University of Southern California Dissertations and Theses

Transport studies of phase transitions in a quasi-1D hexagonal chalcogenide

(USC Thesis Other)

Transport studies of phase transitions in a quasi-1D hexagonal chalcogenide

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content

Transport Studies of Phase Transitions in a Quasi-1D Hexagonal Chalcogenide

by

Huandong Chen

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATERIALS SCIENCE)

May 2023

Copyright 2023 Huandong Chen

ii

Dedication

To my family

iii

Acknowledgements
First of all, I would like to express my gratitude to Prof. Jayakanth Ravichandran for his
invaluable guidance and support throughout my PhD journey. As my advisor, he has
always been so insightful, supportive, nice, and patient. I really appreciate the freedom
and encouragement that Jayakanth provided me to explore my interests, while keeping
me focused on important aspects of research. From him I have learnt a lot not only on
how to critically think of and creatively solve a research problem, but also about how to
make the right decision, how to properly handle work-life balance, human relationships,
etc. I feel extremely fortunate to have him as my advisor, and I believe without his
mentorship and guidance, I would not have grown as a researcher and a person to the
extent that I have. I would also like to extend my appreciation to Prof. Jongseung Yoon
for his guidance and training on how to become a serious experimentalist. His philosophy
of “尽人事，听天命” (do one’s level best and leave the rest to God’ will) has inspired me
to stay strong and calm in the face of obstacles both in research and in life.
Furthermore, I would like to thank all the excellent collaborators and friends who
have worked with me and helped me during my PhD. Thanks to Shanyuan, Tom, Yang,
Mythili, Boyang, Yan-ting, Shantanu and Harish for their friendship, support, and
invaluable contributions as lab-mates in Ravichandran’s group. I really enjoyed our
scientific discussions as well as random chats in the lab! I also must thank Dongseok,
Haneol, Boju, Lauren, Qian, Wanting for their continuous help and friendship. I am also
privileged to have collaborated with exceptional researchers from different fields, including
Prof. Rohan Mishra at Washington University in St. Loius, Prof. Han Wang at USC, and
Prof. Nuh Gedik at MIT, whose expertise ranges from DFT, microscopy, to electronic
devices and optical characterizations. Many thanks to all of them and their group members,
and it has been such a great pleasure working with them! Thanks to Guodong, Gwan-
Yeong, Nan, Hefei, Jiang-bin and Batyr!
Last, I must thank my family for their continuous support regardless of my
situation. Thanks mom and dad for being always so supportive at even 6,500 miles away.
I own my grandparents a visit and many video calls. I wish I could have spent more time

iv

with them. Many thanks to my fiancée, Xinyue, for her continuous support through many
years’ long-distance relationship and during the Covid time. Thank you all!!!

Huandong Chen
Los Angeles, April 2023

v

Table of Contents

Dedication .................................................................................................................................................... ii
Acknowledgements ...................................................................................................................................... iii
List of Figures ........................................................................................................................................... viii
Abstract ..................................................................................................................................................... xv
Preface ...................................................................................................................................................... xvii
Chapter 1 Introduction and background ...................................................................................................... 1
1.1 Theoretical concepts of CDW ............................................................................................................ 1
1.1.1 One-dimensional electron gas and instability .............................................................................. 2
1.1.2 Electron-phonon coupling and Kohn anomaly ............................................................................ 5
1.1.3 Connection to superconductivity ................................................................................................. 7
1.2 Experimental signatures ..................................................................................................................... 9
1.3 Emerging CDW in “semiconducting” systems ................................................................................... 12
1.3.1 Unconventional CDWs ............................................................................................................... 13
1.3.2 Opportunities in developing electronic devices ........................................................................... 16
1.4 Quasi-1D hexagonal chalcogenides .................................................................................................... 16
Chapter 2 Crystal growth and characterization .......................................................................................... 20
2.1 Single crystal growth ......................................................................................................................... 20
2.1.1 Chemical vapor transport .......................................................................................................... 21
2.1.2 Molten flux growth .................................................................................................................... 23
2.2 Chemical and structural characterization ......................................................................................... 25
2.2.1 Energy- and wavelength- dispersive spectroscopy ...................................................................... 25
2.2.2 Single crystal X-ray diffraction .................................................................................................. 27
2.2.3 Transmission electron microscopy .............................................................................................. 29
2.3 Optical characterization .................................................................................................................... 30
2.3.1 Fourier-transform infrared spectroscopy .................................................................................... 30
2.3.2 Raman spectroscopy ................................................................................................................... 31

vi

2.4 Electrical transport measurements .................................................................................................... 32
2.4.1 Bulk resistivity and its temperature dependence ....................................................................... 32
2.4.2 Hall measurements ..................................................................................................................... 34
2.4.3 Resistivity anisotropy ................................................................................................................. 36
2.4.4 DC sweeps and pulsed I-V measurements .................................................................................. 37
Chapter 3 A polymeric planarization strategy for multiterminal transport studies on small, bulk
crystals ........................................................................................................................................................ 39
3.1 Crystal planarization using polyimide and device fabrication ........................................................... 40
3.1.1 Motivation .................................................................................................................................. 40
3.1.2 Planarization processes .............................................................................................................. 43
3.1.3 Device fabrication and contact optimization .............................................................................. 47
3.2 Micro-structure patterning using plasma-FIB ................................................................................... 51
3.3 Integration of van der Waals contacts on planarized bulk crystals ................................................... 53
3.4 Encapsulation strategy for handling ‘sensitive’ materials ................................................................. 55
Chapter 4 Charge-density-wave order and electronic phase transitions in a dilute d-band Semiconductor
.................................................................................................................................................................... 59
4.1 Transport signatures of phase transitions in BaTiS3 ......................................................................... 60
4.2 Structural characterization ................................................................................................................ 64
4.3 Mechanism of phase transitions in BaTiS3 ........................................................................................ 67
4.4 Conclusion ......................................................................................................................................... 71
Chapter 5 Novel electrical functionalities in BaTiS3 ................................................................................... 73
5.1 Charge-density-wave switching and voltage oscillations ................................................................... 73
5.1.1 Reversible resistive switching ..................................................................................................... 75
5.1.2 Mechanism of electrical switching .............................................................................................. 76
5.1.3 CDW voltage oscillations ........................................................................................................... 78
5.1.4 Effect of thermal managements and channel sizes ..................................................................... 80
5.1.5 Conclusion .................................................................................................................................. 81
5.2 Multilevel memristive switching ........................................................................................................ 82
5.2.1 Memristive switching by DC sweeps .......................................................................................... 82

vii

5.2.2 Pulsed I-V measurements and switching mechanism ................................................................. 85
5.2.3 Lifetime of intermediate states ................................................................................................... 86
5.2.4 Conclusion .................................................................................................................................. 87
Chapter 6 Flux growth of BaTiS3 crystals .................................................................................................. 88
6.1 Crystal growth and chemical analysis ............................................................................................... 89
6.2 X-ray diffraction and electron microscopy ........................................................................................ 92
6.3 Structural and optical anisotropies ................................................................................................... 94
6.4 Conclusions ....................................................................................................................................... 95
Chapter 7 Concluding remarks and outlook ................................................................................................ 98
7.1 Concluding remarks .......................................................................................................................... 98
7.2 Outlook ............................................................................................................................................. 99
Bibliography .............................................................................................................................................. 102

viii

List of Figures
Figure 1.1 Illustration of Peierls instability in a 1D atomic chain. A lattice distortion or dimerization
is energetically favorable as the electronic energy saved due to the new bandgaps overweighs the elastic
energy consumption from lattice reconstruction, hence, the total energy is minimized. Ref.[5] ................... 1
Figure 1.2 (a) Normalized Lindhard response function for different dimensional free electron gas at
zero temperature. For 1D, the response function diverges at 2𝑘𝐹. (b) Nesting-induced Kohn anomalies.
Ref. [6] .......................................................................................................................................................... 6
Figure 1.3 (a) Phase diagram of 1T-TaS2. Superconductivity is introduced by pressure. (b) Phase
diagram of CuxTiSe2. Superconductivity is promoted by Cu intercalation. Ref.[10,12] .............................. 8
Figure 1.4 Transport signatures of several CDW systems. (a) Quas-1D organic compound TTF-TCNQ
shows a metal-to-insulator transition. (b) NbSe3 reveals two transport anomalies while the system is
kept metallic. (c) No anomaly is found in temperature-dependent resistivity in NbSe2. Ref.[13,17] ............ 9
Figure 1.5 𝒒-dependent electron-phonon coupling in NbSe2. CDW formation in NbSe2 is not explained
by the Fermi surface nesting mechanism as no local maxima is observed in either real or imaginary
parts of the 𝜒𝒒 at 𝒒𝐶𝐷𝑊. Indeed, the Kohn anomaly-like strong phonon softening is due to the peak
of 𝒒-dependent EPC matrix element g𝒒2. Ref.[4,8] .................................................................................... 11
Figure 1.6 (a) Temperature dependent resistivity of bulk 1T-TaS2, showing several metal-to-insulator
transitions and an overall semiconducting / insulating transport behavior. (b) Schematic illustration
of Ta atoms displacements that form the David-star clusters in CCDW phase of 1T-TaS2. (c)
Illustration of band structure in 1T-TiSe2. Bonded states of electron-hole pairs (excitons) spontaneously
condense when electrons and holes bind between the two bands near the Fermi level, connected by a
wavevector 𝒒𝟎. (d) Schematic of the collective excitations of an exciton condensate coupled to lattice
distortion. Both plasmon and phonon modes soften at 𝒒𝟎 near the phase transition temperature.
Ref.[10,36,43] ............................................................................................................................................... 13
Figure 1.7 (a) Schematic showing biologically inspired neuromorphic computing. (b) Physical
mechanisms of electronic devices that switch between high-conductivity and low-conductivity states,
mimicking synaptic behavior. Different Electrical resistance R versus applied voltage V of a non-volatile

ix

memristor (left) showing multiple resistance states, and a volatile memristive switch (right) with
negative differential resistance (NDR). (c) Memristive switching achieved in a 1T-TaS2
nano-thick
crystal. (d) Voltage oscillations of a 1T-TaS2 oscillator device performed at room temperature.
Ref.[37,49,53] ............................................................................................................................................... 15
Figure 1.8 Calculated band gap of a list of TMPCs with different phases. Quasi-1D hexagonal phase
of BaTiS3 is highlighted in red circles. Ref.[59] ........................................................................................... 17
Figure 1.9 Schematic of BaTiS3 crystal structure, showing hexagonal symmetry. 1D chains of TiS6
octahedra are highlighted. ........................................................................................................................... 17
Figure 1.10 (a) Calculated electronic band structure of BaTiS3 at room temperature with energy band
gap Eg highlighted. (b) Experimentally measured refractive index (n) and extinction coefficient (k) of
BaTiS3 for polarization parallel and perpendicular to the c axis, exhibiting a high optical anisotropy.
An optical bandgap is extracted to be ~ 0.3 eV along the c axis from absorption edges indicated in the
plot. Ref.[57] ................................................................................................................................................ 18
Figure 2.1 Schematic of the crystal growth process with chemical vapor transport. Ref.[72] ..................... 21
Figure 2.2 Different morphologies of CVT-grown BaTiS3 crystals. Optical images of (a) thin BTS needle,
(b) thick BTS needle and (c) BTS platelet. For ‘needle’-like samples, c-axis follows the direction of
long edges and is easy to determine. Edges of terraces on BTS plates are useful in assigning the crystal
orientations, which can be further confirmed by polarization-dependent Raman spectroscopy. ................. 22
Figure 2.3 Schematic of the design principle of molten flux growth. Ref.[76] ............................................. 24
Figure 2.4 Schematic showing resolving capabilities between WDS and EDS. In this case, WDS is able
to discriminate between Te (L𝛼) and Sb (L𝛽1) peaks and has better peak-to-background ratios. Source:
e-probe.epss.ucla.edu ................................................................................................................................... 25
Figure 2.5 Schematic of experimental procedures for single crystal X-ray diffraction. Ref.[77] .................. 28
Figure 2.6 Schematics of working principles of TEM (left) and STEM (right). Figure credit: Matthew
Mecklenburg. (from lecture note of MASC 535L class at USC) .................................................................. 30
Figure 2.7 Schematic illustration of resistivity measurement of a bulk sample using equally spaced
colinear four probes. Ref.[79] ....................................................................................................................... 32

x

Figure 2.8 Optical images of (a) the closed-cycle cryostat used for temperature dependent resistivity
measurements, and (b) a bulk BaTiS3 device bonded onto a chip carrier using Au wires and Ag epoxy,
which is ready to be loaded into the cryostat for transport measurements. ................................................ 34
Figure 2.9 Schematic illustration of a six-contact and eight-contact Hall bar geometry used for Hall
measurements. Image credit: Lake Shore 7500/9500 series Hall system user’s manual. .............................. 35
Figure 2.10 The conformal mapping function that uniquely maps the ratio Raa/Rcc to 𝐵𝛼,𝑘, which is
later used to calculate the anisotropy 𝜌𝑎/𝜌𝑐. Ref.[60] ................................................................................ 37
Figure 3.1 (a) Schematics of the fabrication process flow for a bulk BaTiS3 device utilizing PI as the
embedding medium. (b) Schematic illustration of PI peeling off step with a 5 × 5 arrays of crystals
processed at the same time. (c) Photographic image of multiple BaTiS3 devices fabricated for transport
studies. ........................................................................................................................................................ 44
Figure 3.2 (a) Surface profile scans of an as-grown BaTiS3 crystal placed on a PDMS stamp and after
polyimide embedding and RIE cleaning. (b) Optical micrographs of a BaTiS3 crystal after crystal
embedding (top left), surface cleaning (bottom left), metallization with (top right) and without (bottom
right) a thin PI dielectric on the channel region. ........................................................................................ 45
Figure 3.3 (a) A cross-sectional illustration of a BaTiS3 device embedded in polyimide for transport
studies. (b) and (c) Optical microscopic images of BaTiS3 devices with various electrode designs. Both
devices are contacted directly with channel region exposed. ....................................................................... 48
Figure 3.4 Total resistance (R) as a function of metal pad spacing (L) from standard transfer length
method (TLM) measurements, where Ti/Au (3 nm/300 nm) were deposited on SF6-cleaned crystal
surface. This specific device has an extracted contact resistance of 370 Ohm and a contact resistivity
of 0.015 Ω∙cm2. .......................................................................................................................................... 50
Figure 3.5 SEM images of various BaTiS3 microstructures fabricated by PFIB with geometries of (a)
‘clover-leaf’ shape, (b) 6-terminal Hall bar and (c) 8-terminal Hall bar. ..................................................... 52
Figure 3.7 (a) A cross-sectional illustration of a BaTiS3 device embedded in polyimide with a ‘VIA
holes’ scheme. (c) and (e) Optical microscopic images of BaTiS3 devices with various electrode designs
after ‘VIA’ holes formation. (b) Schematic illustration of a BaTiS3 device contacted through polyimide
‘VIA’ holes, with channel regions encapsulated. (d) and (f) Optical microscopic images of the
corresponding BaTiS3 devices after metal deposition. ................................................................................. 56

xi

Figure 4.1 Illustration of representative temperature dependent electrical resistivity of BaTiS3 crystal
along c-axis. Abrupt and hysteric jumps in resistance are shown near 150-190 K (Transition I), and
240-260 K (Transition II). Inset shows optical microscopic image of a BaTiS3 device used for transport
measurements. ............................................................................................................................................. 60
Figure 4.2 Reproducible transport measurements of BaTiS3. (a) Temperature-dependent electrical
resistance (normalized by R (300 K)) measured from three different BaTiS3 devices. The transport
behavior is qualitatively consistent with each other. (b) Transport behavior of a needle-like device
contacted by hand-bonding method using silver epoxy and Au wires. (c) Transport measurements from
different thermal cycles. (d) Cooling rate-dependent transport on BaTiS3. Neither of the transitions
are suppressed or altered using cooling rate up to 5 K/min. ....................................................................... 61
Figure 4.3 Temperature dependence of the mobility, µ, and carrier concentration, n, of the dominant
carrier, extracted from Hall measurements during a warming cycle. .......................................................... 62
Figure 4.4 (a) Plot of Hall voltage Vxy with magnetic field from -6 T to 6 T at different temperatures.
Hall data was collected form the Sample C, with its temperature-dependent longitudinal resistance
illustrated in Figure 4.2a. (b) The measured data (blue) was fitted linearly to extract the carrier
concentration n and mobility µ. .................................................................................................................. 63
Figure 4.5 Thermal activation energy analysis of BaTiS3. Transport data from Figure 4.3 is used for
analysis. ....................................................................................................................................................... 64
Figure 4.6 CDW order evolution revealed by single crystal XRD. Precession images from single-crystal
X-ray diffraction measurements along hk2 projection at 298 K, 220 K and 130 K. The bottom left plots
the X-ray intensity cut along the direction as indicated in precession images. ........................................... 65
Figure 4.7 DFT-calculated electronic band structure of different phases of BaTiS3 with (a) P63cm, (b)
P3c1, and (c) P21. The contribution of Ti d-state and S p-sates to the band structure are highlighted
with blue and red colors, respectively. The band gap (Eg) calculated at the PBE level is provided
underneath the plots. The vertical arrows indicate the changing band gap at the G point. The horizontal
arrows show the symmetry direction along the chain-parallel- (‘chain(∥)’) and chain-perpendicular-
plane (‘chain(⊥)’) from the zone-center (G point) in the first Brillouin zone .............................................. 66

xii

Figure 4.8 (a) Illustration of unit cell evolution of BaTiS3 at different temperatures. (b) Summary of
electronic phases and phase transitions. The bandgap values (Eg) are taken from DFT-calculated band
structures using PEB exchange-correlation functional. ............................................................................... 67
Figure 4.9 In-plane electrical conductivity anisotropy analysis using Montgomery method. (a) Measured
van der Pauw resistance Raa and Rcc as a function of temperature. The transport data was collected
from a BaTiS3 platelet device with van der Pauw geometry (l = w = 20 µm). (b) The conformal
mapping function that uniquely maps the ratio of Raa / Rcc to 𝐵𝛼,𝑘, which is later used to calculate
the anisotropy 𝜌𝑎/𝜌𝑐 . ................................................................................................................................ 68
Figure 4.10 rs and Fröhlich electron-phonon coupling constant values for various semiconductors.
Experimentally reported or DFT-calculated parameters including carrier concentration n, static and
high frequency dielectric constant 𝜀𝑠 and 𝜀∞, effective band mass mb, and longitudinal optical phonon
frequency 𝜔𝐿𝑂 were used for calculations. .................................................................................................. 70
Figure 5.1 Transport anomalies and reversible resistive switching in BaTiS3 (a) Representative
temperature dependent electrical resistance of BaTiS3 crystal along c-axis. Transport anomalies with
abrupt and hysteric jumps near 240 -260 K reveal the existence of a phase transition. The inset shows
an optical microscopic image of a typical BaTiS3 device. (b) Illustration of unit cell evolution of BaTiS3
across the CDW phase transition. (c) and (d) I-V characteristics of a two-terminal BaTiS3 device at
230 K by sweep voltage and current, respectively. Negative differential resistance (NDR) regions are
observed in I-mode. ..................................................................................................................................... 75
Figure 5.2 Joule heating mechanism behind CDW resistive switching in BaTiS3. (a) Four-probe I-V
characteristics of a BaTiS3 device at different temperatures. (b) Extracted threshold voltages at the
corresponding temperatures for both forward and reverse sweeps. (c) Calculated temperature-
dependent thermal power at threshold fields (𝑷𝒕𝒉). A linear relationship is found between 𝑷𝒕𝒉 and
temperature. (d) Pulsed I-V measurement of a two-terminal BaTiS3 device at 210 K. The pulse voltage
was ramped linearly from 0.8 V to 1.8 V, with the pulse width t = 8 ms and pulse period p = 10 ms.
(e) Reconstructed I-V characteristics of BaTiS3 from pulse measurements with pulse width varying
from 8 ms to 1 ms, while the pulse period was maintained at 10 ms. Dashed line shows the DC I-V
scan on the same device for comparison. ..................................................................................................... 77

xiii

Figure 5.3 CDW voltage oscillation in bulk BaTiS3. (a) I-V characteristics of a two-terminal BaTiS3
device at 220 K, with the inset showing the circuit for oscillation measurements. (b) Representative
oscillation waveform of BaTiS3 with a frequency of 16 Hz. ......................................................................... 79
Figure 5.4 Oscillation frequency optimization in BaTiS3. (a) to (c) Effect of operating temperature.
The frequency increases from 67 Hz to 910 Hz by reducing the measurement temperature from 200 K
to 130 K. (d) Effect of device channel size. The oscillation frequency increases more than three times
when reducing the channel size from 10 µm to 5 µm. ................................................................................. 80
Figure 5.5 (a) Illustration of representative temperature dependent resistance of BaTiS3 crystal from
120 K to 200 K, showing the structural transition between the CDW state and the high-µ state with
exceptionally large thermal hysteresis window. The inset illustrates the CDW domain formation in
BaTiS3 with applied DC voltages. (b) Transport measurement of BaTiS3 resetting process after the
system is set to different intermediate states DC voltage sweeps or pulse. ................................................. 83
Figure 5.6 Non-volatile resistive switching in BaTiS3 by DC sweeps. (a) and (b) Setting processes of
conductance states by consequential DC sweeps with gradually increased set voltages. (c) and (d)
current-voltage and resistance-voltage characteristics of conductance state readout processes performed
at 100 mV. .................................................................................................................................................. 84
Figure 5.7 (a) Conductance state modulation with a large DC set voltage. The transition region is
highlighted by dashed lines (orange), where the current level is mostly maintained. (b) More than 20
intermediate states achieved by continuous I-V sweeps with the same set voltage. ................................... 85
Figure 5.8 (a) Readout processes after applying pulse voltages up to 2 V with 1 ms pulse width. The
sample conductance is modulated continuously. (b) Readout processes after applying pulse voltages up
to 8 V with 10 µs pulse width. No further tuning of the conductance state was observed due to
significantly reduced Joule heating. ............................................................................................................ 86
Figure 5.9 Time-dependent resistance level of BaTiS3 crystal. Pulses (width of 1 ms) with different
amplitudes of voltages were applied to drive the system into various intermediate states. Each state is
maintained for at least an hour. .................................................................................................................. 87
Figure 6.1 Single crystal growth of BaTiS3 using KI flux and chemical composition analysis. (a)
Schematic illustration of KI flux growth of BaTiS3 crystals using a vertical geometry. Optical image of
a representative flux grown BaTiS3 crystal (~ 6 mm long and half a millimeter in both width and

xiv

thickness) is displayed in the top right. (b) Perspective view of BaTiS3 crystal structure along the c-
axis. (c) EDS mapping of barium (red), titanium (yellow) and sulfur (purple) elements on a thick
BaTiS3 crystal (top left). (d) EDS spectrum of KI flux-grown BaTiS3 crystal, showing Ba to Ti ratio
as 1 : 1.02. ................................................................................................................................................... 90
Figure 6.2 X-ray diffraction characterization. (a) - (c) Precession images from single-crystal X-ray
diffraction characterization of KI-grown BaTiS3 crystals along 0kl, h0l, and hk0 projections (from left
to right) at 300 K. (d) Out-of-plane X-ray diffraction scan of a thick BaTiS3 needle-like crystal (~
300 µm in width) ......................................................................................................................................... 93
Figure 6.3 (a) and (b) Atomic-resolution HAADF-STEM image of a KI-grown BaTiS3 crystal viewed
along the [001] axis and the corresponding FFT pattern. (c) High magnification HAADF-STEM image
of BaTiS3 acquired from the region highlighted with yellow box in (a). ..................................................... 94
Figure 6.4 Vibrational anisotropy. Polar plot of the Raman spectra intensity of the A1 versus the
polarization angle at the 532 nm excitation. The red dots are the experimental data, while the blue
line represents the fitted curve. ................................................................................................................... 95
Figure 6.5 Optical anisotropy. (a) Infrared reflection and (b) transmission spectra of a KI-grown BaTiS3
crystal with incident light polarized parallel and perpendicular to the c axis, respectively. ....................... 96

xv

Abstract

Transport Studies of Phase Transitions in a Quasi-1D Hexagonal
Chalcogenide
by
Huandong Chen

Doctor of Philosophy in Materials Science
University of Southern California

Thesis advisor: Prof. Jayakanth Ravichandran

Materials with strong electron-lattice coupling, such as complex oxides and low-
dimensional metals, often exhibit unique phenomena including phase transitions and
charge ordering, which distinguish them from most semiconducting compounds. The
coupling between electron and lattice degrees of freedom can be tuned by external fields
such as pressure, strain, and doping, which greatly enrich the electronic properties of the
material and extend the functionalities. Charge density wave (CDW) is a periodic
modulation of electron density with the underlying lattice distortion, which has been
extensively studied in metallic model systems such as quasi-1D metals, doped cuprates,
transition metal dichalcogenides, and more recently, in Kagome lattice materials. However,
CDW in semiconducting systems is rare. Recently, there has been a growing interest in
CDW systems with semiconducting transport behavior such as 1T-TaS2, 1T-TiSe2, and
EuTe4. The origin of the CDW transitions in these materials presumably go beyond the
q-dependent electron-phonon coupling mechanism. Those materials exhibit electron-hole

xvi

coupling, resistive switching, toroidal dipolar structures, and wide hysteretic transitions,
which have led to a vigorous debate over the mechanism of these CDW transitions. The
confluence of CDW order and semiconducting behavior is not only scientifically interesting
but also may lead to new applications of CDW.
BaTiS3 is a small bandgap semiconductor with an energy gap of approximately 0.3
eV, which has attracted significant research attention due to its giant optical anisotropy
and potential applications in infrared detection. Recent reports of abnormal glass-like
thermal transport properties and atomic tunneling in BaTiS3 have raised questions about
its electronic properties. However, no phase transitions have been theoretically expected
or experimentally reported before.
In this thesis, the electronic transport properties of BaTiS3 in the form of bulk
single crystals were studied and two phase transitions were observed at low temperatures.
The experimental results show that CDW charge ordering emerges in BaTiS3 below ~240
K from a high-temperature semiconducting phase (Transition II, 240-260 K), which
persists until ~150 K and is suppressed by a structural transition (Transition I, 150-190
K) upon further cooling, resulting in a more conductive state. Moreover, novel electronic
functionalities such as reversible resistive switching, voltage oscillations and memristive
switching have been experimentally demonstrated in BaTiS3. These studies establish
quasi-1D hexagonal chalcogenides such as BaTiS3 as a new model platform to explore rich
electronic phases, phase transitions and electronic functionalities associated with CDW in
dilute filling.

xvii

Preface
Upon joining the Ravichandran group in the summer of 2019, I made the decision to write
a new thesis solely based on a series of materials known as “quasi-1D chalcogenides”, with
a specific emphasis on their electrical properties. Although I did not initially realize the
risk involved in starting over, I soon discovered the immense potential for exploring
beautiful physics and functionalities in those materials, particularly the model system of
“BaTiS3” that I focused on in this thesis
Compared to well-established materials systems such as III-V and perovskite oxides,
where high-quality, large-area materials synthesis, basic material properties, and device
fabrication have mostly been figured out, research on those newly synthesized
chalcogenide crystals, especially in terms of their transport properties and potential device
applications, was still in its early stage.
This thesis is organized as follows: In Chapter 1, I elaborate a detailed theoretical
background and experimental signatures of CDW and provide an introduction to the
material system of quasi-1D hexagonal chalcogenides. In Chapter 2, I review the
experimental methods and techniques utilized in this study, such as materials synthesis,
characterization, and transport measurements. In Chapter 3, I describe the polymeric
planarization strategy developed for the fabricating bulk BaTiS3 devices. From Chapter
4 to Chapter 6, I present the major experimental studies conducted on BaTiS3, including
the observation of phase transitions, the demonstration of novel electrical functionalities,
and single crystal growth using molten flux. Finally, Chapter 7 provides concluding
remarks and outlooks for future studies.

