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Non-adiabatic molecular dynamic simulations of charge carrier dynamics in two-dimentional transition metal dichalcogenides

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Non-adiabatic molecular dynamic simulations of charge carrier dynamics in two-dimentional transition metal dichalcogenides

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NON-ADIABATIC MOLECULAR DYNAMIC SIMULATIONS OF
CHARGE CARRIER DYNAMICS IN TWO-DIMENTIONAL TRANSITION
METAL DICHALCOGENIDES
by
Linqiu Li

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
(CHEMISTRY)

May 2020

ii
Acknowledgements
First of all, I would like to thank Professor Oleg V. Prezhdo, my advisor, who has contributed
greatly to my research work. It was a great honor to work with him. I really appreciate his advice
and support, especially his big scope of research projects, which always lead me to the right
direction. Also, I would like to thank him for recommending me for those great internship
opportunities at Gilead Science, Los Alamos National Lab and Lawrence Livermore National Lab.
I also thank all the members in Oleg’s group, Professor Alexey V. Akimov, Professor Run Long,
Professor Linjun Wang, Professor Joanna Jankowska, Dr. Weibin Chu, Dr. Yi-siang Wang, Dr.
Jin Liu, Dr. Andrew Sifain, Dr. Parmeet Kaur Nijiar, Dr. Chuanjia Tong for their help throughout
the projects, as well as others for stimulating discussions not only about science but also life in the
U.S. Besides, I am grateful to my internship mentors, Dr. Yu Zhang and Dr. Xiaohua Zhang.
Without their patient guidance and help, I would not be able to finish my internship projects.
I also thank our collaborators on the transition metal dichalcogenides project, Professor Priya
Vashishta, Professor Rajiv Kalia, Professor Aiichiro Nakano for valuable discussions, Subodh C.
Tiwari, Kuang Liu for technical supports, and Dr. Ming-Fu Lin for pushing me to come up with
novel ideas and to build better models.
I thank my friends, Shuming Hao, Wei Jiang, Fang Fu for their company and support during 5.5
years of my Ph.D. research. Last but most importantly, I would like to thank my parents in China
for always respecting my decisions and making it all possible.

iii
Contents
Acknowledgements ii
List of Tables v
List of Figures vi
Abstract ix
Chapter 1: Introduction and Methods ........................................................................................ 1
1.1 Properties of Transition Metal Dichalcogenides ................................................................................. 1
1.2 Methods of Non-adiabatic Molecular Dynamics ................................................................................ 3
1.2.1 Real-Time Time-Dependent Density Functional Theory ............................................................................ 3
1.2.2 Fewest Switch Surface Hopping .................................................................................................................. 5
1.2.3 Decoherence Induced Surface Hopping ...................................................................................................... 6
1.2.4 Global Flux Surface Hopping ...................................................................................................................... 7
Chapter 2: Charge Separation and Recombination in Two- Dimensional MoS2/WS2
Heterojunction ............................................................................................................................. 10
2.1 Introduction ....................................................................................................................................... 10
2.2 Simulation Details ............................................................................................................................. 12
2.3 Results and Discussion ..................................................................................................................... 13
2.3.1 Electronic Structure of the MoS2/WS2 Heterostructure ............................................................................ 13
2.3.2 Electron-Phonon Interactions ................................................................................................................... 15
2.3.3 Charge Separation ..................................................................................................................................... 18
2.3.4 Electron-Hole Recombination .................................................................................................................. 20
2.4 Conclusion ........................................................................................................................................ 21
Chapter 3 Sulfur Adatom and Vacancy Accelerate Charge Recombination in MoS2, but by
Different Mechanisms ................................................................................................................. 23
3.1 Introduction ....................................................................................................................................... 23
3.2 Simulation Details ............................................................................................................................. 24
3.3 Results and Discussion ..................................................................................................................... 25
3.4 Conclusion ........................................................................................................................................ 33
Chapter 4 Why CVD grown MoS2 samples outperform PVD samples ................................. 35
4.1 Introduction ....................................................................................................................................... 35
4.2 Simulation Details ............................................................................................................................. 36
4.3 Results and Discussion ..................................................................................................................... 37
4.4 Conclusion ........................................................................................................................................ 47
Chapter 5 Phonon-Suppressed Auger Scattering of Charge Carriers in Defective Two-
Dimensional Transition Metal Dichalcogenides ....................................................................... 49
iv
5.1 Introductions ..................................................................................................................................... 49
5.2 Experimental Results ........................................................................................................................ 52
5.3 Theoretical Results ............................................................................................................................ 56
5.3.1 Simulation Details .................................................................................................................................... 56
5.3.2 Results and Discussion ............................................................................................................................. 59
5.4 Conclusion ........................................................................................................................................ 67

References .......................................……………………………………………...…..................69

v
List of Tables
2.1 Coherence time, non-adiabatic coupling, and timescales for hole transfer, electron
transfer and electron-hole recombination in MoS2/WS2 heterojunction ....................................... 17
3.1 Non-adiabatic coupling and coherence time for charge carriers trapping and
recombination dynamics in perfect and defective MoS2 monolayers. .......................................... 31
4.1 Non-adiabatic coupling for the charge carriers trapping and recombination dynamics
in CVD and PVD grown MoS2 samples. ...................................................................................... 44
4.2 Coherence times for the charge carriers trapping and recombination dynamics in CVD
and PVD grown MoS2 samples. .................................................................................................... 45
5.1 Non-adiabatic coupling (NAC) for charge carriers trapping and recombination
processes in perfect and defect MoTe2 bilayers. ........................................................................... 63
vi
List of Figures
2.1 Schematic views of the MoS2/WS2 heterojunction and its electronic energy levels
involved in charge carrier dynamics ............................................................................................. 11
2.2 Partial density of states of the MoS2 and WS2 monolayers and charge densities of the
key states in the MoS2/WS2 heterostructure ................................................................................. 14
2.3 Un-normalized autocorrelation functions, dephasing functions and influence spectra
for hole transfer and electron transfer ........................................................................................... 16
2.4 Hole and electron dynamics following photo-excitation. Hole transfer takes 61 fs.
Electron transfer is an order of magnitude longer ........................................................................ 19
2.5 Population of the excited state, pure-dephasing function and phonon influence
spectrum of electron-hole recombination dynamics ..................................................................... 20
3.1 Electronic energy levels involved in the charge carriers trapping and relaxation
dynamics ....................................................................................................................................... 25
3.2 Side and top views of the perfect MoS2 monolayer, MoS2 monolayer with an S adatom
(Ad_S), and MoS2 monolayer with an S vacancy (V_S). Defects are highlighted with red
arrows and red circles ................................................................................................................... 26
3.3 Density of states and charge densities of perfect MoS2 monolayer, Ad_S and V_S.
Inserts show charge densities of the defect states ......................................................................... 27
3.4 Charge carriers trapping and recombination dynamics in perfect MoS2 monolayer,
Ad_S and V_S. ............................................................................................................................. 29
3.5 Phonon modes involved in the charge carrier dynamics in perfect MoS2 monolayer,
Ad_S and V_S. The peak height is characterizes the strength of electron-phonon coupling.
vii
The adatom allows many phonon modes to couple to the charge carriers, accelerating the
recombination ............................................................................................................................... 32
4.1 Electronic energy levels involved in charge carriers trapping and relaxation. Defects
create electron and hole trap within the band gap ......................................................................... 38
4.2 Side and top views of the perfect MoS2 monolayer, MoS2 monolayer with one Mo
replacing one S atom (MoS), MoS2 monolayer with one Mo replacing two S atoms (MoS2).
MoS2 monolayer with one S vacancy (VS), MoS2 monolayer with two S vacancies on the
opposite sides (VS2_opp), and MoS2 monolayer with two S vacancies on the same side
(VS2_same). Defects are highlighted with red arrows and red circles .............................................. 39
4.3 Density of states of perfect MoS2 monolayer, MoS, MoS2, VS, VS2_opp, and VS2_same.
The vertical black dashed lines represent the Fermi energy ......................................................... 40
4.4 Charge densities of perfect MoS2 monolayer, MoS, MoS2, VS, VS2_opp and VS2_same.
The antisite defects create localized hole and electron trap states. The vacancy defects are
less localized ................................................................................................................................. 42
4.5 Charge carriers trapping and recombination dynamics in perfect MoS2 monolayer,
MoS, MoS2, VS, VS2_opp and VS2_same. Shown are time-dependent populations of the ground
state and three types of trap states, involving either electron, or hole, or both electron and
hole trapping. When multiple hole or electron traps are present, their populations are
summed up for clarity. .................................................................................................................. 43
5.1 Schematics of charge carrier energy loss to phonons in a pristine TMD crystal and a
defective TMD crystal with trap levels residing inside the band gap ........................................... 50
viii
5.2 Optical pump and THz probe measurements of ~9 nm thick 2H-phase MoTe2. The
THz probe beam is normal incident to the sample surface and the transmitted THz field
is measured by the electro-optic sampling method ....................................................................... 53
5.3 Structures and density of states of pristine MoTe2 bilayer with calculated band gap of
0.95 eV between valence band maximum (VBM) and conduction band minimum (CBM),
MoTe2 bilayer with one Te vacancy (VTe). The vacancy is denoted with a red circle ................. 60
5.4 Simulations of phonon-induced charge carrier recombination and trapping dynamics
in pristine MoTe2 bilayer and MoTe2 bilayer with tellurium vacancy, VTe .................................. 62
5.5 Simulations of electron trapping in the MoTe2 bilayer with the tellurium vacancy ............... 64
5.6 Density of states of defective MoTe2 bilayer with two adjacent Te vacancies. Many
trap states appear near band edges, facilitating fast phonon-trapping and further
suppressing Auger trapping. ......................................................................................................... 65

ix
Abstract
The thesis consists of three parts. The first part focuses on the non-adiabatic molecular dynamic
(NAMD) simulations of the MoS2/WS2 heterojunction. The second part is on the defect
engineering of the charge carrier dynamics in two-dimensional transition metal dichalcogenides
(TMDs). The third part is about the Auger process in TMDs.
Our motivation for studying NAMD in TMDs arises from the powerful potentials of TMDs.
After the success of graphene, TMDs have been extensively studied due to their tunable band gaps,
good catalytic performance and great potentials in photovoltaic devices. Despite promising
potentials for applications in electronics and optoelectronics, however, TMDs are still limited by
their low electrical mobility, short-lived free charge carrier and low photoluminescence quantum
efficiency. Deterioration of the radiative quantum efficiency and charge carrier lifetime is
attributed to charge scattering, that is, electron-phonon coupling. NAMD is a good way to measure
electron-phonon coupled dynamics. NAMD simulations could provide theoretical insights into the
diverse charge carrier dynamics in TMDs and generate guidelines to improve the performance of
TMDs based materials. Chapter 1 discusses general properties of TMDs and mathematical
foundations of NAMD simulations.
Through coupling different two-dimensional TMDs together, heterostructure with improved
electronic and optical properties can be achieved, which becomes the basis of modern devices.
Experiments detected an ultrafast charge separation and a long-lived charge separated state in the
MoS2/WS2 heterojunction. These phenomena are rather surprising. Because the interlayer
interaction between MoS2 and WS2 layers is weak. And electron and hole in this heterojunction is
located closely. In Chapter 2, we present the time-domain ab initio study of charge carrier
dynamics in the MoS2/WS2 heterojunction. We found that the ultrafast charge transfer results from
x
significant delocalization of the photoexcited state between the donor and acceptor materials. The
electron-hole recombination is slow because the initial and final states are localized strongly within
different materials.
Chapter 3 discusses the effects of two defects, that is, adatom and vacancy, on charge carrier
dynamics in MoS2 monolayer. We found that adatom could greatly accelerate electron-hole
recombination, compared with vacancy. This is because adatom could strongly perturb the TMDs
layer, break its symmetry and allow more phonon modes to couple to the electronic subsystem. In
contrast, vacancy accelerates charge recombination through traditional defects assisted trapping
and recombination, which results from delocalized electron traps. As a result, to make high-
performance TMDs based devices, adatom should be strongly avoided. Chapter 4 talks about two
kinds of defects due to different manufacturing methods. Chemical vapor deposition (CVD)
samples maintain a high concentration of vacancy defects while physical vapor deposition (PVD)
samples mainly contain antisite defects. Our simulations show that antisites are much more
detrimental than vacancies. Antisites create deep traps for both electrons and holes. Those electron
and hole trap pairs are close to the Fermi energy, allowing fast trapping by thermal activation from
the ground state and strongly contributing to charge scattering. Antisites also strongly perturb
band-edge states, creating significant overlap with the trap states. In comparison, vacancy defects
overlap much less with the band-edge states and only accelerate charge recombination by less than
a factor of 2. Our simulations demonstrate a general principle that missing atoms are significantly
more benign than misplaced atoms and rationalize general experimental observations that CVD
samples outperform PVD samples.
Chapter 5 explores the diverse roles played by phonons and Auger processes in TMDs. High
carrier concentration and long lifetimes is a must to produce high-performance devices. However,
xi
high concentrations usually accelerate energy exchange between charge carriers through Auger-
type processes, especially in TMDs where many-body interactions are strong. As a result, Auger-
process dominate high carrier density region. Surprisingly, experiments detect non-pure Auger
type dynamics. Our simulations show that phonon-driven trapping competes successfully with the
Auger process, given the common existence of point defects. Defects create shallow traps close to
band edges, and phonons accommodate efficiently the electronic energy during the trapping.
Besides, trap states localize around defects, decreasing the overlap of trapped and free carriers and
carrier-carrier interactions. At low carrier densities, phonons provide the main charge loss
mechanism. At high carrier densities, phonons suppress Auger processes and lower the
dependence of the trapping rate on carrier density.
1
Chapter 1: Introduction and Methods
1.1 Properties of Transition Metal Dichalcogenides
After the success of graphene, other two-dimensional materials like transition metal
dichalcogenides (TMDs) have appeared on the horizon of materials science and solid-state physics
due to their superior properties and diverse applications.
1-8
TMDs have the general formula MX2,
where M = Mo, W and X= S, Se. About 40 different TMDs have been synthesized so far, though
only some of them are two-dimensional layered solids.
9-10
To be qualified as a layered TMD, the
metal atoms have to be sandwiched between two hexagonally ordered planes of chalcogen atoms.
In layered TMDs, in-plane atoms are covalently bonded. TMDs layers are stacked together through
weak out-of-plane van der Waals interactions. Going from the bulk crystal to the single-layer limit,
TMDs properties change substantially. The bandgaps of most layered TMDs undergo direct to
indirect transitions, resulting in a higher photoluminescence efficiency.
10-11
Monolayer TMDs are
reported to be marginally stronger than the bulk crystal.
12
TMDs based devices outperform other
three-dimensional materials in electronic and transistor applications.
6, 13-15

