi heterostructures annealed at 350 °C 
n c-axis Total Thickness 
lattice thickness / c-axis 
(nm) (nm) 
4 5.73(5) 40.3(1) 7.0 
7 7.57(7) 34.1(1) 4.5 
9 9.13(7) 36.6(2) 4.0 
 
 153 
Figure 7.4 Plot of c-axis lattice parameter vs n for the three films shown in 
Figure 7.3 The slope of the line represents the average c-axis lattice 
parameter for the individual TiSe2 layers (0.675 nm), while the y-intercept 
indicates the average thickness of the a-Si layers (2.98 nm).  
 
Figure 7.5 Representative grazing-incidence in-plane x-ray diffraction 
patterns for as-deposited (grey) and annealed (black) (TiSe2)nSi 
heterostructure. All observed reflections can be indexed to a hexagonal unit 
cell with dimensions matching those expected for TiSe2.  
Hypothetically, it is possible to synthesize a superlattice by layering one 
amorphous and one crystalline layer to build up a heterostructure. Assuming 
that one can deposit multiple identical crystalline and amorphous layers (with 
the same number of atoms in each layer), this would create a film that 
 154 
contains a single average periodic structure. Figure 7.1 shows a schematic 
depiction of the reaction to form this theoretical “perfect” 
amorphous/crystalline heterostructure created from ~3 nm layers of 
amorphous Si and ~2.5 nm layers of crystalline TiSe2 (4 Se|Ti|Se trilayers). 
The as-deposited Si|Ti|Se repeating units (RU) are visible on the left, along 
with small areas of crystallized TiSe2. After annealing, the majority of the 
Ti|Se layers have been crystallized into TiSe2, as depicted on the right. In this 
sample, the correct number of atoms have been deposited in each Ti and Se 
layer such that they react to form an integer number of crystalline TiSe2 layers 
AND the same number of Si atoms have been deposited in each Ti|Se|Si 
sequence, hereafter referred to as a repeating unit (RU). However, this 
structure is an unrealistic depiction of the experimental structure since it is 
extremely unlikely that one will be able to deposit the exact number of atoms 
in each of the repeatedly deposited layers. 
Figure 7.6 Simulated x-ray reflectivity (XRR) patterns for (TiSe2)n|Si 
heterostructures with “perfect” nanoarchitecture. The models were generated 
from either 4, 5, or 7 repeating units (RU) deposited on Si/SiO2 for the n = 9, 7, 
and 4 films, respectively. Each RU consists of n layers of crystalline TiSe2 (c = 
0.603 nm) plus one a-Si layer (c = 3.0 nm). Generally, the number of repeating 
units in each film can be obtained by taking x + 1, where x is the number of 
minima between each Bragg reflection. For example, between each Bragg 
reflection in the n = 4 film, there are 6 minima, indicating that there are 7 total 
TiSe2|Si repeating units in the film.  
 155 
The resulting simulated x-ray reflectivity (XRR) pattern for the 
described “perfect” film (using 7 total Si|TiSe2 repeating units instead of the 
2 depicted to ensure a more realistic film thickness) are shown in Figure 7.6. 
The plot also contains two other simulated XRR patterns created from model 
heterostructures with 7 and 9 TiSe2 layers in each repeating unit. As one 
would expect from Bragg’s Law, the heterostructures with thicker repeating 
units have Bragg reflections that are spaced more closely together and begin 
at lower angles. For all crystalline heterostructures, the number of unit cells 
present in the heterostructure can always be obtained by counting the 
number of minima that are observed between each Bragg reflection. 
Interestingly, this does not appear to be the case for these heterostructures, 
as one can count both three and four minima that appear between each Bragg 
reflection in the n = 9 film (blue trace, Fig. 7.6.).  
However, unlike a typical thin film superlattice created from two 
crystalline layers, the average structure of the crystalline / amorphous 
heterostructures do not necessarily have to be identical in each repeating 
unit. This is because the crystalline component experiences a strong energetic 
driving force (i.e. its crystal structure and electron configuration) which 
effectively forces it to increment its own layer thickness in steps of ~0.6 nm 
(equal to one three-atom thick trilayer unit cell). The amorphous component 
lacks this driving force, with no impetus to be any particular thickness 
beyond maintaining the requisite tetrahedral bonding dictated by Si’s valence 
shell. This implies that the thickness of each a-Si layer can be any value 
greater than the thickness of a single Si atom, and this thickness will be 
dictated solely by the amount of Si atoms deposited in each layer.  
Figure 7.7 shows a schematic depiction of another possible structure 
for the n = 4 heterostructure, in which the amount of Si deposited in each a-
Si layer varies, resulting in slightly different thicknesses for each of the Si 
layers. In this hypothetical sample, it is assumed that amount of Ti and Se 
 156 
deposited in each RU is identical. Figure 7.8 shows the simulated XRR 
patterns from n = 4 heterostructures, where Δ represents the standard 
deviation of the Si layer thickness. It is easy to see how increasing the 
variance of the Si layer thickness destroys the intensity of the Bragg 
reflections – for the film with Si layers that were 3.0 ± 0.3 nm, there is only a 
single coherent Bragg reflection visible, as all of the subsequent reflections 
are split or have significantly less intensity. Another interesting side effect of 
decreasing the homogeneity of the Si layers is the increased amount of the 
~0.6 nm Fourier component, as shown by the increased intensity of the 
reflections in the XRR patterns around 14 ° 2θ. 
 
Figure 7.7 Schematic depiction of a n = 4 heterostructure, depicting 3 out of 
the 7 actual RU’s. In this schematic, there was poorer control over the amount 
of Si atoms deposited in each layer, leading to a distribution of thicknesses 
around the average a-Si layer thickness of 3.0 nm.  
 157 
Figure 7.8 Simulated x-ray reflectivity (XRR) patterns for (TiSe2)n|Si 
heterostructures with variance in the thickness of each a-Si layer. Δ is the 
standard deviation of the thickness of each of the a-Si layers throughout the 
film, although all models have an average a-Si layer thickness of 3.0 nm.   
Another possibility that might occur when depositing these 
heterostructures is that one is unable to deposit the identical quantities of Ti 
and Se atoms in each RU. As discussed above, the TiSe2 layer thickness 
should increment in 0.6 nm steps, based on the number of Ti and Se atoms 
deposited in each layer, which dictates the number of layers of Se|Ti|Se 
trilayers that nucleate and grow in each RU. However, if one deposits a 
precursor with enough Ti atoms required to form 4.5 TiSe2 layers, what 
happens to the “extra” 0.5 layer’s worth of atoms during annealing (assuming 
Ti is limiting reactant)? One possibility is that during heating, they diffuse 
towards the other “extra” Ti atoms, forming a fifth TiSe2 in every other RU. 
Another possibility is that they grow 5 layers of TiSe2 over half of the area of 
the film, creating islands of TiSe2 that stick up into each amorphous Si layer 
– effectively roughening the TiSe2|Si interface. As a gedanken experiment, 
Figure 7.9 depicts a schematic for a n = 4 heterostructure that depicts the 
first scenario described above. The bottom and top RU’s depicted is the n = 4 
structures, while the middle RU shows the n = 5 structure.  Figure 7.10 shows 
the predicted XRR patterns for several model heterostructures that contain 
 158 
different numbers of TiSe2 layers in each RU. Similarly to the effects observed 
by increasing the variance in the thickness of the a-Si layers, the most 
obvious effect of the increased variance in the crystalline layers is significant 
dampening of the Bragg reflection intensities. 
Figure 7.9 Schematic depiction of a n = 4 heterostructure, depicting 3 out 
of the 7 actual RU’s. In this schematic, there was poorer control over the 
amount of Ti atoms deposited in each layer, leading to a distribution in the 
number of layers of crystalline TiSe2 that form in each RU. The bottom and 
top RU’s depicted show the n = 4 structures, while the middle RU shows the 
n = 5 structure.   
 
 
 159 
Figure 7.10 Simulated x-ray reflectivity (XRR) patterns for (TiSe2)n|Si 
heterostructures with variance in the number of TiSe2 layers crystallized in 
each RU.  
 
7.3 Conclusion 
Based on the relatively close matches between the simulated and 
experimental reflectivity patterns, we can conclude that the superlattice 
structure proposed in this work are stable up to 350 °C. However, more work 
is needed to understand the differences between the gedanken models and 
simulated reflectivity patterns and the actual film structure and experimental 
patterns. Additionally, lots of obvious electrochemical work can be completed, 
such as characterizing the electrical transport properties of these films. An 
initial lithium intercalation experiment under constant current showed that 
the heterostructure was stable towards reversible lithium intercalation, but 
more efforts are required to understand how the lithium intercalation 
capacity of this structure scales with cycle number.  
However, the initial synthetic results are encouraging and show that 
these novel heterostructures can be synthesized with n = 4, 7, and 9 – 
although the optimal thicknesses of each constituent layer for 
electrochemical applications is not yet understood and remains a future goal.  
 160 
7.4 Bridge 
This chapter described the synthesis and characterization of several a-
Si(TiSe2)n heterostructures which have not been reported in the literature to 
the best of this author’s knowledge. The next chapter presents the synthesis 
of a family of six isomer heterostructures with a unit cell consisting of 
different layering of four TiSe2 layers and four PbSe layers. 
  