1

Chapter 1 Introduction and background
1.1 Theoretical concepts of CDW
The idea of charge density wave (CDW) dates back to the discussions initiated by Peierls
in the 1930s[1]. He asserted that at low temperatures, a metallic one-dimensional atomic
chain would be inherently unstable, resulting in a spontaneous dimerization and gap
opening at the zone boundary. The argument is that the lattice distortion becomes
energetically favorable when the gain in electronic energy due to the new band gaps
outweighs the elastic energy cost of lattice reconstruction. In the 1950s, Frohlich
introduced the concept of density wave and a moving collective behavior known as CDW
sliding, which was proposed to explain superconductivity before the BCS theory was
developed[2].
Figure 1.1 Illustration of Peierls instability in a 1D atomic chain. A lattice distortion or dimerization
is energetically favorable as the electronic energy saved due to the new bandgaps overweighs the
elastic energy consumption from lattice reconstruction, hence, the total energy is minimized. Ref.[5]

2
Peierls’ model of CDW identifies several key features, including 1) Fermi surface
nesting in electronic structure, 2) a sharp peak in Lindhard function, 3) a Kohn anomaly
in phonon spectra, 4) a structural transition in the lattice, and 5) a metal-insulator
transition with anomalies in resistivity. However, in real materials, many physical
properties are strongly dependent on the specific system and may not strictly adhere to
Peierls’ prediction. In this section, I will introduce basic theoretical concepts necessary for
understanding the formation of CDW and clarify the role of Fermi-surface nesting and
electron-phonon coupling as the two most important driving forces. Detailed discussions
and derivations can be found in Reference[3] and[4].

1.1.1 One-dimensional electron gas and instability
We start by considering a 1D free electron gas model, where the dispersion relation is
given by 𝜖
!
= ℏ
"
𝑘
"
/2𝑚, and its Fermi surface consist of two points, ±𝑘
#
, as illustrated
in Figure 1.1[5]. In the reciprocal space of a 1D chain with total length L, the total number
of filled quantum states within a distance 2𝑘
#
(including spin) equals to the total number
of the electrons 𝑁
$
, with
𝑁
$
=
2𝑘
#
2𝜋/𝐿
×2 ( 1 )
Hence, the Fermi wavevector 𝑘
#
is
𝑘
#
=
𝑁
$
𝜋
2𝐿
( 2 )
The density of states for one spin direction is

𝑛(𝜖)=
𝜕𝑁
𝜕𝜖
=
𝜕(𝑘𝐿/𝜋)
𝜕𝜖
=
𝐿
𝜋ℏ
3
𝑚
%
2𝜖
4
&/"
=
𝐿
𝜋ℏ𝑣

( 3 )
where the velocity v is given by 𝑚
%
𝑣 = ℏ𝑘.

3
We first recall the Lindhard susceptibility 𝜒(𝒒) that describes how charge density
responds to an external perturbation in the lattice potential
𝜌
()*
(𝒒) = 𝜒(𝒒)𝜙(𝒒) ( 4 )
The total potential seen by the electrons, 𝜙(𝒒), consists of an external potential 𝜙
%+,
(𝒒)
and an induced potential 𝜙
()*
(𝒒) from the charge density fluctuation 𝜌
()*
(𝒒), by 𝜙(𝒒) =
𝜙
%+,
(𝒒)+𝜙
()*
(𝒒). The 𝜙
()*
(𝒒) and 𝜌
()*
(𝒒) are related by
𝜙
()*
(𝒒) = −g 𝜌
()*
(𝒒) ( 5 )
where g is a positive electron-phonon coupling term and is assumed to be constant. After
rearranging equation (4) and (5), we have
𝜌
()*
(𝒒) = >
𝜒(𝒒)
1+𝑔𝜒(𝒒)
A𝜙
%+,
(𝒒) ( 6 )
From this equation, we learn that the instability condition may be reached when 1+
𝑔𝜒(𝒒) = 0, for a system with large electronic susceptibility (large 𝜒(𝒒)) or strong electron-
phonon coupling (large g), considering 𝜒(𝒒)< 0.
The explicit form of the static Lindhard function for 1D system is given by
𝜒(𝑞) = 2E
𝑑𝑘
2𝜋

𝑓(𝜖
!
)−𝑓H𝜖
!-.
I
𝜖
!
−𝜖
!-.
( 7 )
where 𝑓(𝜖
!
) is the Fermi-Dirac distribution with 𝑓(𝜖
!
) = (1+𝑒𝑥𝑝[(𝜖
!
−𝜖
#
)/𝑘
/
𝑇])
0&
. 𝜖
#

is the Fermi energy or chemical potential, 𝑘
/
is the Boltzmann constant and the factor of
2 is from the spin polarization. We can rewrite equation (7) as

𝜒(𝑞)= 2E
𝑑𝑘
2𝜋
P
𝑓(𝜖
!
)
𝜖
!
−𝜖
!-.
−
𝑓H𝜖
!-.
I
𝜖
!
−𝜖
!-.
Q
= 2E
𝑑𝑘
2𝜋
P
𝑓(𝜖
!
)
𝜖
!
−𝜖
!-.
−
𝑓(𝜖
!
)
𝜖
!0.
−𝜖
!
Q
( 8 )

4
At 𝑇 = 0 𝐾, 𝑓(𝜖
!
)= 1 for 𝜖
!
< 𝜖
#
. Near 𝑞 = 2𝑘
#
, we have

𝜒(𝑞)= −2
2𝑚
ℏ
"
E
𝑑𝑘
2𝜋𝑞
S
1
2𝑘+𝑞
−
1
2𝑘−𝑞
T
!
!
0!
!
= −
2𝑚
ℏ
"
𝜋𝑞
lnW
2𝑘
#
+𝑞
2𝑘
#
−𝑞
W
≈ −
𝑚
ℏ
"
𝜋𝑘
#
lnW
2𝑘
#
+𝑞
2𝑘
#
−𝑞
W = −
1
ℏ𝜋𝑣
#
lnW
2𝑘
#
+𝑞
2𝑘
#
−𝑞
W
= − 𝑛(𝜖
#
) lnW
2𝑘
#
+𝑞
2𝑘
#
−𝑞
W
( 9 )
where 𝑛(𝜖
#
) is the density of states at the Fermi energy. Hence, at 𝑞 = ±2𝑘
#
, the 1D
response function diverges logarithmically, as illustrated in Figure 1.2a[6]. This divergence
of 𝜒(𝑞) at 𝑞 = 2𝑘
#
is due to the particular topology of the Fermi surface, sometimes it is
called perfect nesting. On the other hand, in higher dimensions, the number of such states
is significant reduced, leading to the removal of the singularity at 𝑞 = 2𝑘
#
.
While at finite temperatures, the response function is given by

𝜒(2𝑘
#
,𝑇)= − 𝑛(𝜖
#
)E
tanh𝑥
𝑥
𝑑𝑥
1
"
"!
#
2
$
= − 𝑛(𝜖
#
)P(tanh𝑥 ln𝑥)
$
1
"
"!
#
2
−E
ln𝑥
cosh
"
𝑥
3
$
𝑑𝑥Q
≈ − 𝑛(𝜖
#
)S1×ln`
𝜖
$
2𝑘
/
𝑇
a−0−ln3
𝜋
4𝑒
4
$
4T
= − 𝑛(𝜖
#
) ln`
2𝑒
4
$
𝜖
$
𝜋𝑘
/
𝑇
a = − 𝑛(𝜖
#
) ln
1.134𝜖
$
𝑘
/
𝑇

( 10 )
where 𝛾
5
≈ 0.5772 is Euler’s constant, and 𝜖
$
is an arbitrarily chosen cutoff energy and
is often taken to be equal to 𝜖
#
.
Recall the instability condition reaches when 1+g 𝜒(𝑞,𝑇) = 0. By plugging in the
expression of 𝜒(2𝑘
#
,𝑇) from Equation (10), we obtain

5
1−g 𝑛(𝜖
#
) ln
1.134𝜖
#
𝑘
/
𝑇
= 0 ( 11 )
and the mean field transition temperature 𝑇
6#
is given by

𝑘
/
𝑇
6#
= 1.134 𝜖
#
𝑒𝑥𝑝3
0&
7 )(1
!
)
4
( 12 )

1.1.2 Electron-phonon coupling and Kohn anomaly
As the name of CDW suggests, this ground state consists of a periodic charge density
modulation accompanied by a periodic lattice distortion. Hence, both the electron and
phonon spectra are strongly modified by the formation of CDW through electron-phonon
interactions. In the late 1950s, Kohn first stated that the phonon spectra would give direct
information about the shape of Fermi surface due to the abrupt change in screening effects
of conduction electrons[7]. The phonon spectrum undergoes strong renormalization due to
the electron-phonon interaction (g), as well as the divergent electronic response at 𝑞 =
2𝑘
#
in one dimension (𝜒(𝑞,𝑇)), which is commonly known as the Kohn anomaly, as
illustrated in Figure 1.2b. The renormalized phonon frequency is given by

𝜔
;%),.
"
= 𝜔
.
"
+
2g
"
𝜔
.
ℏ
𝜒(𝑞,𝑇)
( 13 )
where 𝜔
.
is the normal mode frequency and g is the 𝒒-independent electron-phonon
coupling constant.
For one-dimensional electron gas, the electronic response function 𝜒(𝑞,𝑇) reaches
its maximum value at 𝑞 = 2𝑘
#
, hence, the softening or reduction of the phonon frequencies
will be most pronounced at those wavevectors. Following the explicit expression of 𝜒(𝑞,𝑇)
derived in the last section, the phonon frequencies at 𝑞 = 2𝑘
#
is given by

6
𝜔
;%),"!
!
"
= 𝜔
"!
!
"
−
2g
"
𝑛(𝜖
#
) 𝜔
"!
!
ℏ
ln
1.134𝜖
#
𝑘
/
𝑇
( 14 )
The renormalized frequency of the phonons decreases as the temperature is lowered. A
transition temperature is defined when 𝜔
;%),"!
!
→ 0, indicating the happening of a frozen-
in lattice distortion
𝑘
/
𝑇
6#
= 1.134 𝜖
#
𝑒
0&/=
( 15 )
where 𝜆 is the dimensionless electron-phonon coupling constant
𝜆 =
2g
"
𝑛(𝜖
#
)
ℏ𝜔
"!
!
( 16 )
As previously discussed in the context of the free electron gas model, the electron-
phonon coupling constant g is assumed to be 𝒒-independent, and we have been using the
zero-frequency limit of the Lindhard function 𝜒(𝒒,0). Now we write a general form for
the renormalized phonon frequencies using 𝒒-dependent coupling constant g(𝒒) and
interacting electronic response function 𝜒(𝒒,𝜔)
𝜔
;%),.
"
= 𝜔
.
"
+2𝜔
.
|g(𝒒)|
"
Re[𝜒(𝒒,𝜔)] ( 17 )
Figure 1.2 (a) Normalized Lindhard response function for different dimensional free electron gas at
zero temperature. For 1D, the response function diverges at 2𝑘
%
. (b) Nesting-induced Kohn
anomalies. Ref. [6]

7
In the Fermi surface nesting (FSN) mechanism for CDW, the real part of the electronic
response function, Re[𝜒(𝒒,𝜔)], diverges at the nesting vector, and the Kohn anomaly is
often attributed to this feature. However, in many real CDW materials such as NbSe2,
perfect FSN or peaks at either Re[𝜒(𝒒,𝜔)] or Im[𝜒(𝒒,𝜔)] are not always observed
experimentally[4,8], contrary to what the simple Peierls’ picture suggests. In such cases,
a large peak in the 𝒒-dependent electron-phonon coupling constant g(𝒒) could effectively
reduce the energy of the acoustic phonon to zero[8], thereby driving the lattice distortion
or CDW phase transition.

1.1.3 Connection to superconductivity
In many materials, charge density waves and superconductivity are found to compete with
each other at low temperatures[9,10]. Suppression of CDW order in such materials has
led to the emergence or enhancement of superconductivity, and vice versa. This
phenomenon is not surprising, as both CDW and superconductivity rely on strong
electron-phonon interactions and require an adequate electronic density of states at the
Fermi level[3,5]. It is also interesting to note that the transition temperature for
superconductivity, as predicted by the BCS theory[11], has a similar form to that for
mean-field Peierls transition:
𝑘
/
𝑇
>
= 1.134 𝜖
?
𝑒𝑥𝑝3
0&
7 )(1
!
)
4 ( 18 )
where g is the electron phonon coupling constant, 𝑛(𝜖
#
) is the electronic density of states
at the Fermi level, as defined before, and 𝜖
?
is the Debye energy taken as the cutoff energy
for the integration. The absolute values of Debye energy are typically orders of magnitude
smaller than those of the Fermi energy, hence it is reasonable to expect a much higher
transition temperature for CDW formation than that for superconducting transition.

8
Several external parameters, such as pressure and doping, have been utilized in
many CDW systems to promote superconductivity by suppressing CDW transitions[10,12],
as illustrated in Figure 1.3. One popular approach involves applying hydrostatic pressure,
typically through the use of a diamond anvil cell apparatus, in which a high pressure (up
to a few hundred GPa) can be achieved by exerting moderate force over a small sample
area. For example, in 1T-TaS2, it has been reported that the commensurate CDW phase
and the Mott localization are fully suppressed at pressures above 0.8 GPa, and
superconductivity develops from an incommensurate CDW phase near 5 K throughout
the entire pressure range of 3 – 25 GPa[10]. Another strategy is to leverage the effects of
chemical pressure through small ion intercalation or substitution of elements with different
sizes into CDW materials. For instance, controlled intercalation of quasi-2D 1T-TiSe2
with Cu has been shown to continuously suppress the CDW transition in CuxTiSe2,
leading to the emergence of a new superconducting state near x = 0.04, which also
coincides with the onset of an incommensurate structure observed from diffraction. A
maximum transition temperature 𝑇
>
of 4.15 K was obtained at x = 0.08, accompanied by
a classic dome-like phase diagram of superconductivity[12].

Figure 1.3 (a) Phase diagram of 1T-TaS2. Superconductivity is introduced by pressure. (b) Phase
diagram of CuxTiSe2. Superconductivity is promoted by Cu intercalation. Ref.[10,12]

9
1.2 Experimental signatures
As briefly mentioned earlier, the ideal Peierls model predicts several key features of charge
density waves. Many of these features can be experimentally probed using techniques such
as transport, diffraction, and spectroscopy to confirm the presence of CDW, although not
all of these features need to be present in real materials. In this section, I will discuss
several experimental signatures directly or indirectly associated with the underlying
periodic modulation of either electron density or lattice. Details of the specific
characterization techniques used in this thesis will be presented in Chapter 2.
Transport measurements are commonly utilized to investigate the metal-insulator
transition that is associated with CDW and to accurately determine the transition
temperatures[13-15]. Similarly, measurements of thermophysical properties such as heat
capacity across the transition temperatures can also confirm the phase transition[16].
However, it is important to note that observing transport anomalies in temperature-
dependent resistivity does not necessarily indicate CDW formation. Indeed, not all CDW
materials exhibit metal to insulator transitions as a result of opening a gap at the Fermi
level. For instance, in classic qusai-1D CDW system NbSe3, there are two anomalies at
Figure 1.4 Transport signatures of several CDW systems. (a) Quas-1D organic compound TTF-
TCNQ shows a metal-to-insulator transition. (b) NbSe3 reveals two transport anomalies while the
system is kept metallic. (c) No anomaly is found in temperature-dependent resistivity in NbSe2.
Ref.[13,17]

10
149 K and 59 K, respectively, corresponding to transitions contributed from different
atomic chains, but no clear signatures of metal-insulator transition[17]. Only a part of the
Fermi surface of NbSe3 is gapped across the transition, and hence, the system remains
metallic. Furthermore, in two-dimensional CDW system NbSe2, there is even no transport
anomaly observed at the CDW transition temperature[13]. This is due to the fact that
the CDW-induced gaps are small and only exist in certain points on the Fermi surface,
which is not captured experimentally from transport measurements.
Diffraction measurements using X-rays, electrons, or neutrons can provide
convincing evidence for the CDW transition by detecting the appearance of superlattice
peaks, which arise from the CDW-associated periodic lattice distortion[18-20]. Analysis of
the diffraction pattern below the transition temperature allows for the determination of
the CDW wavevector 𝑞
>?@
, at which both a local maximum in the Lindhard response
function and Kohn anomaly are expected. The temperature dependence of the satellite
peak intensities further verifies the phase transition temperatures obtained from transport
measurements[18]. Compared with the main Bragg diffraction peaks, the superlattice
peaks from a diffraction pattern are often much weaker, with several orders lower in
intensities, and in some cases, difficult to observe. Hence, high-intensity sources such as
synchrotron-based sources are highly preferred. Differences in the response to external
perturbations in Bragg peak and superlattice peak intensities are utilized to study the
dynamics of CDW in measurements such as ultrafast electron diffraction (UED)[21].
Angle-resolved photoemission spectroscopy (ARPES) is a powerful technique to
directly probe the electronic structure of materials[22,23]. By measuring both the energy
and momentum of photoemitted electrons, it can map out the full electronic band
structure and Fermi contour of a material, providing direct evidence of the energy gap
opening at Fermi level due to CDW formation[24,25]. Moreover, the measured electronic

11
band structure can be used to calculate the non-interacting Lindhard response function
with the zero-frequency limit 𝜒
$
(𝒒), both the real part Re[ 𝜒
$
(𝒒)] and the imaginary part
Im[ 𝜒
$
(𝒒)][8]. A divergence or a peak in response function at the CDW wavevector (𝒒
>?@
)
provides strong evidence for the FSN mechanism.
Inelastic neutron or X-ray scattering measures the phonon dispersion, which can
be used to probe the Kohn anomaly. Moreover, the measured phonon linewidth contains
the information of 𝒒-dependent electron-phonon coupling (EPC) matrix element following
the relation suggested by Grimvall[26]
Γ
ABC
(𝒒) = −2|g(𝒒)|
"
Im[𝜒(𝒒,𝜔)] ( 18 )
where Γ
ABC
(𝒒) is the phonon linewidth. For an acoustic phonon, the zero-frequency limit
Im[ 𝜒
$
(𝒒)] provides a good approximation to Im[𝜒(𝒒,𝜔)], which can be obtained from the
measured band structure and then be used to estimate the values of |g(𝒒)|
"
. An interesting
example of this is seen in NbSe2, where the observed strong Kohn-like anomaly is caused
Figure 1.5 𝒒-dependent electron-phonon coupling in NbSe2. CDW formation in NbSe2 is not
explained by the Fermi surface nesting mechanism as no local maxima is observed in either real or
imaginary parts of the 𝜒(𝒒) at 𝒒
&'(
. Indeed, the Kohn anomaly-like strong phonon softening is
due to the peak of 𝒒-dependent EPC matrix element |g(𝒒)|
)
. Ref.[4,8]

12
by the 𝒒-dependent EPC matrix element |g(𝒒)|
"
with a peak at 𝒒
>?@
, rather than from
a peak at Re[ 𝜒
$
(𝒒)] due to conventional Fermi surface nesting[4,8], as illustrated in
Figure 1.5.
Scanning tunneling microscopy (STM) offers unique opportunities in visualizing
individual single-atom defects and CDW directly in real space[27,28]. Additionally, it
allows the measurement of the density of states near the Fermi level through tunneling
spectroscopy, which can be also utilized to observe the opening of the energy gap during
CDW formation[29]. One important consideration for STM measurements is the surface
quality of the sample, which must be freshly exposed by mechanical cleavage due to the
high surface sensitivity of the technique.
Several other techniques can also be employed to provide supporting evidence for
the formation of CDW. For instance, Raman scattering measurements[30,31] and optical
spectroscopy can be utilized to detect the presence of periodic lattice distortion and the
opening of the energy gap[32], respectively.

1.3 Emerging CDW in “semiconducting” systems
Most of the charge density waves to date have been observed in low-dimensional metallic
systems where CDW formation can be attributed to either Fermi surface nesting or 𝒒-
dependent electron-phonon coupling[1,5,33]. Recently, there is a growing interest in CDW
systems that exhibit semiconducting transport behavior, such as 1T-TaS2[10,34] and 1T-
TiSe2[35,36]. The origin of CDW formation in these materials presumably extends beyond
the 𝒒-dependent electron-phonon coupling mechanism. These materials exhibit unique
properties, including electron-hole coupling[36], resistive switching[34,37], toroidal dipolar
structures[38,39], and wide hysteretic transitions[40], which have led to a vigorous debate

13
over the mechanism of these CDW transitions and largely expanded the electronic
functionalities of CDWs.