Owing to their excellent optical and electric properties, TMDs are promising building blocks
for a new generation of electronic and optoelectronic materials. Numerous experiments have been
carried out to make high-performance TMDs based applications. The electronic transport of MoS2
field-effect transistors shows a steeper subthreshold swing and a higher on/off ratio.
15
TMDs lead
to flexible electronics with much better transport properties, compared to other materials such as
organic semiconductors.
16
TMDs based electron- and photocatalysts have demonstrated promising
results for the hydrogen evolution reactions.
7, 17
TMDs based piezoelectric, optoelectronic, and
spintronic devices also exhibit great potentials.
8, 18-19

2
Despite those great potentials, however, practical performance of TMDs based devices are much
lower than the theoretical potentials. For example, the charge carrier mobilities of chemical vapor
deposition (CVD), physical vapor deposition (PVD) and mechanically exfoliated (ME) grown
TMDs samples are measured to be 45 cm
2
V
-1
s
-1
, < 1 cm
2
V
-1
s
-1
and 81 cm
2
V
-1
s
-1
respectively,
whereas the theoretical value is reported to be 410 cm
2
V
-1
s
-1
.
20
Various approaches are developed
to tackle this problem. The first approach is to couple different TMDs layers together to make
heterostructures with improved electronic and optical properties. Both MoS2/WS2 and
MoS2/MoSe2 heterostructures maintain a long-lived charge separation, compared with pure TMDs
layers.
21-22
The second approach is to apply defect engineering. TMDs performance depend
strongly on its quality and morphology. Various defects and impurities are present in the material.
Through exploring the role of different defects, various manufacturing procedures are proposed to
get rid of detrimental defects. Doping, annealing and coating are demonstrated to be efficient ways
to improve TMDs performance.
23-26
The last approach is to create high carrier concentrations to
provide sufficient free charge carriers. However, high concentrations always accelerate energy
exchange between charged particles via Auger-type process, lowering TMDs performance in the
end.
27-28
In this case, charge carrier concentration needs to be skillfully adjusted in a range, where
the concentration is high enough to provide free charge carriers but not too high to promote Auger
process.
Theoretical study could provide more insights into the extensive experimental efforts. The true
two-dimensional nature put tangent equipment requirements in measuring behaviors, properties
and dynamics of TMDs. Ab initio simulations, on the other hand, provides an easy to study TMDs.
Because TMDs applications mostly relate to carrier dynamics, non-adiabatic molecular dynamic
(NAMD) simulation is required to model TMDs behaviors. Note that there exist a large amount of
3
ambiguities and controversies in TMDs studies. For example, it was believed that chalcogen
vacancy is the intrinsic point defect in TMDs.
29
Until recently it is shown that oxygen substituting
chalcogen is the most abundant point defect in CVD grown samples.
23
And chalcogen vacancies,
which are absent in as-grown samples, can be created by high-temperature annealing under
vacuum.
23
Meanwhile, exciton dynamics dominate TMDs dynamics, rather than the free electron-
hole-pair recombination.
30
I have to admit that this thesis bases on previous experimental results.
But it does not mean this thesis is useless. Rather, this thesis initializes the theoretical studies of
TMDs and provides useful and necessary insights for researchers to dive deeper into TMDs studies.
1.2 Methods of Non-adiabatic Molecular Dynamics
1.2.1 Real-Time Time-Dependent Density Functional Theory
The time-dependent (TD) Schrodinger equation is expressed as:

𝑖ħ
𝜕
𝜕𝑡
𝛹
'
(𝐫,𝑡) =𝐻(𝐫,𝐑,𝑡)𝛹
'
(𝐫,𝑡)
( 1.1 )

where 𝐫 and 𝐑 are the coordinates of n electrons and N nuclei, respectively. The Hamiltonian,
𝐻(𝐫,𝐑,𝑡), depends on the total electron density, its gradient, etc. It is time dependent due to the
external potential created by nuclear motions. The time-dependent Kohn-Sham (KS) orbitals,
𝛹
'
(𝐫,𝑡), are described by the linear combinations of adiabatic KS orbitals, 𝛷
0
(𝐫,𝐑,(𝑡)), which
are calculated as eigenstates of the KS Hamiltonian for the current atomic positions R. Atomic
positions R are obtained from the molecular simulations (MD).

𝛹
'
(𝐫,𝑡) =1 𝐶
'0
(𝑡)
0
𝛷
0
3𝐫,𝐑,(𝑡)4 ( 2.2 )

Here 𝐶
'0
(𝑡) represents vibrational levels which are associated with the electronic states.
4
The dynamics of nuclear wavepackets associated with different electronic states can be obtained
through the combination of eq 1.1 and eq 1.2:

𝑖ħ
𝜕
𝜕𝑡
𝐶
5
(𝑡)=1 𝐶
0
(𝑡)3𝜀
0
𝛿
50
+𝑑
50
4
0
( 3.3 )

where 𝜀
0
is the energy of the adiabatic state 𝑘. 𝑑
50
is the NA coupling between adiabatic states k
and j. It arises from the nuclear motion R and is calculated numerically as the overlap between
wave functions k and j at sequential time steps

𝑑
50
=−𝑖ħ< 𝛷
5
= ∇
𝑹
= 𝛷
0
@∙
𝑑𝑹
𝑑𝑡
=−𝑖ħB𝛷
5
C
𝜕
𝜕𝑡
C𝛷
0
D
( 4.4 )

One thing to note here is that nuclear degrees of freedom are treated classically. That is,
𝛷
0
(𝐫,𝐑,(𝑡)) indicates functional dependence of the electronic wave functions 𝛷
0
on the
electronic coordinates, r, but is parametric dependent on the nuclear coordinates, R. This
simplification gets rid of the strong back-reaction of the electronic degrees of freedom on the
nuclear motions. It is valid in condensed matter systems, because variations in the nuclear
geometry for different electronic states are much smaller than the thermal fluctuations of atoms.
As a result, back-reaction is negligible. This is also known as classical path approximation (CPA).
CPA greatly reduces computational costs, and is the only way to study electron-nuclear dynamics
in sufficiently large systems like TMDs.
The result of solving eq 1.3 gives us electron population change. The electron density, 𝜌(𝐫,𝑡), is
expressed as a sum of the densities of the single-electron KS orbitals, 𝛹
'
(𝐫,𝑡), occupied by 𝑁
G

electrons.

𝜌(𝐫,𝑡) = 1 |𝛹
'
(𝐫,𝑡)|
I
J
K
'LM

( 5.5 )

5
1.2.2 Fewest Switch Surface Hopping
Rewriting eq 1.3 in the equivalent density matrix notation gives us:

𝑖ħ𝐴
̇ 50
=1 P𝐴
Q0
R𝜀
5Q
−𝑖ℏ𝑹𝑑
5Q
T−𝐴
5Q
[𝜀
Q0
−𝑖ℏ𝑹𝑑
Q0
]W
Q
( 6.6 )

where 𝐴
50
=𝑐
5
𝑐
0
∗
. 𝑑
05
∗
=−𝑑
50
because basis functions 𝛷
5
are orthonormal. The probability of
transition between adiabatic states j and k during time interval 𝑑𝑡 is defined in the fewest switch
surface hopping (FSSH) approach through the wave function expansion coefficients and coupling
as:

d𝐏
50
=
−2Re(𝐴
50
∗
𝑑
50
𝑹)
̇ 𝐴
50
𝑑𝑡
( 7.7 )

FSSH minimizes the number of switches and maintains the correct statistical distribution of
state populations at all times.
31-32
Transitions between states take place in the form of “hops”. A
uniform random number 𝜉 between 0 and 1 is generated. 𝐏
50
is set to be zero if 𝐏
50
is negative. A
state switch will be invoked if 𝐏
50
is greater than the random number 𝜉. Meanwhile, if at the
current atomic positions R where potential energy surface (PES) is different between states j and
k, a velocity adjustment is made to conserve total energy. Instead of using velocity adjustment, in
this thesis we use Boltzmann factor to rescale the transition probabilities.

𝐏
50
`
=𝐏
50
𝑏
50

( 8.8 )

𝑏
50
=b
𝑒𝑥𝑝f−
𝜀
0
−𝜀
5
𝑘
g
𝑇
i 𝜀
0
>𝜀
5
1 𝜀
0
<𝜀
5

( 9.9 )

Elimination of velocity rescaling provides computational advantage over initial velocity rescaling.
The former is a single number and can be easily computed along the MD trajectory. The latter
requires a large number of electronic structure calculations.
6
The transition probabilities are computed on the fly for the current nuclear configuration.
Electron population is propagated along the classical MD nuclear configurations. This procedure
is repeated until certain criterion is appropriate. The sequence is then repeated for as many
independent trajectories as needed to obtain statistically significant results. Note here electronic
density matrix elements 𝐴
50
are integrated continuously, without resetting, irrespective of state
switches. Therefore electronic quantum coherence are maintained. Correction is required to get rid
of this artificial quantum coherence, which is discussed in the following section.
1.2.3 Decoherence Induced Surface Hopping
Coherence problem arises due to classical nuclear MD trajectories. Using MD trajectories, we
collapse nuclear wavefunctions into points, thus neglecting the influence of nuclear functions on
electronic dynamics. Decoherence induced surface hopping (DISH) is a technique to reproduce
quantum mechanical effects. DISH is developed upon the concept that decoherence provides the
physical mechanisms for the hops.
33
Because electron-hole recombination needs long time-scale,
where quantum decoherence tends to take place. We usually use DISH to investigate electron-hole
recombination process. Given the energies of states j and k as functions of time from MD
trajectories, we compute fluctuation of their difference:

𝛿𝜖
50
=∆𝜀
50
(𝑡)−〈∆𝜀
50
(𝑡)〉 ( 10.10 )

where <> denotes time-averaging and 𝜀
q5
(𝑡)=𝜀
q5
(𝑡)−𝜀
5
(𝑡). The unnormalized autocorrelation
function (AF) of the energy difference fluctuation could be used to compute the decoherence time.

𝐶
50
(𝑡)= 〈∆𝜀
50
(𝑡′)∆𝜀
50
(𝑡−𝑡′)〉
s`
( 11.11 )

𝐷
50
(𝑡) =𝑒𝑥𝑝u−
1
ℏ
I
v 𝑑𝑡′
s
w
v 𝑑𝑡′′𝐶
50
(𝑡′′)
s`
w
x
( 12.12 )

7
The decoherence rate 𝑟
50
could be obtained through Gaussian fit of D(t). And the decoherence time
𝜏
5
for state j is defined as:

𝛿
1
𝜏
5
= 1 |𝑐
0
(𝑡)|
I
𝑟
50
'
0LM
5{0

( 13.13 )

At each decoherence event, the wave function propagates according to one of two projections.
With the probability of = 𝑐
5
(𝑡)=
I
, wave function collapses to state j. Or the state is projected out by
setting 𝑐
5
=0. Then we renormalize the resulting wavefunctions. The trajectory mush hop to a
new state if the wave function collapses to state j, and state j is different from current state. If state
j is projected out while the current nuclear trajectory was associated with this state, the trajectory
must hop to a state i≠j, with the probability given by |𝑐
q
(𝑡)|
I

Fourier transform of the normalized AF gives the phonon influence spectrum, known as phonon
spectral density. Phonon spectral density depicts phonon modes which contribute to the electronic
state switches.

𝛿𝐼(𝑤)=
1
√2𝜋
v 𝑑𝑡𝑒
qs
𝐶(𝑡)

I

( 14.14 )

1.2.4 Global Flux Surface Hopping
Global flux surface hopping (GFSH) maintains FSSH features like minimization of hops, internal
consistency and detailed balance, but also captures the superexchange mechanism between
particles.
34
Superexchange is a type of dynamical processes, where electronic states are coupled
indirectly through intermediate high energy states. Hopping to the intermediate virtual states
generates a higher energy barrier, thus is classically forbidden in the standard FSSH.
GFSH is similar to FSSH, except for surface hopping probabilities. GFSH hopping probabilities
are set according to the global flux of population change, rather than the state-to-state flux change.
8
Eq 1.7 shows that the FSSH hopping probability between states j and k depends explicitly on the
coupling between these states. GFSH, on the other hand, examines the population change of all
quantum states. GFSH classifies states into two subgroups: group A with reduced population and
the other group B with increased population. Conservation of the total population of all states is
always valid, thus, the gross population decrease in group A equals to the total population increase
in group B. As a result, the surface hopping probability from j in group A to any state k in group
B should be proportional to the population increase of state k. Besides, this increase could come
from all possible states in group A, in which the contribution from state j depends on the ratio of
its population decrease with respect to the total population reduction in group A. Therefore, the
surface hopping probabilities in GFSH is expressed as:

𝑔
50
=
∆𝐴
00
𝐴
55
∆𝐴
55
∑ ∆𝐴
qq q∈

( 15.15 )

All other types of state switches, for example, switches between states within the same group or
from group B to A, are not allowed to happen.
When considering only two quantum states, GFSH is identical to FSSH. For system with more
than two quantum states, according to eq 1.7, we have 𝐏
50
=−𝐏
05
and 𝐏
55
=0. When 𝑗 ≠𝑘,
either 𝑔
50
or 𝑔
55
is positive and the other one is zero. For any state j, we classify all other states
into two subgroups: one with 𝑔
50
>0 as group A, and the other one with 𝑔
50Lw
as group B. In
group A, surface hopping happens from j to other states, and the total fraction of trajectories to
hop out from state j is:

1 𝑔
50
=−1 𝑑𝑡𝑃
50
0∈ 0∈
( 16.16 )

It is opposite to state in group B, where state switches from other states to j. The total fraction of
trajectories hopping into state j is:
9

1 𝑔
05
= 1 𝑑𝑡𝑃
50
0∈g 0∈g
( 17.17 )

Therefore, the net change in probability to state on surface j is

1 𝑑𝑡𝑃
50
0∈g
−−1 𝑑𝑡𝑃
50
0∈
= 1 𝑑𝑡𝑃
50
0

( 18.18 )

According to eq 1.7, this change in the fraction of trajectories is equal to the population change of
FSSH. This phenomenon holds for all quantum states, and thus, GFSH is valid.
In GFSH, there exists only one channel to change the fraction of trajectories in state j from group
A to states in group B. The total fraction change is:

1 𝑔
50
𝐴
55
0∈g
= 1
∆𝐴
00
∆𝐴
55
∑ ∆𝐴
qq q∈
0∈g

( 19.19 )

Because the total population is always conserved, the total population reduction is the same as the
total population increase, that is,

1 ∆𝐴
55
=−1 ∆𝐴
00
0∈ 5∈g
( 20.20 )

The total fraction of trajectories to hop out of state j becomes:

1 𝑔
50
𝐴
55
=−∆𝐴
55
0∈g
( 21.21 )

which equals the inverse number of population change based on the Schrodinger equation.
Similarly, the total fraction of trajectories from all possible states in group A to state k is:

1 𝑔
50
𝐴
55
=1
∆𝐴
55
∆𝐴
00
(∑ ∆𝐴
qq q∈
)
=∆𝐴
00
5∈ 5∈

( 22.21 )

which is also consistent with the population change of state k according to the Schrodinger
equation. GFSH could properly deal with particle-particle interactions, which play a big role in
Auger process. Therefore, GFSH outperforms FSSH in simulating Auger affected dynamics.
34-35