 161 
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 164 
CHAPTER VIII 
SYNTHESIS AND CHARACTERIZATION OF [(PBSE)1+δ]4[TISE2]4 ISOMERS 
8.0 Authorship Statement 
Chapter VI was published in Inorganic Chemistry in 2020. Danielle Hamann, 
and David C. Johnson are the main contributors to the text. I performed data 
analysis and performed modeling. J. Ditto and Daniel B. Moore contributed 
experimental data. 
8.1 Introduction 
Molecular chemists have developed synthetic methods to prepare kinetically 
stable compounds with designed structures. This permits them to prepare 
multiple compounds containing the same number and type of elements 
connected in various arrangements. 1–3 The local arrangement of atoms in a 
compound determines the physical, electronic, and biological properties it 
exhibits.4–11 For example, the five different structural isomers of hexane (hexane, 
2-methylpentane, 3-methylpentane, 2,2-dimethylbutane, and 2,3-
dimethylbutane) all have different melting and boiling points as a consequence 
of their varying local arrangements.12–15 The ability to predict metastable–stable 
compounds via simple bonding rules (i.e., each carbon must have four bonds, 
each oxygen two bonds, and each hydrogen one bond) combined with an 
understanding of how to control the kinetics by manipulating reaction conditions 
(solvents, protecting groups, catalysts) enables molecular chemists to propose 
and test structure–property relationships toward optimizing desired properties. 
2,16–18 
It is more challenging to prepare structural isomers of inorganic compounds 
with extended structures, known as polymorphs.19 Some well-known examples 
of polymorphs are vaterite, calcite, and aragonite. These compounds are different 
structural forms of calcium carbonate which exhibit different properties and free 
energies of formation.20–23 Typically, polymorphs are prepared by changing the 
reaction conditions (temperature, pressure, composition of the reacting system, 
 165 
etc.) so that the desired product is the most thermodynamically stable product 
in that reacting system. The structure of the product cannot be predicted from 
simple bonding rules or reaction conditions but is instead determined 
experimentally. For compounds only stable at high temperature or pressure, 
quenching the system to room temperature and pressure often traps the now 
metastable polymorph. The lack of knowledge of how to control reaction kinetics 
to obtain targeted inorganic, extended, structures severely limits the number of 
polymorphs that can be prepared.24–27 The holy grail in the synthesis of 
compounds with extended structures is a design and mechanism-based 
approach to the synthesis of metastable compounds with targeted structure.28 
Presented here is the synthesis and characterization of six different structural 
isomers of the compound [(PbSe)1+δ]4[TiSe2]4, which have the same composition 
and unit cell sizes, but the sequence of PbSe bilayers and TiSe2 trilayers vary 
between isomers. The different isomers were prepared from precursors with 
sequences of an elemental layer designed to mimic the nanoarchitecture of the 
targeted isomer. While the amount of Pb and Ti in the deposited precursors was 
insufficient to make the desired number of repeating units, the artificial layering 
pattern of deposited layers still directed the self-assembly of the desired isomers. 
X-ray diffraction and HAADF-STEM data support the formation of the desired 
isomer nanoarchitectures with a decreased number of unit cells and additional 
impurity phases present on the top and bottom of the sample. As-deposited 
structural characterization indicated that TiSe2 and PbSe crystallized during the 
deposition and were organized in stacking sequences consistent with the 
targeted isomer. Unexpectedly, Ti2Se also crystallized during deposition at the 
interface with the substrate. The HAADF-STEM images suggest that the sample 
crystallizes from the bottom to the top, with the concentration gradients created 
at the growth front driving diffusion of Pb and Ti to the growing isomers. The 
measured electrical transport properties systematically vary as a consequence of 
changes in the nanoarchitecture, with lower resistivity and higher carrier 
concentrations found in compounds with a higher density of PbSe|TiSe2 
 166 
interfaces within the isomer’s unit cell. This is likely the result of charge transfer 
from PbSe to TiSe2 being dependent on interfacial interactions. This work 
indicates that the self-assembly process begins during the deposition itself, 
driven by the heat of formation of the constituent layers. The nanoarchitecture 
of the precursor is sufficient to direct the formation of the targeted structure 
isomers, even if the composition of the precursor deviates significantly from that 
of the product, suggesting that the compounds are significant local energy 
minima in the free energy landscape. 
8.2 Materials & Methods 
The [(PbSe)1+δ]4[TiSe2]4 heterostructure isomer precursors were prepared from 
physical vapor deposition of elemental layers onto silicon and fused silica 
substrates. Elemental Pb and Ti were evaporated from electron beam guns 
operating at 6 kV. Elemental Se was deposited from a Knudsen effusion cell. All 
elements were purchased from Alfa Aesar and were greater than 99.95% purity. 
Shutters above each evaporating source were programmed to sequentially open 
for the period of time required to deposit the appropriate thickness of each 
element to form either bilayers of PbSe or trilayers of TiSe2. The thickness of the 
elemental layers deposited was monitored by quartz crystal microbalances. PbSe 
bilayers were deposited with a Pb|Se shutter sequence and TiSe2 trilayers with 
a Ti|Se shutter sequence. The sequence of Pb|Se and Ti|Se layers was 
controlled such that the nanoarchitecture of the precursor resembled the 
structure of the targeted isomer.29 The sequence of Pb|Se and Ti|Se layers for 
each isomer was repeated 11 times to build a film that was approximately 550 Å 
thick. The elemental precursors were annealed at 350 °C for 30 min in an N2 
atmosphere to promote self-assembly into a crystalline heterostructure.30–35 
Amount of material per unit area was determined for each heterostructure 
using wavelength dispersed X-ray fluorescence (XRF) data. The data were 
analyzed using a previously published method in which the raw intensity of each 
sample is determined by integrating under the signal curve and subtracting the 
background signal.36 Calibration curves for each element were used to relate the 
 167 
measured signal to the number of atoms per unit area in each film. 
Locked-coupled θ–2θ and grazing-incidence in-plane X-ray diffraction (XRD) 
data were both collected using laboratory Cu–Kα radiation with parallel beam 
optics on Bruker D8 Discover and Rigaku Smartlab instrumentation, 
respectively. Grazing-incidence scans were carried out with an incident angle of 
1.0° and the detector 4.0° above the sample plane. Ab-initio X-ray reflectivity 
(XRR) patterns from the idealized targeted structures were generated with the 
Bede REFS modeling software assuming bulk densities. 
High-angle annular dark-field scanning transmission electron microscopy 
(HAADF-STEM) images were collected using a probe aberration corrected FEI 
Titan 80–300 (300 kV, 120 mm camera length, Cs < 1 μm). Energy dispersive X-
ray spectroscopy (EDS) data were acquired with a 2.3 ms dwell time per pixel 
and summed over several drift-corrected frames. Cross-sectional lamellae for 
STEM imaging were made using an FEI Helios 600 Nanolab dual-beam FIB.37 
Electrical measurements were carried out on a house-built closed-cycle He 
cryostat using a 1.5 T magnet. Van der Pauw resistivities and Hall resistivities 
both were collected on cross-pattern films through Cu wires and In contacts. 
Reported values were calculated using thicknesses from reflectivity 
measurements of the annealed films. Seebeck coefficients were also measured 
using a house-built system. One edge of the film was cooled slightly, and both S 
and ΔT were measured between two type-T thermocouples. 
8.3 Results & Discussion 
XRR and XRD data indicate that the as-deposited precursors have a more 
complex structure than elemental layers in a particular pattern. Figure 8.1 
contains a representative XRR pattern of an as-deposited [(PbSe)1+δ]4(TiSe2)4 
isomer precursor (the 211211 isomer is shown). The pattern contains Kiessig 
fringes consistent with the 11 layers deposited, the first several Bragg reflections 
from the element layering, and Laue oscillations between the Bragg maxima. A 
film composed of 11 repeat units of a [(PbSe)1+δ]4(TiSe2)4 isomer is expected to 
 168 
have a total film thickness of ∼535 Å, slightly lower than the observed film 
thickness for the as-deposited isomers which range from 544 to 557 Å. The 
thickness of the elemental layering determined from the position of the first-
order Bragg reflection is slightly higher than the targeted value expected for a 
[(PbSe)1+δ]4(TiSe2)4 repeat unit, 48.68 Å, in all of the samples (ranging from 49.19 
to 50.81 Å). However, the observed Laue oscillations indicate that there are only 
10 layers present in the repeating elemental modulation, requiring that one of 
the as-deposited layers differs from what was intended. Representative XRD 
patterns, Figures 8.1 and B1, for as-deposited [(PbSe)1+δ]4(TiSe2)4 isomer 
precursors indicate that PbSe and TiSe2 have nucleated during deposition and 
that there are already coherent blocks of the [(PbSe)1+δ]4(TiSe2)4 isomer 
heterostructure before annealing. Surprisingly, there are also reflections 
consistent with the formation of a crystallographically aligned Ti2Se impurity 
phase which has a c-axis lattice parameter of 15.6 Å. XRR, XRD, and HAADF-
STEM images (discussed in subsequent paragraphs) all show that annealing the 
precursors at 350 °C for 30 min in an N2 atmosphere provides enough energy for 
the self-assembly of the elemental precursors into the desired [(PbSe)1+δ]4(TiSe2)4 
isomer structure, although only 8–9 layers of the intended isomers form and the 
presence of the Ti2Se impurity phase remains. 
Figure 8.1. Representative as-deposited XRR and XRD for a 211211 isomer 
 169 
demonstrating behavior observed in all of the [(PbSe)1+δ]4(TiSe2)4 isomer 
heterostructures. The 00l reflections, corresponding to the artificial layering, the 
crystallized [(PbSe)1+δ]4(TiSe2)4 isomer heterostructure, and the impurity Ti2Se 
phase, are indexed in black, blue, and green, respectively. Additional as-
deposited XRR patterns can be found in the Supporting Information, Figure B1. 
 
The annealed heterostructures were analyzed by XRF to quantify the amount 
of material present in each film, and the results are summarized in Table 8.1. 
While the targeted isomer structures all had the same number of total atoms/Å2 
for each element (see Table 8.2), there is a large variation in the actual amount 
of material measured in the films after deposition, reflecting the challenges of 
reproducibly depositing monolayer amounts of various elements (∼10–7 
grams/cm2). We use quartz crystal microbalances (QCMs) to monitor the amount 
of material incident upon the substrate, which have about a 5% measurement 
error for the nanogram sensitivities required. However, the QCMs need to be 
located adjacent to the sample substrates, making this an indirect measurement 
that is sensitive to deviations in the flux within the plume of vaporized atoms. 
The spatial distribution of fluxes within the plume typically remains constant 
within a set of samples, resulting in a constant proportionality between the 
amount of material incident on the QCM to the amount incident on the 
substrate. Unfortunately, the spatial distribution of fluxes within the plume 
changes with time as the source size decreases and with a number of 
experimental parameters (beam raster area and raster rates, impurities on 
source surfaces, etc.). Pb is the limiting element in all of the films, and there is 
not enough Pb, Ti, or Se in any of the films to form 11 unit cells of any of the 
targeted isomers (see Table 8.2). Insufficient Pb, Ti, and Se in the precursors 
explains why fewer unit cells formed compared to what was targeted. To form, 
the intended isomers required diffusion within and between deposited layers to 
provide Pb to the nucleation sites. This results in less than 11 repeating units 
forming. Surprisingly, the deposited nanoarchitecture and initial layer growth in 
 170 
the precursors was sufficient to direct the formation of the targeted isomers 
despite atoms diffusing between deposited layers and fewer than the targeted 
number of isomer layers forming. 
Table 8.1. Total Atoms/Å2 in Each of the Annealed [(PbSe)1+δ]4(TiSe2)4 Isomer 
Filmsa 
Atoms/Å2 
Isomer 
Pb Ti Se 
221111 3.61(1) 3.65(1) 9.82(2) 
211211 3.64(1) 3.74(1) 10.28(2) 
3311 3.71(1) 3.61(1) 9.78(2) 
3212 3.65(1) 3.59(1) 10.02(2) 
2321 3.60(1) 3.87(1) 10.33(2) 
44 3.38(1) 4.02(1) 10.47(2) 
aThe error in the conversion factor between XRF intensity and number of 
atoms per unit area is 2-3%. 
 