1.3.1 Unconventional CDWs
Mean field theories, as discussed in Section 1.1., may not be sufficient to explain the
formation of CDW in systems with strong electron correlations, as the assumption of a
simple one-electron picture is no longer valid. In the case of unconventional charge
ordering or CDWs in cuprates such as YBa2Cu3O6+x (YBCO), phonon softening, and
Figure 1.6 (a) Temperature dependent resistivity of bulk 1T-TaS2, showing several metal-to-
insulator transitions and an overall semiconducting / insulating transport behavior. (b) Schematic
illustration of Ta atoms displacements that form the David-star clusters in CCDW phase of 1T-
TaS2. (c) Illustration of band structure in 1T-TiSe2. Bonded states of electron-hole pairs (excitons)
spontaneously condense when electrons and holes bind between the two bands near the Fermi level,
connected by a wavevector 𝒒
𝟎
. (d) Schematic of the collective excitations of an exciton condensate
coupled to lattice distortion. Both plasmon and phonon modes soften at 𝒒
𝟎
near the phase transition
temperature. Ref.[10,36,43]

14
linewidth broadening have been observed[41,42]. However, the electron-phonon coupling
in these materials is not strong enough to drive the phonon frequency to zero and initiate
the CDW transition, unlike in a typical Kohn anomaly scenario. Therefore, it is believed
that electron correlation plays a significant role in the formation of CDW in such
materials[4,6].
Moreover, I will discuss two examples of unconventional CDW systems that exhibit
semiconducting transport behavior. In the case of 1T-TaS2, every 13 Ta atoms form a
star-of-David structure, with 12 surrounding Ta atoms slightly shrinking towards the Ta
atom at the center, resulting in a √13×√13 superlattice reconstruction[10]. Surprisingly,
transport measurements indicate that the system is insulating in the commensurate CDW
phase at low temperatures, despite the electronic band being nominally half-filled, as
illustrated in Figure 1.6a. This half-filled insulating state of 1T-TaS2 can be explained
within the frame of Mott physics, where Coulomb repulsion is responsible for pushing the
system into the strong-correlation limit. However, the mechanism for the CDW formation
in 1T-TaS2 is still under debate due to the complexity of the system.
1T-TiSe2 is another prominent exception. One promising alternative explanation
for the formation of CDW in 1T-TiSe2 is the excitonic insulator mechanism[36,43], as
illustrated in Figure 1.6c. In a small band semiconductor or a semimetal with small band
overlap, the carriers in separate bands near the Fermi surface level, which is connected
by a finite wavevector 𝒒
𝟎
, can form bound states of electrons and holes, i.e., excitons, as
long as the indirect gap is smaller than the exciton binding energy. This results in the
removal of the charge carriers from the Fermi surface, leading to an insulating state. On
the other hand, it is experimentally challenging to distinguish an exciton condensate from
a CDW driven by electron-phonon interaction since both phases exhibit similar physical
observables, such as the presence of superlattice and a single-particle energy gap opening.

15
The characteristic feature for an electronic condensate is the plasmon-like mode softening
near the transition temperature, analogous to the Kohn anomaly for Peierls transition, as
illustrated in Figure 1.6d. The softening of this mode can be experimentally measured by
momentum-resolved electron energy loss spectroscopy (EELS)[43], which is more sensitive
to valence band excitons than inelastic X-ray or neutron scattering, which mainly couple
to lattice modes.
Figure 1.7 (a) Schematic showing biologically inspired neuromorphic computing. (b) Physical
mechanisms of electronic devices that switch between high-conductivity and low-conductivity
states, mimicking synaptic behavior. Different Electrical resistance R versus applied voltage V of a
non-volatile memristor (left) showing multiple resistance states, and a volatile memristive switch
(right) with negative differential resistance (NDR). (c) Memristive switching achieved in a 1T-TaS2

nano-thick crystal. (d) Voltage oscillations of a 1T-TaS2 oscillator device performed at room
temperature. Ref.[37,49,53]

16

1.3.2 Opportunities in developing electronic devices
The research of CDW materials has been primarily focused on the fundamental physical
properties of these systems over the past few decades[44-46]. For CDW systems that
exhibit transport anomalies or metal-to-insulator transitions resulting from strong
electron-phonon coupling or electron-electron interactions, there are additional
opportunities for electronic device applications[47-49], as illustrated in Figure 1.7. One
such example is the two-dimensional 1T-TaS2, which undergoes several CDW phase
transitions along with the metal-to-insulator transition and hysteresis[13]. The phase
switching in 1T-TaS2 can be controlled by various external parameters, such as
temperature[10,13], electrical field[50,51], and light irradiation[34,52]. Moreover, by
leveraging the stable bi-state switching and the thermal hysteresis of the transitions,
researchers have realized self-sustained oscillators[53-55] and CDW-based
memristors[37,56] using this material. Recently, EuTe4, a layered semiconductor, has
demonstrated an exceptionally large hysteresis window, making it an attractive candidate
for memory devices[40].

1.4 Quasi-1D hexagonal chalcogenides
Quasi-1D hexagonal chalcogenides are a class of d
0
materials with a general formula of
ABX3, where A is an alkaline earth metal such as Ba or Sr, B is an early transition metal
such as Ti, and X is either S or Se[57,58]. Those materials belong to a subgroup of
transition metal perovskite chalcogenides (TMPC), which also includes distorted
perovskite phases and needle-like phases. BaZrS3 with distorted perovskite phase is one
of the most studied TMPCs due to its suitable bandgap for photovoltaic applications[59],

17
as illustrated in Figure 1.8. When the B site is occupied by smaller transition metals such
as Ti, these compounds tend to stabilize in the hexagonal phase, which adopts the BaNiO3
structure and a typical space group of P63/mmc. In this phase, TiX6 octahedra are
connected by sharing faces, forming parallel 1D atomic chains that are arranged in a
hexagonal symmetry while separated by A-site chains[57,60], as illustrated in Figure 1.9.
Single crystals of several quasi-1D hexagonal chalcogenides including BaTiS3, Sr1+xTiS3,
Figure 1.9 Schematic of BaTiS3 crystal structure, showing hexagonal symmetry. 1D chains of TiS6
octahedra are highlighted.
Figure 1.8 Calculated band gap of a list of TMPCs with different phases. Quasi-1D hexagonal phase
of BaTiS3 is highlighted in red circles. Ref.[59]

18
and BaTiSe3 have been synthesized, and characterized both structurally and optically in
our lab over the past few years[57,58,61].
This thesis focuses on the BaTiS3 system and presents comprehensive electrical
transport studies associated with the two newly discovered phase transitions. Figure 1.10a
plots the calculated electronic band structure of BaTiS3 at room temperature, which
indicates a small direct band gap with Eg of approximately 0.3 eV[57]. To experimentally
estimate the optical bandgap, we employed polarization-resolved Fourier-transform
infrared (FTIR) spectroscopy to obtain the reflectance and transmittance spectra parallel
and perpendicular to the c-axis of BaTiS3. Further, by combining the ellipsometry
measurement up to 1.5 µm, optical constants of refractive index (n) and extinction
coefficient (k) were fitted and extracted within the range up to 16.7 µm, as illustrated in
Figure 1.10b. The dispersion relation of extinction coefficient clearly shows two absorption
edges at approximately 0.3 and 0.8 eV for polarization parallel and perpendicular to the
Figure 1.10 (a) Calculated electronic band structure of BaTiS3 at room temperature with energy
band gap Eg highlighted. (b) Experimentally measured refractive index (n) and extinction coefficient
(k) of BaTiS3 for polarization parallel and perpendicular to the c axis, exhibiting a high optical
anisotropy. An optical bandgap is extracted to be ~ 0.3 eV along the c axis from absorption edges
indicated in the plot. Ref.[57]

19
c-axis, respectively. In addition, BaTiS3 exhibits giant optical birefringence, with a value
of Δ𝑛 up to 0.76, in the mid to long infrared region. This is the highest birefringence value
reported among many optically anisotropic materials[57].
Regarding the phase transitions in BaTiS3, although CDW has been observed in
the isostructural d
1
system BaVS3[62,63], no lattice instability has been theoretically
predicted or experimentally observed before. This is due to the fact that the material is
nominally empty in the conduction band. Several groups have previously studied physical
properties of BaTiS3, including its heat capacity and electrical resistivity, in the form of
both powder and single crystals at cryogenic temperatures[63,64]. However, the phase
transitions were not observed in these studies, likely due to limitations in sample quality
and the experimental probes. Our good control over single crystal growth, improvement
in device fabrication and contact optimization, and stress-free characterizations have led
us to observe those phase transitions reliably. Detailed explanations of our findings will
be presented in the following chapters.

20

Chapter 2 Crystal growth and
characterization
2.1 Single crystal growth
High quality single crystals are essential in the research of novel materials due to several
advantages over polycrystalline forms[65,66]. First, a single crystal has significantly lower
impurities or defects than polycrystals. This is critical for many quantum materials that
are sensitive to defects. Secondly, high-purity single crystalline samples are critical for
many measurement techniques. For example, single-crystal X-ray diffraction, which
provides information about fine crystal structures and subtle atomic displacements,
requires single-crystalline samples with high purity and ideally a single domain to obtain
good structural refinement. Additionally, single crystals feature sizable and atomically
ordered surfaces, which are important for surface-sensitive measurements such as
ARPES[67,68] and STM[69,70]. These powerful techniques provide direct information on
electronic structure, gap size, and atomically resolved surface arrangement, which can
only be applied to a perfectly and freshly cleaved surface that exists only in a single-
crystalline sample. Last, but not the least, a single crystal has a well-defined orientation,
which is important for measurements performed on highly anisotropic materials such as
BaTiS3[57]. The orientation can be confirmed either by optical or diffraction techniques,
or sometimes it can directly be distinguished from crystal morphologies.

21
Single crystals of BaTiS3 used in this thesis, from Chapter 3 to Chapter 5, were
synthesized by an I2-assisted chemical vapor transport growth method, unless otherwise
specified. Attempts to grow large BaTiS3 crystals using molten flux are discussed in
Chapter 6 in details.

2.1.1 Chemical vapor transport
Chemical vapor transport is a commonly used method for growing high-quality single
crystals of various materials[71,72]. In this technique, solid precursors are volatilized in
the presence of a gaseous transport agent and redeposited elsewhere, as illustrated in
Figure 2.1. Commonly used transport agents include halogens and halogen compounds.
The setup typically consists of a two-zone furnace, where the source and sink temperatures
can be controlled independently to form a temperature gradient. Alternatively, one can
also use a single-zone furnace and leverage the natural temperature gradient generated
from the hot center zone and environment without using a thermo block. The reactant
and transport agent are typically sealed in a quartz ampule for an enclosed reaction
environment and to avoid oxidation. Ampule cracking during growth can lead to oxidized
materials and transport agent leakage, and it should be avoided. To achieve a successful
CVT growth, various growth parameters such as growth temperature, transport direction,
rate of mass transport and choice of transport agent must be optimized. If the reaction
Figure 2.1 Schematic of the crystal growth process with chemical vapor transport. Ref.[72]

22
between transport agent and source material is endothermic, the reaction leading to
redeposition shall be exothermic. In this scenario, temperature for volatilization needs to
be higher than that for redeposition. Conversely, if the volatilization reaction is exothermic,
the temperature should be chosen the other way around.
Following the growth recipe reported elsewhere[57], 0.5 g stoichiometric powders
of barium sulfide (Sigma-Aldrich, 99.9%), titanium (Alfa Aesar, 99.9%), and sulfur pieces
(Alfa Aesar, 99.999%) were weighted and loaded into a necked quartz tube of 19 mm in
diameter and 2 mm in thickness, along with about 15 mg iodine in a N2-filled glove box.
After sealing using a blowtorch, the tube (about 10 cm in length) was loaded into a 1-
inch tube furnace, heated to 1040˚C over a period of 20 hours and held at 1040˚C for
100 hours. The samples were then cooled to room temperature naturally by turning off
the furnace.
Various morphologies of BaTiS3 crystals were obtained from the CVT
growth[57,60], as shown in Figure 2.2. The first morphology is the “thin needle” type,
which typically has a width and thickness of 10 - 30 µm and can grow up to 1 cm in
length. This morphology is the most frequently obtained from the growth, representing
the quasi-1D nature of BaTiS3. However, it is not uncommon to observe the formation of
Figure 2.2 Different morphologies of CVT-grown BaTiS3 crystals. Optical images of (a) thin BTS
needle, (b) thick BTS needle and (c) BTS platelet. For ‘needle’-like samples, c-axis follows the
direction of long edges and is easy to determine. Edges of terraces on BTS plates are useful in
assigning the crystal orientations, which can be further confirmed by polarization-dependent Raman
spectroscopy.

23
holes at the center of needle-like crystals, which can be confirmed through tilted or cross-
sectional views under a microscope. The formation of these holes may be related to the
specific growth mechanism of quasi-1D BaTiS3 during CVT growth and requires further
investigation. For transport studies, we carefully examined the “thin needle” crystals under
an optical microscope and selected the ones without holes, which usually has a diameter
of 10 – 15 µm. The second type of morphology is the “thick needle”, which typically has a
width of 50 – 100 µm, a thickness of 10 – 20 µm, and can grow up 1 - 2 mm in length
without any holes at the center. The terms “thin” and “thick” here refer to the width of
needles along the a-axis, as per convention. These types of crystals were used in most of
the transport studies presented in this thesis. The last morphology is the BaTiS3 “platelet”,
which typically has a thickness of 5 – 15 µm, and can grow up to a few hundred microns
in both length and width. These crystals are particularly useful for studying optical
anisotropy and in-plane electrical conductivity anisotropy.

2.1.2 Molten flux growth
Flux growth is a high temperature solution growth method that involves the precipitation
of solids form a supersaturated solution[73-75]. The flux can be a metal, oxide, or salt
with good solubility for other compounds and a relatively low melting temperature. At
high temperatures, all constituent elements are dissolved in the flux to form a uniform
solution. As the temperature gradually decreases, the solubility of the target compound
also decreases, as illustrated in Figure 2.3[76]. Below a certain critical temperature, the
desired compound starts to nucleate and precipitate from the supersaturated solution, and
the crystals keep growing as the temperature is lowered further. The crystal size primarily
depends on the number of nucleation sites and the cooling rate. In the metastable
nucleation region between the equilibrium solubility and the limiting super-solubility

24
curves, the driving force for nucleation is low, resulting in slow nucleation and growth.
This condition is critical in obtaining large and strain-free crystals. Both too large an
initial concentration or too fast a cooling rate will lead to small and imperfect crystals.
The selection of an appropriate flux is also vital in crystal growth. Ideally, the flux
should possess a low melting temperature and a high boiling temperature, be easily
separable from the final products, and not form stable compounds with the reactants. One
approach is to use a “self-flux”, where an excess of one or more constituent elements of
the desired compound is used as the solvent. To some extent, the self-flux strategy is
preferred as it avoids introducing extraneous elements into the melt, which could lead to
undesired impurities in the resulting crystals. However, sometimes the self-flux may have
a melting temperature that exceeds the working temperatures of ampules or furnaces,
typically 1100˚C, or too high of a vapor pressure that causes safety concerns. Therefore,
oftentimes, non-self-fluxes are also used. Depending on the specific flux used, the crystals
can be separated by either centrifuging the melt at high temperatures (for example, Te
Figure 2.3 Schematic of the design principle of molten flux growth. Ref.[76]

25
or Sn), or by washing in DI water or a chemical etchant if salt fluxes are used. The flux
growth of BaTiS3 crystals utilizes molten potassium iodide (KI, 𝑇
E
= 681 ℃) as salt flux.
The detailed growth processes and material characterizations of flux-grown BaTiS3
crystals will be discussed in Chapter 6.

2.2 Chemical and structural characterization
2.2.1 Energy- and wavelength- dispersive spectroscopy
Energy-dispersive X-ray spectroscopy (EDS) and wavelength-dispersive X-ray
spectroscopy (WDS) are commonly utilized techniques for identifying elements in a sample.
EDS measures X-rays of all wavelengths using a semiconductor detector and is often used
for rapid identification of elements. On the other hand, WDS employs analytical crystals
to isolate wavelengths of characteristic X-rays, which are then measured by gas-flow
proportional counters, making it more suitable for quantitative analysis. In terms of
energy / wavelength resolution, or peak-to-background ratio, WDS is always better, as
Figure 2.4 Schematic showing resolving capabilities between WDS and EDS. In this case, WDS is
able to discriminate between Te (L𝛼) and Sb (L𝛽
+
) peaks and has better peak-to-background ratios.
Source: e-probe.epss.ucla.edu

26
illustrated in Figure 2.4. However, it is much slower and highly sensitive to changes in
specimen height (e.g., sample surface is not flat), which can significantly impact signal
collection. Recently, with improved detector technology, proper calibration, and data
analysis algorithm, EDS can achieve reasonably accurate results as well.
We employed both EDS and WDS to characterize our BaTiS3 crystals. After the
growth process, EDS was used for a rapid assessment of the chemical composition and to
confirm the Ba/Ti/S ratio. For quantifying the doping level and atomic ratio in BaTiS3,
particularly for newly synthesized BaTiS3 using KI flux, we utilized WDS. CVT-grown
crystals were also characterized by WDS, which served as a reference for EDS
measurements.
EDS measurements were performed using an energy dispersive detector (UltimMax,
Oxford) with highest detection resolution of about 80 eV, mounted on a scanning electron
microscope (Helios G4 PFIB/SEM). Numerical fitting with the known spectra of all
elements was performed by the analysis software to determine the elements and the ratios.
WDS measurements were performed on a JEOL JXA-8200 Superprobe (at UCLA). The
probe has several analytical crystals integrated to measure the intensity of the emission
at a particular wavelength, with a typical resolution of about 10 – 20 eV. Each element
of interest needs to be calibrated with a standard before the measurement on a real sample.
Small crystals were placed on a silicon wafer with carbon tape for mounting. It is
extremely important to make sure the top surfaces are horizontal under an optical
microscope, in order to maximize the signal collection. The measurements obtained the
relative intensity compared to the standard and calculated the percentage of each element
in the specimen.

27
2.2.2 Single crystal X-ray diffraction
Single crystal X-ray diffraction (SC-XRD) is a widely used technique in crystallography
for degerming the crystal structure, i.e., the arrangement of atoms within the unit cell.
The crystal structure of a material can be described by three key components: 1) the space
group, from which the crystal system, the crystal class, and the appropriate symmetry
elements can be deduced, 2) the unit cell dimensions, and 3) a list of atomic coordinates.
In SC-XRD measurements, X-rays interact with the electron clouds of atoms in a
crystal, and produces constructive interference when conditions satisfy the Bragg’s law
with 𝑛 𝜆 = 2𝑑
F!G
sin𝜃, which relates the wavelength 𝜆 to the diffraction angle 𝜃 and the
lattice spacing 𝑑
F!G
in a crystalline sample. Each set of ℎ𝑘𝑙 planes within the crystal
produces a corresponding diffraction spot on the detector. The intensity of each spot, 𝐼
F!G
,
is proportional to the square of the amplitude of the structure factor.
𝐼
F!G
∝|𝑭
F!G
|
"
( 2.1 )
The structure factor 𝑭
F!G
has the expression of

𝑭
F!G
= |𝑭
F!G
|𝑒
(H
, -.
=| 𝑓
I
𝑒
"J(KF+
/
-!L
/
-GM
/
N
I

( 2.2 )
where 𝑓
I
is the atomic form factor, or atomic scattering factor of the 𝑗
th
atom in the unit
cell, and directly associates with the electron charge density distribution of the atoms.
The electron density at a given point xyz within the unit cell 𝜌
+LM
is related with
the structure factor 𝑭
F!G
by

𝜌
+LM
=
1
𝑉
| 𝑭
F!G
F!G
𝑒
0"J((F+-!L-GM)

( 2.3 )
The position of highest density is assumed to be the center of the atom and therefore the
location of the nucleus. Hence, if a structure factor 𝑭
F!G
is known, it is easy to calculate

28
the electron density map, and the structure can be determined. However, 𝑭
F!G
contains
information of both an amplitude and a phase, as shown in Equation 2.2, and only the
amplitudes can be obtained from the experimental diffraction pattern. Without the phase
information, the structure cannot be directly determined. This so-called “phase problem”
can be solved by simply guessing a starting structure, then matching the calculated
intensities with the measured intensities.
Figure 2.5 shows a schematic of experimental procedures for performing single
crystal X-ray diffractions[77]. We first map out the reflection peaks in the entire 3D
reciprocal space, and then reduce the raw integrated intensities, 𝐼
F!G
, to the structure
factor amplitudes |𝐹
O
|. An electron density map is produced by coupling the starting
phases (as input) and the measured amplitudes, which will reveal the number of electrons
and positions of many of the atoms if the phases are nearly correct. These atoms can be
used to calculate the structure factor |𝐹
P
| and for improved phases; This process is cycled
until all the atoms are located; hence, a crystal structure is refined. One useful indicator
of the agreement between the calculated and observed structure factor amplitudes, |𝐹
P
|
and |𝐹
O
|, is known as the residual index with
Figure 2.5 Schematic of experimental procedures for single crystal X-ray diffraction. Ref.[77]

29
𝑅 =
∑ |𝐹
O
|−|𝐹
P
|
F!G
∑ |𝐹
O
|
F!G
( 2.4 )
Favorable matches yield low values of R, generally from 0.02 to 0.07.

2.2.3 Transmission electron microscopy
Transmission electron microscopy (TEM) is an advanced microscopy technique where an
accelerated electron beam (100 – 300 keV) is transmitted through a “thin” specimen to
form an image[78]. For a specimen to be transparent to electrons, it must be thin enough
to transmit sufficient electrons such that enough intensity falls on the screen. Typically,
specimens below 100 nm should be used whenever possible, and in specific cases such as
when doing high-resolution TEM or electron spectroscopy, sample thicknesses <50 nm
are essential. For materials that are not easily exfoliable down to sub-100 nm region such
as BaTiS3, TEM samples were prepared by focused ion beam (FIB) lift-out, followed by
a final thinning step with Ar ion milling before imaging.
An electron source at the top of the microscope emits electrons that travel in the
column of the microscope. In conventional TEM, electromagnetic lenses are used to focus
the electrons into a very thin beam, which is then directed through the specimen of interest
and collected by a detector for imaging; while in scanning transmission electron
microscopy (STEM), the electron beam is focused to a fine spot (with the typical spot
size 0.05 – 0.2 nm) which is then scanned over the sample in raster mode. Along with
other analytical techniques such as Z-contrast annular dark-field imaging (HADDF), and
spectroscopic mapping by electron energy loss spectroscopy (EELS) and energy-dispersive
x-ray spectroscopy (EDS), TEM / STEM can provide in-depth structural and chemical
information of the specimen under investigation.

30
2.3 Optical characterization
2.3.1 Fourier-transform infrared spectroscopy
Infrared spectroscopy techniques measure the interaction of infrared light with material
by absorption, emission or reflection, and often provide information of characteristic
molecular vibrational modes that are IR active. Regular dispersive spectrometer uses a
grating to generate monochromatic light and measure for each wavelength at a time,
similar to UV-Vis spectroscopy. In contrast, Fourier-transform infrared spectroscopy
(FTIR) uses a broadband infrared beam, which is guided through a Michelson
interferometer and then through the sample. A moving mirror inside the apparatus alters
the distribution of infrared light that passes through the sample, due to wave interference.
The raw signal recorded represents the light output intensity as a function the moving
Figure 2.6 Schematics of working principles of TEM (left) and STEM (right). Figure credit:
Matthew Mecklenburg. (from lecture note of MASC 535L class at USC)

31
mirror position, which is then converted to a desired spectrum mathematically using
Fourier transform. FTIR has several advantages over regular dispersive measurements,
including higher speed and signal-to-noise ratio, as the information at all frequencies is
collected simultaneously.
In our applications of FTIR on BaTiS3 crystals, we utilize its wavelength range
from near-infrared to mid-infrared to probe the small optical bandgap of the material.
Polarization-dependent transmission or reflection spectra of BaTiS3 further provides
insights on its optical anisotropy nature.

2.3.2 Raman spectroscopy
Raman spectroscopy is based on an inelastic scattering process of photons, known as
Raman scattering. When an incoming laser interacts with molecular vibrations, phonons
or other excitations in the system, the energy of photons is shifted, providing information
about the vibration modes. Raman spectroscopy detects vibrations involving a change in
electric dipole – electric dipole polarizability in the system, and the intensity of Raman
scattering is proportional to this polarizability change.
In highly anisotropic single crystals such as quasi-1D BaTiS3, the polarizability of
a vibrational mode is not equal along and across the chain axis. Thus, the intensity of the
Raman scattering will be different when the laser’s polarization is varied. This effect has
been utilized to cross-check the crystal orientations of BaTiS3 samples, especially in the
morphologies of platelets or mechanically cleaved flakes.

32
2.4 Electrical transport measurements
Electrical measurements are widely used for characterizing the physical properties of a
material associated with electron transport, such as resistivity, carrier concentration, and
mobility[79]. In this section, I will introduce several commonly used transport
measurement methods and discuss some aspects that are specifically related to
characterizing the bulk BaTiS3 crystal.