10
Chapter 2: Charge Separation and Recombination in Two-
Dimensional MoS2/WS2 Heterojunction
2.1 Introduction
Isolated transition metal dichalcogenides (TMDs), which are already remarkably complex, can
stack in sequence to make even more complex heterostructures. Numerous experiments have been
carried out to investigate the properties of TMD heterostructures and, in particular, MoS2/WS2. Ab
initio analysis shows that the MoS2/WS2 bilayer is a direct bandgap semiconductor with the type-
II band alignment, in which the valence band maximum (VBM) and the conduction band minimum
(CBM) reside in different monolayers, Figure 2.1. The VBM and CBM offsets between the
materials are 0.39 eV and 0.35 eV, respectively.
36
The MoS2/WS2 bandgap is 1.097 eV,
37
which
is significantly smaller than the bandgap of the individual monolayers.
In recent experiments, Hong et al. investigated the dynamics of hole transfer in MoS2/WS2
heterostructures using femtosecond pump-probe spectroscopy.
21
They reported that hole transfer
from the MoS2 layer to the WS2 layer takes less than 50 fs after photoexcitation. Other experiments
showed sub-picosecond hole and electron transfer in MoS2/MoSe2
22
and an extremely long
timescale for electron-hole recombination in MoSe2/WSe2 heterostructures, ranging from 240 ps
22
to 1.8 ns.
38
Theoretical studies of the photo-induced charge separation and recombination
dynamics in layered TDM heterostructures lag behind the extensive experimental efforts. A
microscopic understanding of the dynamic processes is desired, in particular, in order to establish
the mechanisms of the ultra-fast sub-100 fs charge transfer, occurring despite the weak van der
Waals coupling between the layers, and the extremely long-lived charge separation, observed
despite the low dielectric screening of Coulomb interactions and close proximity of the charges.
11

Figure 2.1: (a) Electronic energy levels involved in the photo-induced charge transfer and
non-radiative charge recombination at the MoS2/WS2 interface. Absorption of a photon, hv,
by either MoS2 or WS2 leads to ① hole transfer or ② electron transfer. Following the charge
transfer, electron and hole can recombine at the interface ③. (b) Top and (c) side views of
the MoS2/WS2 heterostructure. Mo is purple. W is grey. S is yellow.

Here, we model the photo-induced charge separation and recombination dynamics at the
MoS2/WS2 bilayer heterojunction at the ab initio, atomistic level of detail and explicitly in the
time-domain, directly mimicking the time-resolved optical experiments. We analyse the
MoS2/WS2 electronic structure, nuclear dynamics, elastic and inelastic electron-phonon
interactions, charge separation and charge recombination. The charge transfer mechanisms are
analysed by considering the effects of electronic and electron-phonon coupling, acceptor state
density, and quantum coherence.
12
2.2 Simulation Details
The electronic structure and adiabatic MD trajectories were computed with the Quantum Espresso
program
39
using a converged plane-wave basis set. The generalized gradient approximation of
Perdew, Burke and Ernzerhof (PBE),
40
and projector-augmented wave (PAW)
41
pseudopotentials
were used. The van der Waals interaction was described by the semi-empirical potential introduced
by Grimme’s in the DFT-D2 method.
42
The approach gives a good description of the electronic
structure and intermolecular interactions of the van der Waals heterojunction. While more
advanced electronic structure methodologies, such as hybrid and screened-hybrid DFT functionals
and GW theory, can provide a more accurate description of the electronic properties of the system
under investigation,
36, 43
they are significantly more computationally demanding and cannot be
combined with NAMD that requires thousands of electronic structure calculations. A vacuum layer
of 9 Å was placed in the direction perpendicular to the bilayer, Figure 2.1, in order to avoid
spurious interactions between adjacent images. The calculations were performed with the
12×12×1 k-point mesh. The structure was fully relaxed until the calculated Hellmann-Feynman
force was smaller than 0.05 eV/Å. The system was then heated to 300 K through repeated velocity
rescaling. A 6 ps adiabatic MD trajectory with a 1 fs atomic time-step was produced and used to
perform the NAMD simulations with the Pyxaid package.
44-45
100 initial conditions were sampled
randomly from the first 1 ps of the 6 ps trajectory, and NAMD simulations were performed starting
from each initial condition and using 1000 random number sequences to sample the surface
hopping probabilities.
13
2.3 Results and Discussion
Our work is motivated by the recent experiment,
21
showing that hole transfer at the MoS2/WS2
interface takes less than 50 fs. This was surprising, because the donor-acceptor interaction between
the layers is weak, and because the driving force, given by the energy offset between the VBMs
of MoS2 and WS2, is small according to the calculations.
36
The mechanism for the ultrafast charge
transfer was unclear. Our work is also closely related to the pump-probe experiments showing sub-
picosecond hole and electron transfer in MoS2/MoSe2,
22
and long 1.8 ns timescale for electron-
hole recombination in MoSe2/WSe2.
38

The processes under investigation are depicted on the energy level diagram shown in Figure
2.1a. Excitation of MoS2 induces hole transfer from MoS2 to WS2, ①. Excitation of WS2 leads to
electron transfer from WS2 to MoS2, ②. After the charge separation, the electron and hole can
recombine at the interface, ③. The top and side views of the MoS2/WS2 simulation cell are shown
in Figures 2.1b and 2.1c, respectively. The transition metal atoms of one layer are on the top of the
chalcogen atoms of the other layer, which is consistent with the earlier theoretical studies.
36, 46

2.3.1 Electronic Structure of the MoS2/WS2 Heterostructure
Figure 2.2a shows the projected density of states (PDOS) of the MoS2/WS2 heterostructure at 300
K. The contribution of the MoS2 and WS2 monolayers are given by the black and red lines. The
PDOS demonstrates that MoS2/WS2 is a type-II heterojunction, which is consistent with the
experimental result.
21
The lowest excited state is formed at the interface when the electron is
localized at the MoS2 CBM and the hole is localized at the WS2 VBM. The canonically averaged
VBM and CBM band offsets are 0.39 eV and 0.42 eV, respectively, indicating that about 0.4 eV
of energy is lost to vibrational motions during the charge transfer events.
14

Figure 2.2. (a) Partial density of states (PDOS) of the MoS2 and WS2 monolayers in the
MoS2/WS2 heterostructure at 300K. The donor-acceptor band edge energy offsets determine
the driving force for the charge separation and recombination. (b) Charge densities (red) of
the key states at the MoS2/WS2 junction: 1. Valence band maximum (VBM) of MoS2. 2. VBM
of WS2. 3. Conduction band minimum (CBM) of MoS2. 4. CBM of WS2. The electron and
hole donor orbitals are delocalized between MoS2 and WS2. Mo is purple. W is grey. S is
yellow.

To elucidate the origin of the fast charge separation dynamics, charge distributions of the donor
and acceptor states in the MoS2/WS2 bilayer are shown in Figure 2.2b. The arrows connecting top
and bottom panels relate the charge distributions with the state energies. The donor orbitals
involved in the separation dynamics are delocalized between the MoS2 and WS2 monolayers. The
delocalization can be considered surprising, since the layers are coupled only weakly by a van der
Waals interaction. The delocalization of the photo-excited donor state into the acceptor can be
rationalized by the fact that the acceptor has a significantly higher DOS than the donor, and even
the weak coupling is sufficient to produce the effect. The delocalization of the photo-excited state
15
onto the charge acceptor material indicates that a fraction of the charge is transferred during the
excitation process. Note that the initial state of the hole, state 1 in Figure 2.2b, contains density on
the sulfur of both bilayers pointing towards each other. In contrast, the initial state of the electron,
state 4, has no density between the bilayers. As a result, the interlayer coupling is stronger for hole
than electron transfer.
The final states of the charge separation processes, states 2 and 3 in Figure 2.2b, are localized
strictly within a single material. This is expected since the complementary materials have no states
at these energies. States 2 and 3 are the initial states of the recombining hole and electron. Since
these states exhibit no appreciable overlap, the donor-acceptor interaction leading to the electron-
hole recombination is weak, and the recombination is slow.
2.3.2 Electron-Phonon Interactions
The charge separation and recombination processes are governed by both electronic interactions
between the donor and acceptor states, and electron-phonon interactions. The latter are particularly
important for the recombination process. The photo-induced electron and hole transfer at the
MoS2/WS2 interface lead to losses of about 0.4 eV of electronic energy into heat. The earliest
stages of the transfer occur iso-energetically, because both materials have states at the initial
energy. However, it is energy relaxation into phonons that prevents back-transfer of the charges
and allows for a long-lived charge separation. The non-radiative electron-hole recombination
occurs across a 1 eV energy gap. This energy is deposited into multiple phonon quanta.
Both elastic and inelastic electron-phonon interactions contribute to the photo-induced charge
transfer dynamics at the MoS2/WS2 interface. Elastic interactions randomize phases of electronic
wave-function phase, resulting in loss of quantum coherence. Loss of coherence is key for the slow
electron-hole recombination process. The quantum Zeno effect presents the extreme example of
16
how quantum coherence loss decreases a transition rate.
47
Inelastic electron-phonon scattering is
responsible for losses of electronic energy to heat. It takes place during both charge separation and
recombination.

Figure 2.3. Un-normalized autocorrelation functions (top panels), dephasing functions
(middle panels) and influence spectra (bottom panels) for (a) hole transfer and (b) electron
transfer. The dephasing functions are fitted by eq 7, giving time constants 29.1 fs for hole
transfer and 10.0 fs for electron transfer. Both hole and electron transfer couple primarily
to the optical phonon mode near 400 cm
-1
, characteristic of the out of plane A1g motion of
MoS2 and WS2.

We estimate the timescale of elastic electron-phonon scattering using the optical response theory
formalism, by computing the pure-dephasing time
48
for pairs of initial and final states for each
process under consideration, Figure 2.1. The pure-dephasing functions, D(t), shown in Figure 2.3,
demonstrate that coherence is lost faster during electron than hole transfer. Generally, one can
attribute fast decoherence to either a rapid loss of correlation in the oscillation of the relevant
energy gap, or a large oscillation magnitude.
49
Both factors are reflected in the unnormalized
autocorrelation functions (ACFs), Cun(t), also shown in Figure 2.3. Both ACFs decay on similar
Electron Hole
17
timescales; however, the initial ACF magnitude is significantly larger for the electron ACF, 0.0037
eV
2
, than the hole ACF, 0.0015 eV
2
. The initial magnitude equals to the canonically averaged
squared gap, and characterizes the gap fluctuation. Thus, it is the larger charge-phonon coupling
and rapid ACF decay, typically associated with involvement of a broader range of phonon modes,
that makes decoherence faster for the electron transfer.
The pure-dephasing functions were fitted by a combination of a Gaussian and an exponent.
48

𝑓(𝑡) =𝐵𝑒𝑥𝑝f−
𝑡
𝜏
G
i +(1−𝐵)exp −
1
2
u
𝑡
𝜏

x
I

1+𝐴𝑐𝑜𝑠(𝜔𝑡)
1+𝐴

(2.1 )

In eq 2.1, B is the magnitude of exponential decay, while 1-B represents the magnitude of the
Gaussian component. The normalized cosine term accounts for oscillations which correspond to
the vibrational modes observed in the phonon spectral density, Figure 2.3. The pure-dephasing
time constant is defined as the weighted average 𝜏=B𝜏
G
+(1-B) 𝜏

. The fitting results are presented
in Table 2.1.
Table 2.1. Pure-dephasing (decoherence) time, average absolute value of non-adiabatic
coupling (NAC), and timescales for hole transfer, electron transfer and electron-hole
recombination

Hole transfer Electron transfer Electron-hole recombination
Dephasing time (fs) 29.1 10.0 27.2
NAC (meV) 9.17 1.64 0.17
Transfer time (ps) 0.061 0.747 2,200

Table 2.1 also presents the canonically averaged absolute values of the NA coupling for the
charge separation and recombination processes. Charge separation involves transitions between
multiple states within the conduction and valence band manifolds, and the reported values are
averaged over the transitions encountered during the NAMD simulations. The NA electron-
phonon coupling is five times larger for the hole than electron transfer, and is an order of magnitude
smaller for the recombination than separation. These results are consistent with the state densities
18
depicted in Figure 2.2. For instance, there is practically no overlap between states 2 and 3,
explaining why the NA coupling value for the recombination is so small, 0.17 meV.
Fourier transforms (FT) of ACFs, or similarly, of the corresponding energy gaps, characterize
the phonon modes that couple to the electronic subsystem. The resulting spectrum is known as the
influence spectrum, or spectral density. The ACF FTs are presented in the bottom panels of Figure
2.3. Both hole transfer and electron transfer couple primarily to phonons near 400 cm
-1
. This
frequency corresponds to the out-of-plane A1g modes of MoS2 (404.1 cm
-1
) and WS2 (420.4 cm
-
1
).
50-51
The involvement of the out-of-plane mode in the interfacial charge transfer dynamics is
reasonable. By modulating the interlayer distance, the out-of-plane motion influences the
electronic state energies and NA coupling, affects electron and hole transfer. A weak participation
of low frequency modes, below 100 cm
-1
, is seen for both electrons and holes. The relative
contribution of the low frequency modes is greater for the holes, rationalizing why the hole ACF
decays slightly faster, Figure 2.3.
2.3.3 Charge Separation
Figure 2.4 characterizes the photo-induced charge separation processes that result from photo-
excitation of either MoS2 or WS2, Figure 2.1. The curves show an initial Gaussian decay that
rapidly turns into exponential dynamics. The amplitude of the Gaussian component is small.
Therefore, we fit the curves of Figure 2.4 using a exponent rather than a more complicated equation,
such as eq 2.1. The 61 fs hole transfer time agrees well with the experimental data, indicating a 50
fs transfer time.
21
Recall that, according to our simulations, a fraction of the hole is transferred
from WS2 to MoS2 already during the photo-excitation process. In experiment, the photo-
excitation timescale is given by the width of the laser pulse, which was 250 fs in the experiment.
21

19
The sub-picosecond electron transfer agrees with the experimental and theoretical work on the
closely related MoSe2/MoS2 system.
22, 52

Figure 2.4. (a) Hole and (b) electron dynamics following photo-excitation. Hole transfer takes
61 fs, in agreement with the experiment.
21
Electron transfer is an order of magnitude longer,
due to weaker NA coupling, shorter coherence time, Table 2.1, and lower acceptor state
density, Figure 2.2. Note that a fraction of electron or hole is transferred already during the
photo-excitation, since the donor states are delocalized between the two materials, Figure 2.2.