Table 8.2. Calculated Number of Atoms/Å2 for Each Element in the 
[(PbSe)1+δ]4(TiSe2)4 Isomers for Different Film Thicknesses 
2
No. of Atoms/Å  
[(PbSe)1+δ]4(TiSe2)4 
Pb Ti Se 
repeating units 
8 3.39 2.91 9.19 
9 3.82 3.28 10.34 
10 4.24 3.64 11.49 
11 4.37 4.00 12.64 
XRR patterns of the annealed films provide insight into the complex structure 
of the products that formed during annealing. Information contained in the XRR 
 171 
patterns is detailed in Figure 8.2, using the 3212 isomer pattern as a 
representative example. The 3212 isomer has a layer sequence of aaabbabb, 
where the thicknesses of the PbSe component in the unit cell (a) has a normal 
typeface and the TiSe2 (b) is bold in the 3212 abbreviation. Bragg maxima from 
the self-assembled product are observed in the XRR pattern, and the position of 
these maxima yield a c-axis lattice parameter of 48.60(1) Å, which is consistent 
with the expected unit cell of a [(PbSe)1+δ]4(TiSe2)4 isomer composed of four layers 
of TiSe2 and four layers of PbSe. The XRR pattern also has smaller maxima, 
which come from two different effects. Near the critical angle, these smaller 
maxima are called Kiessig fringes, and they are a consequence of the X-ray 
interference reflecting from the top and the bottom of the film. At higher angles, 
the smaller maxima between the Bragg reflections, called Laue oscillations, 
result from incomplete destructive interference from the finite number of unit 
cells in the film. The number of Laue oscillations between consecutive Bragg 
reflections depend on the number of complete unit cells contributing to the 
interference effect. The top left panel of Figure 8.2 shows that a film thickness of 
484.4 Å results in Kiessig fringes that match those observed for the 3212 isomer. 
A film that is composed of nine unit cells contributing to the total thickness does 
not match the experimental low angle data between the critical angle and the 
first Bragg reflection. The top right panel of Figure 8.2 compares simulations of 
the Laue fringes for a heterostructure with the targeted 11 unit cells and a 
heterostructure with 9 unit cells contributing to the interference effect with the 
experimental data for the 3212 isomer. Simulations for a film composed of 9 
repeating unit cells matches the observed experimental data, while simulations 
for 11 repeating unit cells do not. 
 172 
Figure 8.2. Experimental and simulated XRR patterns for the 3212 structural 
isomer. The upper left panel focuses on the Kiessig fringes, indicating that the 
total film thickness is 491.4 Å. The upper right panel emphasizes the Laue 
oscillations, showing that 9 unit cells are present, not the 11 expected from the 
deposition sequence. The bottom panel compares the simulated and 
experimental patterns based on the complete model described in the text. 
Since Kiessig fringes are extremely sensitive to the quality of interfaces 
(roughness) while the Laue oscillations are sensitive to the number of unit cells 
interfering in the sample and the extent of their disorder, the experimental low 
angle patterns reflect the changing contributions of both diffraction effects 
throughout the presented angular range. The discrepancy between the total film 
thickness and the number of repeating units indicates that there is extra 
material present in the films. This extra material can exist either above and/or 
below the nine unit cells of the 3212 isomer. The relative thickness of the top 
and bottom impurity layers influences the rate of decay of the intensity above 
the critical angle. The roughness of the layer on top of the 3212 block determines 
the angular dependence of the relative contributions of the Kiessig and Laue 
interference effects. The bottom panel in Figure 8.2 shows a simulated pattern 
containing nine unit cells of the 3212 isomer with 47 Å of extra thickness divided 
between a 35 Å layer underneath and a 12 Å layer with a roughness of 5 Å on 
 173 
top. The positions of the maxima line are consistent between the simulated and 
experimental patterns. The magnitude of the Laue oscillations is larger in the 
simulated pattern because the 3212 block was modeled as an ideal film. The 
intensity of the Laue oscillations can be suppressed and the intensity of the 
fourth-order Bragg reflection can be increased by adding roughness to one or 
more of the unit cells. The 35 Å layer underneath the 3212 isomer block is likely 
the Ti2Se impurity phase observed in the as-deposited XRD and is likely 
responsible for the as-deposited XRR patterns containing Laue fringes for only 
10 layers. 
Similar models were created for all of the targeted [(PbSe)1+δ]4(TiSe2)4 
heterostructure isomers. The stacking sequence of the 8-layer blocks within the 
repeating unit were varied and we assumed atomically sharp interfaces between 
the constituent structures. Also assuming a constant electron density within 
each constituent results in a square-wave function for the electron density as 
shown in Figure 8.3. This simple model assumed the c-lattice parameters for the 
heterostructures were equal and the interfaces between the eight constituent 
unit cells occurred at intervals of 1/8th of a unit cell. Within the unit cell, 
221111 and 211211 compounds have five interfaces, the 3311, 3212, and 
2321compounds have three interfaces, and the 44 profile has one interface. The 
Fourier transform of the electron density of each [(PbSe)1+δ]4(TiSe2)4 
heterostructure isomer is different due to the distinctive placement of the eight 
constituent layers within the unit cell. Consequently, the pattern of intensities 
of the 00l reflections in the specular diffraction will be unique for each structural 
isomer. 
Experimental XRR patterns for each of the [(PbSe)1+δ]4(TiSe2)4 isomers are 
shown in Figure 8.4 along with simulated patterns using both the electron 
density profiles determined from Figure 8.3 and the parameters gathered using 
the method described for the 3212 isomer. Bragg reflections observed in the XRR 
patterns occur at nominally the same 2θ angle for all of the [(PbSe)1+δ]4(TiSe2)4 
isomers, indicating that the repeating unit is similar. Relative patterns of the  
 174 
Figure 8.3. Schematic representation of the variation of electron density through 
a unit cell for each of the [(PbSe)1+δ]4(TiSe2)4 isomers. 
Bragg reflection intensities correlate well between the models and experimental 
data. Small intensities experimentally observed when the models predict zero 
intensity result from approximations made for the models shown in Figure 8.3. 
For the model it was assumed the interfaces were located at exactly 1/8th 
intervals of the unit cell, but experimentally the Se–Ti–Se trilayer and a Pb–Se 
bilayer thicknesses are not equal. Another assumption used in the model is that 
the layers are perfectly smooth, when in reality some roughness is observed. The 
positions of the Laue oscillations in the models were adjusted by varying the 
number of unit cells of each isomer to match the experimental data. Positions of 
Kiessig fringes in the model were manipulated to match the experimental data 
by varying the total sample thickness via the excess material on the top or bottom 
of the film. STEM images of each isomer were used as a guide to approximate 
the amount of extra material present. The patterns are somewhat insensitive to 
the exact ratio of thickness of the top/bottom impurity layers, so the decay of 
the intensity from the critical angle to the first Bragg maxima was adjusted by 
varying the exact thicknesses of the top and bottom impurity layers. Roughness 
of the layer on top of the isomer block was adjusted to match the observed 
 175 
change from Kiessig fringes to Laue oscillations, which differs based on impurity 
thicknesses and number of unit cells. Parameters from the models for each 
isomer are summarized in Table 8.3. All of the [(PbSe)1+δ]4(TiSe2)4 isomers have 
fewer unit cells in the isomer blocks than the targeted number. The total 
thicknesses of the isomers are all less than what was measured for the as-
deposited samples as a result of Se loss during annealing in an open system. It 
was determined, via XRR simulations and HAADF-STEM, that all 
[(PbSe)1+δ]4(TiSe2)4 isomers have impurity layers above and below the block of 
repeating units. 
 