2.4.1 Bulk resistivity and its temperature dependence
Electrical resistivity (𝜌) is a fundamental property of a material that measures its ability
to resist the electric current, which inversely proportional to the electrical conductivity
(𝜎). The measurement of resistivity for bulk materials is typically carried out by linear
four-probe method to eliminate the parasitic effects from contact and wiring resistances.
The four-probe geometry consists of colinearly arranged four electrodes with equal spacing
of s, which are placed on top of the sample with thickness t, as illustrated in Figure 2.7.
The bulk resistivity is obtained by
𝜌 =
𝑉
𝐼
𝜋𝑡
ln{[sinh(𝑡/𝑠)]/[sinh(𝑡/𝑠)]}
( 2.5 )
Figure 2.7 Schematic illustration of resistivity measurement of a bulk sample using equally spaced
colinear four probes. Ref.[79]

33
For thin sample limit with 𝑡/𝑠 ≤ 1/2, the equation 2.5 reduces to
𝜌 =
𝑉
𝐼
𝜋𝑡
ln(2)
≈ 4.532∙𝑡∙
𝑉
𝐼
( 2.6 )
One of the most basic and informative transport measurements is the temperature-
dependence of electrical resistivity. This measurement can quickly determine whether the
system is metallic or semiconducting and can provide information about the thermal
activation behavior whenever applicable. Furthermore, it is the gold-standard for
identifying and demonstrating emergent quantum properties such as metal-to-insulator
transitions and superconductivity from anomalies of the transport behavior.
We performed temperature dependent resistivity measurements of BaTiS3 in a
JANIS 10 K closed-cycle cryostat, as shown in Figure 2.8a. This cryostat can carry out
transport measurements over a wide temperature range from 10 K to 800 K while keeping
the sample under vacuum to avoid water condensation or device degradation. Prior to
loading the device into the cryostat for transport measurements, it needs to be electrically
bonded to a chip carrier using Au wires and two-part Ag epoxy. Large metal bonding
pads with sizes larger than 500 µm × 500 µm were fabricated to facilitate hand bonding.
Conventional ultrasonic wire bonding technique was not applicable for most of the cases
presented in this thesis due to the low bonding yield onto soft polymeric substrates.
Standard low-frequency (𝑓 = 17 Hz) AC lock-in techniques (Stanford Research
SR830) were used to measure sample resistance in four-probe geometry. An excitation
current of about 100 nA was used to avoid non-linear effects at higher fields, which may
arise from Joule heating and CDW sliding. We typically measure resistivity of BaTiS3
from 300 – 100 K for both cooling and warming cycles. The phase of lock-in signals was
maintained below 1 - 2˚ throughout the measurement range. At even lower temperatures,

34
the out-of-phase of lock-in signals increased quickly due to the freezing of contacts or
carriers, and the AC lock-in measurements became no longer reliable.

2.4.2 Hall measurements
From Hall measurements, one can accurately determine the carrier type, carrier
concentration and the mobility. Under moderate magnetic fields, the Hall coefficient RH
is given as
𝑅
Q
=
𝑝−𝑛𝑏
"
𝑒(𝑝+𝑛𝑏)
"
( 2.7 )
where 𝑏 = 𝜇
)
/𝜇
R
, and n is the electron concentration, p is the hole concentration, and e
is the elementary charge. For an n-type material with 𝑛 ≫ 𝑝, it reduces to
𝑅
Q
= −
1
𝑒𝑛
( 2.8 )
Experimentally, the Hall coefficient is determined as
Figure 2.8 Optical images of (a) the closed-cycle cryostat used for temperature dependent resistivity
measurements, and (b) a bulk BaTiS3 device bonded onto a chip carrier using Au wires and Ag
epoxy, which is ready to be loaded into the cryostat for transport measurements.

35
𝑅
Q
=
𝑡𝑉
S
𝐵𝐼
( 2.9 )
where 𝑡 is the sample thickness, 𝑉
S
is the Hall voltage, 𝐵 is the perpendicular component
of an applied magnetic field, and 𝐼 is the sourced current. A six-contact or eight-contact
Hall bar geometry is commonly used for Hall measurements, as the sample dimensions
labeled in Figure 2.9. The electrical resistivity 𝜌 is also obtained concurrently by
𝜌 =
𝑉
++
𝐼
×
𝑤𝑡
𝑏
( 2.10 )
where 𝑉
++
is the measured longitudinal voltage drop with sourced current 𝐼. From the
equation 2.8 to 2.10, both carrier concentration and mobility can be obtained by 𝑛 =
−1/(𝑒𝑅
Q
) and 𝜇 = 𝑅
Q
/𝜌. For actual device geometry with finite size of voltage contacts,
the following aspect ratios are preferred to minimize the geometrical errors in Hall bar
samples: 𝐿/𝑤 ≥ 4, 𝑤/𝑐 ≥ 3, and 𝑝 ≈ 𝑐.
We carried out Hall measurements of BaTiS3 crystals in a PPMS (Quantum Design)
equipped with a 14 T magnet. An AC current was generated by a lock-in amplifier and
passed through the device, with 𝑉
++
, 𝑉
+L
, and the sourced AC current 𝐼 being recorded
simultaneously. Carrier concentration 𝑛 and mobility 𝜇 were extracted assuming a single
carrier model. The detailed results of Hall measurements in BaTiS3 will be discussed in
Chapter 4.
Figure 2.9 Schematic illustration of a six-contact and eight-contact Hall bar geometry used for Hall
measurements. Image credit: Lake Shore 7500/9500 series Hall system user’s manual.

36

2.4.3 Resistivity anisotropy
Electrical resistivity anisotropy, which is defined as the resistivity ratio along different
crystal orientations (𝜌
T
/𝜌
P
), is an important transport parameter of a material that relates
to its structural and electronic anisotropy. One way to obtain the resistivity anisotropy is
by directly measuring resistivity along both a- and c-axis on the same crystal using
standard four-probe method, provided such a pattern can be properly fabricated. However,
direct measurements require samples with large lateral sizes (several millimeters) along
both directions. For small-sized samples, the Montgomery analysis is particularly useful
in obtaining their anisotropic resistivity tensors. Both methods have been applied to
measure the in-plane resistivity anisotropy of small-sized BaTiS3 crystals. The polymeric
planarization strategy has been adopted to lithographically define and fabricate all
electrodes for the measurements, which will be discussed in the next Chapter.
Here, we briefly introduce the in-plane resistivity anisotropy analysis using the
Montgomery method[80]. As shown in the inset of Figure 2.10, a rectangular-shaped
sample with length 𝑙 and width 𝑤 has four point-contacts placed at each corner, inspired
from the van der Pauw method. The basic idea of this analysis is that the resistivity
tensor of an anisotropic material can be conformally mapped to an isotropic “equivalent”
sample with resistivity 𝜌
(UO
. The elements of the resistivity tensor are related to 𝜌
(UO
by a
conformal mapping function 𝐵
V,!
as follows:

𝜌
LL
=
𝑙
𝑤
∙𝐵
V,!
∙𝜌
(UO

𝜌
++
=
𝑤
𝑙
∙𝐵
V,!
0&
∙𝜌
(UO

𝜌
+L
= 𝜌
L+
= 0
( 2.11 )

37
Note that 𝐵
V,!
is a function of 𝑅
TT
/𝑅
PP
and is mathematically correlated, as plotted in
Figure 2.10. Hence, by experimentally measuring 𝑅
TT
and 𝑅
PP
, one can calculate the
resistivity anisotropy through
𝜌
T
/𝜌
P
= 𝜌
LL
/𝜌
++
= (𝑙/𝑤)
"
∙𝐵
V,!
"
( 2.12 )
For actual measurements, the van der Pauw electrode patterns are typically designed with
𝑙 = 𝑤 such that the equation 2.12 can be reduced to 𝜌
T
/𝜌
P
= 𝐵
V,!
"
.

2.4.4 DC sweeps and pulsed I-V measurements
The interaction between the CDW and DC electric field is also an area of interest. DC I-
V sweeps have commonly been used to characterize the “CDW sliding effect” in many
quasi-1D CDW systems, such as NbSe3 and TaS3, where the electrical conductivity
increases dramatically above a certain threshold field due to the depinning of CDW from
defects. At the same time, during I-V sweeps, particularly at high fields, the local
temperature can rise substantially due to Joule heating effects, which has been utilized to
electrically trigger CDW phase transitions in systems such as 1T-TaS2. For BaTiS3, we
Figure 2.10 The conformal mapping function that uniquely maps the ratio Raa/Rcc to 𝐵
0,2
, which
is later used to calculate the anisotropy 𝜌
3
/𝜌
4
. Ref.[60]

38
used DC I-V sweeps to reveal non-linear transport behavior in the system and to
characterize both volatile and non-volatile resistive switching for electronic device
demonstration.
In pulsed I-V measurements, voltage or current pulses with width ranging from
milliseconds to hundreds of nanoseconds are generated and applied on the test device.
The local Joule heating effects can be largely reduced by using short pulses, which is
crucial for distinguishing the contributions from Joule heating or field effects to various
CDW resistive switching behaviors. Moreover, by injecting ultrashort electrical pulses,
one may be even able to access metastable or hidden states that are not attainable under
equilibrium conditions.

39

Chapter 3 A polymeric planarization
strategy for multiterminal transport
studies on small, bulk crystals
In the previous chapter, I have shown that the sizes of as-grown BaTiS3 crystals are
typically only a few hundred microns laterally yet ranging from microns to tens of microns
in thickness. Such small lateral size of these bulk crystals poses significant challenges for
fabricating multiterminal devices for transport studies using conventional hand bonding
method. On the other hand, due to the substantial crystal thickness, standard cleanroom
processing such as lithography cannot be directly applied on BaTiS3 to fabricate multi-
terminal electrical contacts. In section 3.1, I will introduce a simple method that was
developed during my PhD to achieve the surface planarization of small, bulk crystals by
polymeric embedding. This method allows for standard lithography and microfabrication
techniques can be readily applied, as in large-scale wafers and 2D material systems.
Cleanroom processes of BaTiS3 bulk device fabrication and contact optimization are
presented in details. Furthermore, building on this planarized platform of bulk crystals,
advanced micro-structure patterning using Plasma FIB (PFIB), heterogeneous integration
of van der Waals electrodes on bulk BaTiS3 crystals, and strategies for handling air- or
water sensitive crystals are discussed from Section 3.2 to Section 3.4, respectively.

40
3.1 Crystal planarization using polyimide and device fabrication
In section 3.1.1, I will elaborate the general motivation and significance of realizing
planarized crystal surfaces for conducting multi-terminal transport studies on small, bulk
crystals such as BaTiS3. Then I will present the detailed processing conditions for
embedding bulk BaTiS3 crystals in low-stress polyimide in section 3.1.2. This method
works best for crystals with a thickness of up to 30 µm and can be potentially applied to
other strain-sensitive quantum materials as well. After the BaTiS3 crystal surface being
planarized, we use standard photolithography, dry etching, and deposition tools in a
cleanroom to make electrical contacts to BaTiS3. Detailed device fabrication procedures
and contact optimizations are presented in Section 3.1.3. All the BaTiS3 devices used for
transport measurements in this thesis were fabricated based on the polyimide embedding
method unless otherwise mentioned.

3.1.1 Motivation
Electrical transport measurements not only play an important role in understanding the
nature of electronic phases[81-83] and identifying phase transitions[9,10,84], but also
provide supporting experimental evidence for phenomena such as symmetry breaking[85-
87]. For many decades, epitaxial semiconductor thin films and heterostructures such as
GaAs/AlGaAs two-dimensional electron gas (2DEG) systems were the only few material
platforms available for electrical transport studies, especially quantum transport,[88,89]
before low-dimensional nanomaterials such as carbon nanotube[90], graphene[91,92] and
transition metal dichalcogenides (TMD)[93,94] emerged. Recent advancements in
nanomaterials synthesis, mechanical exfoliation and lithography techniques over the past
few decades have successfully expanded transport studies to a large class of nano-scale

41
and exfoliable layered materials[90-94]. On the other hand, there are also a large variety
of newly synthesized or theoretically predicted crystals that are not easily exfoliable down
to lithographically compatible thicknesses such as many quasi-one-dimensional (quasi-1D)
and 3D crystals[95-97], and hence, multi-terminal electrical transport studies are limited
on those materials.
Manual bonding is still the most widely adopted method for making electrical
contacts to those bulk crystals[97-99], where thin metal wires such as gold, platinum, or
indium are directly bonded onto the crystals using conductive epoxy or self-melting
methods. Sometimes a pre-sputtered Au layer through a shadowing mask is also applied
to further reduce the contact resistance[100]. To make a four-probe measurement contact
geometry, this manual bonding method would usually require at least mm-scale crystal
size and significant user skills[98]. However, newly synthesized crystals from either CVT
or flux growth methods are typically small and in a range of a few hundred micrometers.
Extensive growth condition optimizations are required to achieve crystals larger than a
millimeter in lateral dimensions[74,101]. Even for quasi-1D morphology crystals such as
BaTiS3 that are long enough for standard four-probe geometry, achieving more
complicated electrode designs such as Hall bar geometry and angular dependent electrodes
is still challenging due to geometrical limitations on other directions[99]. Conventional
bottom contact method with prepatterned electrodes is also challenging for handling µm-
thick bulk crystals due to the difficulties of making conformal contact between a rigid
bulk crystal and bottom electrodes, although it works very well for contacting thin 2D
flakes[102]. Another option is to use a prefabricated SiNx shadowing mask, but electrode
patterning accuracy, alignment, and crystal handling remain critical limitations.
On the other hand, the simple idea of crystal embedding using epoxy resin has
been applied to handle small bulk samples in situations such as microtome

42
sectioning[103,104] and crystal surface polishing for chemical analysis[105], but its
applications toward electronic device fabrication or electrical transport measurements
have not been explored extensively. Recently, Kang et al reported the fabrication of
lithography-defined GaAs photoelectrodes[106] by embedding freestanding microcells (500
µm in lateral dimension and 4-5 µm thick) in UV-curable epoxy NOA. However, these
epoxies typically exhibit relatively large CTE (coefficient of thermal expansion, ~ 80
ppm/K for NOA 61), and a significant amount of thermal strain (~ 1.6% at 100 K for
NOA) could be introduced at low temperatures. To obtain reliable and reproducible
transport measurements on quantum material systems that typically have strong electron-
lattice interactions and are sensitive to strain fields, low-stress embedding medium is
needed.
Here, we adopt the polymeric embedding approach and demonstrate a simple
crystal planarization strategy that uses a low-stress polymer as the embedding medium,
which allows reliable lithography-compatible multi-terminal electrical transport studies
on small, bulk single crystals. We have chosen the quasi-1D hexagonal chalcogenide
BaTiS3 as a model non-exfoliable quantum material system for this demonstration.
Although the CTE of BaTiS3 is not known from the literature, we choose a low-CTE
polyimide (~3 ppm/K) as the embedding medium, considering most of inorganic single
crystalline materials have CTE values below 10 ppm/K. Moreover, we are using the
following two criteria to determine whether the crystal is in nearly stress-free status: 1)
the transport behavior from embedding method is consistent with the conventional
handing bonding contacting method using silver epoxy and Au wires; And 2) the transport
behavior is reproducible between different heating/cooling cycles.

43
3.1.2 Planarization processes
As already mentioned in Section 2.1, different morphologies of BaTiS3 crystals have been
obtained from CVT growth. Among these, needle-like BaTiS3 crystals with 10-20 µm thick,
40-60 µm wide, and 200-300 µm long have been selected for most of the electrical transport
studies presented in this thesis, including regular transport along c-axis, Hall
measurements, resistive switching etc. Besides, BaTiS3 platelets with 100-200 µm in both
lateral directions are ideal for in-plane conductivity anisotropy studies using orientation-
resolved four-probe geometries, and thin needles with mm long are best for studying
uniaxial strain effects.
Figure 3.1a illustrates a schematic of the device fabrication process flow for
embedding a bulk BaTiS3 crystal in a polyimide medium, which consists of the following
steps:
1. Attach the picked crystal to a polydimethylsiloxane (PDMS) elastomer stamp and
then load the PDMS/glass stack onto a home-built transfer stage. A clean, flat
crystal surface that is planned as the top surface for contacts shall face downwards
in this step.
2. Apply a thin layer of uncured polyimide (PI 2611, HD Microsystems) on a pristine
Si wafer (4 cm × 4 cm) and spread as adhesive using a Q-tip (TX751B, Texwipe).
3. Roughly align the crystal to the substrate under a stereomicroscope and then lower
the stage till the crystal is in contact with the PI adhesive.
4. Hold for ~30 s, and then slowly lift the stage, leaving a BaTiS3 crystal printed on
the Si substrate.
5. Partially cure the PI on a hot plate at 120˚C for 5 min to fix the crystal in place.

44
6. Spin-coat the same PI precursors consecutively for four times at 1500 rpm to
completely cover the crystal, with a soft-bake step at 170˚C for 5 min (5˚C/min
ramp rate) after each coating.
7. Cure the whole substrate at 200˚C for 15 hr (5˚C/min ramp rate).
8. Gently cut and peel off the PI film (6 mm × 6 mm) from the Si substrate, leaving
a freestanding PI chip with the top surface of the BaTiS3 crystal planarized. Note
that no silane-based adhesion promoter (VM 651, HD Microsystems) was applied
prior to PI spin-coating for a higher peeling-off yield.
9. Flip the PI chip and attach it to a 5 mm × 5 mm sapphire substate with two-part
thermally conductive epoxy (Thermo-bond 180) or silver epoxy (EPO-TEK H20E).
Double sided thermal release tape can also be used for temporary bonding to go
through lithography and metal deposition processes, resulting in a BaTiS3 device
on a freestanding PI chip with metal contacts.
Figure 3.1 (a) Schematics of the fabrication process flow for a bulk BaTiS3 device utilizing PI as
the embedding medium. (b) Schematic illustration of PI peeling off step with a 5 × 5 arrays of
crystals processed at the same time. (c) Photographic image of multiple BaTiS3 devices fabricated
for transport studies.

45
(*All the processing steps listed above including transfer and PI coating are performed
in a fume hood environment with good ventilation to avoid inhalation of n-methyl-2-
pyrollidone (NMP), which is the main solvent of the PI precursor.)

Multiple crystals can be processed on the same Si substrate by repeating crystal
transfer and releasing steps (Step 1 to 5). As the schematic illustrated in Figure 3.1b, 5
× 5 arrays of crystals are usually prepared on the same wafer to save total processing
time. Figure 3.1c shows a photographic image of multiple devices fabricated from the same
batch of PI embedding processing. A typical polyimide film thickness of about 60 µm from
the above processing conditions provides sufficient mechanical support and is suitable for
crystals with thicknesses below 30 µm. For even thicker crystals, the conformal coating of
PI may become an issue and lead to a lower yield. As we mentioned earlier, surface
planarization is critical in enabling successful application of lithography techniques on
sub-mm bulk crystals. Here, we have taken advantage of the controllable adhesion
strengths between a PI film and the flat silicon wafer, which serves as the crystal’s
temporary molding surface. The step height of the BaTiS3 crystal-substrate boundary is
Figure 3.2 (a) Surface profile scans of an as-grown BaTiS3 crystal placed on a PDMS stamp and
after polyimide embedding and RIE cleaning. (b) Optical micrographs of a BaTiS3 crystal after
crystal embedding (top left), surface cleaning (bottom left), metallization with (top right) and
without (bottom right) a thin PI dielectric on the channel region.

46
reduced from the as-grown crystal thickness (5 – 20 µm) to typically less than 200 nm
after embedding. After the removal of the PI adhesive residual layer and sometimes
surface oxides by RIE dry etching, the edge step can still be maintained below 400 nm,
as shown by the surface profile scans in Figure 3.2a. On the other hand, as the polyimide
itself is a good dielectric and protects the crystal surface against exposure to air or water,
sometimes it is preferred to remove the PI residuals in the contact regions only. Figure
3.2b illustrates the optical micrographs of BaTiS3 devices at various processing steps.
Detailed cleanroom processes including RIE dry etching and metal deposition will be
presented later in Section 3.1.3.
The use of a polyimide planarization method in bulk crystal device fabrication
provides several advantages over conventional hand bonding techniques. This process no
longer needs large mm or cm scale crystals for transport studies, which requires extensive
expertise and efforts in single crystal growth optimization. As a result, it allows for more
research groups to be involved in and thereby accelerates the search for new exciting
material systems. Moreover, being fully compatible with lithography, this technique offers
new opportunities in terms of flexibility and complexity in device geometry. In addition
to regular linear four-probe measurements, one can now easily study Hall effects and
angular dependence of conductivity on bulk crystals, as easily as on 2D systems. Besides,
as the polyimide itself is a low-stress polymer as well as a good dielectric and protection
material, this planarization strategy enables more possibilities of performing advanced
transport studies even on strain-sensitive, air- or water-sensitive material systems that
were previously very difficult to work with. Down sides of this technique include the
limited crystal thickness (below 30 µm) it can work with, significantly increased processing
time and the need for expertise in device fabrication.

47
3.1.3 Device fabrication and contact optimization
A BaTiS3 crystal with proper morphology and thickness is first selected under an optical
microscope, and then embedded in polyimide following the fabrication steps described in
Section 3.1.2. The resulting sample that is ready for photolithography is a crystal-
embedded PI film bonded onto a 5 mm × 5 mm sapphire substrate. A thin layer of
polyimide, typically around 100 nm thick, is usually present on top of the crystal as the
adhesive residue, as shown in Figure 3.2b (top left). An optional surface cleaning step
may be performed to freshly expose the crystal surface using a short-time reactive ion
etching (RIE) treatment with a mixture of O2 and CF4. Importantly, the surface profile
of the crystal-polymer boundary needs to be confirmed before proceeding with further
metallization. Ideally, the boundary step height should be below 500 nm such that it can
be conformally covered by a ~300 nm thick metal layer without any discontinuity.
Despite the relative stability of BaTiS3 crystals in ambient conditions, a thin
amorphous oxide layer can still form on the crystal surface over time, resulting in increased
contact resistance and hence degradation in transport study quality. In extreme cases,
this oxide layer can even smear the phase transitions that we are interested in. To
effectively remove the surface oxide layer on BaTiS3, we applied RIE treatment using SF6
gas in contact regions before metal deposition. Detailed fabrication procedures are as
follows:
1. Clean the polyimide substrate using acetone, isopropyl alcohol (IPA), deionized
(DI) water and dehydrate at 110˚C for 1 min.
2. Spin-coat a negative photoresist (AZ nLOF-2070, Merck KGaA) on polyimide
substrate at 4000 rpm, and soft bake on a hot plate at 100˚C for 7 min, which
yields a 6 µm flat film.
3. Align and expose the photoresist with i-line mask aligner at 240 mJ/cm
2
.

48
4. Post-exposure bake (PEB) at 110˚C for 45 s.
5. Develop in tetramethyl ammonium hydroxide (TMAH)-based developer (AZ 726
MIF) for 2 min to form the electrode patterns. Carefully check under optical
microscope and make sure all the developed patterns are clear and sharp.
6. Clean the polymer residue in contact regions using RIE. A typical dry etching
recipe for etching polyimide is O2/CF4 = 45/5 sccm, 100 W, 100 mTorr, 30 s. This
recipe has an etch rate at ~0.4 µm/min and may also oxidize the crystal surface,
hence the etching time need to be minimized to just expose the crystal surface.
7. Remove the surface oxide layer by SF6-based RIE treatment, so that fresh BaTiS3
surface is exposed. A commonly used etching recipe is Ar/SF6 = 50/15 sccm, 100
W, 200 mTorr, 1 min.
8. Load the sample to the Ebeam evaporator (Kurt Lesker) immediately after the dry
etching and pump until low 10
-6
Torr pressure range to minimize contamination of
the freshly exposed surface.
9. Deposit Ti (3 nm, 0.5 Å/s) and Au (300 nm, 2 Å/s) consecutively by electron beam
evaporator.
10. Lift-off photoresist in acetone at room temperature for 10 min.

Figure 3.3 (a) A cross-sectional illustration of a BaTiS3 device embedded in polyimide for transport
studies. (b) and (c) Optical microscopic images of BaTiS3 devices with various electrode designs.
Both devices are contacted directly with channel region exposed.