Several factors rationalize why the hole transfer is faster than the electron transfer. First, the
donor-acceptor interaction is stronger for the hole transfer. The photo-generated hole has density
extending into the interlayer space, state 1 in Figure 2.2. This is not the case for the photo-generated
electron, state 4 in Figure 2.2. Second, the NA coupling is stronger for the hole transfer, Table 2.1.
Third, quantum coherence is longer lived. Finally, the acceptor state density is higher for the hole.
20
Consider the peak in the WS2 DOS near the valence band edge, and the absence of a similar peak
in the MoS2 DOS near the conduction band edge, Figure 2.2.
2.3.4 Electron-Hole Recombination

Figure 2.5. Electron-hole recombination dynamics: (a) population of the excited state; (b)
pure-dephasing function; and (c) phonon influence spectrum. The recombination data is
fitted by the short-time linear approximation to the exponential decay, giving the time-
constant of 2.2 ns, in agreement with the experimental data on the closely related
MoSe2/WSe2 system.
38
The pure dephasing-function is fitted to eq 7, giving the timescale is
27.2 fs. Similarly to the electron and hole transfer, Figure 2.3, the recombination process is
facilitated by the 400 cm
-1
out of plane A1g modes.

Non-radiative electron-hole recombination constitutes the main source of charge losses and energy
dissipation in solar energy and electronics applications. The charge recombination across the
MoS2/WS2 interface is characterized in Figure 2.5. The calculated 2.2 ns recombination time is
consistent with the 1.8 ns timescale reported experimentally for the similar MoSe2/WSe2
interface.
38
The shorter, 240 ps recombination time reported
22
for MoSe2/WSe2 can be attributed
to existence of defects in the experimental samples. MoS2 defects are known
29
and can accelerate
the charge recombination dynamics.
28
We plan on investigating the role of defects in future work.
21
Similarly to the charge separation, the non-radiative electron-hole recombination is promoted
primarily by the 400 cm
-1
out-of-plane A1g modes of the two materials,
50-51
Figure 2.5c. Quantum
coherence is maintained during the recombination for about 30 fs. This value is typical for electron-
hole recombination in many nanoscale materials at room temperature.
48, 53-54

Conclusion
Using a combination of real-time time-dependent density functional theory and non-adiabatic
molecular dynamics, we investigated the photo-induced electron and hole transfer, and subsequent
non-radiative electron-hole recombination in a MoS2/WS2 heterojunction. The calculations
rationalize why experiments observe ultrafast charge separation, despite only a weak van der
Waals interaction between the layers, and why the charge separated state is long-lived, even though
the electrons and holes are located close to each other. The separation is fast, because the photo-
excited charges are delocalized between the donor and acceptor materials. The hole transfer is
faster than the electron transfer, since the donor-acceptor interaction is stronger, the non-adiabatic
coupling is larger, the quantum coherence is longer-lived, and the density of acceptor states is
higher. The non-radiative electron-hole recombination is slow, because the initial and final states
are strongly localized within each layer, and the non-adiabatic coupling is very small, about 0.1
meV. In addition, the electron-phonon energy exchange is a high order process, requiring
excitation of about 20 vibrational quanta. Both charge separation and recombination couple to the
400 cm
-1
out-of-plane motions of two-dimensional materials. In all cases, quantum coherence lasts
for 10-30 fs. The reported time-domain ab initio calculations agree well with the available
experimental data, mimic the time-resolved experiments in a most direct manner, generate
valuable mechanistic insights into the photo-induced electron-vibrational dynamics, and provide a
22
tool for screening and predicting excited state dynamics in novel nano-materials. The fast photo-
induced charge separation and the slow charge recombination indicate that hetereojucnctions
involving MoS2, WS2 and other two-dimensional transition metal dichalcogenide semiconductors
are excellent candidates for applications in photovoltaics, photo-catalysis, electronics and related
areas.

23
Chapter 3 Sulfur Adatom and Vacancy Accelerate Charge
Recombination in MoS2, but by Different Mechanisms
3.1 Introduction
The small thickness, mechanical stability, strong interaction with light and interesting electronic
properties make MoS2 a promising building block for a new generation of optoelectronic materials.
MoS2 performance depends strongly on its quality and morphology. Various defects and impurities
are invariably present in the material.
20
By altering mechanical and chemical properties of MoS2
and creating electronic trap states, defects undermine material stability and lead to charge carrier
losses. Santosh et al. calculated formation energies of various defects and found that a sulfur
adatom (Ad_S) and a sulfur vacancy (V_S) are among the most energetically favorable point
defects.
55
Wu et al. detected several intrinsic point defects in monolayer MoS2 synthetized via
chemical vapor deposition (CVD).
29
S vacancy was frequently observed in all their samples. Since
charge transport and optical properties of semiconductors are closely related to dynamics of
excited charge carriers, numerous experiments have been carried out to study such dynamics in
MoS2.
27-28, 56
It is generally accepted that defects introduce charge traps and accelerate electron-
hole recombination; however, the atomistic mechanisms of these processes are not well understood.
For example, it is not known whether all defects are equally detrimental to material’s electronic
and optical properties, or whether certain defect types are particularly important and why. Such
understanding is essential to guide synthetic efforts in producing higher quality materials.
Here, we use ab initio quantum dynamics calculations to show that sulfur defects accelerate
nonradiative electron-hole recombination in MoS2; however, the acceleration mechanisms are
different for adatom and vacancy. The hole trap state created by the adatom is very localized, and
24
therefore, it couples weakly to charge carriers and is barely populated. Still, the adatom accelerates
charge recombination because it distorts the symmetry of the MoS2 layer, introduces new phonon
modes that couple to the electronic subsystem, and increases the non-adiabatic charge-phonon
coupling. The sulfur vacancy creates a deep, fairly localized electron trap and a shallow, less
localized hole trap that can couple well to the free hole. As a result, charge recombination through
the hole trap dominates in MoS2 with sulfur vacancies. Our calculations show that the sulfur
adatom is more fatal in reducing the lifetime of charge carriers in MoS2 than sulfur vacancy, even
though the adatom trap state is not populated. Hence, sulfur adatoms should be avoided to produce
high quality TMD materials and devices
3.2 Simulation Details
The geometry optimization, electronic structure and adiabatic MD trajectories were computed
using the Quantum Espresso program with a converged plane-wave basis set.
39
Interactions
between ionic cores and valence electrons were described by the projector-augmented wave (PAW)
method.
41
The nonlocal exchange-correlation interactions were treated with the Perdew, Burke and
Ernzerhof (PBE) DFT functional.
40
A vacuum layer of 20 Å was placed in the direction
perpendicular to the monolayer to avoid spurious interactions between the periodic images.
All structures were fully relaxed at 0K until the calculated Hellmann-Feynman forces were
smaller than 0.05 eV/Å. Then, the systems were heated to 300 K through repeated velocity
rescaling. 5 ps adiabatic MD trajectories with a 1 fs atomic timestep were produced and used to
calculate the state energies and NACs. To simulate the charge carrier trapping and relaxation
processes over a nanosecond timescale, the 5 ps NA Hamiltonians were iterated 201 times. The
DISH simulations were performed using the Pyxaid package.
44-45
50 initial conditions were chosen
25
randomly from the first 5 ps of the NA Hamiltonian data to sample the canonical distribution of
the atomic coordinates. After that, 2000 random number sequences were used for each initial
condition to sample the surface hopping probabilities.
3.3 Results and Discussion

Figure 3.1. Electronic energy levels involved in the charge carriers trapping and relaxation
dynamics. After photo-excitation, electrons in the conduction band (CB) can directly
recombine with holes in the valence band (VB) ①. A fraction of photo-excited electrons can
get trapped by the unoccupied defect levels (electron trap states) ②. Following the trapping,
electrons can undergo recombination with the VB holes ③. Similarly, holes can get trapped
by the occupied defect levels (hole trap states) ④ and then recombine with the CB electrons
⑤ or the trapped electrons ⑥. Electron is orange. Hole is emerald.

Figure 3.1 shows a diagram of the electronic energy levels involved in the charge carrier trapping
and relaxation dynamics for the perfect and defective MoS2 monolayers. A laser pulse excites
26
electrons from valence band (VB) to CB. The excited electrons in the CB can directly recombine
with the VB holes. Defects can create occupied and unoccupied levels inside the MoS2 band gap,
which serve as hole and electron traps, respectively. The numerals ①–⑥ denote various
processes possible in systems with electron and hole traps. The population of a trap state is
determined through competing trapping and detrapping processes.

Figure 3.2. Side and top views of the (a) perfect MoS2 monolayer, (b) MoS2 monolayer with
an S adatom (Ad_S), and (c) MoS2 monolayer with an S vacancy (V_S). Mo is green and S is
yellow. Defects are highlighted with red arrows and red circles at the side and top views,
respectively.

Figure 3.2 depicts the side and top views of the perfect, Ad_S and V_S MoS2 monolayers.
Defects are denoted with red arrows and circles. DFT calculations predict the formation enery of
Ad_S to be 0.989 eV. This is less than half of the formation energy of V_S, which is 2.57 eV.
55

V_S is frequently observed in MoS2 monolayer samples.
29, 57
The extra S atom in the Ad_S system
is rather mobile. Its potential of binding to the MoS2 surface is shallow, and the adatom can
undergo large scale anharmonic motions. A sulfur vacancy creates unsaturated chemical bonds at
the Mo atoms, which attempt to interact with adjacent S atoms, amplifying their motions. Both
27
adatom and vacancy perturb the symmetry of the MoS2 layer and give rise to phonon modes that
are not available in the pristine system.
The single point defects are introduced in our calculations within the 5×5 supercell of the MoS2
monolayer, corresponding to the defect concentration of 4.6·10
13
defects/cm
2
. The defect
concentration is high, due to the computational limintations associated with modeling of large
simulation cells. Such defect concentration can have a strong influence on device perfomence.
18,
55

Figure 3.3. Density of states (left panel) and charge densities (right panel and inserts) of (a)
perfect MoS2 monolayer, (b) Ad_S and (c) V_S. Inserts show charge densities of the defect
states. The right panel shows charge densities of band edge states. Ad_S has a shallow
localized hole trap state next to the VB edge. V_S has two trap states: a shallow hole trap
close to the VB edge and a deep localized electron trap 0.6 eV below the CB edge. The charge
densities of the VB edge states are strongly perturbed by defects, while CB edge states remain
unchanged.

Figure 3.3 shows the densities of states (DOS) of the perfect, Ad_S and V_S MoS2 monolayers.
The charge densities of the VB and CB edge states in each system are shown to the right of the
28
DOS plots. The inserts within the DOS plots present charge densities of the defect levels. The
calculated band gap of the perfect MoS2 monolayer is 1.724 eV, which is consistent with the
previously reported results.
58-60
The shallow hole trap state introduced by the S adatom narrows
the band gap by 0.069 eV. The S vacancy creates two trap states: a shallow hole trap, which shrinks
the band gap by 0.030 eV, and a deep electron trap 0.54 eV below the CB edge. The changes in
the band gaps obtained in our calculations are small and consistent with the results of the more
advanced electronic structure calculations.
55, 61

The VB and CB edge states are delocalized within the monolayer, and the CB edge states are
barely perturbed by the defects. The VB edges are perturbed more strongly, because both Ad_S
and V_S create defect energy levels close to the VB edge. These shallow hole trap states hybridize
with the VB edge states. The shallow hole trap state created in the Ad_S system is strongly
localized. In comparison, the shallow hole trap observed in the V_S system is much more
delocalized, Figure 3.3 Even the deep electron trap created by the sulfur vacancy is quite
delocalized, compared to the hole trap in the Ad_S system. The latter fact is unexpected, because
deep traps cannot hybridize with CB and VB states, while shallow traps can and, hence, should
delocalize by borrowing density of the delocalized CB and VB orbitals.
Figure 3.4 presents evolution of populations of the key states involved in the electron-hole
recombination dynamics in the three systems, including populations of the electron and hole trap
states and the ground state. The shown timescales are obtained by exponential fitting of the data.
The ground state populations are fitted by a single exponent. The trap states are populated
transiently, involving both rise and decay of the population. In these cases, the rise and decay are
fitted by separate exponents, and the reported times are the sums of the times of the two exponential
fits. These times provide a measure of how long the trap states are populated.
29

Figure 3.4. Charge carriers trapping and recombination dynamics in (a) perfect MoS2
monolayer, (b) Ad_S and (c) V_S. Electron-hole recombination is shown by black lines
(process ① in Figure 3.1). Hole trapping and hole trap-assisted recombination is red
(processes ④ and ⑤). Electron trapping and electron trap-assisted recombination is blue
(processes ② and ③). Recombination through simultaneous electron and hole trapping is
purple (processes ②+④ and ⑥ in Figure 3.1).

Nonradiative electron-hole recombination constitutes a major pathway for charge losses and
energy dissipation in optoelectronic applications. The direct recombination of a CB electron and a
VB hole, corresponding to process ① in Figure 3.1, needs 388 ps in the perfect MoS2 monolayer.
This timescale is consistent with the experimentally reported recombination times of several
hundreds of picoseconds.
62-64
Both defects accelerate the recombination, Figure 3.4, however, the
mechanisms of the acceleration are substantially different for the adatom and the vacancy.
Traditionally, defect induced acceleration of charge recombination is explained by introduction of
30
energy levels within the semiconductor band gap. It is assumed that the defect levels get populated,
and that the relaxation is faster because it involves transitions across smaller energy gaps. This
mechanism operates with the S vacancy, Figure 3.4c. However, the S adatom creates no states
deep inside the band gap, Figure 3.3b. Moreover, the shallow hole trap is never significantly
populated, Figure 3.4b. Nevertheless, the electron-hole recombination becomes faster by a factor
of 8 in the presence of the S adatom.
The enhancement of the electron-hole recombination rate by the S adatom defect is rationalized
by the stronger non-adiabatic coupling (NAC) between the CB and VB edge states, Table 3.1. The
root-mean-square value of the NAC increases from 2.78 meV to 8.44 meV in the presence of the
adatom. The enhancement occurs because the adatom breaks the symmetry of the MoS2 sheet and
introduces multiple phonon modes that couple to the electronic subsystem. Compare parts a and b
of Figure 3.5. The NAC for the hole trapping in the Ad_S system is very small, 0.82 meV, Table
3.1. This is because the localized orbital of the trap state has negligible overlap with the VB edge
orbital, which exhibits a depletion near the defect, Figure 3.3b. In comparison, the NAC between
the hole trap and the free electron occupying the CB edge is as large (8.41 eV) as the NAC between
the CB and VB edges (8.44 eV). This is because the density of the CB edge orbital has no depletion
near the defect, and exhibits significant overlap with the hole trap density. The difference in the
NAC values for the hole trapping and trap-assisted electron-hole recombination explains why the
population of the hole trap state never builds up above a few percent, Figure 3.4b.

31
Table 3.1. Root-mean-square of non-adiabatic coupling (NAC) and pure-dephasing time for
charge carriers trapping and recombination dynamics.