Table 8.3. Parameters Extracted from the XRR Patterns as Described in the Texta 
#  unit bottom top bottom 
total thickness 
cells in impurity impurity impurity 
sample thickness of isomer 
isomer thickness thickness roughness 
(Å) block 
block (Å) (±5) (Å) (±5) (Å) 
221111 9 514 438 40 36 1.0 
211211 8 498 389 48 34 5.0 
3311 8 482 389 60 40 5.0 
3212 9 484 437 35 12 5.0 
2321 9 481 437 14 30 8.0 
44 9 491 437 27 27 5.0 
aNot shown in the table are parameters that do not vary the model significantly. 
These parameters (the bottom impurity roughness (5 Å) and the roughness of 
the Si substrate (5 Å)) were held constant in all of the models. 
 176 
Figure 8.4. X-ray reflectivity patterns (in color) shown against simulated patterns 
created using models of the targeted isomers (in black) described in Figure 8.3. 
Specular and in-plane XRD patterns of the crystallized isomer 
heterostructures are shown in Figure 8.5. Lattice parameters were determined 
 177 
for each of the [(PbSe)1+δ]4(TiSe2)4 isomers and are summarized in Table 8.4. All 
but three of the maxima in the specular X-ray diffraction patterns can be indexed 
as 00l reflections corresponding to the nanoarchitecture of the targeted isomers. 
The c-axis lattice parameters, determined from the position of the 00l reflections, 
are similar for all of the isomers and are consistent with a repeating unit 
composed of four layers of PbSe and four layers of TiSe2, as was observed in the 
as-deposited data. The three reflections not belonging to the isomer’s unit cell 
can be indexed as 00l reflections from Ti2Se. The lattice parameter obtained, 
14.52(5) Å, matches that expected for Ti Se.382  This is consistent with the excess 
Ti observed in the number of atoms/Å2 determined from the XRF data for the 
annealed compounds and the impurity phase observed in the representative as-
deposited diffraction. All of the reflections in the in-plane diffraction scan can be 
indexed as hk0 reflections from either a hexagonal or square unit cell, whose 
lattice parameters correspond to either TiSe2 or PbSe, respectively (Table 8.4). 
Relative intensities of the reflections from each constituent are constant between 
isomers, indicating that there are similar relative amounts of PbSe and TiSe2 in 
each heterostructure. Both the PbSe and TiSe2 in-plane lattice parameters 
remain constant as the isomer nanoarchitecture is varied, indicating that there 
is no structural change as a function of layer sequence. There are no observed 
reflections corresponding to the Ti2Se impurity phase in the in-plane diffraction. 
The (110) and (310) reflections observed in the square unit cell indicate that PbSe 
does not have the bulk rock salt structure, because these reflections are 
forbidden in the Fm3̅m rock-salt space group. This indicates that the PbSe 
structure has distorted with either Pb or Se no longer on special position sites, 
which is not unexpected for these ultrathin layers. A similar distortion was 
observed in (PbSe)m(MoSe2)n compounds, where atoms moved ∼20 pm from ideal 
rock salt structure positions.39 The structures of the PbSe-TiSe2 isomers studied 
in this paper were not refined due to the large number of crystallographic 
parameters that would be required for these more complicated unit cells and the 
 178 
limited number of reflections observed. 
Figure 8.5. Specular (a.) and in-plane (b.) XRD patterns of the [(PbSe)1+δ]4(TiSe2)4 
structural isomers. The indices of the observed reflections are shown above each 
reflection in the in-plane pattern and representative indices are indicated in the 
specular pattern. 
HAADF-STEM images, collected for each of the [(PbSe)1+δ]4(TiSe2)4 isomers, 
provide local information about defects and overall sample structure. Figure 8.6 
shows a full film image of the 44 [(PbSe)1+δ]4(TiSe2)4 isomer. Rock-salt layers 
containing Pb show up as bright regions due to the higher average atomic 
number relative to TiSe2 layers, which are darker. STEM-EDS data for the 2321  
 179 
Table 8.4. Lattice Parameters for the [(PbSe)1+δ]4(TiSe2)4 Structural Isomers 
Determined from the Annealed Diffraction Patterns 
c-axis PbSe a-axis TiSe2 a-
lattice lattice axis lattice impurity 
sample 
parameter parameter parameter phase 
(Å) (Å) (Å) 
221111 48.66(1) 6.121(1) 3.560(1) 14.41(4) 
211211 48.64(1) 6.132(1) 3.566(1) 14.54(1) 
3311 48.62(1) 6.131(1) 3.561(1) 14.53(3) 
3212 48.60(1) 6.134(1) 3.563(1) 14.55(2) 
2321 48.56(1) 6.128(2) 3.561(2) 14.54(1) 
44 48.52(2) 6.132(1) 3.560(1) 14.55(1) 
isomer, shown in Appendix B, confirms this assignment. Distinct bright atomic 
columns of atoms can be seen in regions where the electron beam aligns with a 
crystallite’s zone axis. Different layers and regions within the same layer have 
different orientations, indicating both rotational disorder and some stacking 
defects. The majority of the film consists of nine unit cells of the isomer, which 
is consistent with the XRR data discussed previously. At the top and bottom of 
the film there is material that is not consistent with the repeating blocks of the 
isomer. In the layer closest to the substrate there are regions where Ti2Se grains 
can be found in addition to smaller regions of TiSe2 and (PbSe)1(TiSe2)1. These 
observations are consistent with the analysis of the XRF, XRR, and XRD data 
discussed previously. 
Figure 8.7 shows HAADF-STEM images of all [(PbSe)1+δ]4(TiSe2)4 structural 
isomers. These images demonstrate that the films consist of different sequences 
of PbSe and TiSe2 layers with sharp planar interfaces between them. The 
different layering schemes for each of the six isomers can be clearly identified 
and are further supported by the EDS profile shown in Figure B3. There is 
extensive rotational disorder occurring between the different constituent layers 
in each block, evident by zone axis orientations appearing in only some of the  
 180 
 
Figure 8.6. HAADF-STEM image of the 44 [(PbSe)1+δ]4(TiSe2)4 structural isomer 
showing the entire film from substrate to surface. 
layers. As observed in the specular XRD patterns, the thickness of the repeating 
layer schemes are the same for all six isomers. The majority of the samples are 
composed of a central block of the targeted isomer and the number of unit cells 
in the blocks agrees with that determined from the Laue fringes in the XRR 
patterns. While there are stacking defects in all of the isomer domains, it is quite 
surprising that the imperfect 11 repeating sequences deposited in the precursors 
contain sufficient information to direct the self-assembly of 8–9 unit cells into 
the targeted isomer stacking sequences. 
The structural data presented above provide insight into the isomers’ growth 
from the deposited precursor. It suggests that Ti2Se forms at the substrate 
surface when Se is deposited onto the initial Ti layer. We tested this in a separate 
experiment, showing that Ti2Se forms when depositing Se on Ti in a Ti–Se 
precursor, even when the Ti to Se ratio is 1:2. Forming Ti2Se as the initial layer 
results in an excess Se concentration since the amount of Ti and Se deposited  
 181 
 
Figure 8.7. HAADF-STEM images of each isomer heterostructure highlighting 
the formation of the targeted nanoarchitecture, sharp interfaces between 
constituents, and rotational misregistration between layers. 
was intended to form a TiSe2 layer in the isomer samples. When Pb intended to 
form PbSe in the first repeat unit is deposited, it reacts with the excess Se from 
the first Ti|Se layer to form a PbSe layer. When the next layer of Ti is deposited 
(intended for the second repeat unit), it is deposited on a Se rich layer which 
allows the formation of TiSe2 to occur. The TiSe2 grows out horizontally from its 
nucleation site. Since the repeating sequence is low on Ti, the formation of the 
growth stops when the Ti at the growth front has been depleted, leaving some 
amorphous material in the layer. Similar behavior occurs for the next Pb|Se 
layer, but the TiSe2 basal plane surface results in the formation of 
crystallographically aligned PbSe at the interface. Since the repeating sequence 
is also low on Pb, the formation of the growth stops when the Pb at the growth 
front has been depleted, leaving some amorphous material in the layer. This 
process continues, on average, for about four unit cells, which corresponds to a 
crystallite size of ∼200 Å perpendicular to the substrate. Subsequent deposited 
layers are more disordered. 
 182 
A schematic illustrating the as-deposited structure and how it evolves is 
shown in Figure 8.8. To simplify the image a [(PbSe)1+δ]1(TiSe2)1 repeating unit 
structure was used in place of the more complex [(PbSe)1+δ]4(TiSe2)4 isomer 
structure. When the temperature is increased during annealing, the 
concentration gradients drive diffusion of Pb and Ti to the growth front. In 
addition to growth parallel to the substrate, additional layers crystallize 
perpendicular to the substrate and facilitate further growth of the 
heterostructure. Around the crystallized structure is a region that is metal 
poor/Se rich as a result of the nucleation site stealing metal from the 
surrounding area to form the structure. The requirement to steal material from 
the surrounding area is the result of the wrong atoms/Å2 being deposited per 
layer in the precursor. Since all of the samples were most deficient in Pb, it is 
the species that will be depleted first, leaving a Ti|Se top layer which reacts with 
oxygen during annealing to form an amorphous oxide. We anneal our films in an 
N2 environment with <1 ppm of O2, which is insufficient to prevent formation of 
a surface oxide during annealing. The thickness of the isomer layer therefore 
ends up being 2 or 3 unit cells less than the 11 that were targeted, consistent 
with the number of Laue oscillations seen in the XRR scans and the HAADF-
STEM images. The ability to prepare the metastable isomers without being 
precisely on composition is an advantage in the quest to find new material 
phases, since it is challenging to precisely control the absolute amount of an 
element at the monolayer level. These metastable compounds have a broad 
enough energy minimum in the free energy landscape that the system still forms 
the targeted isomer even if the composition deviates from the target, as long as 
the nanoarchitecture resembles the targeted compound. 
 183 
Figure 8.8. Atomistic picture demonstrating the initial crystallization in the 
isomers (a) and a snapshot showing the movement of atoms and further crystal 
growth upon annealing (b). The arrows demonstrate the concentration gradient 
of the metals and point to where the metals are diffusing. On deposition a layer 
of Ti2Se forms and persists even after annealing. Pb atoms are shown in red, Ti 
atoms in blue, and Se atoms in gray. 
Temperature-dependent resistivity graphs for the six [(PbSe)1+δ]4(TiSe2)4 
isomers are shown in Figure 8.9. The isomer with the smallest number of 
 184 
interfaces per unit cell, the 44 isomer, has the highest resistivity, while the 
221111 isomer, which has the most interfaces, has the lowest resistivity at all 
temperatures. The magnitude of the resistivity and the slow decrease in 
resistivity as temperature is decreased from room temperature suggest that these 
samples are metallic. At low temperatures, however, all the samples have an 
increase in resistivity similar to those observed in the previously reported 
[(PbSe)1+δ]m(TiSe 31,33,34,402)n compounds.  The similarity of the normalized 
resistivity versus temperature plots, Figure 8.9b, suggests that the same 
phenomena are occurring in all of the isomers. Minima in the resistivity for the 
isomers occur between 50 and 100 K, with the 44 isomer, having the highest 
temperature minima, and the 221111 isomer, the lowest. 
Figure 8.9. Temperature-dependent resistivity of six [(PbSe)1+δ]4(TiSe2)4 isomer 
heterostructures, with both measured (a) and normalized (b) values. 
 185 
Hall coefficients were measured as a function of temperature to provide more 
information about the increase in resistivity at low temperatures. The Hall 
coefficients were negative for all isomers over the entire temperature regime, 
indicating that electrons dominate the electrical transport. Carrier 
concentrations were calculated from the Hall data, assuming a single band 
model, and are plotted as a function of temperature in Figure 8.10a. The carrier 
concentrations slowly decrease as temperature is decreased in all of the samples. 
The decrease in carrier concentration has a very weak temperature dependence, 
suggesting that an activated process is not the source of the increasing carrier 
concentration with increasing temperature. Isomers with the same number of 
interfaces in the unit cell have similar carrier concentrations, with the 44 
structure having the lowest and the 221111 and the 211211 isomers the 
highest. Carrier mobility, calculated from the resistivity and Hall data, is shown 
in Figure 8.10b. The mobility values and their temperature dependences are 
similar for all of the isomers, with mobility increasing with decreasing 
temperature before becoming constant below 50 K. At low temperatures, higher 
mobilities correlate with increasing buried interface density. This is somewhat 
surprising as more interfacial scattering from the layers, which should be 
relatively temperature independent, unlike other mechanisms (e.g., electron–
electron or electron–phonon scattering), would be expected for structures with 
high interface density. The minima in the resistivity appears to be a consequence 
of the interplay between the decreasing carrier concentration and increasing 
mobility as temperature is decreased. As the temperature decreases the mobility 
increases at a faster rate than the carrier concentration decreases, resulting in 
observed resistivity decrease. At low temperatures, the decreasing carrier 
concentration and plateau of the mobility result in the resistivity increase. 
The room-temperature Seebeck coefficient was collected for each isomer 
compound, and the values are shown in Figure 8.11. Several [(PbSe)1+δ]4(TiSe2)4 
isomers were measured to explore how much the room temperature transport 
measurements varied between samples. There was a 5% variation of the Seebeck  
 186 
Figure 8.10. Temperature-dependent carrier concentration (a) and mobility (b) 
of six [(PbSe)1+δ]4(TiSe2)4 isomer heterostructures. Values are calculated 
assuming a single n-type band. 
coefficient between the four samples measured. The negative Seebeck 
coefficients obtained for all of the isomers agree with the Hall measurements, 
indicating that electrons are the majority carrier type. The magnitude of the 
Seebeck coefficients systematically decrease as the interface density decreases 
in the [(PbSe)1+δ]4(TiSe2)4 isomers. This and the Hall data suggest that band 
alignments in [(PbSe)1+δ]4(TiSe2)4 isomers result in charge transfer from PbSe into 
TiSe2. The PbSe-TiSe2 bilayers should be thought of as a conducting entity due 
 187 
to charge transfer between the constituents. The more PbSe-TiSe2 interfaces 
there are, the higher the carrier concentration as charge transfer occurs at each 
interface, as shown schematically in Figure 8.12. The unusual decrease in the 
carrier concentration with temperature may be a consequence of the two 
structures changing independently with temperature, resulting in a change in 
the amount of charge transfer between the two constituents as a function 
temperature. 
Figure 8.11. Room-temperature Seebeck coefficients for each of the 
[(PbSe)1+δ]4(TiSe2)4 isomer heterostructures. Colors correspond to the 
nanoarchitecture, and symbols correspond to the precursor parameters. 
 
 188 
Figure 8.12. Schematic demonstrating charge donation occurring in isomers 
containing different numbers of buried interfaces, e.g., the 44 (a) and the 221111 
(b). The SnSe layers are shown in red and the TiSe2 in blue, and purple arrows 
depict the charge donation from the SnSe to the TiSe2 layers. The purple boxes 
indicate a single isomer repeating unit. 
8.4 Conclusion 
This work investigated the synthesis, formation, structure, and transport 
properties of [(PbSe)1+δ]4(TiSe2)4 isomers. While the correct amount of material 
deposited was not enough to form 11 repeat units of a [(PbSe)1+δ]4(TiSe2)4 
isomers, the intended nanoarchitectures still formed albeit with fewer unit cells 
than targeted. During deposition, an impurity Ti2Se phase formed at the 
substrate interface and there was initial crystallization of both TiSe2 and PbSe 
in sequences that match the structure of the targeted isomers. Both the initial 
layering scheme and the heat of formation of the targeted isomers drives the 
formation of the resulting material. XRR, XRD, and HAADF-STEM analyses 
confirm the formation of approximately eight or nine repeating units with the 
correct nanoarchitecture, with thin impurity phases present on the top and 
bottom. Transport data collected for the isomers indicate that the resistivity and 
carrier concentration depend on the number of interfaces in the unit cell of the 
 189 
isomers. This suggests that charge transfer between the constituent layers is the 
source of the electrons. The mobility and carrier concentration vary inversely 
with temperature, resulting in a minimum in the resistivity between 50 and 100 
K. The ability to prepare metastable isomers provides a new handle for tuning 
properties in thin film materials, and the tolerance of the self-assembly process 
to deviations from stoichiometry facilitates the discovery of new compounds 
using this synthesis approach. 
8.5 Bridge 
This chapter described the synthesis and characterization of a series of six 
isomer heterostructures constructed from four TiSe2 layers and four PbSe layers. 
The next chapter describes the synthesis of a novel heterostructure with a unit 
cell consisting of MoSe2, BiSe, and Bi2Se3. 
 
  
 190 
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 196 
CHAPTER IX 
SYNTHESIS AND ELECTRICAL PROPERTIES OF A NEW COMPOUND 
(BISE)0.97(BI2SE3)1.26(BISE)0.97(MOSE2) CONTAINING METALLIC 1T-
MOSE2 
9.0 Authorship Statement 
Chapter IX was published in Chemistry of Materials in 2021. Marisa Choffel 
and David Johnson are the main contributors to the text. Renae Gannon, Fabian 
Gohler, Douglas Medlin, and Thomas Seyller collected experimental XPS and 
HAADF-STEM data. I performed electrical transport measurements of the novel 
compound synthesized in this chapter. 
9.1 Introduction 
Group 6 semiconducting transition metal dichalcogenides have been the 
subject of extensive research over the last several decades due to their potential 
applications in catalysis1–3, photovoltaics4, supercapacitors5, and rechargeable 
battery systems.6 The structure of these MX2 compounds (where M = Mo, W and 
X = S, Se) consists of a hexagonal layer of metal atoms sandwiched between two 
hexagonal chalcogen layers.7,8 Depending on the stacking of these trilayers, 
several polymorphs are possible, with the semiconducting 2H polymorph being 
the most common with ABA BAB stacking. This stacking results in trigonal 
prismatic coordination of the metal.9,10 The recent discovery that the group 6 
compounds transition from an indirect to a direct band-gap semiconductor when 
the bulk material is scaled down to a monolayer has created significant 
excitement as one of the first examples of an emergent property in a 
monolayer.11–13 The transition from an indirect to a direct band-gap 
semiconductor, which increases absorption and photoluminescence, has great 
promise for applications in optical devices.12,14–16 
Ternary and higher-order compounds containing the group 6 X–M–X trilayers 
can also have ABC stacking of the layers, resulting in octahedral coordination of 
the metal and metallic conductivity.3,17–20 These structural and electronic 
 197 
changes were first discovered in the alkali intercalation of the group 6 
compounds.18,21,22 The ability to vary the intercalant, change carrier 
concentration by varying the amount of the intercalate, and the discovery of 
superconductivity in these compounds resulted in a surge of activity.18,23,24  
Haering and co-workers recognized the potential of these compounds as battery 
cathodes, leading to the first commercialized lithium-ion batteries.25 More 
recently, there has been a surge in publications on single- and few-layered 1T-
MX2 compounds due to improved catalytic properties for hydrogen evolution2,3 
and reduced contact resistances in 1T–2H–1T source–channel–drain field-effect 
transistors.19,26 
The high mobility and the volatility of alkali metal intercalants create 
challenges in their synthesis and in subsequent processing steps when adjacent 
to other compounds.27 An alternative way to create 1T-MX2 layers is the presence 
of an adjacent strong electron-donating layer. MSe layers, where M = Sb, Bi, or 
a rare earth metal, have been reported to donate charge to neighboring 
dichalcogenide layers in misfit layered compounds.28 These MSe layers have 
much lower vapor pressures than typical intercalants and are much less likely 
to diffuse. A recent paper on (BiSe)0.97(MoSe2) reported a 40/60 ratio of 1T/2H 
polymorph in the MoSe2 layer, with a significant reduction in electrical resistivity 
relative to 2H-MoSe2.29 To increase the fraction of 1T-MX2, more charge donation 
is required. However, [(BiSe)1+x]n(MoSe2) compounds cannot be made, as multiple 
layers of BiSe are not stable next to each other.30 
In this paper, we report the synthesis, structure, and properties of 
(BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2), probing how increasing the ratio of 
BiSe/MoSe2 layers affects the percentages of 2H and 1T polymorphs in the MoSe2 
layer. (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) was targeted as isostructural 
compounds that have been previously reported.31 The synthesis of the desired 
heterostructure is nontrivial, as it is only kinetically stable and avoiding the 
formation of [(Bi2Se3)1+y]2(MoSe2) requires excess Bi and Se in the precursor. 
(BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) formed crystallographically aligned with 
 198 
respect to the substrate, but this is due to the morphology of the precursor, not 
epitaxial growth. The extensive turbostratic disorder between the constituent 
layers indicates that epitaxial growth does not dominate the self-assembly of the 
precursor into the heterostructure. High-angle annular dark field-scanning 
transmission electron microscopy (HAADF-STEM) images confirm the layered 
nature of (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) and indicate that two different 
polymorphs of MoSe2 are present. X-ray photoelectron spectroscopy (XPS) data 
also indicate that 1T-MoSe2 is present in increased quantities relative to 
(BiSe)0.97(MoSe2). Resistivity measurements of (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) 
show it is metallic, which are consistent with the increased amount of 1T-MoSe2 
in the heterostructure. The Hall data are more complicated due to the 
heterogeneous mix of phases in the structures, resulting in a change in the 
carrier type as temperature is varied. 
9.2 Methods & Materials 
Precursors targeting (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) were synthesized via 
physical vapor deposition of the elements at pressures below 5 × 10–7 Torr, using 
the repeating sequence Mo|Se|Bi|Se|(Bi|Se|Bi|Se)|Bi|Se. Bismuth and 
molybdenum were deposited using an electron beam gun and selenium was 
deposited using a Knudson effusion cell. A Si (100) wafer with a native oxide 
layer and fused quartz were used as substrates. The bulk crystalline structures 
of the individual constituents were used to calculate the desired amount of 
material in each layer such that each Mo|Se layer had the number of atoms 
required to form a single Se–Mo–Se trilayer of MoSe2, each Bi|Se layer had the 
number of atoms required to form a bilayer of a rock salt-structured BiSe, and 
each (Bi|Se|Bi|Se) had the number of atoms required to form a quintuple Se–
Bi–Se–Bi–Se layer of Bi2Se3. A previously published calibration method was used 
to optimize the deposition parameters.32 X-ray fluorescence (XRF) intensities 
were collected using a Rigaku ZSX Primus-II with a rhodium X-ray tube to 
determine the amount of each metal deposited. The proportionality constant 
between XRF intensity and the amount of Mo and Bi in the film was determined 
 199 
by preparing samples of MoSe2 and Bi2Se3 and using the Se proportionality 
constant previously reported.32 
X-ray reflectivity (XRR) and specular X-ray diffraction (XRD) data were 
collected on a Bruker D8 Discover diffractometer using Cu Kα radiation. Grazing 
incidence in-plane XRD information was collected using a Rigaku SmartLab with 
a Cu source. 
Precursors were annealed at targeted temperatures for 15 min in a glovebox 
with a nitrogen atmosphere where O2 pressure was below 0.5 ppm to promote 
their self-assembly into the crystalline products. 
A cross section of the sample was prepared with an FEI Helios Nanolab 600i 
dual-beam scanning electron microscope (SEM)/focused ion beam (FIB) using 
the standard lift-out method.33 A protective layer of Sharpie carbon and FIB-
deposited carbon was applied to the surface. High-angle annual dark field-
scanning transmission electron microscopy (HAADF-STEM) images of the cross 
section were collected on a probe-corrected Thermo Fisher Scientific Themis Z 
STEM at 300 keV. 
X-ray photoelectron spectroscopy (XPS) measurements were carried out at 
room temperature at a pressure of less than 3 × 10–10 mbar using Al Kα radiation 
from a SPECS XR-50M X-ray source with a SPECS Focus 500 crystal 
monochromator and a SPECS Phoibos 150 MCD-9 hemispherical analyzer 
equipped with a nine channeltron detector. Cleaving of samples prior to XPS 
measurements was done by mounting the sample between two steel plates using 
a combination of low-degassing EPO TEK H72 and H22 epoxy resins. Breaking 
of the top plate under the flow of dry nitrogen in the load lock of the UHV system 
exposes the buried interfaces of the film. Spectral analysis was carried out by 
fitting the high-resolution core-level spectra with multiple Voigt profiles. 
Lorentzian lifetime widths used in the fits were determined beforehand on 
commercially available single crystals as well as MER-grown binary samples. 
Temperature-dependent resistivity measurements were collected on the 
 200 
samples between 24 and 298 K using the van der Pauw method on a home-built 
system. 
9.3 Results & Discussion 
Six precursors were deposited as we attempted to prepare 
(BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2). The amounts of each element required to 
form 11 and 10 layers of a (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) heterostructure 
were estimated using the lattice parameters and structures of the binary 
constituents and/or structurally related compounds (Table 1). The compositions, 
total thickness, and repeating layer thickness of each precursor are summarized 
in Table 9.1. The fluctuation of the measured amounts for the precursors around 
the targeted values reflects the reproducibility of the deposition but is valuable 
as our initial target value is only an estimate. Compositions for each precursor 
were determined from the XRF intensities of each element for the total film and 
the previously described calibration method.32 The precursors were closer in 
composition to the stoichiometry of (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2)than to the 
composition estimated for 11 or 10 layers of [(Bi2Se3)1+y]2(MoSe2), a potentially 
competing local free-energy minima. The XRR patterns of all of the precursors 
contained a first-order Bragg reflection from the sequence of deposited layers, 
indicating that the elements in the precursor did not completely mix during the 
deposition. The thicknesses of all of the repeating sequences of elemental layers 
were close to the estimated c-axis lattice parameter for the 
(BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) heterostructure (28.06 Å) determined by 
adding c-axis lattice parameters of the constituents. The amounts of each 
element deposited in the repeating sequence 
Mo|Se|Bi|Se|(Bi|Se|Bi|Se)|Bi|Se suggest that forming 10 or 11 layers of 
(BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) would involve the smallest diffusion distances 
for the elements. 
 
 
 201 
Table 9.1. Amounts of Material and Repeating Thicknesses for Samples 
Targeting the (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) Nanoarchitecture 
atoms/Å2 per layer in precursor before annealing 
Bi M Se Total # # Repeatin
thickness layers layers g 
deposi crystall thickness 
sample -ted -ized (Å) 
sample 1 3.88(8) 1.15(2) 6.5(3) 309.7(9) 11 10 28.37(2) 
sample 2 3.53(7) 1.37(3) 6.6(3) 308.7(5) 11 10 27.69(2) 
sample 3 3.19(6) 1.21(2) 7.6(4) 312.9(8) 11 10 28.49(2) 
sample 4 3.41(7) 0.90(2) 7.0(3) 291.2(7) 11 10 27.28(2) 
sample 5 3.46(7) 1.22(2) 7.0(3) 302.7(4) 11  27.78(2) 
sample 6 3.54(7) 1.15(2) 7.1(4) 315.0(8) 11  27.89(2) 
targeting 
(BiSe) (Bi 3.71 1.18 6.8  11  1+x
2Se3)1+y(Bi 28.06 
Se)1+x(MoS 3.37 1.07 6.2  10  
e2) 
targeting 2.87 1.18 6.8  11  
[(Bi2Se3)1+y] 25.56 
(MoSe ) 2.61 1.07 6.2  10 
 
2 2
All of the samples were annealed to 350 °C to quickly evaluate what 
compounds self-assembled from the precursors, and the resulting specular and 
in-plane diffraction patterns are shown in Figure 9.1. The reflections observed 
in the specular diffraction patterns of samples 1 and 2 index to single families of 
(00l) reflections with c-axis lattice parameters of 27.97(1) and 27.79(2) Å, 
respectively. Both are close to the estimated c-axis lattice parameter of 
(BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) (28.06 Å). The in-plane reflections can be 
indexed as (hk0) reflections for three different constituents: two hexagonal unit 
cells and a unit cell with a rectangular basal plane. The calculated lattice 
parameters (ahex,1 = 4.170(3) Å, ahex,2 = 3.311(4) Å, arect = 4.600(1) Å and brect = 
4.238(1) Å) are consistent with those expected for Bi2Se3 (a = 4.178(1) Å), MoSe2 
(a = 3.32(1) Å), and BiSe (a = 4.61(1) Å and b = 4.26(1) Å), respectively.29,31 The 
diffraction data indicate that (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) formed from 
these precursors. Surprisingly, samples 3 and 4 formed [(Bi2Se3)1+y]2(MoSe2) 
instead of the targeted compound (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) whose 
composition they were closest to. The evenly spaced reflections in the specular 
 202 
X-ray diffraction yield c-axis lattice parameters of 26.38(1) and 25.96(1) Å, 
respectively, which are close to the estimated c-axis lattice parameter for 
[(Bi2Se3)1+y]2(MoSe2) (25.56 Å). The in-plane maxima can be indexed as (hk0) 
reflections to two different hexagonal unit cells with a-axis lattice parameters of 
4.154(2) and 3.309(5) Å, which are close to those expected for Bi2Se3 and MoSe2, 
respectively.29,31 Intensity at ∼28.6° 2θ suggests that a small amount of BiSe 
may have formed. The specular diffraction scans for samples 5 and 6 have sharp 
reflections at low angles and broader diffraction maxima at high angles, 
suggesting that the samples have not fully self-assembled at this temperature. 
The high-angle reflections yield c-axis lattice parameters of 26.32(1) and 26.27(1) 
Å for samples 5 and 6, respectively, which are close to the estimated c-axis lattice 
parameter of [(Bi2Se3)1+y]2(MoSe2). The reflections observed in the in-plane 
pattern of sample 6 can be indexed to two different hexagonal unit cells. The 
lattice parameters calculated from the peak positions (ahex = 4.158(3) Å, ahex = 
3.304(7) Å) are consistent with those expected for Bi2Se3 and MoSe2. Higher 
intensity at ∼28.6° 2θ suggests that more BiSe is present in this sample than 
found in sample 3. The different products formed show how sensitive the reaction 
pathway is to the composition and structure of the precursors. 
In conventional high-temperature solid-state synthesis, the composition of 
the starting mixture determines the product or the ratio of products that form. 
In reactions of layered precursors, the local compositions and nanoarchitecture 
become important parameters as they control what nucleates and the diffusion 
lengths required for growth. Due to reactions with the substrate and/or 
oxidation at the surface, it is common to form one or more fewer unit cells of the 
intended heterostructure than the number of layers deposited.34 We observed 
this in the precursors studied here, as the Laue oscillations around the (002) 
reflections in samples 1–4 indicate that 10 unit cells formed from the 11 
repeating sequences deposited. Figure 9.2 graphs the amounts of Mo and Bi in 
each of the samples, normalized to the 10 unit cells that crystallized, and arrows 
are used to indicate whether they formed (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) or  
 203 
Figure 9.1. (a) XRR (gray) and specular X-ray diffraction and (b) representative 
in-plane X-ray diffraction patterns of the samples after annealing to 350 °C. 
Asterisks in (a) mark the reflections that result from the Si substrate. The 
reflections for the different components are marked in (b) in varying fonts 
consistent with the labels in the top right corner. 
[(Bi2Se3)1+y]2(MoSe2). Samples 1 and 2 have enough Bi and Mo to make the 10 
layers of (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) that formed.Samples 3–6 are all 
deficient in one element compared to (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2). Instead 
of forming nine unit cells of (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2), they instead 
 204 
evolve into [(Bi2Se3)1+y]2(MoSe2). We speculate that the significant excess of Se (5–
13%) relative to the amounts of Bi and Mo in these precursors may have 
promoted the formation of Bi2Se3 rather than BiSe by Le Chatelier’s principle. 
Since Laue oscillations are observed in samples 1–4, long-range diffusion is 
required to transport the excess amounts of Bi and Mo out of the coherent 
crystalline domains. The excess Se probably acts as a flux. Samples with excess 
Mo relative to the compound formed have broader diffraction maxima, which we 
speculate is due to MoSe2 inclusions, which reduces the size of coherent 
domains. Excess Bi has been observed to form Bi2Se3 on the top of the sample 
in other Bi-containing heterostructures35,36, suggesting that it is more mobile 
than excess Mo. Our results indicate that the local free-energy minima in the 
energy landscape for (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) and [(Bi2Se3)1+y]2(MoSe2) 
are close in energy. 
Figure 9.2. Amounts of Bi and Mo in the samples compared to the estimated 
amounts to form [(Bi2Se3)1+y]2(MoSe2) (red circle) and 
(BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) (blue circle). 
Specular and in-plane XRD scans were collected on sample 1 as a function of 
annealing temperature to determine the optimal formation conditions for 
 205 
(BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) (Figure 9.3). The specular XRD pattern of the 
as-deposited precursor contains reflections from two different sources. The 
sharp first-order Bragg reflection results from the composition modulation of the 
precursor from the deposited sequence of elemental layers. The broader 
diffraction maxima at higher angles result from small crystalline domains that 
nucleated and grew during the deposition process. The broad diffraction maxima 
can all be indexed to a single family of (00l) reflections with a c-axis lattice 
parameter of 28.0(1) Å. This value is close to the estimated c-axis lattice 
parameter for (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) (28.06 Å). Evidence for 
crystallization during deposition is also found in the in-plane XRD pattern. The 
broad reflections are consistent with the (100) and (110) reflections for Bi2Se3 
and the (110) and (020) reflections for BiSe.31 After annealing at 150 °C, there 
are slight increases in the intensity of the existing reflections in both the specular 
and in-plane XRD patterns, but no new reflections are observed. The XRR 
pattern has fewer Kiessig fringes, suggesting that there is an increase in the 
roughness of the film as atoms diffuse. After annealing at 250 °C, the intensity 
of reflections in the specular and in-plane XRD patterns increase, linewidths 
decrease, and additional reflections are visible in both patterns. Even more 
reflections appear after annealing at 350 °C and the existing reflections in both 
patterns increase in intensity and decrease in the linewidth. The XRR pattern 
indicates that the film smoothness increased during annealing at 350 °C. Laue 
oscillations are now apparent between low-angle Bragg reflections, indicating the 
sample is 10 repeating layers thick. The total thickness of the sample based on 
the Kiessig fringes in the XRR pattern is 306.9(3) Å. Based on the c-axis lattice 
parameter and the number of layers indicated from the Laue oscillations, the 
thickness of the crystalline BiSe–Bi2Se3–BiSe–MoSe2 repeating structure is 
∼279.7 Å. The difference, ∼27 Å, is approximately the thickness of three 
quintuple layers of Bi2Se3, which is observed in the STEM images discussed next. 
The lattice parameters calculated from both patterns remain consistent with the 
formation of (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) at this temperature. The (00l) 
 206 
reflections in the specular XRD pattern lose intensity, broaden, and new 
reflections appear after annealing at 400 °C, indicating that 
(BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) is decomposed. The in-plane reflections of 
BiSe decrease in the intensity, suggesting that the decomposition of this layer is 
responsible for the deterioration of the heterostructure. The annealing study 
indicates that (BiSe)1+x(Bi2Se3)1+y(BiSe)1+x(MoSe2) begins to self-assemble during 
the deposition and the self-assembly is completed, and excess Bi and Se diffuse 
to the top of the film after annealing at 350 °C. 
Figure 9.3. (a) XRR (gray) and specular XRD (black) patterns and (b) in-plane 
XRD patterns of sample 1 as a function of temperature. The red lines indicate 
the 2θ values for reflections calculated using the c-axis lattice parameter of the 
structure (27.97(1) Å). Indices are indicated above some reflections. 
 207 
An HAADF-STEM image from a cross section of sample 1 annealed at 350 °C 
is contained in Figure 9.4. The 10 repeating units of 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2), containing a quintuple layer of Bi2Se3, a 
bilayer of BiSe, a trilayer of MoSe2, and a bilayer of BiSe are clearly visible. The 
10 unit cells agree with the number determined from the Laue oscillations in the 
XRD pattern. There is a thin amorphous region present on the bottom of the film 
and two extra Bi2Se3 layers are present on the top of the sample. Similar diffusion 
of excess Bi and Se to the top of a sample forming Bi2Se3 layers was previously 
reported in other bismuth-containing heterostructures.35,36 The first crystalline 
layer in the heterostructure above the substrate is Bi2Se3, which is surprising 
since a Mo|Se layer was first in the deposition sequence. The energy-dispersive 
X-ray spectroscopy (EDS) map shows that the bottom of the film contains an 
amorphous mixture including Mo, Se, Si, and O (Figure C1). The intensity of Se 
on the bottom of the film is less than that of the Se intensity in MoSe2 layers, 
suggesting that at least some of the Mo may react with the SiO2-coated Si surface 
during deposition or annealing. Grain boundaries within layers and varying 
orientations within and between layers are present for all constituents, 
suggesting multiple nucleation sites. The resulting turbostratic disorder is 
commonly found in samples prepared from modulated precursors.37–39 
A higher magnification HAADF-STEM image is shown in Figure 9.5, which 
clearly shows the atomically abrupt interfaces between the structurally different 
layers. Different layers having different zone axis orientations are observed, with 
the orientations changing both within and between layers. A single quintuple 
layer containing a Se–Bi–Se–Bi–Se stacking sequence is observed when the 
Bi2Se3 layer is oriented along a ⟨112̅0⟩ zone axis. Antiphase boundaries are 
clearly visible in BiSe layers when they are oriented along a ⟨110⟩ zone axis. The 
different orientations are thought to result from different nucleation sites both 
in the same and in different layers, resulting in the extensive rotational disorder 
observed. While not both contained in the image in Figure 9.5, we identified 
regions in the sample where small domains of the two different polytypes of  
 208 
Figure 9.4. Representative HAADF-STEM image of the 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) heterostructure annealed to 350 °C on a Si 
substrate with its native SiO2 surface layer. The 10 repeating sequences of layers 
resulting in Laue oscillations are indicated on the left with red dashed lines. 
Figure 9.5. HAADF-STEM image of the (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) 
heterostructure with zone axes labeled for each constituent. Antiphase 
boundaries are observed in regions of the film containing BiSe orientated along 
the [110] zone axis and marked with red arrows. 
 209 
Figure 9.6. HAADF-STEM images, which show a region of (a) 1T-MoSe2 and (b) 
2H-MoSe2. The schematics below the images show the expected [110] zone axis 
images for 1T-MoSe2 and 2H-MoSe2 [Mo (green) and Se (yellow)]. 
MoSe2 could be identified when they are orientated down a ⟨110⟩ zone axis. The 
diagonal slashes shown in Figure 9.6a are consistent with an octahedrally 
coordinated 1T-MoSe2 polymorph, and the chevrons in Figure 9.6b are 
consistent with a trigonal prismatic coordinated 2H-MoSe2 structure. The fact 
that only small local regions are observable with these zone axis orientations 
reflects the small size of the MoSe2 grains. 
XPS of the Mo 3d, Se 3d, and Bi 5d core levels was collected on cleaved films 
to gain information about the electronic states found in 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2), and representative spectra are shown in 
Figure 9.7. Spectral analysis of the Mo 3d core-level spectrum (Figure 9.7a) 
reveals contributions from two different components, with Mo 3d5/2 binding 
energies of 228.25 ± 0.05 and 228.93 ± 0.05 eV. An additional broad component 
 210 
centered at 229.47 ± 0.11 eV is required to account for the signal from an 
overlapping Se 3s core level. The Mo 3d binding energies are consistent with 
those reported previously for 1T- and 2H-MoSe2, both in (BiSe)0.97(MoSe2) (228.3 
± 0.1 and 228.9 ± 0.1 eV) and the individual polymorphs2,29,40, consistent with 
the observations in the HAADF-STEM images. The percentage of each polytype 
can be estimated from the relative intensities of the different MoSe2 components 
in the spectrum. The amount of the 1T polymorph is found to be between 40 and 
60%, which is higher than that observed in (BiSe) 290.97(MoSe2).  Se is expected to 
be in a Se2– oxidation state, regardless of whether it is found in the MoSe2 
polymorphs or the bismuth constituents.41 Previous reports show that the Se 3d 
core levels of 1T- and 2H-MoSe2 are found at slightly different binding energies, 
and that the chemical shift between them is similar to that observed in the Mo 
3d spectrum.2 Any difference in binding energy for Se in Bi2Se3 and BiSe is too 
small to be distinguished. Our fit of the Se 3d5/2 spectrum is shown in Figure 
9.7b, and the Se 3d5/2 binding energies (54.47 ± 0.05 eV for 2H-MoSe2, 53.79 ± 
0.05 eV for 1T-MoSe2, and 53.57 ± 0.05 eV for Se bound to Bi) are consistent 
with those previously reported.29 Two components are required to fit the Bi 5d 
spectrum (Figure 9.7c), as evident by the asymmetry of both the 5d3/2 and 5d5/2 
lines toward lower binding energies. The position of the higher binding energy 
line (24.99 ± 0.05 eV) is consistent with Bi3+, slightly larger than that observed 
in bulk Bi2Se3 (24.75 eV) and close to values reported for Bi atoms in BiSe 
(24.93–25.00 eV). The component at lower binding energy (24.13 ± 0.12 eV) has 
previously been assigned as Bi0 due to Bi atoms at antiphase boundaries 
involved in Bi–Bi bonds between adjacent atoms (23.4–24.3 eV).29,42 From the 
relative intensity of the two components, we can estimate that ∼30–50% of the 
Bi atoms in the BiSe layers are involved in Bi–Bi bonds at antiphase boundaries. 
The percentage of Bi involved in Bi–Bi bonds at antiphase boundaries in 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) is similar to the (BiSe)0.97(MoSe2) 
heterostructure29; however, there are two BiSe layers for each MoSe2 layer in 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2), while there is only one per MoSe2 layer in 
 211 
(BiSe)0.97(MoSe2). Therefore, more charge donation to MoSe2 occurs in 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2), increasing the percentage of 1T-MoSe2. This 
interpretation is supported by density functional theory and crystal orbital 
Hamilton population calculations, which show that both charge donation to 
adjacent layers and antiphase boundary formation stabilize the BiSe rock salt 
structure by acting as “sinks” for excess electrons.40 Charge donation from the 
BiSe layers to MoSe2 layers stabilizes the octahedral 1T polymorph instead of the 
thermodynamic trigonal prismatic 2H polymorph.19,20,29 
Figure 9.7. XPS analysis of the (a) Mo 3d, (b) Se 3d, and (c) Bi 5d core levels. 
Experimental data are shown as a solid black line, while the different 
components of the spectral analysis are in color. 
In-plane electrical resistivity data for several 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) samples are shown in Figure 9.8 along with 
the resistivity reported for (BiSe)0.97(MoSe2). The two compounds have strikingly 
different temperature dependencies. The resistivity of (BiSe)0.97(MoSe2) 
exponentially increases as the temperature is decreased, indicating an activated 
conduction mechanism typical for a semiconductor. (29) Since 2H-MoSe2 is 
semiconducting in the bulk43, the amount of metallic 1T-MoSe 18–202  is not 
enough to create a continuous conducting network. In contrast, the room-
temperature resistivities of the (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) samples are 
all very similar to each other, ∼17(2) μΩ*m, with a near-linear decrease in 
resistivity as the temperature decreases, indicating that this compound is 
metallic. We suspect that the metallic conductivity results from a continuous 
 212 
network of 1T-MoSe2 across the sample, consistent with the significantly higher 
percentage of 1T-MoSe2 determined from our XPS data. While 1T-MoSe2 is 
reported to be metallic18–20, we were unable to find resistivity data as a function 
of temperature for 1T-MoSe2 reported in the literature. We used alkali metal 
intercalates of MoS2, in which the MoS2 has the 1T polymorph due to electron 
donation from the alkali metals, as a comparison instead. These compounds 
have room-temperature resistivities ranging from 25 to 50 μΩ m17, approximately 
twice the resistivity measured here for (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2), 
where the MoSe2 sample is only ∼20% of the volume of the unit cell. 
Figure 9.8. Temperature-dependent resistivity data of three 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) samples (A–C) from precursor 1 are plotted 
as a function of temperature for comparison with the (BiSe)0.97(MoSe2) 
heterostructures. The inset figure graphs the data for the 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) samples on an expanded scale. 
In-plane Hall data were collected on (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) to 
obtain more information about its electrical behavior. The Hall data are 
compared to a structurally similar (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(TiSe2) in Figure 
9.9, as Hall data were not reported for (BiSe) (MoSe ).29,310.97 2  The Hall coefficient 
 213 
is negative for (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(TiSe2) across the temperature range, 
indicating electrons are the majority carrier.31 Charge transfer of electrons from 
BiSe to TiSe2 was suggested as the source of the carriers, with the electrons in 
the TiSe2 layers dominating the conductivity.31 The Hall coefficient of 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) is also negative at room temperature, but 
changes sign as temperature is decreased below 235 K. Interpreting the Hall and 
conductivity data for (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) is complicated since we 
know from the XPS data that this compound contains a heterogeneous mix of 
2H- and 1T-MoSe2. Based on prior reports that 1T-MoSe2 is metallic and 2H-
MoSe2 is semiconducting, the current is likely concentrated in the portion of the 
sample that is the 1T polymorph, which forms a low resistivity percolation 
pathway through the film. The small value of the Hall coefficient is consistent 
with the metallic behavior observed in the temperature dependence of the 
resistivity data. Since the sign of the Hall coefficient changes with temperature, 
the small magnitude of the Hall coefficient may also be a consequence of the 
electrons in the 1T-MoSe2 layer competing with holes in the two BiSe layers in 
the unit cell. 
Figure 9.9. Temperature-dependent Hall data plotted as a function of 
temperature for (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2). Data for the structurally 
similar (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(TiSe2) heterostructures are provided for 
comparison. 
 214 
The structural data, electrical transport data, and XPS results are consistent 
with the BiSe layers donating charge to the MoSe2 layers in 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2). The XPS data show that the amount of 1T- 
MoSe2 relative to 2H-MoSe2 is larger than that observed in (BiSe)0.97(MoSe2), and 
the resistivity of (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) is lower than that of 
(BiSe)0.97(MoSe2). (29,31) However, our understanding of how the properties of 
monolayers change as a result of being adjacent to different substrates and 
constituents is limited. The Hall data indicate that at least two bands contribute 
to the electrical conductivity. We have no data that indicate whether this 
contribution comes from the BiSe or the Bi2Se3 layers. Preparing homologous 
compounds with thicker Bi2Se3 (m) or MoSe2 (n) layers, 
(BiSe)0.97[(Bi2Se3)1.26]m(BiSe)0.97(MoSe2)n, and correlating the electrical properties 
and the resulting percentage of 1T and 2H polymorphs of MoSe2 with the values 
of m and/or n might enable us to better understand the interaction between 
constituent layers. 
9.4 Conclusions 
The new metastable heterostructure (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) was 
prepared by self-assembly from designed precursors. Excess Bi was required to 
obtain (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2), which diffused during growth to 
form a cap of Bi2Se3. The c-axis and in-plane lattice parameters are consistent 
with the formation of (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2). The HAADF-STEM 
imaging indicates that two different polymorphs of MoSe2 form as small domains 
and that the BiSe layers contained antiphase boundaries. The XPS Bi 5d spectra 
contain intensity from two oxidation states of Bi, which is consistent with Bi0 in 
Bi–Bi bonds at the antiphase boundaries of BiSe and Bi3+ in the Bi–Se bonds in 
Bi2Se3 and BiSe. Two oxidation states of Mo were also observed in the XPS Mo 
3d spectra, consistent with the presence of both 2H- and 1T-MoSe2. According 
to XPS, about 40–60% of the MoSe2 in the heterostructure was of the 1T polytype. 
The low resistivity values at room temperature and the metallic temperature 
dependence are consistent with the formation of a continuous network of 1T-
 215 
MoSe2. The heterogeneous mix of MoSe2 polytypes complicates the interpretation 
of the Hall data. The low magnitude is consistent with the metallic behavior 
observed in the resistivity. The change in the carrier type as a function of 
temperature indicates that carriers in more than one band contribute to the 
conductivity. The thermal stability and metallic resistivity of 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2) might make it useful as an Ohmic contact 
for devices containing MoSe2 layers. 
9.5 Bridge 
This chapter presented a study of the synthesis and characterization of a 
novel heterostructure containing BiSe, Bi2Se3 and MoSe2 layers. The next 
chapter summarizes and concludes the work presented in this thesis.  
  
 216 
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CHAPTER X 
CONCLUSIONS AND SUMMARY 
Silicon-based transistors have continued to mature, with their current near-
atomic miniaturization and performance in integrated circuits (IC’s) surpassing 
any of its inventors’ wildest expectations. However, current state-of-the-art 
manufacturing for these devices involves manipulation of materials on such a 
small scale that low-dimensional physics have begun to significantly affect device 
performance. However, our knowledge of these low-dimensional effects and how 
they interact with each other is limited, especially given the nearly infinite 
number of possible low-dimensional structures that exist. Therefore, for 
technology to continue advancing, it is necessary to develop methods for 
consistently synthesizing low-dimensional structures in order to better 
understand the relationship between their structures and their chemical and 
physical properties. This will also necessitate the development of new methods 
for characterizing these materials and their properties.  
One such synthetic technique is the modulated elemental reactants (MER) 
method, which combines the attributes of several more conventional approaches, 
allowing for an unprecedented level of experimental control over the thickness of 
each of the deposited layers (which controls diffusion lengths and nucleation site 
density) and the local composition of the film (which controls which phase 
nucleates). By exploiting these tunable and adaptable experimental parameters 
to drive the reaction towards the desired outcome, MER enables the facile 
synthesis of many novel heterostructures as well as a few metastable compounds 
that were not able to be synthesized via other methods. 
Another critical innovation was the development of an x-ray fluorescence-
based (XRF) technique which enables the facile and non-destructive 
measurement of the absolute number of atoms per unit area in a film, provided 
the film is below a critical thickness (~ 50 nm for most film compositions). This 
method allows for the determination of the film composition with sub-monolayer 
 224 
accuracy, enabling the use of statistical process control principles to maximize 
the synthesis of films with the desired composition. 
This dissertation leverages both MER and the XRF-based composition 
methods to develop and demonstrate a systematic approach to synthesizing and 
characterizing two-dimensional transition metal dichalcogenide films and 
heterostructures. The work opens with a survey of many of the conventional 
synthesis methods, followed by an in-depth discussion which further illustrates 
the principles of MER. After a brief summary of the experimental methods used, 
a method for extracting structural information from x-ray diffraction patterns 
containing Laue oscillations is presented. This method allows for determination 
of the number of unit cells of crystalline material in the film, along with 
confirmation that the entire film thickness consists of the targeted crystalline 
material – which is very useful for detection of small amorphous oxide layers that 
may be difficult to observe via other characterization methods. Next, there is a 
discussion of the automated system for measuring the electrical transport 
properties of a film, which uses the van der Pauw method to determine the 
resistivity and Hall Coefficient. The final half of the dissertation focuses on the 
synthesis and characterization of transition metal dichalcogenide films and 
heterostructures utilizing the methods discussed and presented previously. 
First, an experimental study of single-phase MoSe2 and TiSe2 films is presented, 
demonstrating that depositing precursor films with ~15% excess Se results in 
the highest quality films. After that, various the synthesis and properties of 
several novel structures with more complex nanoarchitectures are presented, 
beginning with a composite film constructed from interleaved ultrathin layers of 
crystalline TiSe2 and amorphous silicon, moving to a series of six isomers 
constructed from different intergrowths of an eight-layer unit cell consisting of 
four TiSe2 layers and four PbSe layers, and ending with a novel heterostructure 
(BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2).  
Overall, this work develops and applies a methodology for synthesizing and 
characterizing crystalline two-dimensional materials and heterostructures, 
 225 
applying the method to several material systems. It is important to continue 
extending our knowledge of the many possible two-dimensional structures that 
exist but have not been experimentally synthesized so that we can exploit their 
properties in future generations of optoelectronic devices.  
  
 226 
APPENDIX A 
 
 
Figure A.1 XRR of Ti|Se annealing study showing evolution of film thickness 
and roughness as energy is applied to the system.  
 
Figure A.2 Specular (a.) and in-plane (b.) XRD patterns for additional Ti|Se 
precursors annealed at 350°C showing the influence of precursor composition 
on structure.  
 227 
 
Figure A.3 XRR patterns for various Ti|Se precursors annealed at 350 °C 
showing the variation in roughness and loss of layers as a function of 
stoichiometry.  
 
 
Figure A.4 Experimental (red) and simulated (black) XRR patterns 
demonstrating effect of oxide growth. Based on the amount of excess material in 
each film, the annealed films developed either a thin (~9 Å) or thick (~60 Å) oxide 
layer.  
  
 228 
APPENDIX B 
Figure B.1 Representative as-deposited XRR patterns demonstrating the initial 
layering and rearrangement occurring in the sample before annealing occurs.  
 
Table B.1. Total Film thickness and repeat layer thickness for representative 
[(PbSe)1+]4[TiSe2]4 isomer heterostructures.  
Isomer As-Deposited As-Deposited 
Total Film Repeat 
Thickness (Å) Thickness (Å) 
221111 557 49.34 
211211 545 49.05 
3311 -- -- 
3212 546 49.34 
2321 544 50.81 
44 553 49.19 
 
The as-deposited total thickness was obtained from BedeREFS by 
assuming an 11-layer isomer block with no impurities and varying the c-lattice 
parameter of the isomer block until the simulated Kiessig fringes between θc 
and the 001 reflection maxima matched those of the experimental XRR pattern. 
The simulated electron density was scaled by a factor of 0.9 – 0.95 to get a 
precise match for the experimental θc. The as-deposited repeat unit thickness 
was calculated using a modified version of Bragg’s Law corrected for refraction, 
and the first two Bragg reflections observed in the low angle diffraction 
patterns. 
 
 
 
 229 
Figure B.2 Representative grazing incidence in-plane diffraction of an as-
deposited [(PbSe)1+]1[TiSe2]1 heterostructure demonstrating the initial 
nucleation of both PbSe and TiSe2 crystallites before annealing.  
Figure B.3 STEM-EDS showing the relative intensity of characteristic X-ray 
signals from Pb and Ti when moving down the k=2321 structure. 
 
  
 230 
APPENDIX C 
 
Figure C.1 Electron dispersive x-ray spectroscopy (EDS) line profile from 
substrate to surface of (BiSe)0.97(Bi2Se3)1.26(BiSe)0.97(MoSe2). 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 231