49
After this step, the device is completed. Figure 3.3 (b) and (c) show optical
microscopic images of BaTiS3 devices embedded in polyimide with various electrode
designs. A cross-sectional schematic of the final device is illustrated in Figure 3.3 (a).
To load the device into our JANIS cryostat for transport measurements, we need
to attach our sample onto a chip carrier (Spectrum Semiconductor, CSB01625) that fits
the cryostat, and electrically connect between them. Normally, this step is done by wedge
bonding, where ultrasonic power is used to bond Aluminum wires to metal pads. However,
as we are using soft polymers as the substrate and only thin layers of Au have being
evaporated for bonding, both the yield and bonding strength of this method are low. To
overcome these issues, we instead utilize the “hand bonding” method, which involves the
use of a two-part silver epoxy (EPO-TEK, H20E) and 1 mil thick Au wire. We first apply
a small amount of premixed silver epoxy on the bonding metal pads of the sample, and
then pickup and drop one end of the Au wires (5-7 mm long) into the silver epoxy using
high precision tweezers with fine tips under microscope. Addition epoxy is added to the
metal pads of chip carrier to bond the other free end of the Au wires. After that, the
entire chip carrier is loaded into a laboratory oven and cured the epoxy at 115˚C for 15
min. The resistance between two bonding pads across the Au wire is typically within a
few ohms after silver epoxy curing. Moreover, to facilitate the “hand bonding” process, we
typically design and fabricate very large metal bonding pads of the sample with lateral
sizes from 0.5 mm to 1 mm, as shown in the photographic image of BaTiS3 devices in
Figure 3.1c.
Obtaining high quality electrical contacts with minimized contact resistances is
critical for devices of semiconducting BaTiS3. The quality of contacts can be quickly
checked after metallization and lift-off by measuring two-probe resistance (Rtwo) between
nearest electrodes. Bulk BaTiS3 devices with Rtwo values ranging from 300 to 500 Ohm

50
(e.g. with 20 µm channel size) are typically considered as “good”, and those with Rtwo up
to 2 kOhm are “acceptable”, both of which are used for further transport measurements.
For electronic device applications such as oscillators and memories (Chapter 6), where the
contact resistance plays an important role, only “good” BaTiS3 devices are used to
maximize the device performance.
In order to quantitatively evaluate the contact resistivity of the BaTiS3 devices,
transfer length method (TLM) analysis was carried out. For a needle-like BaTiS3 sample
(Figure 3.3c) with Ti (3 nm) / Au (300 nm) electrodes deposited on a SF6-cleaned crystal
surface, two-probe resistances between metal pads with varying spacing distances were
measured at room temperature, as illustrated in Figure 3.4. This specific device had an
extracted contact resistance of 370 Ohm and a contact resistivity of 0.015 Ω∙cm
"
. The
relatively large contact resistivity still makes sense because as-grown BaTiS3 are nominally
undoped, which is much harder to form good electrical contacts with low resistivity as in
many other metallic or heavily doped systems. For comparison, typical p-type Ohmic
contact resistivity (Pt/Ti/Pt/Au) on heavily doped GaAs (e.g., p-type doping, ~ 10
19
cm
-
Figure 3.4 Total resistance (R) as a function of metal pad spacing (L) from standard transfer length
method (TLM) measurements, where Ti/Au (3 nm/300 nm) were deposited on SF6-cleaned crystal
surface. This specific device has an extracted contact resistance of 370 Ohm and a contact resistivity
of 0.015 Ω∙cm
)
.

51
3
) is in the range of 10
-3
to 10
-4
Ω∙cm
"
, which is orders of magnitude lower than that of
BaTiS3.

3.2 Micro-structure patterning using plasma-FIB
Before this planarization technique was developed, most of the advanced multi-terminal
electrical transport in bulk single crystals relied on sophisticated sample preparation
methods such as focused ion beam (FIB) micropatterning. This involves lifting out a
lamella with a thickness of a few micrometers from a bulk crystal and carving it into
desired patterns, such as the Hall bar geometry, to investigate its charge transport
behavior. Using that technique, several fascinating quantum systems, including iron
pnictides, semimetals, and heavy-fermion superconductors, have been fabricated into a
variety of microstructures for transport studies. However, the complexity of the lamella
lift-out procedure, which requires extensive experience in TEM sample preparation, limits
the extensive use of this powerful method to only a few research groups. On the other
hand, the milling process on the lamella itself is relatively straightforward and quick.
Here, without going through the time-consuming lamella lift-out procedure, we
demonstrate a simple fabrication process for creating multiterminal microstructures of
BaTiS3 from a prefabricated device with desired metal contacts using plasma FIB (PFIB).
The pre-existing metal contacts provide unique opportunities to investigate the effects of
microstructures and ion implantations on transport behavior through direct comparison
of measurements taken before and after patterning from the same device. This is normally
challenging for regular FIB microstructure patterning technique.
To start with, we first select an as-grown BaTiS3 crystal with a plate-like or needle-
like morphology and thickness below 20 µm under an optical microscope. A thinner crystal
is preferred to minimize the total milling time. We then embed the crystal in polyimide

52
and fabricate the electrodes following the procedures presented in Section 3.1.2 and 3.1.3.
Regular electrical transport measurements (Section 4.1 and 4.2) are carried out as needed
to validate the phase transitions. We use a PFIB system (ThermoFisher Helios G4 PFIB
UXe DualBeam) at USC for micro-structures milling processes. This setup features Ga
+

free sample preparation and precise micromachining, which is most used for high quality
TEM sample preparation. Detailed procedures are as follows:
1. Load the sample in the PFIB system, with the edges of metal contacts grounded
to the stage by carbon tape to mitigate the electron beam charging issue during
processing.
2. Mill the crystal at 30 kV and 15 nA to form desired geometries such as “cloverleaf”
and Hall bar geometry. The milling process is typically done within a few minutes.
3. Deposit addition layer of tungsten (~ 500 nm) on top of the contact region at 8
kV using a MultiChem gas delivery system in the PFIB chamber, to ensure the
electrical connection at the crystal-polymer boundary and to maximize the contact
area.
4. Clean up the damaged regions of the sidewall and crystal surface at 30 kV, 1 nA
as the fine polishing step. An even lower milling voltage for surface polishing could
help reduce extrinsic surface contributions to the transport.
Figure 3.5 SEM images of various BaTiS3 microstructures fabricated by PFIB with geometries of
(a) ‘clover-leaf’ shape, (b) 6-terminal Hall bar and (c) 8-terminal Hall bar.

53

After this point, the device can be reconnected to the chip carrier and is again
ready for transport measurements. Figure 3.8 illustrates scanning electron micrographs of
various microstructures fabricated by PFIB milling on pre-embedded BaTiS3 crystals with
metal contacts for transport measurements.

3.3 Integration of van der Waals contacts on planarized bulk
crystals
In addition to studying the intrinsic physical properties of the quantum material itself,
heterogeneous integration with other interesting systems opens new opportunities for
exploring rich physics from proximity effects and reconstructed electronic properties[107].
The emergence of heterostructures of 2D materials, including the twistronics, has offered
a unique platform with great flexibility for investigating intriguing phenomena such as
superconductivity[108,109] and correlated insulating states[110,111]. The crystal surface
planarization strategy presented here theoretically allows for heterogeneous integration of
2D materials such as graphene and transition metal dichalcogenides onto various bulk
crystals using standard transfer techniques.
Here, we use 50 nm thick Au electrodes as an example and show their integration
on BaTiS3 crystal using the transfer processes modified from the procedures previously
reported[112,113]. We choose photoresist/PPC/PDMS stack to pick up and transfer the
electrodes onto planarized BaTiS3 crystals instead of commonly used PMMA/PDMS for
the ease of processing, as illustrated in Figure 3.6a. Detailed fabrication procedures are as
follows:

54
1. Prepare Au electrodes with desired geometries on a clean silicon wafer using
standard photolithography (or e-beam lithography) and ebeam evaporation.
2. An hexamethyldisilazane (HMDS) vapor treatment was carried out on the silicon
substrate (kept at 130˚C on hotplate) for 20 min to functionalize the whole wafer.
3. Spin-coat photoresist AZ1518 at 4000 rpm on top of metal electrodes, followed by
a spin-coating of a thin PPC layer (4000 rpm). The PPC/PR/Au stack can then
be stored for long time and are ready to use.
4. Clean PI-embedded BaTiS3 crystal gently by SF6 RIE (Ar/SF6 = 50/15 sccm, 100
W, 50 mTorr, 40 s) to expose the fresh surface.
5. Use PDMS stamp to pick up the whole PPC/PR/Au stack, a very high yield of
more than 90% has been achieved without cracking Au electrodes.
6. Without much delay, the PPC/PR/Au electrode stack was aligned and transferred
onto the BaTiS3 crystal using a home-built transfer stage. Then the whole sample
stack was treated at 120˚C for 5 min to release PDMS stamp by melting PPC
layer.
Figure 3.6. (a) Optical microscopic images of BTS crystal after surface planarization and van der Waals
contact integration. (b) current-voltage characteristics of a BTS device contacted by 50 nm transferred
Au electrodes.
-100 -50 0 50 100
-5
5
10
V (mV)
I (µA)
-10
0
transferred Au - BTS
a b
100 µm
100 µm
After planarization After transferred contact integration

55
7. Remove the remaining photoresist by acetone and IPA. A short bake of 110˚C for
30 s is applied to further improve the electrode adhesion.

Two-terminal I-V characterization of a BaTiS3 device with transferred electrodes,
as shown in Figure 3.6b, indicates that there is a conformal contact between the Au
electrodes and the crystal surface, which opens up more opportunities on future
heterogeneous integration of various 2D materials onto bulk crystals, given that the
fabrication processes are very similar to each other.

3.4 Encapsulation strategy for handling ‘sensitive’ materials
In the last few sections, I have demonstrated that the polymeric planarization method has
facilitated the use of standard lithography and microfabrication techniques on many small,
bulk crystals such as BaTiS3, thereby enabling versatile transport studies on these
materials. However, there are also many materials that are highly sensitive to ambient
conditions, heat, chemicals, etc., and may experience severe oxidation and degradation
during the regular fabrication processes presented above. Similar issues have been faced
by researchers in 2D materials community for years when handling thin flakes, especially
monolayers, of transition metal dichalcogenides and other sensitive materials such as CrI3.
To address these issues, h-BN flakes have been extensively used to encapsulate thin 2D
materials, which not only serve as a dielectric for electrostatic gating, but also act as
protective layers against sample degradation and charge disorders from the substrate. In
this section, I will introduce an encapsulation strategy for preventing sample degradation
of air-sensitive bulk crystals, similar to the role of h-BN in 2D systems.
Here, we choose polyimide for encapsulation, which is the same material being used
for crystal planarization. Some common properties have been shared between polyimide

56
and h-BN. For example, both are good dielectrics and can be dry-etched to expose fresh
crystal surfaces for electrical contacts through either vertical interconnect access (VIA)
holes or edge contacts. We start with a bulk crystal embedded in polyimide following
procedures presented in Section 3.1.2. Detailed fabrication processes of polyimide
encapsulation and ‘VIA’ holes formation are as follows:
1. Spin-coat diluted PI precursors (PI2611 precursors: NMP = 1: 1) at 3000 rpm to
form the encapsulation layer.
2. Cure the whole substrate at 200˚C for 15 hr with 5˚C/min ramp rate. The film
thickness is about 1.5 µm after curing.
3. Spin-coat a positive photoresist AZ4620 (Merck KGaA) at 4000 rpm, and soft bake
on a hot plate at 110˚C for 3 min, which yields a 7 µm thick flat film.
Figure 3.7 (a) A cross-sectional illustration of a BaTiS3 device embedded in polyimide with a ‘VIA
holes’ scheme. (c) and (e) Optical microscopic images of BaTiS3 devices with various electrode
designs after ‘VIA’ holes formation. (b) Schematic illustration of a BaTiS3 device contacted through
polyimide ‘VIA’ holes, with channel regions encapsulated. (d) and (f) Optical microscopic images
of the corresponding BaTiS3 devices after metal deposition.

57
4. Align and expose the photoresist with i-line mask aligner at 600 mJ/cm
2
.
5. Develop in aqueous base developer (AZ 400K 1:4, Meck KGaA) for 3 min.
6. Etch the polyimide to form ‘VIA’ holes by RIE etching (O2/CF4 = 45/5 sccm, 100
W, 100 mTorr, 4 min). Carefully check under optical microscope and make sure
the fresh crystal surface has been properly exposed.
7. Remove photoresist with acetone.

The metal deposition procedures beyond this step are the same as the ones
presented in Section 3.1.3. Figure 3.7 (a) shows a cross-sectional schematic of a BaTiS3
after ‘VIA’ hole formation with channel regions encapsulated, and Figure 3.7 (c) and (e)
show optical microscopic images of BaTiS3 devices with various electrode designs at the
same step. Figure 3.7 (b) illustrates the schematic view of a BaTiS3 device after final
metal deposition, and Figure 3.7 (d) and (e) show the corresponding optical microscopic
images. Moreover, the PI ‘VIA’ holes strategy precisely defines the positions and area of
contacting electrodes, which is critical in accurately extracting transport properties from
small crystals.
Among the several quasi-1D hexagonal chalcogenide systems that have been
synthesized in our lab, BaTiSe3, with the S site replace by Se, is the most air-sensitive
material. The crystal surface would from “shinny” into “dark” or even “black” if left in
ambient conditions for more than a day, which has created a lot of challenges for material
handling and device fabrication. One may have to either process entirely in a glovebox
filled with inert gases or encapsulate the sample to minimize exposure to ambient
environment. By adopting the polyimide encapsulation and ‘VIA holes’ strategy, BaTiSe3
devices have been successfully fabricated without severe sample degradation and have

58
been used for transport measurements. Detailed transport properties of BaTiSe3 are not
covered in this thesis and will be presented elsewhere.

59

Chapter 4 Charge-density-wave order and
electronic phase transitions in a dilute d-
band Semiconductor
Charge density wave (CDW) is a periodic modulation of electron density, which is
accompanied by periodic lattice distortions and is often observed in low-dimensional
metals such as NbSe3[1,5,33]. The defining features of CDW from Peierls’ model include
periodic lattice distortion, Fermi surface nesting and a metal-insulator transition[4,8]. In
recent years, there has been growing interest in CDW systems that exhibit semiconducting
transport behavior, such as 1T-TaS2[10,34] and 1T-TiSe2[35,36], whose origin presumably
go beyond q-dependent electron-phonon coupling mechanism. These materials exhibit
electron-hole coupling[36], resistive switching[34,37], toroidal dipolar structures[38,39],
and wide hysteretic transitions[40], which have led to vigorous debates over the
mechanism of these CDW transitions[40,114]. The confluence of CDW order and
semiconducting behavior is not only scientifically interesting but also holds promise for
new applications of CDW.
Here, we report the discovery of CDW order and phase transitions in a non-
degenerate semiconductor, BaTiS3, which broadens the realm of CDW physics,
particularly in semiconducting materials. We observe two hysteretic resistive phase
transitions that correspond to the emergence and suppression of the CDW state using

60
transport measurements. Combining single-crystal X-ray diffraction (XRD), we provide
direct experimental evidence of CDW order in the system and track its evolution in both
electronic and lattice degrees of freedom. Our findings suggest that a combination of
electron-phonon coupling, and non-negligible electron-electron interactions may be
responsible for the observed phase transitions in BaTiS3. Our study establishes
semiconducting BaTiS3 as a new model system for investigating rich electronic phases and
phase transitions in dilute filling and offers new opportunities in electronic device
applications of CDW phase change materials.

4.1 Transport signatures of phase transitions in BaTiS
3

Quasi-one-dimensional (quasi-1D) chalcogenide, BaTiS3, is a small bandgap
semiconductor (Eg ~ 0.3 eV) with a hexagonal crystal structure composed of 1D chains
of TiS6 octahedra, stacked between Ba chains. Recently, a giant optical anisotropy[57]
and abnormal glass-like thermal transport properties[64] were reported in this material,
Figure 4.1 Illustration of representative temperature dependent electrical resistivity of BaTiS3
crystal along c-axis. Abrupt and hysteric jumps in resistance are shown near 150-190 K (Transition
I), and 240-260 K (Transition II). Inset shows optical microscopic image of a BaTiS3 device used
for transport measurements.

61
which imposed questions over its electronic properties. However, no feature indictive of
phase transitions has been reported in BaTiS3 to date. We performed electrical transport
measurements on bulk single crystals of BaTiS3 along the chain axis (c-axis), as shown in
Figure 4.1. Here, we identify two different phase transitions from their non-monotonic
and hysteretic transport behavior. Upon cooling, the electrical resistivity increases, and
the system undergoes a phase transition at 240 K (Transition II) featuring a resistivity
jump. On further cooling, it continuous to increase till 150 K, after which the material
Figure 4.2 Reproducible transport measurements of BaTiS3. (a) Temperature-dependent electrical
resistance (normalized by R (300 K)) measured from three different BaTiS3 devices. The transport
behavior is qualitatively consistent with each other. (b) Transport behavior of a needle-like device
contacted by hand-bonding method using silver epoxy and Au wires. (c) Transport measurements
from different thermal cycles. (d) Cooling rate-dependent transport on BaTiS3. Neither of the
transitions are suppressed or altered using cooling rate up to 5 K/min.

62
undergoes another transition that we call Transition I with a sharp drop in resistivity.
The Transition II (240-260 K) hints at the emergence of a CDW state from a high
temperature semiconducting phase; while at Transition I (150-190 K), the CDW order is
suppressed and the system switches to a more conductive state. Qualitatively reproducible
transport behavior showing two characteristic phase transitions were obtained from
several devices, different fabrication methods, different thermal cycles, and with different
cooling rates, as illustrated in Figure 4.2.
To further understand these observations, we performed Hall measurements to
study the evolution of carrier concentration and mobility across both the phase transitions,
as illustrated in Figure 4.3. At room temperature, the electron concentration is ~1.1×10
18

cm
-3
, and it decreases monotonically as temperature is lowered (n < 10
15
cm
-3
at 100 K).
We did not observe any change in carrier type across the transitions. These observations
confirm the non-degenerate nature of BaTiS3, which possesses one of the lowest carrier
densities among reported CDW compounds. Additionally, we found that the modulation
of electrical resistances of both transitions is primarily due to the Hall mobility, rather
than changes in carrier concentration across the transitions. This is distinctive from many
Figure 4.3 Temperature dependence of the mobility, µ, and carrier concentration, n, of the dominant
carrier, extracted from Hall measurements during a warming cycle.

63
other resistive switching systems such as VO2[115] and 1T-TaS2[116], where the
modulation of carrier concentrations accounts for their large resistance level changes. All
these transport observations are consistent with two phase transitions that lead to a
sequence of electronic phases in BaTiS3, starting from a high-temperature semiconducting
phase that transitions to a CDW phase at intermediate temperatures, and finally to a
high mobility phase at low temperatures.
Figure 4.4 shows supplemental data from magneto-transport measurement. Unlike
many other metallic CDW systems such as 2H-NbSe2[117] and 1T-TiSe2, no carrier type
switching behavior was observed across either of the two phase transitions, indicated by
the plot of Hall voltage Vxy vs. B throughout the whole temperature range. Further, the
temperature evolution of carrier concentration is used to obtain the transport activation
energy by ∆E=−
5(78 (:))
5(+/2
!
=)
. The extracted activation energy before and after Transition II, as
well as after Transition I is 125 meV, 219 meV, and 117 meV, respectively.

Figure 4.4 (a) Plot of Hall voltage Vxy with magnetic field from -6 T to 6 T at different temperatures.
Hall data was collected form the Sample C, with its temperature-dependent longitudinal resistance
illustrated in Figure 4.2a. (b) The measured data (blue) was fitted linearly to extract the carrier
concentration n and mobility µ.

64
4.2 Structural characterization
The superlattice reflections in a diffraction pattern is one of the direct experimental
evidences of CDW formation. These satellite peaks stem from periodic lattice distortions
associated with the charge modulation[18-20]. We performed synchrotron XRD at three
different temperatures to track the structural changes across the phase transitions. Figure
4.6a shows the corresponding precession map projected onto the hk2 reciprocal plane, and
Figure 4.6b illustrates a zoomed-in intensity cut along the direction indicated in Figure
4.6a. A hexagonal array of reflection spots is observed at room temperature consistent
with P63cm space group (a = b = 11.7 Å, c = 5.83 Å). At 220 K, additional superlattice
reflections appear at h+1/2 k+1/2 2 in the precession image, which signals a change in
the periodicity of the lattice (a = b = 23.3 Å, c = 5.84 Å) associated with Transition II
from P63cm to P3c1, consistent with a second-order transition. The intensities of these 2
´ 2 commensurate superstructure reflections are two orders of magnitude lower than that
of the primary reflections and are signatures of the formation of CDW order below
Transition II.
Figure 4.5 Thermal activation energy analysis of BaTiS3. Transport data from Figure 4.3 is used
for analysis.

65
Surprisingly, the unit cell doubling takes place in the a-b plane, rather than along
the chain axis (c-axis), which is usually the case in many other classic quasi-1D CDW
systems such as NbSe3[118] and BaVS3[119]. On further lowering the temperature to 130
K, the superlattice peaks disappeared and a new set of reflections associated with a smaller
"
√X
´
"
√X
unit cell emerged (a = b = 13.4 Å, c = 5.82 Å), which indicates a direct suppression
of the CDW via the structural transition (P3c1 to P21). The low temperature space group
P21 is not a subgroup of P3c1, and we have observed the large thermal hysteresis from
Figure 4.6 CDW order evolution revealed by single crystal XRD. Precession images from single-
crystal X-ray diffraction measurements along hk2 projection at 298 K, 220 K and 130 K. The
bottom left plots the X-ray intensity cut along the direction as indicated in precession images.

66
transport measurements, both of which lead us to the conclusion that the Transition I is
a first-order transition. The observed intermediate steps of Transition I from transport
measurements (Figure 4.1 and Figure 4.2a) are due to percolative nature of the structural
transition. An evolution of unit cell sizes in BTS is summarized in Figure 4.8a.
To further gain insights into the change of electronic structures in BaTiS3 across
these transitions, we calculated the electronic band structure of these three structures,
based on refined crystal structures from XRD, using density-functional theory (DFT), as
shown in Figure 4.7. As temperature is lowered, the bandgap of the system increases from
0.26 eV to 0.3 eV at Transition II and then drops to 0.15 eV across Transition I, which
qualitatively agrees with the evolution of thermal activation barrier from Arrhenius
analysis of transport data.
Single crystal diffraction at 130 K, 220 K and 298 K were carried out on beamline
12.2.1 at the Advanced Light Source (ALS), Lawrence Berkeley National Laboratory.
Figure 4.7 DFT-calculated electronic band structure of different phases of BaTiS3 with (a) P63cm,
(b) P3c1, and (c) P21. The contribution of Ti d-state and S p-sates to the band structure are
highlighted with blue and red colors, respectively. The band gap (Eg) calculated at the PBE level
is provided underneath the plots. The vertical arrows indicate the changing band gap at the G
point. The horizontal arrows show the symmetry direction along the chain-parallel- (‘chain(∥)’) and
chain-perpendicular-plane (‘chain(⊥)’) from the zone-center (G point) in the first Brillouin zone
P2
1
(130 K)
E
g
= 0.15 eV
P3c1 (220 K)
E
g
= 0.30 eV
a b c P6
3
cm (298 K)
E
g
= 0.26 eV
chain(∥) chain(⊥) chain(∥) chain(⊥) chain(∥) chain(⊥)
A B C a b c

67
Note that the refined space group is different from previously reported P63/mmc or
P63mc[57]. It is mainly attributed to the improved brightness and resolution using
synchrotron radiation that allows the observation of weak reflections.
The band structure of BaTiS3 in the three different phases were computed using
DFT. The initial structures were taken from the refined crystal structures from XRD at
different temperatures, which are assigned to have a space group of P63cm (298 K), P3c1
(220 K), and P21 (130 K), respectively. The structures were fully optimized by DFT.
These calculations were done using the Vienna Ab initio Simulation Package (VASP)[120]
with projector augmented wave (PAW) potentials[121]. The exchange-correlation energy
was treated with the generalized gradient approximation (GGA) using the Perdew-Burke-
Ernzerhof (PBE) functional[122].

4.3 Mechanism of phase transitions in BaTiS
3

BaTiS3 is a d
0
semiconductor with a nominally empty conduction band. No phase
transitions have been theoretically expected or experimentally observed in BaTiS3 before,
Figure 4.8 (a) Illustration of unit cell evolution of BaTiS3 at different temperatures. (b) Summary
of electronic phases and phase transitions. The bandgap values (Eg) are taken from DFT-calculated
band structures using PEB exchange-correlation functional.