The acceleration of the electron-hole recombination by a factor of 1.7 due to the S vacancy
follows the traditional mechanism. First, the shallow hole trap is populated, red line in Figure 3.4c.
Second, the deep electron trap is populated, purple line in Figure 3.4c. Finally, electrons and hole
recombine, black line in Figure 3.4c. The electron trapping and electron-hole recombination
exhibit similar timescales, and therefore, about half of electron-hole recombination events bypass
the electron trap state. In contrast, hole trapping is involved in most recombination events in the
V_S system. The NAC values are 2.5-4 meV for all processes observed in the V_S system, with
exception of the electron trapping, which involves a 0.9 meV NAC, Table 3.1. The pure-dephasing
times, representing elastic electron-phonon scattering, are on the order of 10 fs in all cases. Such
values are typical of many nanoscale materials.
47, 49, 52-53, 65
Both S adatom and vacancy defects
accelerate the electron-hole recombination within the MoS2 monolayer. The calculated few ten to
hundred picoseconds recombination timescales are consistent with the experimental results.
8, 64,
66-67

perfect Ad_S V_S
recombination
of CB e and
VB h

recombination
of CB e and
VB h

hole
trapping
recombination
by h-trapping
recombination
of CB e and
VB h

hole
trapping
recombination
by h-trapping
electron
trapping
recombination
by e-trapping
recombination
by e and h
trapping
NAC
(meV)
2.78 8.44 0.82 8.41 3.67 4.01 2.53 0.92 4.01 2.56
Pure-
dephasing
(fs)
7.28 7.48 9.80 5.65 6.81 11.46 12.84 6.69 7.00 7.38
32

Figure 3.5. Phonon modes involved in the charge carrier dynamics in (a) perfect MoS2
monolayer, (b) Ad_S and (c) V_S (two bottom rows). The peak height is characterizes the
strength of electron-phonon coupling. The adatom allows many phonon modes to couple to
the charge carriers, accelerating the recombination (Figure 3.4).

In order to provide further insights into the nonradiative relaxation and recombination of the
charge carriers in the pristine and defected MoS2 we computed Fourier transforms of the
fluctuations of the energy gaps between the relevant energy levels, Figure 3.5. Electron-hole
recombination in the pristine MoS2 monolayer is promoted by the 400 cm
-1
phonon, which
corresponds to the out-of-plane A1g mode of MoS2 with the 404.1 cm
-1
frequency.
68
Similar
findings have been reported in other TMD systems.
52, 69
The S adatom perturbs the symmetry of
the MoS2 layer and introduces new phonons that couple to the electron and hole. The adatom is
33
loosely bonded to the monolayer and vibrates at low frequencies that contribute strongly to the
overall electron-phonon coupling. The effect is seen with all transitions in the Ad_S system,
including recombination directly between CB and VB edges, and via hole trapping. The spectrum
amplitude for the hole trapping process is small, in agreement with the small value of the NAC,
Table 3.1. The CB to VB charge recombination in MoS2 with the S vacancy is also promoted by
the 400 cm
-1
out-of-plane mode. The processes involving electron and hole traps are facilitated by
a wider range of phonons, including both the 400 cm
-1
phonon and other vibrations that are
typically at lower frequencies. The higher frequency modes are more important for hole trapping
than electron trapping. Because the NAC is proportional to nuclear velocity, higher frequency
modes create larger NAC at a given temperature. The differences in the spectrum intensities for
the higher and lower frequency modes involved in electron and hole trapping, Figure 3.5c, are
consistent with the corresponding NAC values, Table 3.1.
3.4 Conclusion
To summarize, we have investigated how the two most common intrinsic point defects, S adatom
and S vacancy, influence charge carrier trapping and recombination in the MoS2 monolayer. We
have found that both defects can accelerate electron-hole recombination, but the acceleration
happens through different mechanisms. The adatom enhances the recombination by a factor of 8,
while the vacancy does so only by a factor of 2. Surprisingly, the shallow hole trap state created
by the adatom is never significantly populated during the relaxation dynamics. Nevertheless, the
recombination becomes much faster. The wavefunction of the trap state created by the S adatom
near the VB edge is very localized, and therefore, it very weakly overlaps with the delocalized VB
wavefunctions. The trap-VB coupling is weak, and the trapping is slow. The acceleration arises
34
because the S adatom perturbs strongly the structure and symmetry of the MoS2 layer. In addition
to the 400 cm
-1
out-of-plane phonon that operates in pristine MoS2, the adatom introduces many
other vibrational modes that couple strongly to the electronic subsystem and induce electron-hole
recombination directly between the CB and VB edges. In contrast, the S vacancy creates both
electron and hole traps, and these traps are populated during the nonradiative relaxation process.
The electron-hole recombination proceeds by the traditional mechanism in this case. First, the hole
is trapped by the shallow state, then, the electron is trapped by a state deep inside the band gap,
and finally, the charges recombine.
The novel mechanism of the defect induced charge carrier losses in MoS2, uncovered by the
reported simulations, can operate in most semiconductors. It should be particularly important for
TMD and other two-dimensional materials, because they have extremely high surface-to-volume
ratio and are prone to mechanical deformation. A single adatom can strongly influence the phonon
spectrum of a two-dimensional material, by perturbing the system symmetry and geometry, and
introducing new, highly anharmonic motions. The modified ensemble of phonons promotes
nonradiative energy losses. From the practical perspective, the reported results indicate that S
vacancies should be much more benign to performance of TMD devices than S adatoms. The MoS2
properties can be adjusted significantly by small variations in the layer stoichiometry. Our results
agree well with the available experimental data, demonstrate how point defects influence the
properties of the MoS2 monolayer, generate theoretical insights into defect engineering and excited
state dynamics in TMDs, and suggest routes for optimizing performance of TMD based electronic
and photovoltaic devices.
35
Chapter 4 Why CVD grown MoS2 samples outperform PVD samples
4.1 Introduction
MoS2 is a promising building block for a new generation of electronic and optoelectronic materials.
Devices based on mechanically exfoliated MoS2 exhibit good electric performance. However, the
thickness, shape and number of layers of mechanically exfoliated MoS2 are not controllable.
70
For
large-scale applications though, large area and continuous thin films of MoS2 are a must, limiting
applicability of mechanically exfoliated MoS2. On the other hand, physical vapor deposition (PVD)
and chemical vapor deposition (CVD) enable controlled growth of large area TMD films with
precise atomic scale thickness.
71-72
At the same time, the charge carrier mobility are much lower
in PVD and CVD grown samples than in mechanically exfoliated samples. The highest reported
mobility reaches 81 cm
2
V
-1
s
-1
for mechanically exfoliated samples, 45 cm
2
V
-1
s
-1
for CVD grown
samples and <1 cm
2
V
-1
s
-1
for PVD grown samples. This is significantly lower than the theoretical
limit of 410 cm
2
V
-1
s
-1
.
20

Deterioration of the charge mobility has been attributed to charge scattering off short-range
disordered defects. Hong et al. reported that the antisite defects with one molybdenum atom
replacing one or two sulfur atoms (MoS or MoS2) are the dominant point defects in PVD grown
MoS2 monolayers, while sulfur vacancies are predominant in mechanically exfoliated and CVD
grown samples.
20, 29, 55, 57, 73
The work of Zhou et al. confirmed existence of one sulfur vacancy
(VS) and two sulfur vacancies, on opposite (VS2_opp) or same (VS2_same) side, in CVD grown MoS2
monolayers.
29
Having identified the defect types, one needs to estimate the rates of charge
scattering and energy losses at these defects. Since it is very difficult to disentangle the
36
contributions of different defects experimentally, the task can be achieved by atomistic
calculations.
Here, we use ab initio quantum dynamic calculations to study the role of different point defects
on charge carrier dynamics in monolayer MoS2, and rationalize why CVD grown samples are
superior to PVD samples. We demonstrate that all defects are bad for MoS2 quality, but antisite
defects are more detrimental than vacancy defects. Antisites creates trap states for both electrons
and holes deep within the bandgap, opening up extra charge carrier relaxation pathways. They also
perturb wavefunctions of the band edge states in a way that allows free charge carriers to couple
to the defects states. The simplest antisite defect generates a pair of electron and hole traps at the
Fermi energy, such that the traps can be populated already by thermal activation at room
temperature. As a result, the excited state lifetime is decreased by a factor of 8.3 due to antisite
defects. In contrast, vacancies decrease the lifetime only by a factor of 1.7. Conduction band (CB)
edge states are perturbed little by vacancies. Only shallow hole traps couple strongly to the valence
band (VB) edge. Electron is hard to trap, and its mobility remains high. Charge recombination in
vacancy MoS2 monolayers occurs primarily through hole traps. In general, misplaced atoms,
including adatoms and antisites, perturb charge carrier dynamics much more strongly than missing
atoms, and therefore, should be avoided.
4.2 Simulation Details
The Quantum Espresso program was used to perform geometry optimization, density functional
theory (DFT) calculations and adiabatic molecular dynamics.
39
The projector-augmented wave
(PAW) method was employed to treat interactions between ionic cores and valence electrons.
41

The Perdew, Burke and Ernzerhof (PBE) DFT functional was selected to represent nonlocal
37
exchange-correlation terms.
40
It provides a practical middle ground between accuracy and
computational efficiency. In order to avoid spurious interactions between periodic images of the
systems, a 10 Å vacuum layer was placed in the direction perpendicular to the MoS2 plane.
All structures were fully relaxed at 0K until the calculated Hellmann-Feynman forces were
smaller than 0.05 eV/Å. Then the systems were heated to 300 K through repeated velocity rescaling.
After that, a 5 ps adiabatic MD trajectory was obtained with a 1 fs nuclear timestep, and the
nonadiabatic (NA) coupling matrix elements were calculated along the trajectory. The trajectory
was sufficient to sample phonon induced fluctuations in energy levels and NA coupling. Because
the charge carrier trapping and relaxation processes take hundreds of picoseconds, the NA
Hamiltonian, including the NA coupling matrix elements and the orbital excitation energies, was
iterated, and 700 ps NAMD simulations were performed with the Pyxaid package.
44-45
100 initial
geometries were sampled from the MD trajectory to represent the canonical distribution in the
classical phase space. 1000 random number sequences were used to sample the surface hopping
probabilities for each initial geometry.
4.3 Results and Discussion
Figure 4.1 depicts a diagram of the charge carrier trapping and relaxation dynamics in the perfect
and defective MoS2 monolayers. Defects generally bring in trap states within the bandgap, which
provide extra pathways for charge carrier relaxation. Without trap states, electrons in the CB
directly recombine with VB holes, process ①. In the presence of defects, electrons and holes get
trapped, processes ② and ④. Trapped electrons recombine with free or trapped holes, processes
③ and ⑥, while CB electrons also recombine with trapped holes, process ⑤. The population
of a trap state is determined through competing trapping and detrapping processes.
38

Figure 4.1. Electronic energy levels involved in charge carriers trapping and relaxation.
Defects can create electron and hole trap within the band gap. After photo-excitation,
electrons in the conduction band (CB) can directly recombine with holes in the valence band
(VB) ①. Some electrons can get trapped by unoccupied defect levels (electron trap states)
② and then recombine with the VB holes ③. Similarly, holes can get trapped by occupied
defect levels (hole trap states) ④ and then recombine with the CB electrons ⑤ or the
trapped electrons ⑥. Electron is orange. Hole is emerald.

Figure 4.2 shows the side and top views of the pristine MoS2 monolayer, together with the
antisite and vacancy defects, which are highlighted with red arrows and circles. The considered
defects include antisite defects, in which a Mo atom replaces one (MoS) or two (MoS2) S atoms, as
well as single (VS) and double S vacancies, with the two vacancies being on the same (VS2_same) or
opposite (VS2_opp) sides of the monolayer. DFT calculations predict the formations energies of the
antisite and vacancy defects to be in the ranges of 5.45 eV–6.09 eV and 2.86 eV–4.34 eV,
respectively.
20
The smaller formation energies of the vacancy defects indicate that they are
39
common in MoS2 samples.
29, 55
This is true for mechanically exfoliated and CVD grown MoS2
monolayers, as confirmed, for instance, through the scanning transmission electron microscopy
experiments by Zhou et al.
29
In comparison, the PVD manufacturing process maintains a S-
deficient and Mo-rich conditions, resulting in a high probability of the antisite defects, with the
experimental probability density ratio of MoS2:MoS:VS = 9:2.3:1, indicating that the antisite defects
dominate PVD grown MoS2.
20

Figure 4.2. Side and top views of the (a) perfect MoS2 monolayer, (b) MoS2 monolayer with
one Mo replacing one S atom (MoS), (c) MoS2 monolayer with one Mo replacing two S atoms
(MoS2). (d) MoS2 monolayer with one S vacancy (VS), (e) MoS2 monolayer with two S
vacancies on the opposite sides (VS2_opp), (f) MoS2 monolayer with two S vacancies on the
same side (VS2_same). Mo is green and S is yellow. Defects are highlighted with red arrows
and red circles in the side and top views, respectively.

40
In PVD grown MoS2 monolayers, the antisite Mo atom is loosely bonded to the MoS2 monolayer
and can undergo large scale vibrations. Since Mo is heavier than S, the antisite defects vibrates at
low frequencies. In mechanically exfoliated and CVD grown MoS2 monolayers, the sulfur
vacancies create unsaturated chemical bonds at the Mo atoms, which can interact with adjacent S
atoms and amplify their motions. Both antisite and vacancy defects perturb the symmetry of the
MoS2 monolayer and bring in phonon modes that are not available in the perfect system.

Figure 4.3. Density of states of (a) perfect MoS2 monolayer, (b) MoS, (c) MoS2, (d) VS, (e)
VS2_opp, and (f) VS2_same. The vertical black dashed lines represent the Fermi energy. The
antisite defects (MoS and MoS2) create a deep electron trap and two kinds of hole traps: a
shallow hole trap state close to the VB edge and a deep hole trap near the Fermi energy. The
vacancy defects (VS, VS2_opp, VS2_same) create a shallow hole trap and deep electron traps.

Figure 4.3 shows the densities of states (DOS) of the perfect, antisite and vacancy MoS2
monolayers. The calculated band gap of the perfect MoS2 monolayer is 1.72 eV, which is
41
consistent with the previously published results.
22, 58-59
The antisite defects create a deep electron
trap and two kinds of holes traps: a shallow hole trap attached to the VB edge, and a deep hole trap
close to the electron trap near the Fermi energy. The gap between the deep electron trap and the
deep hole trap is narrowed down by a large extent, especially in MoS in which it is almost zero. As
a result, the NA couplings between the electron and hole trap states are large. Trapped electrons
can quickly recombine with trapped holes, and the electron-hole recombination is accelerated
through both electron and hole trapping. The S vacancies create deep electron traps and shallow
hole traps. The shallow hole traps can efficiently couple to the VB edge states, in contrast to
electron traps, which only weakly couple to the CB edge states. Hole trapping plays a much more
important role than electron trapping in MoS2 with S vacancies.
Figure 4.4 presents the charge densities of states involved in the charge carrier trapping and
relaxation dynamics for the perfect and defective MoS2 monolayers. The VB and CB edge states
are delocalized within the whole monolayer, while the trap states are localized around defects. In
antisite MoS2, all states are strongly perturbed by the misplaced Mo atom, even the VB and CB
edge states gather more charge densities near the defect region. Consequently, the band edge states
overlap well with the defect states, and the NA couplings leading to charge trapping are relatively
large, Table 4.1. The MoS system has an unusually large NA coupling between the electron and
hole traps, because these states are nearly degenerate, Figure 4.3b. In vacancy MoS2 monolayers,
the CB edge states remain unperturbed. In comparison, the VB edges are perturbed, because the
vacancies create shallow hole traps next to VB edge states. The shallow hole trap states hybridize
with the VB edge and are more delocalized than the deep electron trap states. Therefore, the NA
coupling is larger for hole than electron trapping in the S vacancy systems, Table 4.1, and
nonradiative recombination of free charge carriers is mediated primarily by hole traps.
42

Figure 4.4. Charge densities of (a) perfect MoS2 monolayer, (b) MoS, (c) MoS2, (d) VS, (e)
VS2_opp and (f) VS2_same. The antisite defects create localized hole and electron trap states. The
vacancy defects are less localized. In antisite MoS2, both VB and CB edge states are
perturbed by the defects, with electron density gathering near the defects. In vacancy MoS2,
only the VB edge states are perturbed by defects, and the CB edge states remain unchanged.

Figure 4.5 depicts time evolution of populations of the key states involved in the electron-hole
recombination dynamics in the perfect and defective MoS2 monolayers, including electron trap
states, hole trap states, states with electron and hole trapped simultaneously, and the ground state.
In systems that exhibit multiple electron or hole traps, Figure 4.3, the populations are added up to
obtain the total population of all electron traps, all hole traps, and all states with both electron and
hole trapped. The times presented in the figure are obtained through exponential fitting of the data,
as follows. The ground state populations are fitted by a single exponent. The populations of the
43
trap states are characterized by the competing rise (trapping) and decay (detrapping) processes.
The rise and decay parts are fitted separately, and the reported times are the sum of the times of
the two exponential fits. These timescales provide a measure of how long the trap states are
populated. The height of the curves represents the maximum average population of the traps.

Figure 4.5. Charge carriers trapping and recombination dynamics in (a) perfect MoS2
monolayer, (b) MoS, (c) MoS2, (d) VS, (e) VS2_opp and (f) VS2_same. Shown are time-dependent
populations of the ground state and three types of trap states, involving either electron, or
hole, or both electron and hole trapping. When multiple hole or electron traps are present,
their populations are summed up for clarity. The corresponding processes are depicted
schematically in Figure 4.1.

Nonradiative electron-hole recombination is a major mechanism for charge losses and energy
dissipation in solar, optoelectronic and other TMD applications. The calculation shows that direct
recombination of electrons and holes, corresponding to process ① in Figure 4.1, needs 388 ps in
the perfect MoS2 monolayer. This time scale is consistent with the previously reported
44
experimental results of several hundreds of picoseconds.
62-64
Both antisite and vacancy defects
introduce energy levels within the bandgap and accelerate charge carrier relaxation, but the degree
of the accelerations is different. The antisites can speed up the recombination by a factor of up to
8.3, while the vacancies decrease the time constants only by 1.7, Figure 4.5.

Table 4.1. Root-mean-square of nonadiabatic coupling (meV) for the charge carriers
trapping and recombination dynamics.

Hole trap assisted recombination dominates in MoS2 monolayers with the S vacancies. First, the
shallow hole trap is populated, red lines in Figure 4.5d-f. Second, the deep electron trap is
populated, purple lines. At the same time, the trapped holes start recombining with free electrons.
Recombination of trapped holes with free and trapped electrons gives rise to the ground state
population, black lines in Figures 4.5d-f. The electron trapping is slow due to small NA coupling
of the electron trap with the CB edge, Table 4.1, originating from relatively large energy separation
and differences in the charge density localization. In addition, the quantum coherence (pure-
dephasing) times for electron trapping are shorter than for hole trapping and other dynamics, Table
System
recombinatio
n of CB e
and VB h
hole
trappin
g
recombinatio
n by h-
trapping
electron
trappin
g
recombinatio
n by e-
trapping
recombination
by e and h
trapping
perfect 2.78
MoS 1.78 4.58 3.56 4.29 2.73 144.58
MoS2 1.56 4.42 4.22 4.95 2.52 4.95
VS 3.67 4.01 2.53 0.92 4.01 2.56
VS2_opp 3.35 4.87 3.46 1.09 3.51 3.58
VS2_same 3.62 3.97 1.74 0.82 3.61 1.70
45
4.2. As a result, less than half of recombination events involve electron trapping. In contrast, hole
trapping is involved in most recombination events in the MoS2 monolayers with the S vacancies.
The NA coupling values are around 4 meV for transitions involving hole traps, and the
corresponding pure-dephasing times are fairly long, Table 4.2. Hole trapping accelerates electron-
hole recombination by a factor of 1.4-1.7, Figure 4.5d,e, and can even delay the ground state
recovery, Figure 4.5f. Mobility of free positive charge carriers is reduced by trapping in vacancy
MoS2, while mobility of free negative charge carriers changes little. The excited state lifetime is
decreased by a small extent.

Table 4.2. Pure-dephasing times (fs) for the transitions involved in the charge carriers
trapping and recombination dynamics.

System
recombinatio
n of CB e
and VB h
hole
trappin
g
recombinatio
n by h-
trapping
electron
trapping
recombinatio
n by e-
trapping
recombinatio
n by e and h
trapping
perfect 7.28
MoS 13.23 23.85 9.00 9.83 12.10 13.56
MoS2 16.12 26.76 4.62 15.47 7.35 5.09
VS 6.81 11.46 12.84 6.69 7.00 7.38
VS2_opp 10.19 35.56 12.67 10.42 10.36 10.19
VS2_same 22.77 32.58 35.95 13.10 15.93 15.69

A recent publication
74
reported an increase in the photoluminescence quantum yield of
monolayer MoS2 to nearly unity, following treatment with organic superacids that probably
passivate defect sites. The corresponding photoluminescence lifetime increased to up to 10 ns for
low excitation fluences, at which bimolecular exciton-exciton annihilation is negligible. Our
46
calculated nonradiative lifetime for pristine MoS2 is shorter than the measured lifetime most likely
due to the small simulation cell size. The small cells confine electrons and hole to an area that is
less than the exciton size in the infinite material, thereby enhancing both electron-hole and
electron-phonon interaction. Further, the small cell size does not allow for exciton dissociation
into free charge carriers that is possible in a large sample due to entropic effects, since two free
charges have a larger entropy than an exciton. The simulation cell size is sufficient to capture the
defect properties, because the defects are strongly localized.
The reported calculations use a pure DFT functional used that tends to underestimate energy
gaps and does not include explicitly excitonic effects. More accurate hybrid DFT functionals are
expensive with periodic systems. Excitonic effects, described by the Bethe-Salpether theory, are
extremely expensive to incorporate into MD dynamics. Nevertheless, the methodology provides
correct semi-quantitative description. The DFT functional allows us to distinguish between deep
and shallow trap states, and between electron and hole traps, since they are determined by chemical
properties of the atoms. In particular, the S vacancies create deep electron traps, because the MoS2
CB arises due to Mo atoms, and unsaturated Mo bonds create empty states within the gap.
Perturbation to the VB caused by S vacancies is small, because the VB arises from S atomic
orbitals, and all S atoms remain chemically saturated. In comparison, the occupied and vacant
orbitals of the antisite Mo atoms interact strongly with the surrounding atoms, perturbing the MoS2
VB and CB edges. The antisite defects create deep trap states for electrons and holes, because the
extraneous Mo atoms contain both occupied and vacant orbitals separated by gaps that are much
smaller than the MoS2 bandgap.
47
4.4 Conclusion
We have used NA molecular dynamics and time-dependent DFT to investigate the influence of
two defect types, antisites and vacancies, on charge carrier recombination dynamics in MoS2
monolayers. We have found that defects generally accelerate electron-hole recombination, but
antisite defects are much more detrimental than vacancy defects. On one hand, antisites can speed
up the recombination by more than a factor of 8. On the other hand, vacancies accelerate the
recombination by less than a factor of 2, and even delay the ground state recovery. This is because
the antisite defects create both electron and hole traps deep within the bandgap, reducing the energy
gaps for the phonon-mediated charge relaxation. In addition, the CB and VB edge state are
perturbed by the antisite defects in a way that creates significant overlap with the trap states. In
comparison, vacancies create deep electron but not hole traps, and the CB and VB edge states
remain delocalized, showing weaker overlap with the defect wavefunctions. Moreover, the
simplest antisite defect with one Mo atom replacing one S atom creates a pair of electron and hole
traps close to the Fermi energy, allowing charge trapping by thermal activation from the ground
state.
Our simulations rationalize the better performance of CVD grown MoS2 monolayers over PVD
grown monolayers. PVD samples contain many antisite defects, which greatly decrease charge
carrier lifetimes and mobilities. In contrast, CVD samples contain primarily vacancy defects that
have a much weaker effect on carrier lifetimes, and influence primarily holes but not electrons.
Our analysis suggests that the performance of PVD grown MoS2 samples can be improved by
introduction of extra S during the growth process or post-growth treatment, to minimize
appearance of Mo atoms in place of S atoms. At the same time, our previous publication shows
that S adatom can greatly, by a factor of 8, accelerate charge recombination,
75
which is comparable
48
to the acceleration induced by MoS. Therefore, the manufacturing process should be tuned to
prevent formation of both antisite and adatom defects. In other words, missing atoms are more
benign than misplaced atoms. The conclusions obtained in this work for MoS2 should be applicable
to the other closely related materials, such as WS2, WSe2 and MoSe2, because the chemistries
during their PVD and CVD production are similar. Showing good agreement with the existing
experimental data, our results provide theoretical insights into defect engineering in TMDs, and
suggest routes for improving MoS2 quality for applications in low-dimensional electronic,
optoelectronic and solar energy devices.

49
Chapter 5 Phonon-Suppressed Auger Scattering of Charge Carriers
in Defective Two-Dimensional Transition Metal Dichalcogenides
5.1 Introductions
TMDs are promising building blocks for a new generation of optoelectronics. However, the
reported photoluminescence quantum efficiencies of as grown TMD materials are typically in the
range from 10
-4
to 10
-2
, which limits their applications in realistic devices.
76
Deterioration of the
radiative quantum efficiency is attributed to charge scattering off short-range disorder defects, such
as vacancies, anti-sites and adatoms. Chalcogen vacancy defects are frequently observed in
chemical vapor deposition (CVD) grown TMD samples, and previous theoretical studies show that
the vacancy accelerates charge carrier recombination nonradiatively.
29, 75
Later Bajar et al. found
that chalcogen vacancies are passivated by oxygen atoms.
77
However, mid-gap trap states are
commonly observed in TMDs.
78-84
Even when chalcogen vacancies are passivated by oxygen, O2
molecules can embed into defect sites to form Te-O and Mo-O bonds, which also create mid-gap
states.
85
Here, we use Te vacancy as the model system to study the general TMDs mid-gap
defective systems. In addition to the direct energy losses to phonons as shown in
Figures 5.1(a)-1(b), the strong quantum confinement and reduced dimensionality of TMDs
significantly enhance many-body interactions, which facilitates energy exchange between charge
carriers and enables efficient Auger recombination,
86-87
as displayed in Figure 5.1(c). For example,
rapid Auger-type annihilation has been detected in photoexcited MoS2.
64

50

Figure 5.1. Schematics of charge carrier energy loss to phonons in (a) a pristine TMD crystal
and (b, c) a defective TMD crystal with trap levels residing inside the band gap. After
photoexcitation, excited electrons in the conduction band (CB) recombine nonradiatively
with holes in the valence band (VB) through channel ①, phonon-driven channel. Defects
generate trap states within the bandgap. A fraction of photoexcited electrons gets trapped
through channel ②, and recombines with the VB holes ③. Auger-type carrier trapping takes
place at high carrier densities, as shown in channel ④ (i.e. one electron is trapped, denoted
as 1
st
electron, while the other electron is excited into deep CB, denoted as 2
nd
electron).
Electron and hole are displayed in yellow and emerald, respectively. Red arrows represent
electron relaxation in the energy domain.

In addition to the recombination dynamics, fast charge trapping is widely detected in TMDs on
a 1~2 ps timescale.
27-28, 67, 88-89
Wang et al. and Kar et al. attribute these fast dynamics to Auger
trapping of free carriers.
27-28, 67
Defects in TMDs introduce mid-gap states that can trap electrons
from CB, and utilize the released energy to excite free CB electrons to higher energy states.
Surprisingly, these fast dynamics are nearly independent of the pump fluence, which contradicts
relaxation by the Auger mechanism. Since Auger processes involve scattering between two or
more charge carriers, the rate of Auger trapping should grow as the pump fluence increases, since
51
more charge carriers are produced at higher fluences. Meanwhile, phonon-driven trapping is
independent of pump fluence, because it involves scattering of individual carriers by phonons. For
this reason, Xing et al. and Docherty et al. believe these fast dynamics are driven by phonons.
88-89

However, on the one hand, our previous calculations show that purely phonon-driven trapping of
charge carriers takes longer time.
75, 90
On the other hand, Auger processes can become quite
important at high carrier densities, as more carriers can be involved in the dynamics. Therefore, it
is not yet known whether these fast dynamics are phonon-driven or Auger-driven, or whether both
mechanisms are influential. A detailed understanding of the interplay between the Auger-type and
phonon-driven charge trapping processes is still lacking. Kinetic rate equations could provide
simple models of the charge carrier dynamics. A thorough atomistic understanding of interactions
between carriers, phonons and traps requires an ab initio level of description.
Here, we employ time-domain ab initio calculations to rationalize the time-resolved optical
pump and THz probe transient absorption measurements on charge carrier trapping in multi-layer
MoTe2, performed in the high carrier density regime with the densities ranging from ~10
19
to 10
21

cm
-3
. Note that the experimental part is carried out by my collaborator Ming-Fu Lin. I only
contribute to the computational part. There is a very weak dependence of the charge carrier lifetime
on the carrier density. This fact is surprising, since straightforward models predict quadratic
density dependence of charge-charge scattering. The observation is explained by our time-domain
ab initio simulations of charge carrier dynamics in defective MoTe2. The simulations show that,
first, charge trapping facilitated by phonons is already quite fast but still cannot explain our
observations. Second, charge trapping via Auger-type carrier-carrier scattering is strongly
influenced by phonons. The excited carrier in the Auger process accepts about 50% of the trapped
carrier energy, with more than half of the energy dissipated directly to phonons. The Auger-type
52
mechanism accelerates the carrier trapping by a factor of four, and the simultaneous phonon-driven
and Auger-type trapping occur within ~2 ps, in agreement with the experimental results. Phonons
participate strongly because trap states are relatively shallow, and phonons accommodate
efficiently the electronic energy loss during the trapping. Trapped electrons localize around defects,
decreasing the overlap of wavefunctions between trapped and free carriers and reduces carrier-
carrier scattering. Thus, phonons-driven electron trapping suppresses the Auger mechanism at high
carrier densities and lowers the dependence of the carrier lifetime on the carrier density. Our time-
domain atomistic modeling is consistent with the unexpected experimental trend and provides a
detailed analysis of the strongly coupled charge-phonon and charge-charge scattering processes
that are common to majority of nanoscale materials.
5.2 Experimental Results
Note that the experimental measurements are carried out by my collaborator Ming-Fu Lin.
Transient absorption measurements using terahertz (THz) pulses provide a direct probe of
photoconductivity in a material induced by the optical excitation. Photoconductivity is a product
of free carrier mobility and concentration. Thus, it is a sensitive measurement of free charges.
25, 91-
93
In these experiments, we characterize the THz field transmitted through the sample at each
pump-probe delay step and convert the obtained THz field in the time domain to the spectral
domain. The procedure allows us to catch the short-lived carrier lifetime without the complication
of the THz field phase drift at a single point measurement of the maximum field. Optical excitation
at 800 nm (1.55 eV) is employed to generate free carriers over the band edge of MoTe2. Note that
at high pump fluences in this experiment, the generated excitons dissociate into free carriers.
94
The
estimated Mott density for exciton dissociation to occur is at ~10
18
cm
-3
based on the Mott criterion
53
NMott=(0.25/aBohr)
3
,

where aBohr is the Bohr radius of exciton in bulk 2H-phase MoTe2 (i.e. 2.5
nm).
95
The pump-probe kinetics at different effective carrier densities are shown in Figure 5.2(a),
with the charge carrier density increasing from top to bottom by over a factor of ~100. The red and
blue curves represent the experimental results and best least-square-fits, respectively. Each fit is
performed with inclusion of a convolution between the instrument response function of ~0.3 ps
and the exponential decay function. The obtained lifetimes as a function of carrier density are
plotted in Figure 5.2(b). Note that each carrier density is calculated by considering the complex
refractive indices of air, MoTe2, and substrates at 800 nm photon energy. This allows us to estimate
the absorption of photons that taking into account the reflection at the interfaces between air,
MoTe2 and substrates.
96
Finally, the saturation effect at the high pump fluence is included so that
the actual absorption correction can be estimated from saturable absorber model. In addition, we
assume that each photon produces one electron-hole pair that dissociates into free carriers.

54
Figure 5.2. Optical pump and THz probe measurements of ~9 nm thick 2H-phase MoTe2.
The THz probe beam is normal incident to the sample surface and the transmitted THz field
is measured by the electro-optic sampling method. (a) The kinetics plots of 2H-phase MoTe2
after optical excitation at 800 nm. These plots are obtained from the integration of
normalized THz spectral intensity change from 0.5 THz to 2.3 THz. Red dots and blue lines
represent the experimental results and overall fits, respectively. Each fit is obtained by
considering a convolution of instrumental response function of ~0.3 ps with an exponential
decay function. The carrier density shown in the plots increases toward the bottom by a
factor of ~100. Note that the unit for the carrier density is in cm
-3
. (b) The time constants
obtained from the fits in (a) as a function of carrier density. The horizontal error bars in the
figure represents the measured uncertainties of pulse energy and pump beam spot size. The
vertical error bars in the lifetime corresponds to the uncertainty obtained from the least-
squared fit of the experimental data points.

The experimental results display ~2 to 3 ps free charge carrier lifetimes in thirteen-layered
MoTe2 at the carrier density from ~10
19
to 10
21
cm
-3
as shown in Figure 5.2(b). The picosecond
lifetimes suggest that the observed dynamics may not be simply attributed to the intraband
relaxation of hot carriers to the band edge via phonon emission, because such process occurs on a
much shorter time scale, 100 fs to 500 fs, and thus, it can be excluded.
97-98
However, this 2 ps time
scale of carrier dynamics may be attributed to the interplay between the electron-phonon scattering
and Auger trapping processes by the defect states.
67, 89, 99
Once the free carriers are trapped, the
photoconductivity decays to zero.
67, 89, 100
Afterwards, the trapped carriers recombine
nonradiatively which is invisible to the THz field. Note that the exciton contribution in our THz
signal is negligible because the intra-excitonic transition requires ~20 meV to 50 meV which is
outside of our THz-probe region (2 meV to 12 meV). In addition, at current excitation densities
the excitons fully dissociate into free carriers based on Mott density estimation using the exciton
Bohr radius in the bulk MoTe2. The two-dimensional nature of MoTe2 enhances many-body
interactions, and at our current carrier density the Auger process becomes efficient, as observed in
a few-layer MoS2.
28, 101

55
In Figure 5.2(b), the measured dependence of the charge carrier lifetimes on the charge carrier
density is weak. Considering a two-particle scattering event, one expects quadratic dependence of
carrier lifetime on the particle density, and the lower than quadratic dependence on the charge
carrier density is surprising. The carrier lifetimes also depend on the density of trap states, Figure
5.1(c). The defect density is maintained constant in our experiments, since we use the same
prepared 9 ±1.1 nm thick polycrystalline MoTe2 samples while varying the pump intensity. Note
that the pump fluence that generates the highest carrier density in the current study is two times
smaller than the damage threshold of MoTe2 samples. A sub-quadratic carrier density dependence
can arise if trapping is purely an electron-phonon scattering event, and charge-charge scattering is
rare. However, this is unlikely for the high carrier densities used in our experiments. Most likely,
the Auger process occurs simultaneously with phonon-driven trapping, and the Auger scattering
is accompanied by charge-phonon scattering of the same type that leads to the sub-picosecond
intraband charge-phonon relaxation.
97-98
An interplay between Auger and phonon scattering has
been established, for instance, during multiple exciton generation
102-103
and Auger-assisted
electron transfer
104-105
in semiconductor quantum dots (QD). Note that compared to the TMDs,
QDs show stronger confinement, but weaker Coulomb interactions due to 3D screening over the
QD volume. The observed 2 to 3 ps time scale as observed in Figure 5.2 cannot be attributed to
direct nonradiative charge recombination in TMDs, which requires much longer time (i.e. ~23
ps).
28, 101

56
5.3 Theoretical Results
5.3.1 Simulation Details
In order to rationalize the weak dependence of the charge carrier lifetime on the carrier density in
MoTe2 we performed time-domain ab initio simulations combining real-time time-dependent (TD)
density functional theory (DFT) with nonadiabatic (NA) molecular dynamics (MD). The electron
and phonon dynamics are directly coupled in the simulation. The MoTe2 structure, including a Te
vacancy defect to create mid-gap states, is represented at the atomistic level, and vibrations are
described fully anharmonically, which is important for modeling defect modes. Experiments
detected the common existence of vacancy defects in chemical vapor grown TMDs samples,
20, 29,55

motivating our model. Among all point defects, one chalcogen vacancy is calculated to have lowest
formation energy.
29
It is reported that oxygen could passivate vacancy defects and recover the no
mid-gap bandstructure.
77
However, oxygen can further interact with the Mo vacancy to create new
mid-gap states.
100
Since vacancies are common and widely studied defects in TMDs, we use
chalcogen vacancy as a model to represent defective systems with mid-gap states. Charge carriers
can also relax into exciton levels. However, the experimental pump fluences are high, and excitons
dissociate into free carriers. Only at low pump fluences, or at later stages of the carrier relaxation
at high pump fluences excitons can provide an efficient channel for carrier trapping.
We used a bilayer MoTe2 in the simulation to mimic the charge trapping dynamics in the
fourteen-layered MoTe2 used in the experiments. While monolayer MoTe2 is a direct bandgap
semiconductor, bilayer MoTe2 already has in indirect bandgap, similarly to multilayer MoTe2, and
the corresponding photoluminescence intensity is low compared to the monolayer.
106-107
Our
Raman spectrum of 2H-MoTe2 shows similar features and intensity as observed from previous
bilayer studies.
107
The TDDFT-NAMD quantum dynamics simulations are computationally
57
intense, involving several thousand nuclear time-steps, each requiring an electronic structure
calculation, and hundreds of thousands electronic time-steps. The bilayer MoTe2 model demands
significantly less computational cost than multilayer MoTe2, making it applicable at the ab initio
level. The bilayer model already captures the overall trend and rationalizes the experimental data.
The DFT calculations and adiabatic MD are performed with the Quantum Espresso program.
39

The TDDFT and NAMD simulations are carried out with the Pyxaid software package.
44-45
The
phonon-driven nonradiative charge trapping and recombination are simulated using the
decoherence-induced surface hopping (DISH) method.
33
DISH has been used to model excited
state dynamics in closely related TMDs systems, such as MoS2 monolayers, and MoS2/WS2 and
MoS2/MoSe2 heterojunctions.
52, 75, 90, 108
Auger-mediated dynamics are computed with the global-
flux surface hopping (GFSH) method.
34
GFSH captures many-particle processes and has been
successful in simulating Auger processes in semiconductor QDs, nanoplatelets and nanotubes.
35,
109-110
This is the first study of Auger-type dynamics in TMDs.
The simulation supercell is obtained through repeating the unit cell of the MoTe2 bilayer 3*3
times. The supercell is a hexagonal structure with the cell constants a=10.73 Å, b=10.73 Å and
c=25 Å. A vacuum of 14 Å is placed on the c direction to avoid spurious interactions between
adjacent images of the bilayer. All calculations are performed with a cutoff energy of 50 Ry. The
Perdew, Burke, and Ernzerhof (PBE) functional is selected to describe the nonlocal exchange-
correlation terms, because it provides a practical middle-ground to balance accuracy and
computational cost. The projector-augmented wave (PAW) method is chosen to treat interactions
between ionic cores and valence electrons. The van der Waals interactions were described by the
semiempirical potential introduced by Grimme’s in the DFT-D2 method with a 200 a.u. cutoff
radius.
58
The Quantum Espresso program is used to perform geometry optimization, electronic structure
calculations and adiabatic molecular dynamics (MD) simulation. The perfect and defective MoTe2
bilayers are fully relaxed at 0 K until the calculated Hellmann-Feynman forces were smaller than
0.05 eV/Å. These optimized structures are used to compute densities of states (DOS) shown in
Figure 5.3 and charge density distributions shown in insets in Figure 5.4. The DOS were calculated
through using a 9´9´1 k-point mesh. Then, the structures are heated to 300 K through repeated
velocity rescaling. Because of thermal fluctuations, the energy gap between the conduction band
minimum (CBM) and the shallow trap state (i.e. the trap state close to the CBM) in the defective
bilayer MoTe2 narrows down by 25%, (from 0.2 eV to 0.15 eV), while other energy gaps remain
similar. After that, a 3 ps adiabatic MD trajectory is computed with a 1 fs nuclear timestep, and
the nonadiabatic (NA) coupling matrix elements are calculated along the trajectory. It is important
to note that the 3 ps trajectory is sufficient to sample phonon induced fluctuations in the energy
levels and NA couplings, because the system is close to harmonic and undergoes oscillations close
to the energy minimum. The NA Hamiltonian, including the NA couplings and excitation energies,
is iterated to model long time NAMD with the Pyxaid package. 1000 initial geometries are sampled
from the MD trajectory to mimic the canonical distribution in the classical phase space. 500
random number sequences are used to sample the surface hopping probabilities for each initial
geometry. The population and energy decay curves, Figures 5.4 and 5.5, represent averages over
these NAMD trajectories. There are two trap states in the defective bilayer MoTe2, see Figure
5.3(b). The population of defect state shown in Figure 5.4(b) is the sum of populations of the two
defect levels. Pure phonon-driven trapping represented in Figure 5.5(a) takes sufficiently long time,
providing enough time for electrons to relax between traps, such that most electrons are in the deep
trap, releasing 0.3 eV of energy to phonons. On the other hand, phonon-suppressed Auger trapping,
59
Figure 5.5(c), finishes in a short time, and ~67% of the trap electron populations is in the shallow
trap. Thus, the trapped electron releases only ~0.2 eV of energy.
5.3.2 Results and Discussion
Figure 5.3 depicts the simulated structure and densities of states (DOS) of the pristine and defective
MoTe2 bilayers. The calculated bandgap of the pristine MoTe2 bilayer is 0.95 eV, which agrees
with the previous experimental and theoretical results within ~0.1 eV.
107, 111
The Te vacancy
creates two trap levels residing approximately ~0.2 to 0.3 eV below the conduction band minimum
(CBM) as shown in Figure 5.3(b). The relatively small energy gap between the CBM and the trap
states suggests fast electron trapping dynamics. The vacancy of Te in the crystal (VTe) creates
unsaturated chemical bonds at Mo atoms, and the compromised lattice structure allows for larger
amplitude, anharmonic motions near the defect site. The defect perturbs symmetry of the MoTe2
bilayer, giving rise to vibrational modes that are not originally available in the defect-free system,
and accelerates nonradiative charge carrier relaxation. By creating a single point vacancy within
the 3×3 supercell of the MoTe2 bilayer, we generate a high defect concentration of 8.3×10
20
cm
-3

in the crystal (i.e. 9.0×10
13
cm
-2
per layer). This defect concentration is similar to the experimental
value of ~3.5×10
13
cm
-2
determined for monolayer MoS2 synthetized by CVD.
20
In addition, by
placing two charges in this supercell we create a high carrier density of ~10
21
cm
-3
, which is falling
within the experimental range, Figure 5.2(b).
Next, we simulate phonon-driven charge carrier recombination and trapping in the pristine and
defective MoTe2 bilayers, respectively, based on the processes ① and ② in Figures 5.1(a) and
5.1(b), without considering the Auger effect. Figure 5.4 presents the simulated time-resolved
populations of the electronic states involved in the charge carrier relaxation dynamics. The insets
show charge densities of the VBM and CBM in Figure 5.4(a), and trap states in Figure 5.4(b),
60
respectively. The time scales presented in the figure are obtained through exponential fittings of
the simulation data. The ground state recovery in the pristine system takes ~23 ps, which is still
one order of magnitude slower than our experimental observation. It is important to note that the
simulation described in Figure 5.4 only allows phonon-driven nonradiatively processes. Thus, the
results of Figure 5.4 mimic high carrier density experiments in which Auger-type charge-charge
scattering is turned off.

Figure 5.3. Structures, top, and density of states (DOS), bottom, of (a) pristine MoTe2 bilayer
with calculated band gap of 0.95 eV between valence band maximum (VBM) and conduction
band minimum (CBM), (b) MoTe2 bilayer with one Te vacancy (VTe). The vacancy is denoted
with a red circle. It creates electrons traps within the bandgap, as are shown in red area in
the bottom. The energy of trap states locates approximately 0.2 to 0.3 eV below the CBM.
Emerald and yellow balls represent Mo and Te atoms, respectively.

61
The phonon-driven nonradiative charge carrier recombination, channel ①, accelerates slightly
in the presence of the VTe defect as shown in the blue curve in Figure 5.4(b). The electron is trapped
from the CB into the defect states within a few picoseconds, and then proceeds to recombine with
the hole in the VB (red curve in Figure 5.4(b)). The fast rise of the defect level population,
compared to the ~21 ps ground state recovery time, and the relatively large transient amplitude of
the defect population, nearly 50%, indicating a significant contribution of carrier relaxation
through the defect level. This conclusion is confirmed further by the values of the non-adiabatic
coupling (NAC) presented in Table 5.1. Defined as 𝑖ħ< 𝛷
5
= ∇
𝑹
= 𝛷
0
@∙
¶𝑹
¶s
, the NAC depends on
overlap of wavefunctions of initial and final electronic states, and reflects the sensitivity of the
wavefunctions to nuclear movements. The NAC is a form of electron-phonon coupling. The NACs
from the trap level to the CBM and VBM are ~20 % larger than the NAC of carriers between the
CBM and VBM. It is important to note that the calculated charge carrier lifetimes in MoTe2 are
shorter than in other TMDs systems.
78
This is because MoTe2 has a significantly smaller band gap
than other TMDs, such as MoSe2 and MoS2. The carrier recombination in defective MoTe2 is
reported to be ~60 ps, which is consistent with our results.
112

The ~8 ps time of phonon-mediated electron trapping is a factor of two to three larger than the
experimentally determined carrier trapping times as displayed in Figure 5.2(b). This is because the
simulation described in Figure 5.4 does not allow for Auger-type carrier-carrier energy exchange
which is actually happening in the experiment at high carrier densities. Next we turn on the Auger
channel and simulate simultaneous phonon-mediated and Auger-mediated electron trapping and
the results are shown in Figure 5.5. Figure 5.1 illustrates three different mechanisms of charge
carrier relaxation, among which the third mechanism including both Auger and phonon-driven
processes is consistent with our THz results.
62

Figure 5.4. Simulations of phonon-induced charge carrier recombination and trapping
dynamics in (a) pristine MoTe2 bilayer based on the model shown in Figure 5.1(a) and (b)
MoTe2 bilayer with tellurium vacancy, VTe, based on the model shown in Figure 5.1(b). Only
a single electron-hole pair is present in this simulation, and Auger processes are not allowed.
The recovery of the ground state (GS) population, shown by the blue lines, occurs on a ~20
ps time scale in both systems. For a defective bilayer, VTe creates electron traps located at
~0.2 to 0.3 eV below the CBM. Carrier relaxation through the trap level is shown by the red
curve. Electrons are quickly trapped in the defect levels within ~8 ps and recombine with
holes at VBM at later time. The insets in (a) show charge densities of the VBM and CBM,
and in (b) the higher energy defect state. Both VBM and CBM delocalize throughout the
whole bilayer, while the electron trap resides locally around the defect and within one layer.

63
Table 5.1. Root-mean-square non-adiabatic coupling (NAC) for charge carriers trapping
and recombination processes.

Pristine bilayer Defective bilayer with V Te
Recombination of
CB (e
-
) and VB
(h
+
)
Recombination of
CB (e
-
) and VB
(h
+
)
VBM to trap CBM to trap
NAC (meV) 4.54 3.88 4.89 4.63
Energy gap (eV) 0.95 0.95 0.65~0.75 0.2~0.3

Figures 5.5(a) and 5.5(c) compare electron trapping driven purely by phonons, channel ② in
Figure 5.1(b), with electron trapping driven by both phonons and electron-electron energy
exchange, channel ④ in Figure 5.1(c), respectively. Note that the hole is not present in the current
simulation so that the blue curve in Figure 5.5(a) does not decay to zero as was observed in the red
curve in Figure 5.4(b). This allows us to reduce computational expense significantly while
maintains the accuracy of simulation for nonradiative carrier relaxation process to the trap levels.
The simulation includes trap states and 30 CB states for each of the two electrons, giving a
32×32=1024 state basis for quantum dynamics. Adding another 30 VB states for the hole would
increase the many-particle basis to ~30,000, greatly increasing the computational cost. Thus,
Auger-type energy exchange occurs between the two electrons present in the simulation. The
simulation already captures the essential physics, and allows not only the pure Auger scattering,
but also Auger scattering that occurs simultaneously with charge-phonon relaxation.

64

Figure 5.5. Simulations of electron trapping in the MoTe2 bilayer with the tellurium vacancy,
VTe. (a, b) Phonon-driven trapping, process ② in Figure 5.1(b). (c, d) Trapping driven
simultaneously by the Auger and phonon mechanisms, process ④ in Figure 5.1(c). Blue
curves in parts (a, c) show the evolution of electron population in the trap state, while parts
(b, d) present the change of electronic energy of carriers. Auger-type energy exchange
between charges accelerates the trapping, bringing agreement with the experiment,
Figure 5.2(b). The solid pink circles in (c) depicts the THz experimental results at the carrier
density of 4.6×10
20
cm
-3
. Note that this kinetics trace is reversed vertically in order to show
the loss of carrier to trap levels (or increase of electron population in trap level). The
dynamics in (d) is not exponential at the beginning, because the system needs time to explore
the Hilbert space of final states. Only half of the trapped electron energy is transferred to
the 2
nd
electron, with the other half going to phonons.

Figure 5.5(a) matches well the rise of the trap state population in Figure 5.4(b), both processes
corresponding to phonon-mediated electron trapping. The key result of the present work is
demonstrated in Figures 5.5(c) to 5.5(d). Figure 5.5(c) shows that Auger-type electron-electron
scattering accelerates the charge carrier trapping to ~2 ps, matching very well with the
experimental data presented in Figure 5.2(b). Figure 5.5(d) demonstrates that only half of the
energy lost by the 1
st
electron during the trapping is deposited into the 2
nd
electron by the Auger-
type scattering (i.e. 0.1 eV). The remaining half of the trapped electron energy is accommodated
by phonons (i.e. 0.1 eV from total available energy of 0.2 eV). Figure 5.5(d) also shows that the
Auger-type scattering continues until the 1
st
electron is fully trapped and with energy fully
65
converted to phonons. The 1
st
electron energy continues to decrease up to 4.5 ps. The energy of
the 2
nd
electron increases concurrently, and after that the energy decreases due to intraband
electron-phonon relaxation. The initial dynamics is not exponential, in particular, since the
quantum system needs time to explore the full Hilbert space of available states. The simulation
results show that the electron-phonon scattering to the trap levels competes strongly with
Auger-type electron-electron scattering, and the overall trapping process can be characterized as
an entangled combination of charge-phonon and Auger scattering.

Figure 5.6. Density of states of defective MoTe2 bilayer with two adjacent Te vacancies. Many
trap states appear near band edges, facilitating fast phonon-trapping and further
suppressing Auger trapping.

The successful competition of the phonon-mediated electron trapping with the Auger-type
electron trapping seen in our simulations can be attributed to the following factors. First, the pure
phonon-mediated electron trapping is already quite fast in bilayer MoTe2 (i.e. ~7 to 8 ps), only a
factor 2 to 3 slower than the Auger-type trapping. This is because the trap states are relatively
shallow, about 0.2 eV to 0.3 eV below the CBM as shown in Figure 5.3(b). Occasionally, thermal
66
atomic fluctuations decrease this energy gap even further. Besides, as defect density increases,
many trap states appear near band edges Figure 5.6. These states speed up phonon-mediated
trapping and further compete with Auger trapping. The NAC between electrons in CBM and trap
states is slightly larger than the direction recombination of NAC between the electrons in CBM
and the holes in VBM as was listed previously in Table 5.1. Since gaps between trap states and
band edges are even smaller in TMDs with high defect concentration Figure 5.6, the NAC for
trapping should be even larger than for direct recombination. Second, the other electron that
accommodates the trapped electron’s energy during the Auger-type scattering evolves into a dense
manifold of CB states (green curve in Figure 5.5(d)). It undergoes rapid electron-phonon relaxation
afterwards
97-98
which is faster than the trapping process itself. The second electron is excited into
vibrationally hot electronic states, with fraction of the energy taken by the vibrational degrees of
freedom. Third, after the 1
st
electron starts to get trapped, its charge density gathers around the
defect and resides only in one layer, as shown in the inset in Figure 5.4(b). The localization of the
trapped electron weakens its coupling to the free electrons, reducing the efficiency of electron-
electron Auger scattering. At the same time, electron localization increases electron-phonon
coupling, as evidenced by the larger NAC for the processes involving the trap states as shown in
Table 5.1. The significant contributions of phonons-driven trapping process rationalize the weaker
than quadratic dependence of the trapping rate on the charge carrier density as was observed in our
experiments in Figure 5.2. Our theoretical results indicate that the Auger channel is notably
suppressed by electron trapping channel that deposit electronic energy to phonon modes quickly.
The time scale of electron-phonon energy redistribution in the defective crystal does not depend
on carrier density. Thus, the lifetime of free charge carriers exhibits very weak carrier density
dependence.
67
5.4 Conclusion
We measured charge carrier lifetimes in few-layer 2H-phase MoTe2 with ultrafast optical pump
and THz probe transient absorption spectroscopy. Our NAMD and real-time TDDFT calculations
show that the observed short carrier lifetime is caused by defects in this system. We find that the
Auger process alone cannot explain the weak dependence of the lifetime of photo-generated
carriers over a factor of 100 variation of carrier density. An efficient energy dissipation into phonon
modes competes successfully with electron-electron scattering, rationalizing the experiments.
Intrinsic defects in TMD samples create trap states that are close in energy to band edges, making
phonon-driven carrier trapping already quite efficient. During the Auger process, the other electron
that accepts the energy of the trapped electron is excited into vibrationally hot states and undergoes
rapid intraband electron-phonon relaxation. As a result, half of the trapped electron energy goes
directly into phonons. Further, as electron gets trapped, it localizes around the defect and only
resides in one layer, decreasing its coupling to the free delocalized charge carriers. The strong
participation of phonons during the trapping process leads us to conclude that charge trapping at
high carrier densities occurs by the phonon-suppressed Auger mechanism that shows weaker
dependence on charge carrier density than the standard Auger-type charge-charge scattering.
We find that defects play a dual role in charge trapping. At low carrier densities, defects provide
an efficient charge relaxation pathway, accelerating nonradiative carrier losses compared to
pristine samples. Charge trapping is mediated by phonons in this regime. As the carrier density
increases, Auger-type charge-charge scattering becomes important, accelerating carrier trapping.
However, instead of the rapid reduction of carrier lifetime with carrier density by the quadratic
law, the rate shows a much weaker carrier density dependence, because the Auger mechanism is
suppressed by active participation of phonons. Our theoretical results show good agreement with
68
the experimental data, provide important mechanistic insights into charge carrier losses in TMDs
at the high carrier density, and suggest routes for improving performance of TMD devices.

69
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Abstract (if available)

Abstract The thesis consists of three parts. The first part focuses on the non-adiabatic molecular dynamic (NAMD) simulations of the MoS₂/WS₂ heterojunction. The second part is on the defect engineering of the charge carrier dynamics in two-dimensional transition metal dichalcogenides (TMDs). The third part is about the Auger process in TMDs. ❧ Our motivation for studying NAMD in TMDs arises from the powerful potentials of TMDs. After the success of graphene, TMDs have been extensively studied due to their tunable band gaps, good catalytic performance and great potentials in photovoltaic devices. Despite promising potentials for applications in electronics and optoelectronics, however, TMDs are still limited by their low electrical mobility, short-lived free charge carrier and low photoluminescence quantum efficiency. Deterioration of the radiative quantum efficiency and charge carrier lifetime is attributed to charge scattering, that is, electron-phonon coupling. NAMD is a good way to measure electron-phonon coupled dynamics. NAMD simulations could provide theoretical insights into the diverse charge carrier dynamics in TMDs and generate guidelines to improve the performance of TMDs based materials. Chapter 1 discusses general properties of TMDs and mathematical foundations of NAMD simulations. ❧ Through coupling different two-dimensional TMDs together, heterostructure with improved electronic and optical properties can be achieved, which becomes the basis of modern devices. Experiments detected an ultrafast charge separation and a long-lived charge separated state in the MoS₂/WS₂ heterojunction. These phenomena are rather surprising. Because the interlayer interaction between MoS₂ and WS₂ layers is weak. And electron and hole in this heterojunction is located closely. In Chapter 2, we present the time-domain ab initio study of charge carrier dynamics in the MoS₂/WS₂ heterojunction. We found that the ultrafast charge transfer results from significant delocalization of the photoexcited state between the donor and acceptor materials. The electron-hole recombination is slow because the initial and final states are localized strongly within different materials. ❧ Chapter 3 discusses the effects of two defects, that is, adatom and vacancy, on charge carrier dynamics in MoS₂ monolayer. We found that adatom could greatly accelerate electron-hole recombination, compared with vacancy. This is because adatom could strongly perturb the TMDs layer, break its symmetry and allow more phonon modes to couple to the electronic subsystem. In contrast, vacancy accelerates charge recombination through traditional defects assisted trapping and recombination, which results from delocalized electron traps. As a result, to make high-performance TMDs based devices, adatom should be strongly avoided. Chapter 4 talks about two kinds of defects due to different manufacturing methods. Chemical vapor deposition (CVD) samples maintain a high concentration of vacancy defects while physical vapor deposition (PVD) samples mainly contain antisite defects. Our simulations show that antisites are much more detrimental than vacancies. Antisites create deep traps for both electrons and holes. Those electron and hole trap pairs are close to the Fermi energy, allowing fast trapping by thermal activation from the ground state and strongly contributing to charge scattering. Antisites also strongly perturb band-edge states, creating significant overlap with the trap states. In comparison, vacancy defects overlap much less with the band-edge states and only accelerate charge recombination by less than a factor of 2. Our simulations demonstrate a general principle that missing atoms are significantly more benign than misplaced atoms and rationalize general experimental observations that CVD samples outperform PVD samples. ❧ Chapter 5 explores the diverse roles played by phonons and Auger processes in TMDs. High carrier concentration and long lifetimes is a must to produce high-performance devices. However, high concentrations usually accelerate energy exchange between charge carriers through Auger-type processes, especially in TMDs where many-body interactions are strong. As a result, Auger-process dominate high carrier density region. Surprisingly, experiments detect non-pure Auger type dynamics. Our simulations show that phonon-driven trapping competes successfully with the Auger process, given the common existence of point defects. Defects create shallow traps close to band edges, and phonons accommodate efficiently the electronic energy during the trapping. Besides, trap states localize around defects, decreasing the overlap of trapped and free carriers and carrier-carrier interactions. At low carrier densities, phonons provide the main charge loss mechanism. At high carrier densities, phonons suppress Auger processes and lower the dependence of the trapping rate on carrier density.

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Asset Metadata

Creator Li, Linqiu (author)

Core Title Non-adiabatic molecular dynamic simulations of charge carrier dynamics in two-dimentional transition metal dichalcogenides

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Publication Date 02/17/2020

Defense Date 01/21/2020

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

Tag defect engineering,non-adiabatic molecular dynamics,OAI-PMH Harvest,phonons,transition metal dichalcogenides

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Prezhdo, Oleg V. (committee chair)

Creator Email linnnankai@gmail.com,linqiuli@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-268966

Unique identifier UC11675177

Identifier etd-LiLinqiu-8183.pdf (filename),usctheses-c89-268966 (legacy record id)

Legacy Identifier etd-LiLinqiu-8183.pdf

Dmrecord 268966

Document Type Dissertation

Rights Li, Linqiu

Type texts

Source 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 a...

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