68
and it was surprising to observe CDW order and phase transitions in such a dilute d-band
semiconductor, although a dynamic lattice instability has been speculated as an
explanation for its abnormal thermophysical behavior[64], and its d
1
counterpart, BaVS3,
is another archetypical CDW system[62]. Several groups in the past have investigated
physical properties of BaTiS3 compound in both polycrystalline powder and single crystal
form at cryogenic temperatures[63,64], but no phase transition was reported. It is likely
that BaTiS3 is sensitive to certain external stimuli such as strain or unintentional chemical
doping, and a good control over BaTiS3 single crystal synthesis, improvement on device
fabrication and contact optimization, and strain-free characterizations at low
temperatures allowed us to observe those phase transitions reliably in this work.
In a gapped semiconductor such as BaTiS3, as revealed by both optical
spectroscopy measurements and DFT calculations, the Fermi level falls in the bandgap
and therefore there is no Fermi surface. Hence, the surface nesting mechanism, which is
the dominant explanation for CDW in quasi-1D metals[118], can be ruled out. One
Figure 4.9 In-plane electrical conductivity anisotropy analysis using Montgomery method. (a)
Measured van der Pauw resistance Raa and Rcc as a function of temperature. The transport data
was collected from a BaTiS3 platelet device with van der Pauw geometry (l = w = 20 µm). (b) The
conformal mapping function that uniquely maps the ratio of Raa / Rcc to 𝐵
0,2
, which is later used
to calculate the anisotropy 𝜌
𝑎
/𝜌
𝑐
.

69
interesting observation in BaTiS3 is its two-dimensional charge ordering in the a-b plane
(Figure 4.6), rather than along the 1D chain-axis. This mismatch in dimensionality further
complicates the understanding of CDW order in this material. To investigate the role of
interchain coupling in stabilizing the CDW phase in BaTiS3, we performed in-plane
conductivity anisotropy measurements using Montgomery analysis[80,123], as illustrated
in Figure 4.9. The measured anisotropy in resistivity (ρa/ρc) was approximiately 4, which
is relatively small compared to other model quasi-1D CDW systems like NbSe3 (ρa/ρc ~
15-20)[99] and (TaSe4)2I (ρa/ρc > 200)[124].
In many real CDW materials, particularly those with higher dimensionalities such
as two-dimensional NbSe2, the CDW order is usually attributed to strong electron-phonon
coupling rather than purely electronically driven Peierls’ instability[44]. On the other hand,
clean semiconductor systems typically lack such coupling. To estimate the strength of
electron-phonon interaction in BaTiS3, we calculated its Frohlich coupling constant 𝛼 =
%
@
ℏZ
"
3
&
[
A
−
&
[
B
4
E
C
Z
"
"ℏ
for each phase[125,126], where the band effective mass mb, static and
high-frequency dielectric constant 𝜀
\
and 𝜀
3
, and the effective polar optical phonon
frequency 𝜔
$
were obtained from DFT. The calculated 𝛼 values of BaTiS3 are 1.36, 1.78
and 1.63 for the P63cm, P3c1, and P21 phases, respectively, indicating intermediate to
relatively strong electron-phonon coupling systems. For comparison, the reported 𝛼 values
for semiconductors such as GaAs, and InP are typically well below 1[127].
Moreover, as a non-degenerate semiconductor with dilute concentration of electrons,
the role of electron-electron interaction in BaTiS3 could be non-trivial unlike most metallic
or semi-metallic CDW systems. One way to evaluate the electron correlation effects in a
material is by calculating the dimensionless parameter 𝑟
U
=

&
D
E
J)
E
/3
]J[ℏ
@
E
C
%
@
4, defined by the
ratio of Wigner-sphere radius (dominated by electron-electron interaction) to Bohr radius

70
for a 3D electronic system[128]. Using the experimentally measured carrier concentration
n, calculated band effective mass mb and static dielectric constant 𝜀 from DFT, we
obtained rs value of BTS close to 4.4 at 200 K (n = 8.2 ´ 10
16
cm
-3
), and it further reaches
18.5 at 90 K (n = 1.7 ´ 10
14
cm
-3
). Although the calculated rs values are still away from
strongly correlated region (rs values ~ 100)[128] within the temperature range of
transitions, one cannot fully rule out the role of the correlation effects like in other metallic
CDW systems. Hence, the origin of CDW order and phase transitions in semiconducting
BaTiS3 can be potentially attributed to combined effects of electron-lattice and electron-
electron interactions.

Figure 4.10 rs and Fröhlich electron-phonon coupling constant values for various semiconductors.
Experimentally reported or DFT-calculated parameters including carrier concentration n, static and
high frequency dielectric constant 𝜀
F
and 𝜀
G
, effective band mass mb, and longitudinal optical
phonon frequency 𝜔
HI
were used for calculations.

71
4.4 Conclusion
In summary, we have investigated the CDW order and phase transitions in a dilute d-
band semiconductor, BaTiS3, by combining transport, XRD measurements and DFT
calculations. The phase transitions in BaTiS3 show several peculiar features: (i) the CDW
phase emerges from a semiconducting phase with a low carrier density, (ii) the structural
transition (Transition II) features an abrupt switching towards a more conductive state
upon cooling, (iii) Transition II has a large thermal hysteresis window of over 40 K, (iv)
the changes of electrical resistance across both transitions are mainly due to the
modulation of Hall mobility, rather than carrier concentrations, and (v) the CDW ordering
is two-dimensional and the electronic anisotropy of BaTiS3 is relatively small, although
structurally and optically being very anisotropic. Our analysis suggests that CDW order
and phase transitions in semiconducting BaTiS3 may be contributed from both electron-
lattice interactions and non-negligible elector-electron interactions. Further experimental
and theoretical studies are necessary to probe the evolution of electronic structure and
phonon dispersion across the transitions, to pin down the origin or driving force of these
transitions. Responses of the phase transitions in BaTiS3 to external fields such as pressure,
strain, and doping, and possible emergence of electronic phases such as superconductivity
are also of interest.
In addition, while CDW phenomena have been extensively studied in various
materials systems, practical electronic device applications based on CDW are still limited
due to the absence of hysteretic resistive transitions in most CDW systems. One notable
exception is the quasi-two-dimensional Mott insulator 1T-TaS2, where the hysteretic
CDW phase transitions have been utilized to develop novel electronics such as phase
change oscillators[53,54] and memory devices[37,56]. In BaTiS3, we have demonstrated
two hysteretic resistive phase transitions, one of which is first-order and the other second-

72
order, making it an ideal candidate for achieving both non-volatile and volatile type
resistive switching in the system. We anticipate that these phase transitions in BaTiS3
will offer new opportunities for achieving neuromorphic functionalities, similar to what
has been achieved with 1T-TaS2. Further research in this direction is necessary to explore
the full potential of CDW-based electronic devices using BaTiS3.

73

Chapter 5 Novel electrical functionalities
in BaTiS
3
In the last chapter, I have shown two unique hysteric resistive phase transitions in
the small bandgap semiconductor BaTiS3, with one CDW transition occurring near 250
K and the other structural transition in the temperature range of 150 K to 190 K. The
CDW ordering and lattice instabilities in BaTiS3 are considered as unconventional and
are potentially connected to non-trivial electron-correlation. In this chapter, I will discuss
about rich electrical functionalities in BaTiS3 such as CDW voltage oscillations and
memristive switching, which are enabled by leveraging the CDW (Transition II) and the
low-temperature structural transition (Transition I), respectively. Our experiments
highlight BaTiS3 as a promising CDW platform for the development of next-generation
computing technologies, such as quantum computing, neuromorphic computing, and
energy-efficient memory and storage.

5.1 Charge-density-wave switching and voltage oscillations
The metal-to-insulator transition is a hallmark phenomenon predicted by Peierls’ theory
for explaining charge density wave (CDW) in ideal one-dimensional metals[3,4]. However,
this transition is not a universal feature in real CDW materials, with some systems failing
to exhibit transport anomalies at the transition temperatures[8,13]. Despite over half a

74
century of study into CDW phases and phase transitions, much of the research has
centered on the physical aspects such as the driving force behind CDW[24,44,45] and its
relation to superconductivity[9,46,129], rather than exploring potential electronic device
applications. Nonetheless, CDW systems with hysteric resistive phase transitions have the
potential to offer unique opportunities for novel electronic device development[47,48]. One
such system that has attracted significant attention is the quasi-two-dimensional Mott
insulator 1T-TaS2, which exhibits several CDW phase transitions with resistivity changes
and hysteresis and has been utilized to construct electronic devices such as phase change
oscillators[53-55] and memristors[37,56].
BaTiS3 is a small bandgap semiconductor[57] that has recently shown unique
resistive phase transitions[60], including one CDW transition near 250 K and another
structural transition emerging at even lower temperatures (from 120 K to 150 K during
cooling cycle). Upon cooling from room temperature, the system switches from a
semiconducting state to a CDW state, resulting in an increase in electrical resistivity,
bandgap opening, and a periodic lattice distortion[60]. This change in electrical resistivity
presents opportunities to create devices that can be modulated by external stimuli such
as electrical and optical fields. In this study, we demonstrate threshold resistive switching
behavior with negative differential resistance (NDR) utilizing the CDW phase transition
in bulk BaTiS3 single crystal. The electrical switching mechanism was extensively
investigated through temperature-dependent current-voltage (I-V) characteristics and
pulsed I-V measurements. Furthermore, voltage oscillations with a frequency close to 1
kHz were observed from a two-terminal BaTiS3 device. Potential strategies for optimizing
device performance, such as reducing channel sizes and optimizing thermal management,
were also explored. Our findings shed light on electronic device applications in CDW
systems.

75

5.1.1 Reversible resistive switching
The phase transition of BaTiS3 near 250 K, referred to as the CDW transition, results in
an abrupt increase in resistance and a thermal hysteresis of over 10 K, both of which are
crucial for its potential applications as an electronic device. Figure 5.1a plots the
temperature-dependent resistance of BaTiS3 along the c-axis from 220 to 280 K, with an
inset showing an optical image of a typical multi-terminal BaTiS3 device with varying
Figure 5.1 Transport anomalies and reversible resistive switching in BaTiS3 (a) Representative
temperature dependent electrical resistance of BaTiS3 crystal along c-axis. Transport anomalies
with abrupt and hysteric jumps near 240 -260 K reveal the existence of a phase transition. The
inset shows an optical microscopic image of a typical BaTiS3 device. (b) Illustration of unit cell
evolution of BaTiS3 across the CDW phase transition. (c) and (d) I-V characteristics of a two-
terminal BaTiS3 device at 230 K by sweep voltage and current, respectively. Negative differential
resistance (NDR) regions are observed in I-mode.

76
channel sizes. Structurally, the unit cell doubles along the a- and b-axis across the
transition (a = 2a0, b = 2b0, c = c0), as depicted in Figure 5.1b.
To demonstrate the resistive switching behavior in BaTiS3, the device was initially
set to the high-resistive CDW state near the completion of the CDW transition (230 K).
A DC current-voltage characterization was performed on a two-terminal BaTiS3 device
by sweeping voltage (V-mode), as illustrated in Figure 5.1c. The system exhibited a
transition to a more conductive state above a certain threshold voltage VF during forward
scan, and it returned to its original high-resistive state below another critical voltage VR
(VR < VF) during reverse scan, forming a characteristic hysteresis window. Additionally,
‘S-type’ negative differential resistance regions (dV / dI < 0) were observed during
transitions when testing in current mode (I-mode) by sourcing current, as shown in Figure
5.1d. This threshold resistive switching behavior with NDR has been previously observed
in other phase change systems such as VO2[130-132] and 1T-TaS2[50,53,133], and is utilized to
construct electronic devices such as oscillators[53,54,131,132].

5.1.2 Mechanism of electrical switching
The mechanism behind such electrical voltage / current resistive switching behavior in
those systems is believed to be primarily due to local Joule heating[133-135], although
there are ongoing debates regarding the potential role of electrical field effect[50] and Mott
transition[131]. The effect of Joule heating is highly dependent on the specific material,
device structure, and bias mode (DC or pulse). In this experiment scheme, where a BaTiS3
crystal is embedded in a polymer medium with low thermal conductivity and the switching
is triggered by DC sweeps, the local Joule heating can be substantial.
To evaluate the contribution of Joule heating to the resistive switching behavior
observed in BaTiS3, we conducted four-probe I-V sweeps at various temperatures across

77
the CDW transition (Figure 5.2a). The results show that the critical voltage required to
switch the resistance state increases as temperature decreases, and there is no threshold
voltage switching observed at a temperature of 260 K. The thermal power generated by
Joule heating at threshold fields were calculated (𝑃
,F
= 𝑉
,F
×𝐼
,F
) and found to exhibit a
linear relationship with temperature, as illustrated in Figure 5.2b and 5.2c. Two
characteristic temperatures of 245 K and 258 K were identified at which the threshold
thermal power approaches zero, which aligns with the transition temperatures observed
Figure 5.2 Joule heating mechanism behind CDW resistive switching in BaTiS3. (a) Four-probe I-
V characteristics of a BaTiS3 device at different temperatures. (b) Extracted threshold voltages at
the corresponding temperatures for both forward and reverse sweeps. (c) Calculated temperature-
dependent thermal power at threshold fields (𝑷
𝒕𝒉
). A linear relationship is found between 𝑷
𝒕𝒉
and
temperature. (d) Pulsed I-V measurement of a two-terminal BaTiS3 device at 210 K. The pulse
voltage was ramped linearly from 0.8 V to 1.8 V, with the pulse width t = 8 ms and pulse period p
= 10 ms. (e) Reconstructed I-V characteristics of BaTiS3 from pulse measurements with pulse width
varying from 8 ms to 1 ms, while the pulse period was maintained at 10 ms. Dashed line shows the
DC I-V scan on the same device for comparison.

78
in the temperature-dependent resistance measurements (Figure 5.1a). This analysis
suggests that the resistive switching in BaTiS3 is primarily driven by Joule heating.
Moreover, pulsed I-V measurements with varying pulse widths were performed to
gain insights into the switching mechanism by deconvoluting the contributions from Joule
heating and electrical field effects. Figure 5.2d shows the results of pulsed I-V
measurements conducted on a two-terminal BaTiS3 device at 210 K. Voltage pulses with
a width of 8 ms and a pulse period of 10 ms were swept between 0.8 V to 1.8 V. In such
pre-defined voltage pulses, less than 10% of the total time was used for cooling. Hence,
similar to that observed in DC sweeps, the hysteretic switching behavior persisted, as
evidenced by the asymmetric measured current profile. To reduce the contribution of
Joule heating, the pulse width was decreased from 8 ms to 1 ms while maintaining the
voltage sweep ranges and pulse period. Figure 5.2e illustrates the reconstructed I-V curves
from pulsed measurements for different pulse widths. As the pulse width was decreased,
the width of the hysteresis window reduced while the switching voltage increased. No
hysteresis was revealed in the I-V curves when the pulse width was 1 ms. These
observations are consistent with the hypothesis of a thermally driven transition, as the
Joule heating power decreased with decreasing pulse width, while the electric field applied
to the BaTiS3 device remained the same.

5.1.3 CDW voltage oscillations
The capability of inducing sustained phase change-based voltage oscillations is crucial for
constructing electronic devices such as oscillators. Systems such as 1T-TaS2 and VO2 have
shown promising results, with the potential for GHz-level switching speeds theoretically
predicted[134,136] and experimentally demonstrated at MHz frequencies[53,131]. In the
case of BaTiS3, we observe stable voltage oscillations at frequencies from 16 Hz to 18 Hz

79
when a two-terminal BaTiS3 device is connected in series with a load resistor (RL = 11.25
kOhm) and a parallel capacitor (CP = 10 µF) and subjected to a DC bias between 16 V
and 23 V. The voltage oscillation is illustrated in Figure 5.3b, with the I-V characteristics
at 220 K and circuit diagram of the oscillation measurements shown in Figure 5.3a,
together with the load line of the resistor. The mechanism behind this voltage oscillation
can be understood as the switching of the BaTiS3 device between its CDW state and
semiconducting state. When the DC voltage reaches a critical value VF, the voltage drop
across the BaTiS3 channel triggers a transition to the semiconducting state, resulting in
a sudden increase in current and a subsequent increase in voltage across the load resistor.
This drives the BaTiS3 device back into the CDW state, and the cycle repeats, leading to
sustained voltage oscillations. The oscillation is not sustained when the DC voltage
exceeds 23 V or falls below 16 V.
On the other hand, although stable voltage oscillations were obtained for the first
time from the CDW transition in BaTiS3, its frequency remains orders of magnitude lower
than the MHz level achieved in VO2 and 1T-TaS2 systems. This low switching speed is
primarily attributed to the poor heat dissipation of the bulk BaTiS3-polyimide system,
Figure 5.3 CDW voltage oscillation in bulk BaTiS3. (a) I-V characteristics of a two-terminal BaTiS3
device at 220 K, with the inset showing the circuit for oscillation measurements. (b) Representative
oscillation waveform of BaTiS3 with a frequency of 16 Hz.

80
which has a low thermal conductivity and results in an inefficient cooling process that
limits its overall performance, despite the effective heating procedure.

5.1.4 Effect of thermal managements and channel sizes
One approach to enhance the switching speed is by improving the cooling efficiency of the
system, for example, by decreasing the operating temperature. Figure 5.4a to 5.4c plot
the voltage oscillations of the same BaTiS3 device measured at 200 K, 170 K and 130 K,
respectively, with an observed increase in frequency from 67 Hz to 910 Hz. However, it is
difficult to maintain this CDW oscillation when the temperature is further reduced, as
the low-temperature structural transition in BaTiS3 begins to interfere and complicate the
0 10 20 30 40
Time (ms)
50
2
4
6
0
V
OUT
(V)
T = 200 K f = 67 Hz
T = 170 K f = 168 Hz
0 10 20 30 40
Time (ms)
50
2
4
6
0
V
OUT
(V)
T = 130 K f = 910 Hz
0 10 20 30 40
Time (ms)
50
2
4
6
0
V
OUT
(V)
T = 170 K
10 µm
5 µm
f = 556 Hz
0 10 20 30 40
Time (ms)
50
2
4
6
0
V
OUT
(V)
c
a
bd
Figure 5.4 Oscillation frequency optimization in BaTiS3. (a) to (c) Effect of operating temperature.
The frequency increases from 67 Hz to 910 Hz by reducing the measurement temperature from 200
K to 130 K. (d) Effect of device channel size. The oscillation frequency increases more than three
times when reducing the channel size from 10 µm to 5 µm.

81
results. Thus, it is challenging to significantly improve the oscillator performance solely
by tuning the measurement temperatures.
Another strategy to further enhance the oscillation frequency is to decrease the size
of the device channel, as has been proven effective in other oscillating systems, such as
VO2[137]. In early days, the voltage oscillation frequency in millimeter-scale VO2 bulk single
crystals was only around 5 kHz[138], while nowadays, MHz-level oscillation frequencies
have been achieved in VO2 thin film devices with sub-micron channels[139]. Figure 5.4d
plots the oscillation waveforms from two different BaTiS3 devices with channel sizes of 10
µm and 5 µm, respectively, both of which were measured at 170 K for direct comparison.
With reduced channel size down to 5 µm, the oscillation frequency increases more than
three times compared to the 10 µm BaTiS3 device. This effect can be understood as the
improved efficiency for both cooling and heating processes as the channel size decreases.
Further reduction of sample sizes both laterally and vertically is expected to result in even
higher oscillation frequencies in BaTiS3.

5.1.5 Conclusion
In conclusion, we have shown reversible threshold switching in the recently discovered
CDW system BaTiS3, driven by DC voltage or current, whose mechanism is consistent
with a Joule heating scheme. Moreover, sustained voltage oscillations were achieved in
BaTiS3 based on bistate resistive switching between the semiconducting phase and CDW
phase. The oscillation frequencies were improved through appropriate thermal
managements and reduced channel sizes. Our work on BaTiS3 opens new opportunities in
electronic device applications of CDW phase change materials beyond 1T-TaS2.

82
5.2 Multilevel memristive switching
Neuromorphic computing is an approach that aims to mimic the operation of brains and
is essential for achieving energy-efficient information processing. One promising solution
for neuromorphic computing is the integration of analog or digital CMOS with memristive
devices, whose non-volatile conductance states can be tuned by electrical voltages. While
oxide-based memristive systems with metal/oxide/metal architecture have gained much
attention, achieving non-volatile resistive switching in phase change materials is also
promising, particularly those with first-order phase transitions and large thermal
hysteresis windows. Recently, memristive phase switching has been demonstrated in
various phase change materials, such as the layered CDW system 1T-TaS2 and the metal-
to-insulator system VO2.
Here, we demonstrate the multi-level non-volatile switching of resistance in the
phase change semiconductor BaTiS3 using both DC and pulsed voltages. We leverage the
first-order structural transition between the CDW and low-T high mobility states (150 -
190 K) to achieve this conductance modulation, mainly by consecutively tuning carrier
mobility. Moreover, the resistance state can be reset by thermal approaches. Each
intermediate state accessed has prolonged lifetime, suggesting a potential for developing
neuromorphic devices. Our results establish quasi-1D BaTiS3 as a model system to explore
and leverage emergent neuromorphic functionalities for next-generation electronic
applications.

5.2.1 Memristive switching by DC sweeps
In BaTiS3, the low-temperature structural transition (Transition I) exhibits an
exceptionally large hysteresis window of 40 K in the phase change loop, as shown in Figure

83
5.5. This suggests that the lattice dynamics are slow and there may be the existence of
metastable states, similar to the case in ultrathin 1T-TaS2[37,94]. The transition is unique
in that the electrical resistivity of BaTiS3 decreases abruptly upon cooling, unlike most
commonly observed resistive phase transitions. This is mainly due to the contribution of
Hall mobility, which is about one order of magnitude larger in the low-T phase, rather
than an increase in carrier concentration across the transition.
To demonstrate the memristive switching in BaTiS3, we first set the device to the
high-µ state at 175 K during warming cycle of the transport measurement. This
temperature is slightly below the transition temperature towards the CDW state (~ 185
K). DC current-voltage sweeps with sequentially increased voltages were then carried out
on a two-terminal device to set its conductance state, as illustrated in Figure 5.6a. Hysteric
I-V characteristics were observed for each sweep and various intermediate conductance
states were accessed before entering the final high resistance state. Another cycle of
sequential I-V scans with selected set voltages was performed after resetting the system
to its original low resistance state, achieving intermediate states similar to the first cycle,
Figure 5.5 (a) Illustration of representative temperature dependent resistance of BaTiS3 crystal
from 120 K to 200 K, showing the structural transition between the CDW state and the high-µ
state with exceptionally large thermal hysteresis window. The inset illustrates the CDW domain
formation in BaTiS3 with applied DC voltages. (b) Transport measurement of BaTiS3 resetting
process after the system is set to different intermediate states DC voltage sweeps or pulse.

84
as shown in Figure 5.6b. A small voltage (e.g. 100 mV) could be applied to read out the
conductance state after each setting process done by large DC voltage sweep. Figure 5.6c
and 5.6d plot the current-voltage and resistance-voltage characteristics of readout
processes after applying a series of setting voltage at a slightly higher temperature at 180
K. Different levels of conductance states could be achieved by tuning both the setting
voltages and operating temperatures, leading to a large number of states in a memory
device.
The resetting process of non-volatile resistive switching in BaTiS3 was realized by
cooling the entire system down to 100 K at a rate of 5 K/min and then warming it up to
the desired temperature, as shown in Figure 5.5b. However, this lengthy resetting
Figure 5.6 Non-volatile resistive switching in BaTiS3 by DC sweeps. (a) and (b) Setting processes
of conductance states by consequential DC sweeps with gradually increased set voltages. (c) and
(d) current-voltage and resistance-voltage characteristics of conductance state readout processes
performed at 100 mV.

85
procedure (~ 30 min total) utilizing purely thermal approaches is not practical for
multilevel memory applications, and alternative faster optical or electrical approaches
need to be developed. Another important aspect of resistive switching memories is the
number of distinguishable states, which is closely related to the physical properties of the
material. Phase change materials with first-order structural transitions have great
potential to achieve a large number of intermediate states due to the percolative nature
of the transitions. To demonstrate this behavior, sequential I-V sweeps were conducted
with the same set voltage, as illustrated in Figure 5.7b. More than 20 states were achieved,
and the modulation of conductance states appeared to be continuous. Figure 5.7a and the
dashed lines in Figure 5.7b represent the overall memristive switching region.

5.2.2 Pulsed I-V measurements and switching mechanism
Furthermore, to achieve a faster and more efficient control of memristive switching, a
pulsed voltage triggering experiment was conducted. Figure 5.8a illustrates the low-field
I-V scans obtained after applying various DC voltage pulses with a width of 1 ms to the
Figure 5.7 (a) Conductance state modulation with a large DC set voltage. The transition region is
highlighted by dashed lines (orange), where the current level is mostly maintained. (b) More than
20 intermediate states achieved by continuous I-V sweeps with the same set voltage.

86
device. As the voltage pulses are applied, the conductance state is gradually modulated,
although a larger amplitude of voltage is required to set the state compared to DC sweep.
This suggests that the non-volatile switching in BaTiS3 is not a pure electric field effect,
but instead, it can be largely controlled by Joule heating. To verify this assumption,
voltage pulses with larger amplitude but two orders smaller pulse width (10 µs) were
applied, which significantly reduces the total Joule heating effects. The BaTiS3 device’s
conductance state cannot be tuned with voltage pulses up to 8 V with the applied short
pulses, after which the contacts are easily damaged by such large voltages.

5.2.3 Lifetime of intermediate states
Additionally, time-dependent experiments on the intermediate states were carried out on
a BaTiS3 device with multi-terminal electrodes, where four-probe electrical resistance was
continuously monitored after the application of each voltage pulse with a width of 1 ms
at the outer leads, as illustrated in Figure 5.9. All intermediate states were maintained
Figure 5.8 (a) Readout processes after applying pulse voltages up to 2 V with 1 ms pulse width.
The sample conductance is modulated continuously. (b) Readout processes after applying pulse
voltages up to 8 V with 10 µs pulse width. No further tuning of the conductance state was observed
due to significantly reduced Joule heating.

87
for at least one hour, indicating a successful demonstration of non-volatile electrical
switching behavior in BaTiS3.

5.2.4 Conclusion
To summarize, we have demonstrated multi-level memristive switching in a phase change
semiconductor BaTiS3, driven by DC sweeps and pulses. The percolative nature of the
first order structural transition and large thermal hysteresis enabled the achievement of
more than 20 distinguishable states in the system. The switching mechanism is consistent
with a partial structural transition assisted by local Joule heating. Furthermore, each
intermediate state is maintained for a prolonged time. Our work on BaTiS3 opens new
opportunities in developing multilevel memories in phase change materials.

Figure 5.9 Time-dependent resistance level of BaTiS3 crystal. Pulses (width of 1 ms) with different
amplitudes of voltages were applied to drive the system into various intermediate states. Each state
is maintained for at least an hour.

88

Chapter 6 Flux growth of BaTiS
3
crystals
Ternary hexagonal chalcogenides, such as BaTiS3 and Sr1+xTiS3, are emerging small
bandgap semiconductors with strong in-plane optical anisotropy in the mid-wave and
long-wave infrared regions[57,58,61,140], making them promising candidates for
polarization-sensitive infrared optical elements and photodetection / imaging devices[141-
143]. To realize these practical applications, high-quality, large-sized single crystals with
well-defined anisotropic crystal orientations are required, as is the case for many other
optical crystals[144,145]. Furthermore, several important materials characterization
techniques used to probe the in-depth structural and electronic properties of these
materials, such as neutron scattering or diffraction, rely on large and thick single
crystals[20,146,147]; Surface-sensitive characterization techniques, such as angle-resolved
photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM), also
benefit from such type of crystals for the ease of mechanical cleavage to expose fresh
surfaces[67-70]. Despite the importance of these large, high-quality single crystals, to date,
the synthesis of BaTiS3 single crystals has only been achieved using the chemical vapor
transport method with iodine as the transport agent[57,60,148]. However, BaTiS3 crystals
grown by this method are typically thin needles or platelets with limited lateral dimensions
and thickness.
The high temperature solution or molten flux growth method is a powerful
technique for synthesizing large-sized crystals with lateral dimensions of several
millimeters or more, benefiting from a reduced number of nucleation sites and a controlled

89
slow cooling rate[73,75]. Although millimeter-sized single crystals of the isostructural
hexagonal chalcogenide BaVS3 have been synthesized using both tellurium[149] and
barium chloride fluxes[150], no successful attempt has been made towards the growth of
BaTiS3 crystals through the flux growth method. Here, we report the successful synthesis
of large-sized BaTiS3 single crystals using potassium iodide (KI) as a salt flux. X-ray
diffraction (XRD) analysis indicates a consistent room temperature structure of P63cm in
KI-grown crystals compared to those grown via chemical vapor transport[57]. The high
crystallinity of the flux-grown crystals is confirmed by atomically resolved imaging of
BaTiS3 from scanning transmission electron microscopy (STEM). Furthermore,
polarization-dependent Raman and infrared spectroscopy reveal the structural and optical
anisotropies of BaTiS3, respectively. Our study provides a feasible route for growing
BaTiS3 crystals via the flux growth method, enabling various advanced characterizations
that require large crystal sizes and facilitating the optical and optoelectronic applications
associated with its optical anisotropy.

6.1 Crystal growth and chemical analysis
Single crystals of BaTiS3 were grown via the molten KI flux method by slowly cooling the
flux with pre-synthesized polycrystalline powders (BaTiS3: KI atomic ratio ~ 1:100) in a
vertical geometry, as illustrated in Figure 6.1a. As-grown crystals were then extracted at
room temperature by washing away excess salt flux in water. The crystals obtained from
the flux growth were mostly thick needles with lengths of a few millimeters, and both
widths and thicknesses up to 500 µm, as depicted in Figure 6.1a. Additionally, thin needles

90
with widths of approximately 40 µm, similar to those obtained from chemical vapor
transport growth[57], were also observed.
The selection of KI salt as the flux material for crystal growth was based on several
important considerations. Firstly, its low melting temperature allows the flux to remain
liquid at temperatures above 700˚C, which enables the crystal growth to occur over a
wide range of temperatures. Secondly, compared to other commonly used salts such as
BaCl2[101,150], KI is less chemically aggressive and does not require the use of doubly
Figure 6.1 Single crystal growth of BaTiS3 using KI flux and chemical composition analysis. (a)
Schematic illustration of KI flux growth of BaTiS3 crystals using a vertical geometry. Optical image
of a representative flux grown BaTiS3 crystal (~ 6 mm long and half a millimeter in both width
and thickness) is displayed in the top right. (b) Perspective view of BaTiS3 crystal structure along
the c-axis. (c) EDS mapping of barium (red), titanium (yellow) and sulfur (purple) elements on a
thick BaTiS3 crystal (top left). (d) EDS spectrum of KI flux-grown BaTiS3 crystal, showing Ba to
Ti ratio as 1 : 1.02.

91
sealed quartz ampules or special crucible materials like alumina. This allows for the
utilization of a larger amount of flux salts to optimize growth conditions such as the
material-to-flux ratio. Finally, the high solubility of KI salt in water (~ 140 g KI / 100
mL water) facilitates the flux removal and crystal extraction steps, resulting in a cleaner
process with minimal crystal exposure time to water. Leaving BaTiS3 crystals in water
for a prolonged time, e.g., tens of minutes or longer, would lead to severe degradation
with crystal surfaces turning blue-like colors. Alternatively, methanol (12.5 g KI / 100
mL water) can also be used to wash off the residual KI flux to minimize the surface oxides
formation.
Energy dispersive X-ray spectroscopy (EDS) measurements were conducted on as-
grown BaTiS3 crystals for a quick assessment of their chemical composition. The mapping
results, as depicted in Figure 1d, indicate the presence of Ba, Ti, and S elements with
uniform distribution throughout the crystals. Figure 1c plots a representative spectrum
showing a Ba to Ti atomic ratio of 1 : 1.02. Importantly, no presence of K or I was
observed within the detection limit of EDS, which indicates that the use of KI as a salt
flux did not introduce a significant number of unintended elements in BaTiS3 crystals.
For a more accurate determination of the chemical composition, we carried out wavelength
dispersive X-ray spectroscopy (WDS) measurements. The analysis showed an average
composition of Ba : Ti : S = 1 : 1.01 : 2.83 for KI flux-grown BaTiS3. Hence, we conclude
that the KI flux growth method produces high-quality BaTiS3 crystals with a
stoichiometry close to 1 : 1 : 3.
Polycrystalline BaTiS3 powders were synthesized by first mixing a stoichiometric
amount of barium sulfide powder (Sigma-Aldrich, 99.9%), titanium powder (Alfa Aesar,
99.9%), with a 5% excess of sulfur (Sigma-Aldrich, 99.998%). The mixture was loaded
into a sealed, evacuated quartz ampule and heated to 1050˚C at a rate of 50˚C/h. The

92
ampule was cooked for 160 h and then quenched in NaCl/ice bath. The resulting material
was in the form of loosely packed black powder.
For single-crystal growth, 10 g pre-dried KI powder (Alfa Aesar, 99.9%) and 200
mg of BaTiS3 (BTS:KI atomic ratio ~ 1:100) were mixed with 10 mg excess S powder in
a N2-filled glovebox. The mixture was then placed in a quartz tube with 19 mm of outer
diameter, 2 mm of wall thickness, and approximately 8 cm in length. The ampule was
sealed under vacuum and placed in a quartz crucible in a box furnace (modified from a 6-
inch three zone tube furnace) with a vertical configuration as illustrated in Figure 6.1a.
The ampule was heated to 1040˚C in 20 hours and hold at 1040˚C for 30 hours, followed
by a slow cooling step to 700˚C at a cooling rate of 1˚C/h before a natural cooling down
process (Figure 6.1a). After approximately 20 days, the ampule was removed from the
furnace and washed with DI water or methanol to remove the remaining salt. Crystals
were picked individually after drying under an optical stereo microscope for further
characterizations.

6.2 X-ray diffraction and electron microscopy
The crystal structure of KI-grown BaTiS3 was analyzed using X-ray diffraction (XRD).
Figure 6.2 shows the precession maps projected onto the 0kl, h0l, and hk0 reciprocal
planes from single crystal XRD measurements. The space group was determined to be
P63cm, with lattice parameters a = b = 11.7 Å and c = 5.8 Å, which agrees with previous
reports on CVT-grown BaTiS3 crystals at room temperature[60]. The detailed
crystallographic data and atomic positions are available elsewhere. In addition, a thin film
out-of-plane XRD scan was performed on a BaTiS3 crystal with large lateral dimensions,

93
as illustrated in Figure 6.2b. A set of narrow 010-type reflections confirms that the crystal
top surface has [010] orientation with the c-axis lying in-plane.
To further assess the crystal quality of flux grown BaTiS3, scanning transmission
electron microscopy (STEM) studies were conducted. Atomically resolved high-angle
annular dark-field (HAADF) image of BaTiS3 along the c-axis and its corresponding fast
Fourier transform (FFT), as shown in Figure 6.3, clearly revealed the hexagonal
arrangement of the chains, consistent with our symmetry assignment from XRD analysis.

Figure 6.2 X-ray diffraction characterization. (a) - (c) Precession images from single-crystal X-ray
diffraction characterization of KI-grown BaTiS3 crystals along 0kl, h0l, and hk0 projections (from
left to right) at 300 K. (d) Out-of-plane X-ray diffraction scan of a thick BaTiS3 needle-like crystal
(~ 300 µm in width)

94
6.3 Structural and optical anisotropies
Polarization-resolved Raman spectroscopy is a powerful technique for characterizing the
anisotropic crystal structure[141,151], and therefore, Raman measurements were carried
out on BaTiS3 using a 532 nm laser as the excitation source. The incident light polarization
was varied from 0˚ to 360˚ by rotating a half-wave plate with a 10˚ step. Here, we
focused on the evolution of the A1 mode peak intensity, which has a well-documented
polarization dependence[57,61]. Figure 6.4 illustrates the polar plot of Raman spectra
intensity of the A1 mode, which shows a maximum intensity at close to 90˚ and a
maximum-to-minimum ratio of I(𝜃)
^_`
/I(𝜃)
^ab
= 2.97, consistent with previous reports
of CVT-grown BaTiS3[57,61].
The optical anisotropy of KI-grown BaTiS3 was studied using polarization-resolved
infrared spectroscopy, where reflectance and transmittance spectra were collected with
Figure 6.3 (a) and (b) Atomic-resolution HAADF-STEM image of a KI-grown BaTiS3 crystal
viewed along the [001] axis and the corresponding FFT pattern. (c) High magnification HAADF-
STEM image of BaTiS3 acquired from the region highlighted with yellow box in (a).

95
incident light polarized both parallel and perpendicular to the c-axis, as illustrated in
Figure 5a. For transmittance measurements, a freestanding thin platelet crystal (~20 µm
thick) was placed on a metal stencil pinhole, and the observed Fabry-Pérot fringes were
associated with the sample thickness. Two distinctive absorption edges at 0.25 eV and 0.8
eV were identified when the polarization was parallel and perpendicular to the c-axis,
which is consistent with previous observations of CVT-grown BaTiS3 crystals[57]. We
further analyzed the absorbance dispersion of BaTiS3 to reveal its broad window of
pronounced linear dichroism. The substantial difference in reflectance spectra and the
peak position shift of the fringes in the NIR regions signal that the KI-grown BaTiS3
crystal is highly birefringent.

6.4 Conclusions
In this work, high-quality, single crystals of optically anisotropic BaTiS3 were synthesized
using a KI flux method, resulting in crystal sizes that are orders larger than those grown
Figure 6.4 Vibrational anisotropy. Polar plot of the Raman spectra intensity of the A1 versus the
polarization angle at the 532 nm excitation. The red dots are the experimental data, while the blue
line represents the fitted curve.

96
using the CVT method. The structure of the flux-grown crystals was refined to P63cm at
room temperature and their high crystallinity was confirmed by XRD analysis and STEM
imaging. The pronounced structural and optical anisotropies of the KI-grown BaTiS3
crystals were further revealed by polarization-resolved Raman and infrared spectroscopy
measurements, which were comparable to those obtained for CVT-grown crystals. The
larger crystal sizes of the KI-grown BaTiS3 crystals allow for in-depth characterizations
of this material and its potential applications in optics and optoelectronics. Moreover, we
anticipate that the KI-based crystal growth method could be broadly applicable for
synthesizing other complex chalcogenide materials, such as Sr1+xTiS3, and may be
superior to using highly corrosive BaCl2. However, unintended potassium doping, or iodine
incorporation could be an issue in certain material systems and would require careful
chemical analysis to clarify.
Further advancements in the crystal synthesis of ternary chalcogenide materials,
such as BaTiS3, towards the growth of even larger crystals would enable more possibilities
in the field. Recently, thin film growth of BaTiS3 has been achieved using pulsed laser
deposition technique[152], but the limited choice of substrates and incompatibility
Figure 6.5 Optical anisotropy. (a) Infrared reflection and (b) transmission spectra of a KI-grown
BaTiS3 crystal with incident light polarized parallel and perpendicular to the c axis, respectively.

97
between chalcogenide films and complex oxide substrates have hindered further
improvement of film quality. For instance, the development of wafer-scale single crystals
of those materials, synthesized though either the Bridgeman method or top-seeded flux
growth, could lead to the growth of versatile epitaxial chalcogenide thin films, opening
the possibility of intriguing physical phenomena from heterogeneous integration or
superlattices of complex chalcogenides.

98

Chapter 7 Concluding remarks and
outlook
7.1 Concluding remarks
In conclusion, the focus of my doctoral research has been on the investigation of B phase
transitions in the semiconducting system BaTiS3. This material exhibits rich physics
associated with both electronic and lattice degrees of freedom at low temperatures, which
requires further in-depth studies in the future. My major contributions presented in this
thesis are as follows:
Firstly, I have developed a novel device fabrication method for multi-terminal
transport studies on small, bulk crystals. Importantly, the platform is not limited to
BaTiS3 and can be generally applied to handle other small-sized, bulk quantum materials,
even for those strain- or air-sensitive systems.
Secondly, I have discovered and studied two unique phase transitions in BaTiS3
using transport methods. These transitions have been leveraged to develop electronic
devices such as oscillators and multilevel memories.
Lastly, I have explored the single crystal growth of BaTiS3 using molten fluxes and
obtained high-quality large-sized crystals up to a few millimeters long and 500 µm in both
width and thickness. Such large crystals are required for advanced materials
characterization such as neutron-based measurements and STM.

99
In addition, the observation of phase transitions in BaTiS3 has also raised several
fundamental questions that require further investigation. For instance, there is a need to
explore the driving force behind these transitions and determine the nature of the
transitions. Moreover, it is essential to identify guidelines for searching similar novel
material systems that exhibit rich physics as well. Answering these questions would not
only deepen our fundamental understandings of BaTiS3 but also contribute to the broader
research in the field of quantum materials.

7.2 Outlook
BaTiS3 has emerged as an exceptional material platform to explore, as it is not only
scientifically interesting but also practically useful. As research into BaTiS3 continuous,
exciting physical properties keep showing up, including giant optical anisotropy, abnormal
thermal transport, phase transitions, and, more recently, the discovery of atomic-scale
polar textures in the system. Despite these discoveries, our understanding of these
phenomena is still in its early stages, and potential device applications require further
exploration. Honestly, I am not sure where it eventually goes, as our understanding of
this system is also evolving so fast. Here, I will just list a few promising directions to
explore following my work:
1. Strain modulation. The material system of BaTiS3 exhibits strong electron-
phonon coupling and is highly sensitive to external strain fields, making it an ideal
platform for studying strain modulation. By introducing uniaxial or biaxial strain fields,
we can study how these phase transitions respond to strain, which can vary due to the
distinctive origin of the transitions. Classic three-stack piezoelectric strain apparatus
designs can be used to introduce uniaxial strain up to 1%. In addition, inspired by the
polymeric embedding technique discussed in Chapter 3, one can introduce substantial

100
amounts of biaxial thermal strain at low temperatures by using epoxies with large thermal
expansion coefficients. For applying extreme strain levels above 5%, the only viable option
is strain fixation. One can potentially embed the thin cleaved BaTiS3 flake (tens of
nanometers or thinner) in a freestanding polyimide layer, and then mechanically stretch
it to achieve an extreme strain state before fixing the strain state using an adhesive.
2. Electrostatic gating. Electrostatic gating of BaTiS3 using either regular oxide
dielectric or ionic liquid is interesting as it provides practical routes towards gated devices,
which can add one more knob on controlling its electrical properties. There are even non-
negligible chances of introducing superconductivity at extreme gating levels, considering
the close relation between CDW state and superconductivity. Superconuctivitiy has
already been demonstrated in other archetypical CDW systems such as 1T-TaS2 and 1T-
TiSe2 using ionic liquid gating techniques. However, due to the non-exfoliable nature of
bulk BaTiS3, the device fabrication processes can be complicated, and effects of
electrostatic gating may not be as substantial.
3. Chemical doping / alloying. Chemical doping / alloying is critical in tuning the
carrier concentration, and hence, tuning the physical properties. Effects of chemical doping
/ alloying on optical anisotropy, tuning phase transitions, and thermoelectric properties
are of particular interest.
4. Heterogeneous integration. Heterogeneous integration of 2D materials on three-
dimensional quantum materials is rarely reported in the literature, which is mainly due
to the limited sample sizes of those small, non-exfoliable bulk crystals. However, with the
development of the crystal planarization method as presented in Chapter 3, heterogeneous
integration of van der Waals materials on BaTiS3 has become possible, which opens up
new opportunities for exploring rich physics and device applications. In section 3.3, we
have already shown the integration of transferred electrodes on BaTiS3 with conformal

101
contact as a demonstration. For instance, one can explore the integration of
superconducting NbSe2 to leverage the proximity effects. Additionally, MoS2/BaTiS3 or
black phosphorus/BaTiS3 heterostructures can be fabricated to improve the performance
of polarization-sensitive photo-detection.
5. High frequency transport measurements. In this thesis, I have mainly focused on
low-frequency AC transport or DC transport. High-frequency transport such as noise
spectra can be useful in study in-depth mechanism of CDW-sliding effects.

All in all, quasi-1D hexagonal chalcogenides, particularly BaTiS3 and its derivatives,
are and will continue to be at the frontier of cutting-edge cross-disciplinary research,
attracting considerable attention from various fields, including materials science,
condensed matter physics, optics and electrical engineering.

102
Bibliography
1 Peierls, R. & Peierls, R. E. Quantum theory of solids. (Oxford University Press,
1955).
2 Fröhlich, H. On the theory of superconductivity: The one-dimensional case.
Proceedings of the Royal Society of London. Series A. Mathematical and
Physical Sciences 223, 296-305 (1954).
3 Gruner, G. Density waves in solids. (CRC press, 2018).
4 Zhu, X., Guo, J., Zhang, J. & Plummer, E. Misconceptions associated with the
origin of charge density waves. Adv. Phys.: X 2, 622-640 (2017).
5 Grüner, G. The dynamics of charge-density waves. Rev. Mod. Phys. 60, 1129
(1988).
6 Chen, C.-W., Choe, J. & Morosan, E. Charge density waves in strongly
correlated electron systems. Rep. Prog. Phys. 79, 084505 (2016).
7 Woll Jr, E. & Kohn, W. Images of the fermi surface in phonon spectra of metals.
Phys. Rev. 126, 1693 (1962).
8 Zhu, X., Cao, Y., Zhang, J., Plummer, E. & Guo, J. Classification of charge
density waves based on their nature. Proc. Natl. Acad. Sci. 112, 2367-2371
(2015).
9 Morosan, E. et al. Superconductivity in CuxTiSe2. Nat. Phys. 2, 544-550 (2006).
10 Sipos, B. et al. From Mott state to superconductivity in 1T-TaS2. Nat. Mater. 7,
960-965 (2008).
11 Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys.
Rev. 108, 1175 (1957).
12 Kogar, A. et al. Observation of a charge density wave incommensuration near the
superconducting dome in CuxTiSe2. Phys. Rev. Lett. 118, 027002 (2017).

103
13 Naito, M. & Tanaka, S. Electrical transport properties in 2H-NbS2, -NbSe2, -TaS2
and -TaSe2. J. Phys. Soc. Jpn. 51, 219-227 (1982).
14 Thompson, A., Zettl, A. & Grüner, G. Charge-Density-Wave Transport in TaS3.
Phys. Rev. Lett. 47, 64 (1981).
15 Wang, Z. Z. et al. Charge density wave transport in (TaSe4)2I. Solid State
Commun. 46, 325-328 (1983).
16 Harper, J., Geballe, T. & DiSalvo, F. Thermal properties of layered transition-
metal dichalcogenides at charge-density-wave transitions. Phys. Rev. B 15, 2943
(1977).
17 Chaussy, J. et al. Phase transitions in NbSe3. Solid State Commun. 20, 759-763
(1976).
18 Di Salvo, F. J., Moncton, D. & Waszczak, J. Electronic properties and
superlattice formation in the semimetal TiSe2. Phys. Rev. B 14, 4321 (1976).
19 Tsutsumi, K. et al. Direct Electron-Diffraction Evidence of Charge-Density-Wave
Formation in NbSe3. Phys. Rev. Lett. 39, 1675 (1977).
20 Moncton, D., Axe, J. & DiSalvo, F. Study of superlattice formation in 2H-NbSe2
and 2H-TaSe2 by neutron scattering. Phys. Rev. Lett. 34, 734 (1975).
21 Sun, S. et al. Direct observation of an optically induced charge density wave
transition in 1T−TaSe2. Phys. Rev. B 92, 224303 (2015).
22 Sobota, J. A., He, Y. & Shen, Z.-X. Angle-resolved photoemission studies of
quantum materials. Rev. Mod. Phys. 93, 025006 (2021).
23 Damascelli, A., Hussain, Z. & Shen, Z.-X. Angle-resolved photoemission studies of
the cuprate superconductors. Rev. Mod. Phys. 75, 473 (2003).
24 Schmitt, F. et al. Transient electronic structure and melting of a charge density
wave in TbTe3. Science 321, 1649-1652 (2008).
25 Ryu, H. et al. Persistent charge-density-wave order in single-layer TaSe2. Nano
Lett. 18, 689-694 (2018).
26 Grimvall, G. The electron-phonon interaction in metals. (1981).

104
27 Carpinelli, J. M., Weitering, H. H., Plummer, E. W. & Stumpf, R. Direct
observation of a surface charge density wave. Nature 381, 398-400 (1996).
28 Wise, W. et al. Charge-density-wave origin of cuprate checkerboard visualized by
scanning tunnelling microscopy. Nat. Phys. 4, 696-699 (2008).
29 Kumakura, T., Tan, H., Handa, T., Morishita, M. & Fukuyama, H. Charge
density waves and superconductivity in 2H-TaSe2. Czech. J. Phys. 46, 2611-2612
(1996).
30 Xi, X. et al. Strongly enhanced charge-density-wave order in monolayer NbSe2.
Nat. Nanotechnol. 10, 765-769 (2015).
31 Goli, P., Khan, J., Wickramaratne, D., Lake, R. K. & Balandin, A. A. Charge
density waves in exfoliated films of van der Waals materials: evolution of Raman
spectrum in TiSe2. Nano Lett. 12, 5941-5945 (2012).
32 Zhou, X. et al. Origin of charge density wave in the kagome metal CsV3Sb5 as
revealed by optical spectroscopy. Phys. Rev. B 104, L041101 (2021).
33 Thorne, R. E. Charge-density-wave conductors. Phys. Today 49, 42-47 (1996).
34 Stojchevska, L. et al. Ultrafast switching to a stable hidden quantum state in an
electronic crystal. Science 344, 177-180 (2014).
35 Cercellier, H. et al. Evidence for an Excitonic Insulator Phase in 1T−TiSe2. Phys.
Rev. Lett. 99, 146403 (2007).
36 Kidd, T., Miller, T., Chou, M. & Chiang, T.-C. Electron-hole coupling and the
charge density wave transition in TiSe2. Phys. Rev. Lett. 88, 226402 (2002).
37 Yoshida, M., Suzuki, R., Zhang, Y., Nakano, M. & Iwasa, Y. Memristive phase
switching in two-dimensional 1T-TaS2 crystals. Sci. Adv. 1, e1500606 (2015).
38 Nakano, A. et al. Antiferroelectric distortion with anomalous phonon softening in
the excitonic insulator Ta2NiSe5. Phys. Rev. B 98, 045139 (2018).
39 Kitou, S. et al. Effect of Cu intercalation and pressure on excitonic interaction in
1T−TiSe2. Phys. Rev. B 99, 104109 (2019).

105
40 Lv, B. et al. Unconventional hysteretic transition in a charge density wave. Phys.
Rev. Lett. 128, 036401 (2022).
41 Blackburn, E. et al. Inelastic x-ray study of phonon broadening and charge-
density wave formation in ortho-II-ordered YBa 2Cu3O6.54. Phys. Rev. B 88,
054506 (2013).
42 Le Tacon, M. et al. Inelastic X-ray scattering in YBa2Cu3O6. 6 reveals giant
phonon anomalies and elastic central peak due to charge-density-wave formation.
Nat. Phys. 10, 52-58 (2014).
43 Kogar, A. et al. Signatures of exciton condensation in a transition metal
dichalcogenide. Science 358, 1314-1317 (2017).
44 Johannes, M. & Mazin, I. Fermi surface nesting and the origin of charge density
waves in metals. Phys. Rev. B 77, 165135 (2008).
45 Rossnagel, K. On the origin of charge-density waves in select layered transition-
metal dichalcogenides. J. Phys.: Condens. Matter 23, 213001 (2011).
46 Fujita, M., Goka, H., Yamada, K. & Matsuda, M. Competition between charge-
and spin-density-wave order and superconductivity in La1.875Ba0.125−xSrxCuO4.
Phys. Rev. Lett. 88, 167008 (2002).
47 Xu, Z. et al. Topical review: recent progress of charge density waves in 2D
transition metal dichalcogenide-based heterojunctions and their applications.
Nanotechnology 32, 492001 (2021).
48 Balandin, A. A., Zaitsev-Zotov, S. V. & Grüner, G. Charge-density-wave
quantum materials and devices—New developments and future prospects. Appl.
Phys. Lett. 119, 170401 (2021).
49 Marković, D., Mizrahi, A., Querlioz, D. & Grollier, J. Physics for neuromorphic
computing. Nat. Rev. Phys. 2, 499-510 (2020).
50 Hollander, M. J. et al. Electrically driven reversible insulator–metal phase
transition in 1T-TaS2. Nano Lett. 15, 1861-1866 (2015).
51 Vaskivskyi, I. et al. Fast electronic resistance switching involving hidden charge
density wave states. Nat. Commun. 7, 1-6 (2016).

106
52 Wen, W., Zhu, Y., Dang, C., Chen, W. & Xie, L. Raman spectroscopic and
dynamic electrical investigation of multi-state charge-wave-density phase
transitions in 1T-TaS2. Nano Lett. 19, 1805-1813 (2019).
53 Liu, G. et al. A charge-density-wave oscillator based on an integrated tantalum
disulfide–boron nitride–graphene device operating at room temperature. Nat.
Nanotechnol. 11, 845-850 (2016).
54 Zhu, C. et al. Light-tunable 1T-TaS2 charge-density-wave oscillators. ACS Nano
12, 11203-11210 (2018).
55 Liu, H. et al. A tantalum disulfide charge-density-wave stochastic artificial
neuron for emulating neural statistical properties. Nano Lett. 21, 3465-3472
(2021).
56 Patel, T. et al. Photocurrent imaging of multi-memristive charge density wave
switching in two-dimensional 1T-TaS2. Nano Lett. 20, 7200-7206 (2020).
57 Niu, S. et al. Giant optical anisotropy in a quasi-one-dimensional crystal. Nat.
Photonics 12, 392-396 (2018).
58 Niu, S. et al. Mid-wave and long-wave infrared linear dichroism in a hexagonal
perovskite chalcogenide. Chem. Mater. 30, 4897-4901 (2018).
59 Sun, Y.-Y., Agiorgousis, M. L., Zhang, P. & Zhang, S. Chalcogenide perovskites
for photovoltaics. Nano Lett. 15, 581-585 (2015).
60 Chen, H. et al. Unconventional charge-density-wave order in a dilute d-band
semiconductor. arXiv preprint arXiv:2207.11622 (2022).
61 Wu, J. et al. Linear Dichroism Conversion in Quasi-1D Perovskite Chalcogenide.
Adv. Mater. 31, 1902118 (2019).
62 Fagot, S., Foury-Leylekian, P., Ravy, S., Pouget, J. P. & Berger, H. One-
dimensional instability in BaVS3. Phys. Rev. Lett. 90, 196401,
doi:10.1103/PhysRevLett.90.196401 (2003).
63 Imai, H., Wada, H. & Shiga, M. Calorimetric Study on Metal-Insulator
Transition of Quasi-One-Dimensional BaVS3. J. Phys. Soc. Jpn. 65, 3460-3463
(1996).

107
64 Sun, B. et al. High frequency atomic tunneling yields ultralow and glass-like
thermal conductivity in chalcogenide single crystals. Nat. Commun. 11, 1-9
(2020).
65 Shi, D. et al. Low trap-state density and long carrier diffusion in organolead
trihalide perovskite single crystals. Science 347, 519-522 (2015).
66 Dong, Q. et al. Electron-hole diffusion lengths> 175 μm in solution-grown
CH3NH3PbI3 single crystals. Science 347, 967-970 (2015).
67 Chen, S.-D. et al. Incoherent strange metal sharply bounded by a critical doping
in Bi2212. Science 366, 1099-1102 (2019).
68 Kang, M. et al. Dirac fermions and flat bands in the ideal kagome metal FeSn.
Nat. Mater. 19, 163-169 (2020).
69 Rosenthal, E. P. et al. Visualization of electron nematicity and unidirectional
antiferroic fluctuations at high temperatures in NaFeAs. Nat. Phys. 10, 225-232
(2014).
70 Du, Z. et al. Imaging the energy gap modulations of the cuprate pair-density-
wave state. Nature 580, 65-70 (2020).
71 Binnewies, M., Glaum, R., Schmidt, M. & Schmidt, P. in Chemical Vapor
Transport Reactions (de Gruyter, 2012).
72 Schmidt, P., Binnewies, M., Glaum, R. & Schmidt, M. Chemical vapor transport
reactions–methods, materials, modeling. (InTech Rijeka, 2013).
73 Canfield, P. C. & Fisk, Z. Growth of single crystals from metallic fluxes. Philos.
Mag. B 65, 1117-1123 (1992).
74 Kanatzidis, M. G., Pöttgen, R. & Jeitschko, W. The metal flux: a preparative
tool for the exploration of intermetallic compounds. Angew. Chem. Int. Ed. 44,
6996-7023 (2005).
75 Klepov, V. V., Juillerat, C. A., Pace, K. A., Morrison, G. & Zur Loye, H.-C.
“Soft” alkali bromide and iodide fluxes for crystal growth. Front. Chem. 8, 518
(2020).

108
76 Pritula, I. & Sangwal, K. in Handbook of crystal growth 1185-1227 (Elsevier,
2015).
77 Hasegawa, K. Introduction to single crystal X-ray analysis. The Rigaku Journal
28, 14-18 (2012).
78 Williams, D. B., Carter, C. B., Williams, D. B. & Carter, C. B. The transmission
electron microscope. (Springer, 1996).
79 Schroder, D. K. Semiconductor material and device characterization. (John
Wiley & Sons, 2015).
80 Borup, K. A., Fischer, K. F., Brown, D. R., Snyder, G. J. & Iversen, B. B.
Measuring anisotropic resistivity of single crystals using the van der Pauw
technique. Phys. Rev. B 92, 045210 (2015).
81 Chang, C.-Z. et al. Experimental observation of the quantum anomalous Hall
effect in a magnetic topological insulator. Science 340, 167-170 (2013).
82 Shekhar, C. et al. Extremely large magnetoresistance and ultrahigh mobility in
the topological Weyl semimetal candidate NbP. Nat. Phys. 11, 645-649 (2015).
83 Deng, Y. et al. Quantum anomalous Hall effect in intrinsic magnetic topological
insulator MnBi2Te4. Science 367, 895-900 (2020).
84 Ortiz, B. R. et al. CsV3Sb5: A Z2 topological kagome metal with a
superconducting ground state. Phys. Rev. Lett. 125, 247002 (2020).
85 Xu, S.-Y. et al. Spontaneous gyrotropic electronic order in a transition-metal
dichalcogenide. Nature 578, 545-549 (2020).
86 Ji, Z. et al. Photocurrent detection of the orbital angular momentum of light.
Science 368, 763-767 (2020).
87 Rees, D. et al. Helicity-dependent photocurrents in the chiral Weyl semimetal
RhSi. Sci. Adv. 6, eaba0509 (2020).
88 Beenakker, C. & van Houten, H. in Solid State Phys. Vol. 44 1-228 (Elsevier,
1991).

109
89 Eber, G., Von Klitzing, K., Ploog, K. & Weinmann, G. Two-dimensional
magneto-quantum transport on GaAs-AlxGa1-xAs heterostructures under non-
ohmic conditions. J. Phys. C: Solid State Phys. 16, 5441 (1983).
90 Laird, E. A. et al. Quantum transport in carbon nanotubes. Rev. Mod. Phys. 87,
703 (2015).
91 Zhang, Y., Tan, Y.-W., Stormer, H. L. & Kim, P. Experimental observation of
the quantum Hall effect and Berry's phase in graphene. Nature 438, 201-204
(2005).
92 Amet, F. et al. Supercurrent in the quantum Hall regime. Science 352, 966-969
(2016).
93 Cui, X. et al. Multi-terminal transport measurements of MoS2 using a van der
Waals heterostructure device platform. Nat. Nanotechnol. 10, 534-540 (2015).
94 Tsen, A. W. et al. Structure and control of charge density waves in two-
dimensional 1T-TaS2. Proc. Natl. Acad. Sci. 112, 15054-15059 (2015).
95 Noguchi, R. et al. A weak topological insulator state in quasi-one-dimensional
bismuth iodide. Nature 566, 518-522 (2019).
96 Liang, T. et al. Ultrahigh mobility and giant magnetoresistance in the Dirac
semimetal Cd3As2. Nat. Mater. 14, 280-284 (2015).
97 Li, Q. et al. Chiral magnetic effect in ZrTe5. Nat. Phys. 12, 550-554 (2016).
98 Gooth, J. et al. Axionic charge-density wave in the Weyl semimetal (TaSe4)2I.
Nature 575, 315-319 (2019).
99 Ong, N. P. & Brill, J. Conductivity anisotropy and transverse magnetoresistance
of NbSe3. Phys. Rev. B 18, 5265 (1978).
100 Chu, J.-H. et al. In-plane resistivity anisotropy in an underdoped iron arsenide
superconductor. Science 329, 824-826 (2010).
101 Niu, S. et al. Crystal growth and structural analysis of perovskite chalcogenide
BaZrS3 and Ruddlesden–Popper phase Ba3Zr2S7. J. Mater. Res. 34, 3819-3826
(2019).

110
102 Liu, F., Navaraj, W. T., Yogeswaran, N., Gregory, D. H. & Dahiya, R. van der
Waals contact engineering of graphene field-effect transistors for large-area
flexible electronics. ACS Nano 13, 3257-3268 (2019).
103 Pease, D. C. & Baker, R. F. Sectioning techniques for electron microscopy using
a conventional microtome. Proceedings of the Society for Experimental Biology
and Medicine 67, 470-474 (1948).
104 Richardson, K., Jarett, L. & Finke, E. Embedding in epoxy resins for ultrathin
sectioning in electron microscopy. Stain Technol. 35, 313-323 (1960).
105 Park, W., Sarrao, J., Thompson, J. & Greene, L. Andreev reflection in heavy-
fermion superconductors and order parameter symmetry in CeCoIn5. Phys. Rev.
Lett. 100, 177001 (2008).
106 Kang, D. et al. Printed assemblies of GaAs photoelectrodes with decoupled
optical and reactive interfaces for unassisted solar water splitting. Nat. Energy 2,
doi:10.1038/nenergy.2017.43 (2017).
107 Lüpke, F. et al. Proximity-induced superconducting gap in the quantum spin Hall
edge state of monolayer WTe2. Nat. Phys. 16, 526-530 (2020).
108 Cao, Y. et al. Unconventional superconductivity in magic-angle graphene
superlattices. Nature 556, 43-50 (2018).
109 Hao, Z. et al. Electric field–tunable superconductivity in alternating-twist magic-
angle trilayer graphene. Science 371, 1133-1138 (2021).
110 Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle
graphene superlattices. Nature 556, 80-84 (2018).
111 Huang, X. et al. Correlated insulating states at fractional fillings of the
WS2/WSe2 moiré lattice. Nat. Phys. 17, 715-719 (2021).
112 Liu, Y. et al. Approaching the Schottky–Mott limit in van der Waals metal–
semiconductor junctions. Nature 557, 696-700 (2018).
113 Wang, Y. et al. Probing photoelectrical transport in lead halide perovskites with
van der Waals contacts. Nat. Nanotechnol. 15, 768-775 (2020).

111
114 Rossnagel, K., Kipp, L. & Skibowski, M. Charge-density-wave phase transition in
1T−TiSe2: Excitonic insulator versus band-type Jahn-Teller mechanism. Phys.
Rev. B 65, 235101 (2002).
115 Rosevear, W. & Paul, W. Hall Effect in VO2 near the Semiconductor-to-Metal
Transition. Phys. Rev. B 7, 2109 (1973).
116 Inada, R., Ōnuki, Y. & Tanuma, S. Hall effect of 1T-TaS2 and 1T-TaSe2. Physica
B+ C 99, 188-192 (1980).
117 Lee, H., McKinzie, H., Tannhauser, D. & Wold, A. The low-temperature
transport properties of NbSe2. J. Appl. Phys. 40, 602-604 (1969).
118 Hodeau, J. et al. Charge-density waves in NbSe3 at 145K: Crystal structures, X-
ray and electron diffraction studies. J. Phys. C: Solid State Phys. 11, 4117
(1978).
119 Inami, T. et al. Symmetry breaking in the metal-insulator transition of BaVS3.
Phys. Rev. B 66, 073108 (2002).
120 Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for
metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6,
15-50 (1996).
121 Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).
122 Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation
made simple. Phys. Rev. Lett. 77, 3865 (1996).
123 Montgomery, H. Method for measuring electrical resistivity of anisotropic
materials. J. Appl. Phys. 42, 2971-2975 (1971).
124 Smontara, A., Tkalčec, I., Bilušić, A., Budimir, M. & Berger, H. Anisotropy of
the thermal conductivity in (TaSe4)2I. Physica B Condens. Matter 316, 279-282
(2002).
125 Devreese, J. T. in Encyclopedia of applied physics: vol. 14 383 (1996).
126 Alexandrov, A. S. & Devreese, J. T. Advances in polaron physics. Vol. 159
(Springer, 2010).

112
127 Iadonisi, G. Electron-phonon interaction: Effects on the excitation spectrum of
solids. La Rivista del Nuovo Cimento (1978-1999) 7, 1-116 (1984).
128 Ceperley, D. M. & Alder, B. J. Ground state of the electron gas by a stochastic
method. Phys. Rev. Lett. 45, 566 (1980).
129 Neupert, T., Denner, M. M., Yin, J.-X., Thomale, R. & Hasan, M. Z. Charge
order and superconductivity in kagome materials. Nat. Phys., 1-7 (2021).
130 Stefanovich, G., Pergament, A. & Stefanovich, D. Electrical switching and Mott
transition in VO2. J. Phys.: Condens. Matter 12, 8837 (2000).
131 Kim, H. T. et al. Electrical oscillations induced by the metal-insulator transition
in VO2. J. Appl. Phys. 107, 023702 (2010).
132 Sakai, J. High-efficiency voltage oscillation in VO2 planer-type junctions with
infinite negative differential resistance. J. Appl. Phys. 103, 103708 (2008).
133 Geremew, A. K. et al. Bias-voltage driven switching of the charge-density-wave
and normal metallic phases in 1T-TaS2 thin-film devices. ACS Nano 13, 7231-
7240 (2019).
134 Mohammadzadeh, A. et al. Evidence for a thermally driven charge-density-wave
transition in 1T-TaS2 thin-film devices: Prospects for GHz switching speed. Appl.
Phys. Lett. 118, 093102 (2021).
135 Zimmers, A. et al. Role of thermal heating on the voltage induced insulator-metal
transition in VO2. Phys. Rev. Lett. 110, 056601 (2013).
136 Zhao, B. & Ravichandran, J. Low-power microwave relaxation oscillators based
on phase-change oxides for neuromorphic computing. Physical Review Applied
11, 014020 (2019).
137 Seo, G. et al. Experimental investigation of dimension effect on electrical
oscillation in planar device based on VO2 thin film. Thin Solid Films 519, 3383-
3387 (2011).
138 Taketa, Y., Kato, F., Nitta, M. & Haradome, M. New oscillation phenomena in
VO2 crystals. Appl. Phys. Lett. 27, 212-214 (1975).

113
139 Mian, M. S., Okimura, K. & Sakai, J. Self-oscillation up to 9 MHz based on
voltage triggered switching in VO2/TiN point contact junctions. J. Appl. Phys.
117, 215305 (2015).
140 Mei, H. et al. Colossal optical anisotropy from atomic-scale modulations. arXiv
preprint arXiv:2303.00041 (2023).
141 Huang, S. et al. In-plane optical anisotropy of layered gallium telluride. ACS
Nano 10, 8964-8972 (2016).
142 Ermolaev, G. et al. Giant optical anisotropy in transition metal dichalcogenides
for next-generation photonics. Nat. Commun. 12, 854 (2021).
143 Tong, L. et al. Stable mid-infrared polarization imaging based on quasi-2D
tellurium at room temperature. Nat. Commun. 11, 2308 (2020).
144 Li, C. et al. Controlled growth of layered acentric CdTeMoO6 single crystals with
linear and nonlinear optical properties. Crystal Growth & Design 18, 3376-3384
(2018).
145 Zhang, W. et al. LiNa5Mo9O30: Crystal growth, linear, and nonlinear optical
properties. Chem. Mater. 28, 4483-4491 (2016).
146 Lovesey, S. W. Theory of neutron scattering from condensed matter. (1984).
147 Goldman, A. et al. Lattice and magnetic instabilities in CaFe2As2: A single-
crystal neutron diffraction study. Phys. Rev. B 78, 100506 (2008).
148 Zhao, B. et al. Orientation-Controlled Anisotropy in Single Crystals of Quasi-1D
BaTiS3. Chem. Mater. 34, 5680-5689 (2022).
149 Kuriyaki, H. et al. Synthesis and characterization of BaVS3 single crystals grown
in melted Te. Synth. Met. 71, 2049-2050 (1995).
150 Gardner, R., Vlasse, M. & Wold, A. Preparation, properties and crystal structure
of barium vanadium sulfide, BaVS3. Acta Crystallographica Section B: Structural
Crystallography and Crystal Chemistry 25, 781-787 (1969).
151 Mao, N. et al. Optical anisotropy of black phosphorus in the visible regime.
Journal of the American Chemical Society 138, 300-305 (2016).

114
152 Surendran, M. et al. Quasi-epitaxial growth of BaTiS3 films. J. Mater. Res. 37,
3481-3490 (2022).

Abstract (if available)

Abstract Materials with strong electron-lattice coupling, such as complex oxides and low-dimensional metals, often exhibit unique phenomena including phase transitions and charge ordering, distinguishing them from most of the well-known semiconducting compounds. Charge density wave (CDW) is a periodic modulation of electron density with the underlying lattice distortion, and it has been extensively studied over the past few decades, mainly in metallic model systems such as quasi-1D metals, doped cuprates, transition metal dichalcogenides, and more recently, in Kagome lattice materials. However, CDW in semiconducting systems is rare. In this thesis, I studied the electronic transport properties of BaTiS3, a small bandgap semiconductor, in the form of bulk single crystals. Two phase transitions are observed at low temperatures. It is shown experimentally that CDW charge ordering emerges in BaTiS3 below ~240 K from a high temperature semiconducting phase (Transition II, 240-260 K), which survives till ~150 K and is suppressed by a structural transition (Transition I, 150-190 K) upon further cooling, with the system switching to a more conductive state. Moreover, novel electronic functionalities such as reversible resistive switching, voltage oscillations and memristive switching have been experimentally realized in BaTiS3. These studies establish quasi-1D hexagonal chalcogenides such as BaTiS3 as a new model platform to explore rich electronic phases, phase transitions and electronic functionalities associated with CDW in dilute filling.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Tailoring asymmetry in light-matter interaction with atomic-scale lattice modulations

PDF

Phase change heterostructures for electronic and photonic applications

PDF

Perovskite chalcogenides: emerging semiconductors for visible to infrared optoelectronics

PDF

Expanding the synthesis space of 3D nano- and micro-architected lattice materials

PDF

Thermoelectric and transport studies of low dimensional materials & hot electron-driven photocatalysis on plasmon-resonant grating nanostructures

PDF

In-situ characterization of nanoscale opto-electronic devices through optical spectroscopy and electron microscopy

PDF

Materials development and characterization of optically-active core-shell nanomaterials

PDF

Nonlinear optical nanomaterials in integrated photonic devices

PDF

Plasma emission across metal nanoparticle surfaces and semiconductor -liquid interface characterizations

PDF

Optoelectronic, thermoelectric, and photocatalytic properties of low dimensional materials

PDF

Corrosion studies of engineered interfaces

PDF

Large-scale molecular dynamics simulations of nano-structured materials

PDF

Surface acoustic wave waveguides for signal processing at radio frequencies

PDF

Atomistic modeling of the mechanical properties of metallic glasses, nanoglasses, and their composites

PDF

Tailoring compositional and microstructural complexity in nanostructured alloys

PDF

Enhanced photocatalysis on titanium oxide passivated III-V semiconductors

PDF

Integration of cost effective luminescent materials into organic light emitting diodes (OLEDs) and molecular approaches to improve the device efficiency

PDF

Integrated photonics assisted electron emission devices

PDF

Efficient yellow and green emitting InGaN/GaN nanostructured QW materials and LEDs

PDF

RF and mm-wave blocker-tolerant reconfigurable receiver front-ends

Asset Metadata

Creator Chen, Huandong (author)

Core Title Transport studies of phase transitions in a quasi-1D hexagonal chalcogenide

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Materials Science

Degree Conferral Date 2023-05

Publication Date 04/13/2024

Defense Date 01/26/2023

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag BaTiS3,electrical transport,hexagonal chalcogenide,OAI-PMH Harvest,phase transitions

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ravichandran, Jayakanth (committee chair), Branicio, Paulo (committee member), Wu, Wei (committee member)

Creator Email huandonc@usc.edu,shiyayewu@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113015391

Unique identifier UC113015391

Identifier etd-ChenHuando-11627.pdf (filename)

Legacy Identifier etd-ChenHuando-11627

Document Type Dissertation

Format theses (aat)

Rights Chen, Huandong

Internet Media Type application/pdf

Type texts

Source 20230414-usctheses-batch-1022 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu