Structure Characterization and Electronic Properties Investigation Of

Structure Characterization and Electronic Properties Investigation of

Two-Dimensional Materials

Fazel Baniasadi

Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State

University in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

Chair: Chenggang Tao

Co-Chair: Kyungwha Park

William Reynolds

Mitsu Murayama

Carlos Suchicital

05/10/2021

Blacksburg, Virginia

Keywords: Two Dimensional Materials, Scanning Tunneling Microscopy, Density

Functional Theory, Raman Spectroscopy, 1T-PtSe2, 2M-WS2

Structure and Electronic Properties Investigation of Two-Dimensional Material

Fazel Baniasadi

ABSTRACT

This dissertation will have three chapters. In chapter one, a comprehensive review on defects in two dimensional materials will be presented. The aim of this review is to elaborate on different types of defects in two dimensional (2D) materials like graphene and transition metal dichalcogenides (TMDs). First, different types of point and line defects, e.g. vacancies, anti-sites, guest elements, adatoms, vacancy clusters, grain boundaries, and edges, in these materials are categorized in terms of structure. Second, interactions among defects are discussed in terms of their rearrangement for low-energy configurations. Before studying the electronic and magnetic properties of defective 2D materials, some of the structures are considered in order to see how defect structure evolves to a stable defect configuration. Next, the influence of defects on electronic and magnetic properties of 2D materials is discussed. Finally, the dynamic behavior of defects and 2D structures under conditions such as electron beam irradiation, heat treatment, and ambient conditions, is discussed. Later as a case study, defects in a two dimensional transition metal dichalcogenide will be presented. Among two-dimensional (2D) transition metal dichalcogenides (TMDs), platinum diselenide (PtSe2) stands at a unique place in the sense that it undergoes a phase transition from type-II Dirac semimetal to indirect-gap semiconductor as thickness decreases. Defects in 2D TMDs are ubiquitous and play crucial roles in understanding and tuning electronic, optical, and magnetic properties. Here intrinsic point defects in ultrathin 1T-PtSe2 layers grown on mica were investigated through the chemical vapor transport (CVT) method, using scanning tunneling microscopy and

spectroscopy (STM/STS) and first-principles calculations. Five types of distinct defects were observed from STM topography images and the local density of states of the defects were obtained. By combining the STM results with first-principles calculations, the types and characteristics of these defects were identified, which are Pt vacancies at the topmost and next monolayers, Se vacancies in the topmost monolayer, and Se antisites at Pt sites within the topmost monolayer. Our study shows that the Se antisite defects are the most abundant with the lowest formation energy in a Se-rich growth condition, in contrast to cases of 2D molybdenum disulfide (MoS2) family. Our findings would provide critical insight into tuning of carrier mobility, charge carrier relaxation, and electron-hole recombination rates by defect engineering or varying growth condition in few-layer 1T-

PtSe2 and other related 2D materials. Also, in order to investigate the layer dependency of vibrational and electronic properties of two dimensional materials, 2M-WS2 material was selected. Raman spectroscopy and DFT calculation proved that all Raman active modes have a downshift when material is thinned to few layers (less than 5 layers). It was proven that there is a strong interaction between layers such that by decreasing the number of layers, the downshift in Raman active modes is mostly for the ones which belong to out-

2 of-plane atomic movements and the most downshift is for the Ag Raman active mode. Also, I investigated the effect of number of layers on the band structure and electronic properties of this material. As the number of layers decreases, band gap does not change until the materials is thinned down to only a single monolayer. For a single monolayer of 2M-WS2, there is an indirect band gap of 0.05eV; however, with applying in-plane strain to this monolayer, the material takes a metallic behavior as the strain goes beyond ±1%.

Structure and Electronic Properties Investigation of Two-Dimensional Material

Fazel Baniasadi

GENERAL AUDIENCE ABSTRACT

Graphite (consisting of graphene as building blocks) and TMDS in bulk form are layered and with exfoliation one can reach to few layers which is called two-dimension. Two dimensional materials like graphene have been used in researches vastly due to their unique properties, e.g. high carrier mobility, and tunable electronic properties. Transition metal dichalcogenides (TMDs) with a general formula of MX2, where M represents transition metal elements (groups 4-10) and X represents chalcogen elements (S, Se or Te), are another family of two-dimensional materials which have been extensively studied in the past few years. Besides exfoliation, there are also synthesis methods to produce two dimensional materials, e.g. chemical vapor deposition and chemical vapor transport.

Normally, after synthesizing these materials, researchers investigate structure and electronic properties of these materials. There might be some atoms which no longer exist in the structure; hence, those are replaced by either vacancies or other elements which all of them are called defects. In chapter 1, defects in graphene and transition metal dichacolgenides were investigated, carefully. Later, dynamic behavior of defects in these materials were investigated and finally, the effect of defects on the electronic properties of the two dimensional materials were investigated. Chapter two talks about a case study which is two dimensional 1T-PtSe2. In this chapter, 5 different kinds of defects were

v studied using scanning tunneling microscopy and spectroscopy investigations and density functional theory was used to prove our assumptions of the origin of defects.

Also, another thing which is investigated by researcher is that how atoms in two dimensional materials vibrate and how the number of layers in the two dimensional material influences vibrations of atoms. Other than this, electronic properties of these materials is dependent upon the number of layers. When these materials are synthesized, there is a stress applied to the material due the mismatch between the material and its substrate, so it is worth investigating the effect of stress (strain) on the structure, and electronic properties of the material of interest. For this purpose, 2M-WS2 was exfoliated on Si/SiO2 substrate and the layer dependency of its vibrational modes was investigated using Raman spectroscopy and density functional theory calculation. Also, in order to investigate the influence of stress (strain) on the electronic properties of two dimensional

2M-WS2, a single monolayer of this materials underwent a series of strains in density functional theory calculations and the effect of strain on the electronic properties of this material was investigated.

DEDICATION

I would like to dedicate this dissertation to my family. Without their special support, I would have never been able to do my best and fulfill the requirements for my study. Their words and encouragement were always with me and I will definitely use them in my future life. So many thanks to all of them.

AKCNOWLEDGEMENT

I would appreciate all the support and help I received from my advisor, Dr. Chenggang

Tao. Also, I would like to express my gratitude to Prof. Kyungwha Park who supported me as my co-advisor and I learned a lot from her.

I would like to thank the rest of my committee members who gave me helpful keys for my

PhD study.

Prof. William Reynolds helped me in different ways. Some days I was depressed, and he was with me. What he did to me was like what a father does toward his son or daughter. I wish I can respond to this much of kindness one day in the near future.

Finally, I would like to thank my lab-mates who were always kind and supportive.

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Attribution

The contributors to the whole work of this PhD dissertation are as follow:

Chenggang Tao – Professor at Virginia Tech, Department of Physics.

William Reynolds – Professor at Virginia Tech, Department of Materials Science and

Engineering.

Kyungwha Park – Professor at Virginia Tech, Department of Physics.

Michael von Spakovsky – Professor at Virginia Tech, Department of Mechanical

Engineering.

Aimen Yunis – Postdoctoral Researcher at Virginia Tech, Department of Mechanical

Engineering.

Jhon A. Montanez-Barrera – Graduate Student at Virginia Tech, Department of

Mechanical Engineering.

Yichul Choi – Graduate Student at Virginia Tech, Department of Physics.

Husong Zheng – Graduate Student at Virginia Tech, Department of Physics.

Dake Hu – Graduate Student at Tsinghua University, Department of Chemistry.

Liying Jiao – Professor at Tsinghua University, Department of Chemistry.

Fang Yuqiang – Researcher at Shanghai Institute of Ceramics.

Fuqiang Huang – Researcher at Shanghai Institute of Ceramics.

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In-detail contribution of my collaborators is as follow:

Chapters 1 and 2: I wrote the review paper from the beginning until the end. Dr. Reynolds and Dr. Tao reviewed it.

Chapters 3 and 4: Husong Zheng did the whole room temperature STM and AFM experiments. We both conducted the low temperature STM measurements, did the analysis on all the experiments, wrote the introduction, experiment methods, result and discussion, and supplementary information parts of the resulting paper. Dr. Tao supervised the experimental part of the project. Dr. Park and Yichul Choi conducted the DFT calculations, did the theoretical part of the project, and wrote the calculation parts of the paper. Dake Hu and Liying Jiao synthesized the material for us.

Chapter 5: Dake Hu and Liying Jiao synthesized the material. Husong Zheng and I conducted the STM and annealing experiments. I identified the types of individual defects with STM, measured the areal densities of individual defects, cataloged the combinations of interacting defects, and analyzed the changes in these characteristics during sequential annealing steps. Dr. Reynolds and I developed a thermodynamic model for this study. I did the DFT calculations to estimate the energies of all the individual defects and all the possible configurations of interacting defects. Dr. Aimen Younis, Dr. von Spakovsky, and

Dr. Reynolds did the SEAQT part of the project. Dr. Reynolds, Dr. von Spakovsky, Aimen

Younis and I wrote the resulting paper from this work which will be submitted to a journal soon.

Chapter 6: Fang Yuqiang and Fuqiang Huang synthesized the material. I did the the rest of the experiments, did the DFT calculation, analyzed the results and wrote the paper of

ix this work. Dr. Reynolds supported the experiment and supervised me for it. Dr. Park supervised my conducting DFT simulations and interpretation of the results. The resulting paper of this work will be submitted to a journal next month.

Table of Contents

INTRODUCTION ...... 1 1.1. TWO-DIMENSIONAL MATERIALS ...... 1 1.2. HOW TO PRODUCE A TWO-DIMENSIONAL MATERIAL...... 1 1.2.1. EXFOLIATION...... 1 1.2.2. SYNTHESIS ...... 2 1.3. DEFECTS IN TWO-DIMENSIONAL MATERIALS ...... 3 1.4. LAYOUT OF MY DISSERTATION ...... 5 REVIEW: DEFECT STUDY OF TWO-DIMENSIONAL MATERIALS...... 6 2.1. ABSTRACT ...... 6 2.2. INTRODUCTION ...... 7 2.3. PHYSICAL PERCEPTION OF DEFECTS ...... 10 2.3.1. POINT DEFECTS ...... 10 2.3.2. LINE DEFECTS ...... 16 2.4. THE INFLUENCE OF DEFECTS ON ELECTRONIC AND MAGNETIC PROPERTIES ...... 24 2.4.1. GRAPHENE ...... 24 2.4.2. TMDs ...... 28 2.5. DYNAMIC BEHAVIOR OF DEFECTS ...... 32 2.5.1. GRAPHENE ...... 32 2.5.2. TMDs ...... 41 2.6. SUMMARY ...... 49

VISUALIZATION OF POINT DEFECTS IN ULTRATHIN LAYERED 1T-PtSe2... 50 3.1. ABSTRACT ...... 50 3.2. INTRODUCTION ...... 51 3.3. METHODS...... 53 3.3.1. EXPERIMENT ...... 53 3.3.2. SIMULATION ...... 53 3.4. RESULTS AND DISCUSSION ...... 55 3.4.1. STM TOPOGRAPHIC IMAGE ...... 55 3.4.2. DFT SIMULATIONS OF INTEGRATED LDOS ...... 60 3.5. CONCLUSION ...... 67

SUPPLEMENTARY INFORMATION FOR “VISUALIZATION OF POINT DEFECTS IN ULTRATHIN LAYERED 1T-PtSe2” ...... 69 4.1. EXTRA EXPERIMENTAL DATA ...... 69 4.2. DFT CALCULATIONS OF FORMATION ENERGIES ...... 73 DEFECT STABILITY AND KINETICS IN TWO-DIMENSIONAL 1T-PtSe2 ...... 82 5.1. INTRODUCTION ...... 82 5.2. METHODS...... 83 5.2.1. SYNTHESIS AND IMAGING ...... 83 5.2.2. DFT CALCULATION ...... 93 5.2.3. THERMODYNAMIC MODEL ...... 96 5.2.4. ENERGY LANDSCAPE ...... 99 5.2.5. KINETIC MODEL AND TEMPERATURE ...... 101 5.3. RESULT AND DISCUSSION ...... 103 APPENDIX A ...... 109 A.1 CHEMICAL POTENTIALS ...... 109

VIBRATIONAL PROPERTIES OF TWO DIMENSIONAL 2M-WS2 FILMS ...... 111 6.1. ABSTRACT ...... 111 6.2. INTRODUCTION ...... 112 6.3. METHODS...... 113 6.3.1. SAMPLE PREPARATION ...... 113 6.3.2. MEASUREMENT METHODS ...... 116 6.3.3. COMPUTATIONAL DETAILS ...... 117 6.4. MEASURED VIBRATIONAL MODES...... 119 6.5. DENSITY-FUNCTIONAL THEORY CALCULATIONS ...... 121 6.5.1. RAMAN ACTIVE MODES ...... 121

6.5.2. ELECTRONIC BAND STRUCTURE OF A SINGLE MONOLAYER OF 2M-WS2 UNDER STRAIN ...... 123 6.6. RAMAN SPECTROSCOPY: SIMULATION AND EXPERIMENT...... 131 6.7. CONCLUSION ...... 133 6.8. ACKNOWLEDGEMENT ...... 133 REFERENCES ...... 134

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INTRODUCTION

1.1. TWO-DIMENSIONAL MATERIALS

Graphene, an ultrathin carbon material produced via graphite exfoliation (delamination), was the first two-dimensional (2D) material which was introduced by Novoselov et.al. [1] which have outstanding electronic and physical properties [2].Actually, what two dimension stands for is atomically thin. Later, other two dimensional materials were explored and introduced for example single to few-layered transition metal dichalcogenides (TMDs), transition metal carbides and notrides (MXenes), 2D mono elemental materials like P, Si and B [3, 4].

1.2. HOW TO PRODUCE A TWO-DIMENSIONAL MATERIAL 1.2.1. EXFOLIATION

There are a variety of methods to produce 2D materials. One method is the delamination of layered materials [5]. For instance, graphite consists of thousands of graphene layers. If one delaminates graphite such that at least one layer of graphene is remaining, then a 2D form of carbon atoms is achieved which we call it a 2D material. In order to delaminate layered materials there are several ways which all of them are almost mechanical [5]. One can use a scotch tape and put the layered material (e.g. graphite) onto it, then fold the tape, unfold it, use another tape, move the delaminated flakes from the previous tape to the new tape and do the folding/unfolding process until flakes reach the thickness of single to few layers [6, 7]. Then, the tape is put on a substrate (e.g. Si/SiO2), rub behind the tape and remove the tape suddenly [8]. This method will leave at least some ultrathin material having single to few layers thickness and is called mechanical exfoliation. Another method of exfoliation is that when we have bulk` layered materials having some elements between layers like MAX materials [8, 9]. MXenes are made through liquid exfoliation. Their precursor is

1 usually a MAX phase. M stands for the transition metal element in their formula, A is an element from group IIIA or IVA, and X is either carbon or nitrogen [9]. In order to do the exfoliation, the

A element must be extracted since it is between layers and once it is extracted, layers become individual and the MAX phase will be converted to MX phase; however, due to analogy with graphene, it is called MXene. This method is a combination of physical and chemical exfoliation, since chemical process is used to extract the A element from interlayer spaces and the liquid also is used to separate 2D layers by sonication [10].

1.2.2. SYNTHESIS

Besides exfoliation, there are other methods to make 2D materials as well. Chemical vapor deposition (CVD) is a method which have been used vastly for the synthesis of these materials

[11]. In this method, we can control the thickness of the material to be either in 2D limit or even thicker. Parameters which control this method are temperature, gas pressure and time. For example, as the temperature goes higher, the deposition rate will be higher as well. By increasing the temperature, however, the chance of the synthesis of other products which are favored at higher temperatures is elevated. Also, the non-uniformity of the 2D material increases too. Hence, finding the appropriate temperature for CVD synthesis of these materials is critical. The same thing is for gas pressure. As the pressure of gas precursors increases, deposition rate and non-uniformity increase. Since, the thickness of 2D materials and their uniformity are very sensitive to the synthesis condition, playing with synthesis parameters is the primary job a researcher does.

Therefore, finding appropriate synthesis conditions are super critical in 2D materials chemical vapor deposition and these conditions need a lot of trial and errors [12-17].

Atomic layer deposition (ALD) [18] and molecular beam epitaxy (MBE) [19] are other synthesis methods to produce 2D form of layered materials [11]. Compared to CVD method, these methods

2 are not used frequently in 2D materials synthesis since the goal is to look for excellent crystal quality, superior yield, and large scale production. Recently, 2D form of non-layered materials have been synthesized via Van der Waals epitaxial (VdWE) growth which has a high potential of anisotropic growth for two dimensional non-layered materials [20].

Actually, what is very important in 2D materials production is that finding the application of the material first, and based on the application one should try to find the most appropriate method of how to reach the 2D form of the material of interest. For instance, if the goal is to make a field effect transistor and if one wants to find the on/off ratio of the transistor, one way is to use exfoliation and then transfer the 2D material to the transistor; however, this method has a lot of uncertainty since it is unknown if we are transferring the material exactly to the desired location and there is no control on contamination [21-23].

1.3. DEFECTS IN TWO-DIMENSIONAL MATERIALS

As discussed above, depending on the application, the method of how to produce a 2D material can change. If I select exfoliation and use a liquid for it, the liquid will do physical and chemical interactions with the layered material. These two kinds of interactions have their own impacts to the material structure. From the chemistry point of view, the liquid can alter the composition of the layer by interacting with other elements of the MAX phase, M and X. These interactions will result in defects in the structure, e.g. vacancies, guest or substitutional elements, line defects and etc. [10, 24, 25].

Also, the liquid can leave some functional groups, being attached to the 2D material after exfoliation, which can alter the physical and chemical properties of the 2D material [26, 27]. If we use mechanical exfoliation, the possibility to introduce defects into the structure is less but still

3 remaining. When doing the mechanical exfoliation, the bulk layered material is torn off several times such that one can reach an ultrathin layer of the material. The process of tearing off will increase the edges of the material. At the edges, elements are not fully bonded to their neighbors and the physical and chemical properties of edges are different from the middle of the 2D material.

Hence, edges could be categorized as a kind of defect in 2D materials [28, 29]. In chemical synthesis of 2D materials, there are more chances of having different kinds of defects due to chemical reactions. There could be vacancies, groups or lines of vacancies, edges, substitutional

(guest) elements, groups (clusters) or lines of substitutional elements, adatoms (atoms which are physically or chemically bonded to the surface of the material) [30], and the effect of the substrate on the material [31] (crystal mismatch and etc.). Defects can change the composition of the 2D material and as the result change the structure and physical and electronic properties of the material. Considering all discussed above, we can conclude that defects have a very important role in defining properties of 2D materials [30, 32].

On the other hand, when doing the exfoliation, it is not easy to control how many layers exist after a specific number of exfoliations and it means that properties can change based on the number of layers [7]. Sometimes, there could be a single monolayer of the 2D material and sometimes it might be few layers. The same thing exists for chemical synthesis methods. The control of thickness besides aiming for high lateral (xy) size is a big challenge in chemical synthesis methods

[12]. Therefore, structure and electronic properties will be layer dependent.

1.4. LAYOUT OF MY DISSERTATION

In order to address the concerns discussed above, the influence of defects on the structure and electronic and physical properties of two dimensional materials and layer dependency of these properties I selected the following route.

First in chapter 2, I did a comprehensive study on defects, their structures and the influence of them on the properties of graphene and 2D transition metal dichalcogenides. Second in chapters 3 and 4, 2D 1T-PtSe2 was synthesized on Mica substrate via chemical vapor transport, its defects were studied using scanning tunneling microscope as the main investigation tool and density functional theory as the complementary effort to be able to justify my experiments. Defects can migrate across the material if the energy for their movement is provided. As, these is heat treatment in chapters 3 and 4, then I could study defect migration and defect combination as the result of which across the material. Therefore, defect combinations, their formation energy and their equilibrium state will be discussed in chapter 5. Finally in chapter 6, 2D 2M-WS2 was selected to investigate the effect of the number of layers on different properties of the material.

REVIEW: DEFECT STUDY OF TWO-DIMENSIONAL MATERIALS

2.1. ABSTRACT

The aim of this review is to elaborate on different types of defects in two dimensional (2D) materials like graphene and transition metal dichalcogenides (TMDs). First, different types of point and line defects, e.g. vacancies, anti-sites, guest elements, adatoms, vacancy clusters, grain boundaries, and edges, in these materials are categorized in terms of structure. Second, interactions among defects are discussed in terms of their arrangement into low-energy configurations. Before studying the electronic and magnetic properties of defective 2D materials, some of the structures are considered in order to see how defect structure evolves to a stable defect configuration. Next, the effect of defects on electronic and magnetic properties of the 2D materials are discussed.

Finally, the dynamic behavior of defects and 2D structures under conditions such as electron beam irradiation, heat treatment, and ambient conditions, are discussed.

Keywords: Two Dimensional Materials, Defects, Graphene, Transition Metal Dichalcogenides

2.2. INTRODUCTION

Two dimensional (2D) materials have attracted materials scientists’ attention because of their special electronic and optoelectronic properties [33-36] . The synthesis of two-dimensional carbon with sp2-bonding, called graphene, in 2004 [1] became the genesis of work on producing other groups of 2D materials (Figure 2.1a) [37] like hexagonal boron nitride (hBN) [38], transition metal oxides [39], transition metal chalcogenides (TMCs) [40, 41] and 2D mono elemental materials like P, Si and B [3, 4]. Graphene received so much attention so quickly because of its combination of peculiar properties including high carrier mobility [42, 43], high in-plane mechanical strength

[44], and sizable band gap [45]. A few years later, transition metal dichalcogenides (TMDs) were introduced. These have the general formula of MX2 (M as the transition metal and X as the chalcogen element) which forms an X-M-X configuration in which M is sandwiched between two

X atomic layers. Both M and X are individually in-plane hexagonal closed pack layers [46]. By reducing the number of stacked layers of MX2, considerable changes are introduced into the properties of these materials e.g. indirect to direct band gap transition and carrier mobility increase

[47]. Depending on the number of stacking layers, there are several structures for TMDs including

1H, 2H, 1T, 1T ՜, 3R and 2M (Figure 2.1b-g) [48, 49]. The problem of defects in compound semiconductor structures like TMDs and the influence of them on electronic properties of 2D materials led researchers to investigate the potential of mono-elemental semiconducting materials.

Phosphorene (P) and Boron (B) are two such single elemental 2D materials that have been studied by researchers [3, 50]. However, B has still remained hypothetical and no one has yet conducted an experimental study of this material. The structure of P consists of buckled hexagons with a rectangular symmetry (Figure 2.1h and 1j) [3]. Recently, other generations of 2D materials have been introduced which are transition metal carbides (TMCs) [51], transition metal Nitrides

(TMNs) [52] and transition metal oxides [39]. Research on these materials, however, have remained at the synthesis step.

The functionality of all 2D materials is highly dependent upon the quality of their structures.

Geometric defects such as grain boundaries, edges, interfaces, dislocations and clusters of point defects can have a negative or a positive influence on the functionality of TMDs, e.g. lowering the carrier mobility or causing large spin-orbit splitting [53][3, 54-58]. Moreover, discrepancies between theory and experiment – like the emergence of an emission peak in the experimental optical band gap [59] lower than expected carrier mobility [60] and changes in Raman active modes – made us think about possible gaps in understanding. There could be different explanations for the mismatch being theory and experiment including instrumental uncertainty and faulty theoretical assumptions. The latter involve assumptions about the nature of the 2D crystal structure which can include defects and different types of crystalline order. Since defects play a very important role in the properties of 2D materials, this review will summarize the available information on defects in the structure of 2D materials and their effects on the electronic and magnetic properties of these materials. Also, finally, I will discuss the dynamic behavior of every individual defect under different conditions.

Figure 2.1: a) The structure of graphene which shows its 3-fold rotational symmetry and honeycomb structure [37]. Different types of perfect TMDs [49], b) trigonal prismatic 1H phase, c)metallic octahedral 1T phase, d) the most stable but distorted configuration of 1T structure which is 1T՜, e) A Bernel stacking (AbA BaB) of two 1H layers making a 2H phase, f) An AbA BcB CaC stacking of three 1H layers making a rhombohedral phase (3R), g) 2M-WS2 crystal structure with a red arrow showing the necessary movement of one layer in order to match with its adjacent layer in the monoclinic (M) structure and a 2 corresponding to the minimum number of layers needed for this structure. h) Phosphorene structure which depicts buckled hexagons having a rectangular symmetry [61]. i) The α- and flat snub-boron sheets [62].

2.3. PHYSICAL PERCEPTION OF DEFECTS

2.3.1. POINT DEFECTS

2.3.1.1. POINT DEFECTS IN GRAPHENE

Defects are typically categorized by their spatial dimensionality. Point defects are zero- dimensional defects [63]. These defects can be divided into different classes: rotated bonds, missing atoms, adatoms attached to the surface, substitutional atoms (one element filling the atomic site of a different element), and interstitial atoms (an atom filling a position located between normal atomic sites). For example, a Stone-Wales defect in graphene is a zero dimensional defect topologically generated by rotating one C - C bond by 90° which results in a 5 - 7 - 7 - 5 (two pentagons and two heptagons) ring fusion (Figure 2.2a) 35,36. As it is known, the formation energy for a vacancy is the amount of energy which is needed for removing one atom from its position and actually the parameter defining the formation energy of each defect is the chemical potential of each component (µX and µM) of the layered materials in compound state [64]. In order to remove one atom from its position, the bonding between that atom and its neighboring atoms must break or change. The amount of energy which is need for breaking or changing bonds is the barrier energy; however, after breaking bonds, new bonds are made which lower the final energy of the whole system. The formation energy is the difference between the final state and initial state of the whole system although the whole system has passed a barrier as well. Therefore, the formation energy of Stone-Wales defect in graphene is about 4.8eV which must overcome the barrier energy of 9.2eV during formation. Actually, the C - C bond should rotate by 90° and during this rotation, the energy barrier changes and reaches its maximum (9.2eV) at 45° and then decreases [65].

Vacancies in graphene are missing carbon atoms (Figure 2.2b). El-Barbary et.al [66] measured the formation energy for a single vacancy to be about 7.5eV (good agreement with experiment [67]),

10 and for the coalescence of two neighboring single vacancies into a divacancy (Figure 2.2c) to be

8.5eV. Dopants like nitrogen and boron (N & B) atoms can make the electronic structure of graphene change and introduce a gap because these two elements have just one electron difference with carbon and can change the position of the Fermi level [68]. Dopants like Si and Fe are also added to graphene during the synthesis process to modify the electronic properties and electronic band structure. Also, Electron or ion beams can be used intentionally to pattern 2D materials [69-

73]. These techniques are used to trap or assemble specific sized atomic clusters that lead to practical applications [74, 75]. Si6 clusters trapped in the nanopores of graphene are one of the material groups being used in nanopore technology which is used in molecular detection and DNA sequencing (Figure 2.2d). During the synthesis process of graphene, some of the carbon atoms may be trapped between graphene layers. L. Li et.al [65] proposed five different positions for such atoms and calculated their corresponding formation energies and concluded that the most stable configuration is the one in which the interstitial carbon atom makes four bonds with its neighboring atoms (two atoms above and two atoms below, Figure 2.2e), and its formation energy is about 6.25 eV. Interstitial atoms are more stable if trapped between two sheared graphene layers (a laterally displaced graphene layer with respect to its adjacent graphene layer). The reason is that interstitial carbon atoms will have more opportunity to bond with more carbon atoms in a sheared configuration. On the other hand, some of additional carbon atoms on the top graphene layer may bond to carbon atoms of that layer (Figure 2.2f) and become stable adatoms. The most stable configuration for adatoms is the bridge position with the formation energy of 6.45 eV, presented in the Figure 2.2f. Other types of adatoms are possible. When the adatom is hydrogen, the most stable configuration is H bonded to a C atom orthogonal to the graphene sheet (Figure 2.2g) [76].

This kind of bonding is used to hydrogenate graphene layer and gives rise to a new D peak in

11 graphene Raman spectroscopy [77]. Fluorination with fluorine adatoms is another method [78] used to tune the electronic properties of graphene. Furthermore, adatoms might be N or B for specific applications [79].

Figure 2.2: a) Stone-Walls defect formation from a pristine single layer of graphene: the left image is pristine lattice and the right is SW-defected lattice [80]. b) Single vacancy formation and new bond formation to create 5-9 ring fusion in graphene [66]. c) Divacancy in graphene [81]. di)

Schematic top view of a Si6 cluster on a graphene pore and dii) Schematic 3-D of the Si6 cluster

[82]. e) The most stable configuration of an interstitial carbon atom in unshreaded graphene [65]. f) The most stable configuration of a carbon adatom on a graphene layer (C՜ is the adatom and C is the graphene atom) [83]. g) Hydrogen atom added to the surface of graphene and bonded to one of the carbon atoms such that the bond is perpendicular to the graphene sheet [76].

2.3.1.2. POINT DEFECTS IN TMDS

The point defects described in graphene are found in TMDs as well. These layered materials are made through either chemical or physical methods, e.g. chemical vapor synthesis (CVD) or

12 exfoliation, respectively [84-86], and the synthesis processes introduce different types of defects in structure of TMDs. MoS2, MoSe2, WS2 and WSe2 are the most investigated layered TMDs [87-

91], but there are also few studies on PtSe2 [92], ReS2 [64], TiSe2 [93] and others. Vacancies are the most frequent point defects in TMDs, even though there are a variety of point defects.

Considering the discussion about the general formula of TMDs (MX2) and all kinds of point defects in TMDs, we have categorized them into several groups, namely single X vacancy (VX in

Figure 2.3a) [64, 92-94], two mono VX (VXX in Figure 2.3b) [64], double X vacancy (VX2 in Figure

2.3c) [64, 94], single M vacancy (VM in Figure 2.3d) [92, 94], a VM and a neighboring VX (VMX in

Figure 2.3e) [64], a VM and a neighboring VX2 (VMX2 in Figure 2.3f) [64], a VM and its triad in- plane bonded X vacancies (VMX3 in Figure 2.3g) [94], a VM and its 6 bonded X vacancies (VMX6 in Figure 2.3h) [94], an M atom substituting a VX (MX in Figure 2.3i), an M atom occupying two

X vacancies (MX2 in Figure 2.3j) [94], single X atom occupying a VM (XM in Figure 2.3k) [92], a pair of X atoms occupying a VM (X2M in Figure 2.3l) [94], and excess M intercalations (Minter in

Figure 2.3m) [93].

Figure 2.3: Point defects in a two dimensional distorted-1T ReS2 [64]: a) VX, b) VXX c), VX2 d) VM, e) VMX, f) VMX2, g) MX, h) X2M. High resolution Scanning transmission electron microscopy

(STEM)-annular dark field (ADF) images of point defects in two dimensional 2H-MoS2 [94]: i)

VMX3, j)VMX6, k) MX2. Atomic resolved scanning tunneling microscopy (STM) images of point defects in two dimensional 1T-PtSe2 [92]: l) XM, and 1T-TiSe2 [93]: m) Minter [93]. n) Possible

14 adsorption sites for 2H-MoS2 [95], in this case TX is TS and TM is TMo. Oi-iii) Atomic model of T0 to T1 transformation. Yellow polygons correspond to double vacancies of X [96].

The formation energy of VX in a 2D-MoS2 synthesized under Mo-rich condition is 1.2eV and it becomes 3eV in S-rich condition [94]. However, in the case of 1T-PtSe2, it becomes 1-1.2eV and

1.5-1.8eV for Pt-rich and Se-rich conditions, respectively [92]. It has been proven that VX in MoS2 has the lowest formation energy amongst all single vacancies. However, using DFT calculation,

Zheng et.al proved that the lowest formation energy belongs to Pt replaced by Se atoms in two dimensional 1T-PtSe2 which is −0.3 eV [92]. Substituting elements are another class of point defects in TMDs. Depending on the elements in the synthesis atmosphere, the substituted elements can differ. For instance, the ratio of Mo/W and the synthesis temperature determine out or in-plane heterostructures of MoS2/WS2 [97]. Also, Se and S alloying elements in TMDs have been used quite a few times in order to tune the electronic properties of layered TMDs [98-100]. However, in 2D-MoS2, other dopant elements like Mn, Fe, Nb, Co, Au and Re have been reported [101-107].

Moreover, dopants of N, P, and As also have been used to replace S vacancies in MoS2 [95]. Host or guest atoms can be adsorbed to the surface of 2D-TMDs which are called adatoms. Depending of the synthesis condition, most of the adatoms are M or X elements, since, for example, in an M- rich condition, the amount of M in the atmosphere would be excess and hence, M atoms can potentially be adsorbed to the surface of the material and therefore, change the electronic properties. There are four positions for adatoms, namely above the X atom (TX), above the M atoms (TM), above or within the hexagonal holes (A), and above the M-X bonds (B) (See Figure

2.3n) [95, 108]. Because of the stacking order of 2H TMDs, TM and TX adatoms are attributed to intercalated atoms [107]. Dolui et.al used DFT calculations and concluded that TM sites are favorable for alkali metals with adsorption energies of −0.8 eV to −1 eV [95]. Because of the

15 polar nature of Stone-Walls defects in TMDs, this kind of defect is not found in TMDs; however, if an M-X bond rotates by 60º, the heteroatomic nature of the bond and the trigonal symmetry of the system is preserved and this rotation will result in a “trefoil”-shaped defect [96]. A trefoil defect is made if the sharing pairs of M-X bonds between three neighboring double vacancies rotate by 60º around the M atom (Figure 2.3oi-iii) [96]. After the first rotation, this defect is called

T1. Next rotations will be discussed later in the section of dynamics of defects.

2.3.2. LINE DEFECTS

2.3.2.1. LINE DEFECTS IN GRAPHENE

Line defects are one-dimensional (1D) defects [63]. In order to investigate 1D defects in 2D materials carefully, it is helpful to consider the building blocks of line defects before investigating whole defects. In order to do so, topological defects are described first. Next, we will discuss different configurations of dislocations and how those are combined to make a line defect. Finally, we will discuss the edges of graphene in either the presence or absence of passivating species like

H atoms.

The first topological defects in graphene are disclinations. A disclination can be made by either adding or removing a semi-infinite wedge to a graphene sheet. A positive 60̊ wedge introduces a pentagon and a negative 60̊ wedge adds a heptagon to the graphene layer (Figure 2.4a).

Figure 2.4: a) Introduction of disclinations to the ideal graphene which produces either a pentagon or a heptagon [109]. b) Atomic

Structure of i): (1, 0) and ii): (1, 1) dislocations [109]. c) The geometry of graphene containing i) eight vacancy unites and ii) two pairs of pentagon-heptagon [110]. d) Two grains (bottom left and top right) with 27̊ missorientation with respect to one another. Red heptagons and blue pentagons are the parts of dislocations in the grain boundary; also, there are some distorted hexagons (colored in green) at the grain boundary [111] (scale bars are 5 Å). e) Grain boundary between two zigzag graphene domains which consists of sp2 hybridized pentagon pairs and octagons [112]. The geometries of graphene edges fi) Zigzag fii) Armchair [113].

As the presence of disclinations introduces curvature into the material and since the total Gaussian curvature should be nearly zero to preserve the dynamical stability of the material, inevitably there cannot be any individual disclinations in the structure of the material. Hence, disclinations will emerge in the structure as dislocations (the combination of a pair of disclinations with total zero

Gaussian curvature). A semi-infinite embedded strip of width b (Burgers vector of the dislocation) is called a dislocation. Since the strain field of a dislocation in 2D materials must embed in the plain of the material, there are just edge dislocations in 2D materials and screw dislocations do not exist in these materials due to their three dimensional strain field [109]. The strip starts with a pair of a pentagon and a heptagon and depending on the distance between these two rings, the Burgers vector corresponding to their pair could be either the smallest possible Burgers vector, b= (1,0), or the largest possible Burgers vector which is b= (1,1) (Figure 2.4bi-ii). As discussed in the point defect section in graphene, vacancies can migrate and coalesce in the 2D material if the migration energy is provided. Coalescence of vacancies potentially can make a line defect inside the graphene layer (Figure 2.4c). However, when the number of vacancies in a zigzag chain goes over ten, dangling bonds around the hole saturate by making bonds between atoms as shown in Figure

2.4c and two pairs of pentagon-heptagons are made at the end of the line defect [110]. Hexagons that are between the pairs of 5-7 rings are slightly strained and as the number of these hexagons increases, the amount of energy needed to make such a pair increases as well. Moreover, due to the lattice mismatch between graphene and its substrate during the growth process, different graphene domains grow and coalesce [114]; hence, grain boundaries between domains are formed and could be a combination of rings and/or dislocations. Considering the case of dislocations and depending on the dislocation density (or the average distance between them) and their corresponding Burgers vector, misorientation angle between grains is different such that as the

18 density increases, the misorientation angle increases as well (Figure 2.4d) [111]. Also, these all factors determine whether the GB is armchair or zigzag [115]. In an experiment done by Lahiri et.al [112], a grain boundary consisting sp2 hybridized pentagon pairs and octagons was seen between zigzag-edged grains (Figure 2.4e).

The last part of line defects in graphene is edges of the 2 dimensional films. Since, zigzag (ZZ), armchair (AC) or a combination of ZZ and AC edges reduce the number of dangling bonds in graphene, grains tend to end up with these two kinds of edges (Figure 2.4f) [113].

2.3.2.2. LINE DEFECTS IN TMDS

Line defects can result from point defects coalescence [116-118], e.g. vacancies agglomeration, or similar to graphene, as the result of the coalescence of multiple 2D grains to make grain boundaries

(GB) [119]. As in graphene, another class of line defects in TMDs are edges which will be discussed at the end of this section. Line defects can also be produced by irradiation. Under electron beam irradiation, vacancies are produced in the structure of TMDs and most of them are

VX, since the electron beam momentum is downward and hence, knocking out the bottommost atoms of the TMD layer is much easier than other atoms [120]. Moreover, under such a condition, vacancies are mobile and tend to agglomerate [117]. Komsa et.al [121] used 80 keV electron beam to irradiate 2D-MoS2 and produced vacancies of sulfide (VS). Increasing the radiation dose makes more vacancies, brings them into lines (Figure 2.5a-c), and if the irradiation continues, double- vacancy (DV) lines are made that are a result of the trade-off between the formation energy of single-vacancy (SV) lines and DV lines (Figure 2.5d). If the numbers of vacancies in an SV line goes beyond 4, DV lines become more favorable since their formation energy is lower than that of

SV lines.

Figure 2.5: (a-d) HR-TEM images showing vacancy formation in MoS2 under electron beam exposure and their migration to make SV and DV line defects [121]. ei) half-line removal of atoms to make dislocations in MoS2 which are eii) removing an armchair half-line

(b=(1, 0)), eiii) removing two parallel zigzag half-lines (b=(1, 1)), eiv) removing an inverted armchair half-line (b=(0, 1)) [122]. f)

Reconstructed dislocation cores at the results of the interaction of generic dislocations with point defects and their corresponding formation energies [122]. g) Energies of GBs as a function of tilt angle [122]. Armchair grain boundaries composed of 5|7 rings depicted

20 with red solid circle, and open circles showing armchair grain boundaries being composed of 4|6 and 6|8 rings degenerate gradually at

60° in all-rhombs grain boundaries. Crosses, blue dashes, and open squares show zigzag grain boundaries composed of 4|6+6|8, 5|7and

4|8 rings, respectively. h) Top and side views of common MoS2 structures [123]. i) cross sectional HRTEM image of MoS2 showing the presence of IDB and its effect on the stacking of layer’s order [124]. j) Possible IDB structures in MoS2 [123].

In order to investigate GBs, similar to graphene, one first needs to find out their building blocks.

Analogous to the case of dislocations in 3D, to make an edge dislocation in 2D, a half-line of atoms must be added or removed; these atoms can be arranged as an armchair half-line, inverted armchair half-line, or two parallel zigzag half-lines (Figure 2.5e). As the material has trigonal symmetry, the resulting dislocations will have trigonality as well which is evident in Figure 2.5e. As it is seen from this Figure, two (1, 0) and (0, 1) dislocations have homo-elemental bonds being M-M and X-

X which make them M-rich and X-rich, respectively. Next step for GBs analysis is to take the interaction of dislocations with point defects into account and then investigate GBs formation energies. Zou et.al [122] considered MoS2 and investigated the interaction of dislocation discussed above with point defects, namely adding one S atom or a pair of S atoms (equivalent to one M vacancy), and adding a 2S pair and removing one M simultaneously to the M-rich dislocation.

Also, the same case is for the S-rich dislocations (Figure 2.5f). By doing so, there are few possibilities for the new reconstructed structures being hexagon-octagons 6|8, 4|6+V2S, and rhomb- hexagons 4|6. Formation energies for all the possible reconstructions are provided in the Figure

2.5f too. It should be noted that if the number of changes to each dislocation increases, the formation energy of that reconstruction increases as well (slopes correspond to the number of changes). There are two kinds of GBs in TMDs, zigzag (Z-GB) and armchair (A-GB), which are made out of dislocations and/or their reconstructions. Based on the interplay between strain and chemical energies, the structure of a GB is determined. One must keep that in mind that predicting the structure of GBs is not based on their energies since this is set by the tilt angle and the tilt angle is set based on the non-equilibrium state of the 2D material growth. Increasing the tilt angle of the

GB would increase its energy as well until the energy reaches its maximum at 60˚, which makes the GB be zigzag with homoelemental bonds (M-M or S-S). A-GBs consist of 5|7 dislocations

22 and/or reconstructions of 4|6 and 6|8. Likewise, Z-GBs consist of 5|7 and 4|8 dislocations and/or

4|6 and 6|8 reconstructions [122]. 6|8 GBs are preferred under S-rich synthesis condition and 4|6 and Mo substituted 4|6 GBs are most likely to be made under M-rich condition [94]. In 2H structure of TMDs, layers are stacked on top of each other in the fashion of AA and in order to preserve this fashion, layers must have different chevron directions, showing the MoS6 prisms parallelism, with respect to their above and below layers (Figure 2.5h). For the case of MoS2 with its another common structure being 3R, all layers have the same chevron direction [123].

Generally, in a single layer of MoS2, this direction does not change; however, somewhere in the

Figure 2.5i, it changes which shows prisms have reached a defect. Where through which the direction of chevrons changes is called inversion domain boundaries (IDB) which possibly undergo stoichiometric changes in sulfur shells [125]. These defects either consist of 558 ring fusions with homoelemental M-M bonds (M-bridge) or 8 rings (S-bridge) and based on the DFT simulation, the GB is mostly probable to be a Mo-Mo bridge [123]. Since the types of coordination of ligand X in TMDs are flexible, different edges for these materials from S-rich to M-rich with different percent of X coverage [126] are possible (Figure 2.6). Also, as it is seen from the part E of the Figure 2.6, there are some vacancies of X on S2 sites which caused the outmost row of M atoms move closer to the second outmost layer of M atoms (reconstructed M-terminated edges)

[127].

Figure 2.6: Side and top views of Mo and S edges with diﬀerent S coverages [94, 128].

2.4. THE INFLUENCE OF DEFECTS ON ELECTRONIC AND MAGNETIC

PROPERTIES

2.4.1. GRAPHENE

Pristine graphene is diamagnetic. A single vacancy in graphene introduces two magnetic components of σ (1μB) and a π (1μB) to the magnetic moments of graphene [129, 130], although in some theoretical calculations it has been reported that the π magnetization component is quenched to 0.5 μB [131]. Actually, 20−60 meV gap between two spin- split polarized vacancy π states close to the Dirac point causes magnetization (Figure 2.7a) [129, 132].

Figure 2.7: a) Ground state band structure of monovacancy in graphene [129]. Band structure of graphene and one dimensional defect containing a pentagon pair and an octagon: b) Band structure of graphene containing the defect which shows a flat band around the

Fermi level, c) Scanning tunneling spectroscopy results showing density of states of a perfect graphene and the line defect which illustrates the metallic characteristic of the line defect [112]. Calculated density of states for d) small angle grain boundaries, and e) large grainj boundaries (LAGB I consists of (1, 1) and LAGB II consists of dispersed (1, 0) and (0, 1) dislocations) [109]. Band structure of f) a ZZ edge and g) a reconstructed (57) ZZ edge [133].

In a single vacancy in graphene, two of the undercoordinated C atoms move a little toward one another and form a bond; however, the third one still remains with the dangling bond (Figure 2.2b).

Localized dangling bond and some delocalized density in the σ network and the π states respectively give rise to magnetic moment which is due to the two unpaired electrons per vacancy

[129].

As discussed above, divacancies have different configuration; however, Amorim et.al [134] proved that configurations of 5-7-5 and 555-777 ring fusions have similar effect on the electronic properties of graphene and their charge transport properties are much similar and close to the metallic carbon nanotubes. Moreover, Ugeda et.al [135] used scanning tunneling microscopy

(STM) to investigate the electronic spectrum on divacancies in an ideal graphene. Their results showed that the nature of spin-degenerated band of π-electron dominated the spectrum which was seen as an empty-states resonance, while magnetic moment around the divacancy was ruled out by calculations. Yazyev calculated magnetic moment of different kinds of defects in graphene and concluded that ferromagnetism is only induced by single-atom defects, e.g. vacancies, hybridization elements (H and F) and interstitial carbon atoms [136]. Also it should be noted that no magnetic moment is seen due to the Stone-Walls defects [137]. Generally, single unpaired electron in functionalizing groups can lead to and stabilize a magnetic state which inhibits nonmagnetic pair formation. As the formation energy of H bonded to carbon atoms in a SW defect decreases to 0.44 eV and a pair of H atoms formation becomes rather difficult than H atoms bonded to other carbon atoms, magnetization will occur if H bonds with carbon atoms in SW defective graphene [138]. Carbon adatoms influence the magnetic properties of graphene such that the ground state of an added carbon atom has a magnetic moment of .45 µB. Adatoms have four electrons that two of them are covalently bonded to two graphene atoms, one of the remaining

2 2 electrons goes to the SP dangling bond, and the SP bond and Pz orbital share the last electron. As the Pz orbital is orthogonal to the surface π orbitals, it is not able to form any bands just in order to maintain the symmetry, and hence, is spin-polarized [139]. In hydrogenation, the hybridization of carbon atoms changes from SP2 to SP3, and therefore the π-bands being conductive are removed and an energy gap is opened [140]. Actually, this gap is opened between the occupied and unoccupied bands of graphene and a spin-polarized gap state accompanies it; however, a Stone-

Walls defect can quench this spin-polarization [137]. Fully-hydrogenation of graphene leads this material to be a wide-gap semiconductor [141], although half-hydrogenated graphene has a gap of

0.43 eV [142]. Furthermore, it has been investigated that a single hydrogen atom covalently bonded to a carbon atom of a 32-carbon-atom slab gives rise to a bandgap of 1.25 eV [137].

Likewise, Charge reduction in the conducting π orbitals, introducing scattering centers, and band gap opening are what fluorine does to graphene if it bonds with carbon atoms. Reduction of conductivity and mobility seen in experiment are proofs for this statement [78].

Depending on the kind of line defects, these defects can have different effects on the electronic properties of graphene. GBs consisting of a pentagon pair and an octagon show metallic behavior such that a flat band located at the center of the Briliouin zone emerges in electronic states close to the Fermi level and this is the reason of metallic behavior of the defect (Figure 2.7b) [112].

Huang et.al [111] investigated the effect of grain boundaries on the resistance of graphene and their work resulted in that the resistance of graphene is more than three times greater than the resistance of GBs. Also, GBs consisting of pentagons and heptagons show a metallic behavior which is consistent with their lower resistance [143]. Small and stable large angle GBs with different configurations show van Hove singularities around the Fermi level (0.5 eV below and above the Dirac point) which are signatures of line defects (Figure 2.7d and e) [109]. Reconstructed

ZZ edges of graphene tremble the conductivity of graphene edges since their dangling bond bands go away from the Fermi level [133]. In a ZZ edge, the so-called “flat bands” are due to the π electrons and are localized at the edges. Also, dangling bond bands are spatially located a bit beyond the edge. However, these bands go away from the Fermi level by lifting the degeneracy by

5eV [133] (Figure 2.7f and 2.7g). Generally, Graphene is a diamagnetic material; however, as I discussed above, defects might show local magnetic moments due to the undercoordinated carbon atoms e.g. undercoordinated atoms at vacancies, dislocations, GBs, edges and other kinds of defects[144]. Also, it is important to mention that at high temperatures (room temperature), graphene mostly tends to be diamagnetic [145].

2.4.2. TMDs

13 Point defects in TMDs are mostly VX [64] and the density of this kind of defect can go up to ~10

-3 cm in MoS2. These defects generally introduce localized states in the band gap of pristine TMD and in MoS2, and can act as electron donor sites which makes the material locally n-doped [146,

147]. However, localized states from VM in WSe2 makes the material locally p-doped [148].

Unoccupied levels of SV line defects cover a portion of the band gap of MoS2 and lower it to 0.5 eV. A double vacancy line levels the band gap completely and makes the material metallic.

Horzum et.al [64] investigated the effect of VS, VS+S, V2S, VRe, VReS, VReS2, ReS, and Re2S on electronic and magnetic properties of 1T´-ReS2 and concluded that these defects do not change the semiconducting of the material; Defects containing Re have localized spin polarized ground states with a magnetic moment between 1 and 3 µB and on the other hand, defects containing S show a nonmagnetic ground state. Moreover, substitutional elements like N, P, As, F, Cl, Br, O and Se do not affect the band gap of the defective material and may shift the Fermi level into the defect bands causing the conductivity to increase [121, 149]. However, replacing S atoms with nonmetals and

Mo substitution with transition metals introduces deep donor levels inside the band gap of pristine

MoS2. Also with substituting Mo with Nb, one can obtain p-type MoS2 and in contrast to Nb, alkali metals can make the MoS2 n-type [95].

Calculated density of states for trefoil-shaped defects in WSe2 are shown in Figure 2.8a [96].

Compared to the pristine material, rotational defects of T1, T2 and T3 introduce new states to the band gap of the material which originate from the corner of the defects, while new states above the valance band maximum and below conduction band minimum can be attributed to the edges made through multiple rotations (see the dynamic behavior of defects part). As the number of rotations increases, the size of the defect increases as well and as the result, the Fermi-level moves toward the valance band maximum meaning the defects lead to p-type doping of the 2D material.

However, tight-binding transport calculation has shown that the conductivity of MoS2 containing large rotational defects decreases [150].

Figure 2.8: a) Calculated density of states for T1, T2 and T3 defects [96], b): Calculated total and partial density of states for pristine

MoS2 and embedded islands interconnected to their surroundings via –S– bridges or Mo-Mo bonds, c): Grain boundaries made from inversion domain boundaries [123].

As it was seen in the part of line defects in TMDs, GBs consist of different structures; however, most of them have been discussed just theoretically. An experiment showing the structure of GBs have been done by Zhou et.al [94]. In this experiment, GBs in 2H-MoS2 consist segments of 4- fold rings being parallel to the zigzag direction which are linked by octagonal kinks. These GBs may share points at S2 sites or at the edges of the rings which are called 4|4P and 4|4E, respectively.

4|4E and 4|4P GBs serve as perfect 1D metallic quantum wires in MoS2 matrix. Octagonal kinks can disturb the electronic behavior of these metallic wires significantly. In contrast, 4|8 GBs only introduce some localized midgap states right above the valance bands and it obviously explains the reason why octagonal kinks disturb the electronic behavior of these metallic wires.

Considering islands of MoS2 interconnected with pristine MoS2 via Mo-Mo bonds or –S– bridges

(IDBs which are GBs with 60º tilt angle), Enyashin et.al [123] calculated the electronic density of states for perfect MoS2, mentioned islands and the IDBs and concluded that there is not an impressive effect of defects on the partial density of states; however, there is a nonzero density of states in the band gap of pristine MoS2. Partial density of states shows that the main contribution to the states in the bang gap is from Mo4d-states of both the islands and their surrounding atoms

(Figure 2.8b and 2.8c). Also, it should be noted that orbitals of Mo atoms located near the edges of both IDBs have the most contribution to the Fermi level. Generally, GBs add localized states to the middle of the pristine material’s gap which in the case of MoS2 are mainly from d orbitals of the metal atom in Mo- and S-rich conditions or p orbitals of S atoms in 6|8 GBs [122].

Using first principle calculations, Zhang et.al [151] investigated the spatial distribution of spin polarization for these localized states in TMDs and concluded that dislocations and GBs show intrinsic magnetism (magnetic moment of about 1 Bohr magnetron) since defects have localized states within the BG of pristine MoS2 which are centered on Mo-4d orbitals. GBs consisting of 5|7

31 dislocations show ferromagnetic spin ordering and their transition from semiconducting to half metallic and then metallic is a function of tilt angle and doping level. However, increasing the tilt angle beyond 47º favors 4|8 pairs due to the structural energetics and then GBs become antiferromagnetic. It has been shown by spin-polarized calculations that bare Mo-terminated edges in MoS2 have ground ferromagnetic states [94, 152]. Non-reconstructed Mo-terminated edges show metallic behavior and symmetric spin-up and spin-down channels with 0.4 μB magnetic moment for every Mo atom at the edge. All magnetic moments disappear in reconstructed Mo- edges, although their metallicity is preserved [94]. Sang et.al [153] synthesized 2D Mo0.95W0.05Se2 and investigated its edge evolution under electron beam irradiation and thermal heating at 500 ºC.

The resulted edges will be discussed in the dynamic part of this review in detail which are four stable edge structures namely zigzag (ZZ) Se edges terminated with nanowires (NW) of MoSe and

Se atoms, ZZMo edges terminated with Se atoms and NWs (Figure 2.12h-k). DFT local density of states calculation shows that the two edges terminating with NWs are conductive which is due to metallic nature of the NWs. Although ZZMo-Se edge is semiconducting (Bandgap= 0.45eV) and ZZSe-Se is metallic.

2.5. DYNAMIC BEHAVIOR OF DEFECTS

2.5.1. GRAPHENE

It has been found that single vacancies in graphene are much more mobile than divacancies because of the relative migration energies associated with these two defects (1.7eV and 7eV, respectively [66]). Under electron beam irradiation [154], C-C bonds rotate to create Stone-Walls defects and with continued irradiation, the reverse transition may occur. Another effect of electron beam irradiation is mono-vacancy formation. If the sample is kept under beam exposure, some of

32 the undercoordinated atoms around monovacancies are ejected and divacancies are formed and their configuration changes while being beam exposed (Figure 2.9a-f).

Figure 2.9: Defect transformations under electron beam irradiation, atom ejection and bond reorganization create defects: (a) Stone-

Wales defect, (b) perfect graphene, (c) single vacancy of V1 (ring 5-9), (d) divacancy of V2 (ring fusion 5-8-5), (e) divacancy of V2

(555-777) as a result of a bond rotation in a (5-8-5) defect, (f) V2 (5555-6-7777) divacancy as a result of a bond rotation in a (555-777) defect (Scale bar is 1 nm) [154]. The inverse SW defect g) side view and h) top view. The I-V pair in two graphene layers stacked in the fashion of ABAB… (i) side view and (j) top view [155]. k-m) Si6 cluster embedded in a pore of graphene shown by STEM-ADF Z-

34 contrast, n) stable configuration with a higher symmetry for the Si6 clusters. Scale bar 0.2 nm [82]. Fe dimers in graphene vacancies

[156]. Smoothed AC-TEM images of a pair of Fe atoms in (o) trivacancy; (p) alternative trivacancy ; (q) quadvacancy and (r) two adjacent monovacancies (scale bar: 0.5 nm) [157]

Adatoms can move and when meeting one another, they can make a dimer and then the SP2 hybridized network. Although, looking at the network from top, it appears like a Stone-Walls defect, but the new rings do not have the same symmetry and arrangement as the rings in a SW defect, and because of that this defect is called an inverse SW (ISW) defect (Figure 2.9g and 2.9h).

On the other hand, the ISW defect formation energy is about 5.8 eV which is higher than SW defect formation energy and thus it can be the reason why the population of such defect is negligible in a flat carbon SP2 hybridized system [158].

An interstitial carbon atom and a single vacancy in graphene can interact and form a new metastable I-V complex (pair) or a Stone-Walls defect. The formation energy for the pair is 10.8 eV which is 2.9 eV less than its isolated constituents. In the form of I-V pair (Frenkel pair), the interstitial cross-links with two neighboring atoms above and below (Figure 2.9i and 2.9j). In the stacking fashion of ABAB… of graphene layers, if the interstitial is a grafted two-coordinated atom, the vacancy and this atom will interact and form a SW defect [155]. Jaekwang Lee et.al [82] used annular dark field (ADF) mode of scanning transmission electron microscopy (STEM) to investigate the dynamic behavior of Si6 clusters under electron beam irradiation. They reported a reversible structure change for these clusters in graphene pores. During beam irradiation, one of the Si atoms oscillates between the ground state (the most stable configuration) of Si6 cluster and a metastable configuration and finally rests at its original position in less than 10s (Figure 2.9k- m). After continued graphene pore exposure to the electron beam, one of the carbon atoms ejects from the pore edge and a new stable configuration with a higher symmetry for the Si6 clusters appears (Figure 2.9n). Based on their calculations, the energy barrier for every configuration of

Si6 clusters is 1.44eV.

Chen et.al [73] investigated the effect of electron beam irradiation on Si nanoclusters covalently bonded to graphene. Their research showed crystalline cubic phases start to emerge as nanoclusters reach 4-10 atoms in size, presumably because of the stronger Si-C bond compared to the Si-Si bond. Under electron beam exposure, anisotropic ordered nanocrystals appear on the surface of the material. In local volume constraints and with oscillations between two geometric conﬁgurations, Si nanoclusters rotate perpendicular to the graphene plane under electron beam irradiation.

He Z et.al. [156] used two Fe atoms to form paired clusters with different geometries within graphene vacancy defects. In order to monitor the atomic structure and real-time dynamics of the clusters, they used aberration-corrected transmission electron microscopy and finally concluded that dimer structures evolve from a single Fe atom trapped in a graphene vacancy and eventually lead to four different stable structures (Figure 2.9o-r), namely two Fe dimer variants in a graphene trivacancy, two adjacent vacancies with an Fe dimer embedded in between, and an Fe dimer surrounded by a quadvacancy. 2.00 or 4.00 μB are the magnetic moments associated with all these structures.

Under certain conditions, some of the edge atoms with a dangling bond can be removed and the configuration of the edge changes. Using transmission electron microscopy, Girit et.al [159] recorded images of atomic bond rearrangements at the edges of graphene, and they found that by migration of carbon atoms along the edges, armchair edges can convert into zigzag edges (Figure

2.10a and b).

Figure 2.10: a) Edge reconfiguration from an armchair to a zigzag edge under electron beam irradiation (blue dots in the upper box change to the red diamonds in the lower box making a zigzag edge). b) Monte-Carlo simulation of edge transformation between a zigzag edge and an armchair edge [159]. Reconstructed geometries of different edges due to carbon atoms migration: c) reconstructed ZZ edge

(57), d) Reconstructed AC edge (677), and e) Reconstructed AC edge (56) [113] (Captured during a 4-min-beam irradiation with 110 frames). f) A perfect 5-7 pair as the result of saturation of dangling bonds in a zigzag chain of vacancies, g) the 5-7 pair migration by

38 rotation of carbon dimers shown by open circles, h) another movement of the 5-7 pair by rotation of carbon dimers shown by filled circles [110]. i-l) HRTEM image of a flowerlike structure inside graphene, its evolution during electron beam exposure and structure models compatible with every structure [160].

Moreover, during beam irradiation, some of carbon atoms may get ejected from the structure (edge or the middle of graphene) and make edges with different configurations [133] as described in

Figure 2.10c-e. In the TEM imaging of graphene edges, ZZ edges are seen much more than AC edges just due to the dynamic and kinematic effect of electron microscopy imaging and it does not have anything to do with lower formation energy [113]. Also, reconstructed ZZ edges are similar to AC edges and this is why they are discriminated by TEM. To repair the reconstructed edges, a reconstructed ZZ edge needs just one carbon atom to make the structure of graphene similar to its pristine structure; however, a reconstructed AC edge needs two C atoms which makes their repair slower. Generally, the formation energy of reconstructed ZZ edge is large such that undoubtedly their existence is unlikely [113]. 5-7 pairs, as the results of dangling bonds saturation in zigzag vacancy chains, can migrate by rotation of C-C bonds. Figure 2.10f-h shows how this kind of line defects can migrate. As seen from the Figure, rotation of the bond between carbon dimers shown by open and filled circles by 90̊ makes the 5-7 pair to move [110].

In order to induce knock-on radiation damage in TEM to make a three-coordinated carbon atom in the graphene structure, the energy of electron beam must be over 80 KeV [161]. However, 80

KeV is also the highest energy which can rotate C-C bonds without removing C atoms from the structure [111, 162, 163]. Although, atoms at the edges of holes are displaced even at this energy[164]. Hence, Kurasch et.al [160] used 80 KeV electron beam accompanying with DFT simulation and proved that by providing enough energy, grain boundaries tend to decrease their

훾 length. Driving force for GB migration is defined by , where 훾 is grain boundary energy per unit 푅 length and R is curvature. For straight GBs (R≅∞), the driving force is almost zero and hence,

GBs will not move, although it fluctuates between different straight configurations. GBs between small grains, in the order of few nanometers, have low R and therefore the driving force will be

40 enough for them to migrate which is done by C-C bond rotations. Considering a grain of few nanometers embedded inside a larger grain and being exposed by electron beam, Kurasch et.al proved that GBs reach a flowerlike structure as seen in Figure 2.10i-k which can be done by only

6 bond rotations. As the shrinkage of such structure starts, one might expect total disappearance of the grain and this is actually true with some intermediate steps (Figure 2.10l). Each of the intermediate steps reduces the total energy of the whole system until it reaches the original structure. However, the initial stage of bond rotation needs two consecutive rotations each spending 3eV and this is why there is an increase in the energy profile. The flowerlike structure at first transforms into a divacancy with a 555-777 ring fusion structure and an adatom pair and then to the pristine graphene. Shrinkage of the interior GBs will result in vacancy production and in order to accommodate the excess volume, adaoms are good candidates [160].

2.5.2. TMDs

In order for TMD defects to migrate and arrange in new configurations, sufficient energy must be provided to overcome barriers to defect motion. Vacancies are one of the most common defects in

TMDs that migrate across the material if the diffusion barrier energy is provided. As observed earlier, VX in MoS2 appear during electron beam irradiation and if the irradiation continues, VX migrate and agglomerate in the material. Since the electron beam momentum is downward and perpendicular to the two dimensional film, vacancies are mostly VX. DFT molecular dynamics calculations show the energy barrier for VX diffusion in MoS2 is 2.3eV. The diffusion of single vacancies makes SV lines, which this process is fairly slow compared to DV line formation.

Because the alignment of single vacancies is sluggish and the barrier energy for vacancy diffusion in this material is high, we cannot conclude that agglomeration is only from the diffusion of single vacancies. On the other hand, when the number of single vacancies increases, the diffusion barrier

41 decreases to 0.8eV (Figure 2.11a)[121]. The stress field around the vacancies is isotropic; however, around the lines of vacancies, this field is anisotropic. Generally, introducing a vacancy introduces a tensile stress in the material. To reduce this stress, vacancies may rearrange in lines, supercells contract perpendicular to these lines and thereby release most of the stress. On the other hand, the stress may also be released at the edges of the material; hence, SV or DV lines are often parallel to the edges of the material (Figure 2.11b).

Figure 2.11: a) Energy needed for diffusion whether or not in the presence of nearby vacancies, on the same side [121], b) High resolution

TEM image of MoS2 flakes confirming vacancy lines mostly oriented parallel to the flake edges [121], c) Different VSe diffusion configurations in two adjacent PdSe2 layers, d) calculated diffusion barrier energies for VSe migration from one configuration to another

43 one [118]. Annular dark field images of WSe2 flakes containing e): SVSe and DVSe (white and yellow polygons respectively), f): T1 defect and then g): T2 defect. h-j): Atomic model of T1 to T2 transformation showing the presence of DVs and bond rotations. k-m): T1 defect gliding by consecutive 5 M-X bond clockwise rotation [96].

Nguyen et.al [118] used STM coupled with first-principle calculations to manipulate VX in two dimensional PdSe2. In this material, every Pd atom is bonded to four Se atoms (two atoms in the top Se layer and two atoms in the bottom Se layer). Depending on the position of the vacancy, the diffusion barrier for VX migration across the material can be from 0.03eV to 1.59eV which is visible in Figure 2.11c and 2.11d. Trefoil defects are M-centered defects and yet X-centered trefoil defects have not been detected by experiments. By continuing electron beam irradiation on a trefoil defects with first rotation (T1), next rotations will happen to the defect and other kinds of T defects,

T2 and T3, will emerge inside the material (Atomic transformation from T1 to T2 defect is shown in Figure 2.11e-j. Actually, two more DVSe around the T1 defect in WSe2 and rotation of seven W-

Se bonds around three W centers will create a T2 defect. For a T2 to T3 transformation, more M-X bond rotations are necessary and hence, more energy is needed to overcome the barrier. Also, the

T1 defect can migrate under electron beam irradiation if the amount of energy for five M-X bond rotations is provided (Figure 2.11 k-m) [96].

In order for a GB to migrate, its component ring fusions (discussed in section 1.3.2.2 about line defects in TMDs) must glide. HRTEM imaging technique has been used to track GBs in a 2D WS2.

The migration of a 12º grain boundary consisting of pairs of 6|8 or 6|8 and S-vacancies (VS) is shown in Figure 2.12 a-f. The movement of dislocations determines the deformation of the material. Different dislocations have their own migration path which depends on the kind of migration (glide or climb) and their Burgers vector. The movement of W atoms is involved in the glide of both cases in the image below (blue circles indicates W). Rearrangement of S atoms

(indicated by red circles) is just needed for 6|8-VS migration. The concerted migration of W and S atoms make the energy barrier foe the migration of 6|8-VS larger than that of 6|8 (Figure 2.12g)

[106].

Figure 2.12: Initial, saddle-point, and ﬁnal structures for the dislocation migration in WS2 showing the presence of (a−c) the 6|8-VS structure and (d −f) the 6|8 structure. (g) Minimum energy paths for the migration of two dislocations [127]. h-k) Different edge configuration in 2D Mo0.95W0.05Se2 under thermal heating and electron beam irradiation, l) Models showing the atomic structure of two edges being Mo-oriented ZZMo (dashed boxes with cyan color) and Se-oriented ZZSe (black dashed boxes) with Mo and Se atoms

46 pointing out normal to the edge, respectively. Also, the three atomic models in the bottom show the atomic structure of MoSe NW constructed on the edges and NW0 and NW30 (two projections which are observed commonly) [153].

GB migration in the same material but for 22º GBs containing 6|8 (1, 0) and 4|6 (1, -1) dislocations has been investigated. If the high angle GB with two or more different class of dislocations moves across the material, it must do so through coupled migration, e.g. 6|8 glides one or two steps along the (1, 0) direction and 4|6 glides and then climbs one step along the (1, -1) direction and one step along the (0, -1) direction, respectively [165].

Sang et.al [153] did an in-situ edge engineering in two dimensional Mo0.95W0.05Se2. In their experiment, 100KeV electron beam and thermal heating up to 500 ºC were used. Since the sample was irradiated by electron beam, Se atoms were removed from the sample and hence, the chemical potential of metal atoms changed which results in edges being either –Se or – MoSe nanowire

(NW) terminated. Therefore, there are four different edges namely zigzag (ZZ) Se edges terminated with nanowires (NW) of MoSe and Se atoms, ZZMo edges terminated with the NWs and Se atoms (Figure 2.12 h-k). As an example, the ZZSe-Mo-NW30 edge (Figure 2.12l) means that a ZZSe edge connected via Mo (W) atoms to a 30° rotated nanowire. In order for the lattice mismatch between the material’s hexagonal lattice and the edges to accommodate, pairs of pentagons and heptagons (5|7) are made at the interface, the same as grain boundaries we discussed earlier [166]. We also discussed the twin grain boundaries which are 4|4 rings [167] connecting the ZZSe edges to –Se termination (Figure 2.12i). µMo is increasing as the heating time increases since Se atoms are being knocked out by the electron beam during beam irradiation; hence, the initial ZZSe-Se edge transforms to a Mo-rich ZZSe-GB4-Se and eventually to a ZZSe-Mo-NW30 edge.

2.6. SUMMARY

As two-dimensional materials are either synthesized directly from chemical reactants or made through exfoliation, the presence of defects is inevitable in them. Graphene has a variety of defects, namely, vacancies, divacancies, Stone-Walls, adatoms, alloying elements, clusters, line defects, dislocation, grain boundaries, and edges. Graphene is a diamagnetic material; however, as I discussed above, defects might show local magnetic moments because of undercoordinated carbon atoms, e.g. undercoordinated atoms at vacancies, dislocations, grain boundaries, edges and other kinds of defects [144]. Also, it is important to mention that at high temperatures (room temperature), graphene mostly tends to be diamagnetic [145].

There can be a variety of defects in a two dimensional transition metal dichalcogenides, namely point defects, line defects, edges, dislocations, grain boundaries, some of these defects result from the migration and combination of other defects. Point defects introduce localized states in the band structure of two dimensional transition metal dichalcogenides that affect electronic properties.

Defect migration mainly occurs when the defect size is not small, since the defect needs a sufficient energy to overcome a migration barrier. Point defects play an important role in defects configuration evolution. Conditions which can provide the required migration energy for defect movement include electron beam irradiation, heat treatment, and even the synthesis process. The electronic and magnetic behavior of two dimensional materials are heavily influenced by defects and defect configurations. Therefore, in order to have a realistic understanding of the two dimensional material’s behavior in applications, we must consider defects, their configuration, and their influence on materials’ properties.

VISUALIZATION OF POINT DEFECTS IN ULTRATHIN LAYERED 1T-PtSe2

3.1. ABSTRACT

Among two-dimensional (2D) transition metal dichalcogenides (TMDs), platinum diselenide

(PtSe2) stands at a unique place in the sense that it undergoes a phase transition from type-II Dirac semimetal to indirect-gap semiconductor as thickness decreases. Defects in 2D TMDs are ubiquitous and play crucial roles in understanding and tuning electronic, optical, and magnetic properties. Here, intrinsic point defects in ultrathin 1T-PtSe2 layers grown on mica through the chemical vapor transport (CVT) method are investigated using scanning tunneling microscopy and spectroscopy (STM/STS) and first-principles calculations. Five types of distinct defects were observed from STM topography images and the local density of states of the defects were obtained.

By combining the STM results with the first-principles calculations, we identified the types and characteristics of these defects, which are Pt vacancies at the topmost and next monolayers, Se vacancies in the topmost monolayer, and Se antisites at Pt sites within the topmost monolayer.

This study shows that the Se antisite defects are the most abundant with the lowest formation energy in a Se-rich growth condition, in contrast to cases of 2D molybdenum disulfide (MoS2) family. The present findings would provide critical insight into tuning of carrier mobility, charge carrier relaxation, and electron-hole recombination rates by defect engineering or varying growth condition in few-layer 1T-PtSe2 and other related 2D materials.

Keywords: 2D materials, 1T-PtSe2, point defects, scanning tunneling microscopy, scanning tunneling spectroscopy, first-principles calculations

3.2. INTRODUCTION

Transition-metal dichalcogenides (TMDs) with a general formula of MX2, where M represents transition metal elements (groups 4-10) and X represents chalcogen elements (S, Se or Te), are a family of two-dimensional (2D) materials being extensively studied in the past few years [56, 168-

170]. A single TMD layer consists of a hexagonal layer of the M atoms sandwiched between two hexagonal layers of the X atoms. Neighboring TMD layers are typically coupled via a weak van der Waals interaction. Depending on the number of d electrons and thickness, TMDs can have a variety of electronic properties, namely metallic, semimetallic, semiconducting and superconducting [34, 171]. These 2D materials and their bulk counterparts are markedly different in terms of physical and chemical properties which can be tuned for wide ranges of applications

[172-175].

So far, studies on TMDs have been mostly conducted on MX2 with group VIB transition metals, such as M = Mo, W, and X = S, Se. Recently a new type of TMD, platinum diselenide (PtSe2) in a 1T structure (Figure 3.1a), has been synthesized in bulk form and ultrathin layers [169, 176-178].

Compared to the well-studied TMDs, 1T-PtSe2 has inversion symmetry and it has stronger coupling between neighboring unit layers. Furthermore, this material is unique in the sense that a transition from indirect-gap semiconductor to metal can be driven by simply varying thickness

[179]. Among all the TMDs, PtSe2 has the highest Seeback coefficient good for thermoelectric applications [180] and the extremely high mobility, up to 3000 cm2/V/s, desirable for electronic applications [181]. PtSe2 can be also used in catalysis [169, 182] and as efficient gas sensors because of low adsorption energies for gases like NO, CO, CO2 and H2O [171]. In monolayer 1T-

PtSe2 layer, spin polarization induced by a local Rashba effect was recently observed [178].

Defects are ubiquitous in 2D TMDs, especially those synthesized via chemical vapor deposition

(CVD) or transport (CVT) [183, 184]. Some defects appear from growth or annealing processes

[185], whereas some other defects are naturally or intentionally brought into the structure during investigation [186]. In 2D materials, typical zero-dimensional or point defects constitute vacancies, antisites, adatoms, intercalations, interstitial dopants, and substitutional dopants [170,

187], while one-dimensional defects include grain boundaries, dislocations, and edges [188-190].

Properties of 2D TMDs are very sensitive to defects, especially for 2D semimetals and semiconductors [186, 191-194]. Depending on the properties of interest and desirable applications, defects can be beneficial or detrimental. For instance, 60˚ twin grain boundaries in molybdenum and tungsten dichalcogenides can function as metal wires (conducting pathways) or sinks for carriers [195]. Point defects typically lower the carrier mobility or degrade mechanical properties of 2D materials [196]. On the other hand, under certain conditions, point defects can also be sources of single photon emission [56, 197] and induce large spin-orbit splitting in 1T TMDs [57,

198].

Despite the ubiquity and importance of defects [199], there are no experimental studies of defects in 1T-PtSe2 layers at the atomistic level yet. Here, intrinsic point defects for ultrathin 1T-PtSe2 layers grown on mica through the CVT method are investigated using scanning tunneling microscopy and spectroscopy (STM/STS) and first-principles calculations. Point defects were formed in the structure of 1T-PtSe2 during the growth process. As shown in Figure 3.1a, in a 1T structure, PtSe2 monolayers are stacked in a fashion of A-A. Through STM/STS, five types of dominant point defects were identified and their atomic structures and local density of states were obtained. Characteristics and formation energies of the defects were determined using density- functional theory (DFT). Results may stimulate studies of effects of defects on electronic and

52 optical properties and defect engineering for applications in this interesting new ultrathin 1T-PtSe2 and other 2D TMDs.

3.3. METHODS

3.3.1. EXPERIMENT

Ultrathin PtSe2 flakes were grown on a mica substrate by the CVT method at a growth temperature of 600-700oC. The detailed procedures were reported in our previous papers [200, 201]. Then a stripe of 100-nm thick gold film was evaporated through a shadow mask on the samples as electrodes. The samples were annealed at 250℃ for 2.5 hours in the preparation chamber in a customized Omicron LT STM/AFM system with a base pressure of low 10-10 mbar before transferring it into the STM analysis chamber that is connected to the preparation chamber. In the main text, all the STM and STS results were carried out in the customized Omicron STM/AFM system and all the measurements were performed at 77 K. Room-temperature STM data are provided in the Supplementary Information. STM imaging was carried out at a constant current mode, and STS measurements were done at an open feedback loop using a bias modulation 20 mV with the frequency of 1000 Hz.

3.3.2. SIMULATION

DFT-based simulations were performed including spin-orbit coupling (unless specified otherwise) using VASP [202, 203]. Local-density approximation (LDA) [204] was employed for the exchange-correlation functional and used projector-augmented wave (PAW) pseudopotentials

[205]. LDA was chosen because it gives both in-plane and out-of-plane lattice constants of bulk

PtSe2 closer to the experimental values [206-208] than the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA) [209] upon geometry relaxation, as reported in references [210, 211]. The PBE-optimized out-of-plane lattice constant c for bulk is 27-29% larger

53 than the experimental value, as shown in the literature [210, 211]. The energy cut-off and number of k-points used in references [210, 211] are as follows: 70 Ry with 13131 k-points for slabs and 800 eV with 11116 k-points for bulk. Furthermore, with the PBE-optimized c value, a band gap opens for bulk PtSe2 [210], which is inconsistent with the experimental observation [212, 213].

There are also conflicting results [210, 211] in the improvement of the out-of-plane lattice constant when van der Waals interaction [214, 215] is included within PBE-GGA.

A surface of a thin PtSe2 film was modeled by two 1T-PtSe2 monolayers. Supercells of 5×5 surface atoms were used except for the Pt2 vacancy defect (discussed later), in order to simulate isolated defects. The energy cutoff was set to 260 eV and a k-point mesh of 5×5×1 was used. The supercell structures were fully relaxed until the residual forces were less than 0.01 eV/Å. For the Pt2 vacancy defect, a 7×7 in-plane supercell was used to simulate large-area modulations of the observed STM image near the defect site. Only in this case, spin-orbit coupling was turned off, and an energy cutoff of 230 eV and a k-point mesh of 3×3×1 were employed. For the slab calculations, a vacuum layer thicker than 20 Å was included to avoid interactions between successive images of PtSe2 layers.

To compare with the STM topographic images, applying Tersoff-Hamman approach [216, 217], the DFT-calculated surface local density of states (LDOS) was integrated from the Fermi level to the experimental bias voltage at a plane z = 1 Å above the topmost atomic layer. Although isosurfaces of the integrated LDOS corresponding to constant current are more accurate, the method applied here has been used as a good approximation to STM topographic images in the literature [218-220]. The integrated LDOS images were visualized using VESTA [221]. Also, formation energies of various defects were calculated using the standard method discussed in references [222]. A brief description of the method is shown in the Supplementary Information.

3.4. RESULTS AND DISCUSSION

3.4.1. STM TOPOGRAPHIC IMAGE

The atomic structure of 1cT-PtSe2 is schematically drawn in Figure 3.1a. Atomic force microscope

(AFM) and STM were used to determine the number of layers of PtSe2 flakes (Figures 3.1b, 4.1 and 4.2). Considering the reported thickness of a single PtSe2 layer, 0.507 nm [207], the thickness of flakes in our measurements were determined to range from 5 to 9 layers. A high-resolution

STM topographic image of a defect-free 1T-PtSe2 surface is shown in Figure 3.1c. Similar to previous STM study on monolayer PtSe2 grown though selenization of a Pt(111) substrate and other transition-metal diselenides [169, 223], the hexagonal protrusions in Figure 3.1c represent the topmost Se atoms. From the arrangement of the surface Se atoms, the in-plane lattice constant of 1T-PtSe2 is determined to be 0.375 ± 0.003 nm, which is consistent with previous theoretical and experimental results [169, 182, 224]. Figure 3.2 is an atomically resolved large scale STM image of an area of PtSe2 surface showing various types of defects. Figures 3.2a and 3.2b are the

STM images of the same area obtained at positive (empty states) and negative sample bias voltages

(filled states), respectively. These defects can be visualized at the surface with distinct atomic structures and morphologies at a given bias voltage, marked by arrows in Figure 3.2. The morphology of some types of defects reveals a clear dependence on bias voltage. Combining the defect morphology at the filled and empty states, five dominant types of point defects were identified at the PtSe2 surface, labeled as A, B, C, D, and E, as shown in Figure 3.2. Considering the shape of each defect in a single-crystalline flake as a triangle except for defect A, I noticed that each defect type has the same orientation (see Figure 4.2 in the Supplementary Information). In addition to these five defect types, we occasionally observed a few other defects which can be either combined or new defects. For simplicity, we focus on these five dominant types of defects.

Figure 3.1. (a) Structure model of 1T-PtSe2. (b) Large scale STM image of a few-layer PtSe2 flake, including a step edge indicating that the left area is three-layer thicker than the right area (Vs = 2.0

V, I = 0.3 nA). Inset: line profile along the marked line in the STM image. (c) Atomically resolved

STM image of 1T-PtSe2 surface (Vs = 0.3 V, I = 0.6 nA).

Figure 3.2. STM micrographs of PtSe2 film at 77K. (a) Empty-state image (Vs = 0.4 V, I = 0.7 nA) and (b) Filled-state image (Vs = − 0.4 V, I = 0.7 nA).

Figures 3.3a-e show zoom-in STM images of the five defect types. Defects of type A appear like depressions at both positive and negative bias voltages. Defects of type B, C, and D look like protrusions at both positive and negative bias voltages. For defects of type E, protrusions

(depressions) are shown at negative (positive) bias voltages. All these types of defects have three- fold symmetry. Defects of type A are centered at Setop sites, while defects of type B, C, D, and E are centered at Pt, Sebottom, Pt and Pt sites, respectively, where Sebottom (Setop) is the bottom (top)

Se site of the topmost monolayer, as marked by the dashed triangles in Figure 3.3 (see also Figure

4.3 in the Supplementary Information). In addition to their different sizes, defect type B is centered at Pt site in the topmost monolayer while defect type D is centered at Pt site in the second topmost monolayer. Table 3.1 lists the density of these defects obtained by averaging over STM images of typical regions each with an area of 20 × 20 nm2. Among these five types, defects of type E have the highest density. We now discuss each defect type separately.

Table 3.1. Densities of defects obtained from STM and STEM measurements.

Defects Density obtained from STM

images (1/cm2  1012)

A (VSe1) 2.2 ± 2.0

B (VPt1) 1.2 ± 0.4

C (VSe2) 1.2 ± 0.6

D (VPt2) 3.1 ± 1

E (SePt) 16.4 ± 3.9

Defects of type A show one-site depressions at the surface at both positive and negative bias

(Figure 3.3a). There is not a much difference in the brightness of the STM images at various bias voltages. This defect type could be due to a missing Se atom on the surface of the topmost PtSe2 layer, in other words, a Se vacancy in the top Se layer, labeled as VSe1a.

Defects of type B show 1 × 1 triangular protrusions at both positive and negative bias voltages, although the protrusions are much more apparent at positive bias voltages (Figure 3.3b). There are a few factors affecting tunneling current, such as the height of the atoms at the surface and integrated local density of states [217, 225]. Typically, the higher surface atoms or larger integrated local density of states result in protrusions in STM images. Despite this difficulty, our observation suggests that the defects of type B are electron acceptor defects. Since one cannot determine the orientation of 1-T structure from the top Se layer, each of the three sites may be associated with either (i) Se substituted by a more electronegative element at the bottom atomic layer of the topmost monolayer, or (ii) a Pt vacancy (VPt1) located at the topmost monolayer, noted as Pt1 in

Figure 3.1a. Option (i) is, however, ruled out since there were no other observable more

58 electronegative elements than Se in the growth environment. Option (ii) is more promising since the growth was under a Se-rich condition. The Pt vacancy can build a high acceptor density at the three neighboring Se sites forming the triangle, giving rise to the three protrusions at positive bias.

This analysis is supported by our DFT calculations, as explained later.

Defects of type C show 2 × 2 triangular protrusions at both positive and negative bias voltages

(Figure 3.3c), although the protrusions are much more apparent at positive bias voltages, similarly to defects of type B. Considering that the defects of type C are centered at the bottom Se atoms, there are three possible candidates for the origin of such a defect, such as a bottom Se atom replaced by Pt (Ptantisite, PtSe1b), a bottom Se atom vacancy (VSe1b), or three neighboring Pt vacancies around the center bottom Se atom (V3Pt). Different from MoS2 or TiSe2, O-substituted defects were not observed in the measurements of this research [170, 226].

Figure 3.3. Atomically resolved STM images of five types of defects. Top panel: Empty-state images. (a) Type A (Vs = 0.3 V, I = 0.7 nA). (b) Type B (Vs = 0.2 V, I = 0.7 nA). (c) Type C (Vs

= 0.2 V, I = 0.7 nA). (d) Type D (Vs = 0.085 V, I = 0.7 nA). (e) Type E (Vs = 0.3 V, I = 0.7 nA).

Middle panel: Filled-state images. (a) Type A (Vs = − 0.3 V, I = 0.7 nA). (b) Type B (Vs = − 0.1

V, I = 0.7 nA). (c) Type C (Vs = − 0.2 V, I = 0.7 nA). (d) Type D (Vs = − 0.1 V, I = 0.7 nA). (e)

Type E (Vs = − 0.3 V, I = 0.7 nA).

Dashed lines indicate the size of defects in term of the lattice constant, appearing as 1×1, 2×2 and

3×3 triangles in (b), (c) and (d), respectively. Bottom panel: Top and side view of the models of each type of defects shown in the top and middle panels. The scale bar on the images is 0.5 nm.

Defects of type D show 4 × 4 triangular protrusions at both positive and negative bias voltages

(Figure 3.3d), and they are centered at Pt sites just like the defects of type B. Protrusions are more prominent at the vertices of the triangles, but they are not as strong as those for the defects of type

B and C at positive bias voltages. Compared with the defects of type B and C, topographic images do not show much contrast between positive and negative bias voltages.

Defects of type E appear as 1 × 1 triangular protrusions at negative bias, and show the same triangular protrusion surrounded by depressions at positive bias (Figure 3.3e). Among the five defect types, this type appears with the highest density (Table 3.1), which is consistent with the

DFT-calculated formation energies of defects discussed later. This finding in 1T-PtSe2 layers is in contrast to the trend of defects in group VIB TMD MoS2 family layers where vacancies are the most dominant defects in either Mo- or S-rich condition [56].

3.4.2. DFT SIMULATIONS OF INTEGRATED LDOS

In order to determine the characteristics of the five defect types, DFT calculation was performed.

All possible intrinsic single point defects were considered within a PtSe2 slab of two monolayers as well as Se adsorption based on the Se-rich growth condition. Within each atomic layer, two types of single point defects, vacancy and antisite, were considered. In addition, intercalation of a

Se or a Pt atom within the van der Waals gap was considered. Although the experimental sample

60 flakes are about five to nine monolayers thick, such thick slabs including defects cannot be simulated due to high computational cost. The total DOS for the pristine bilayer was calculated and six monolayer using the LDA-optimized geometries. The partial density of states (PDOS) from

Se and Pt atoms are shown in Figure 4.6 in the Supplementary Information. The overall features of the total DOS for the bilayer are similar to those for the six monolayer, as shown in Figure 4.5 in next chapter.

Figure 3.4 shows integrated LDOS images for five distinct types of defects which are closest to the experimental STM images of defect types A-E at positive and negative bias voltages. These images as well as calculated formation energies in this work (Sec. III. C) bolster the identification of each observed defect type. According to the DFT-calculated LDOS images, defect types A-E correspond to VSe1a, VPt1, VSe1b, VPt2 and SePt1, respectively. Additional integrated LDOS images at different bias voltages are shown in Figure 4.7 in the Supplementary Information.

Defects of type A are indeed from one missing atom at the topmost Se layer, VSe1a, clearly seen in both experimental images and integrated LDOS (Figures 3.3a and 3.4a). In various TMDs [170,

187, 223, 227, 228], defects of this type are the most abundant and produce electron trap states within the band gap. In our experiments, most of type A defects are isolated as shown in Figure

3.3a. Occasionally we also observed paired Vse1a with an extremely low density, similar to the Se- divacancies predicted in reference [199].

Figure 3.4. DFT-calculated integrated local density of states for the five types of defects. Top panel: Empty-state images. (a) Type A at 0.25 eV. (b) Type B at 0.15 eV. (c) Type C at 0.2 eV.

(d) Type D at 0.085 eV. (e) Type E at 0.15 eV. Bottom panel: Filled-state images. (a) Type A at −

0.3 eV. (b) Type B at − 0.1 eV. (c) Type C at − 0.2 eV. (d) Type D at – 0.1 eV. (e) Type E at − 0.3 eV.

For defects of type B, our integrated LDOS images show that VPt1 produces 1 × 1 triangular protrusions at positive and negative bias (Figure 3.4b), similarly to the experimental STM images.

It was also found that after the structural relaxation, three nearest neighboring Se atoms at the topmost Se layer around the Pt vacancy site are expanded outward in plane (~ 0.3 Å) and vertically

(~ 0.1 Å) due to the missing bonds between the Pt and Se atoms. This topographic effect explains why the STM images for defects of type B show 1 × 1 bright triangular shapes at both negative and positive bias as well as the small expansion of the in-plane lattice constant in the triangular protrusions.

For defects of type C, among the three aforementioned possibilities (PtSe1b, VSe1b, V3Pt), we found that VSe1b produces the 2 × 2 triangular protrusions similar to those observed in the STM images at positive and negative bias (Figure 3.4c). Unlike the case of type B defects, changes in the atomic positions near the defect site were negligible upon the structural relaxation. Therefore, the

62 observed STM image is likely to be determined by the influence of the defects on the nearby electronic structure, rather than by mere topographic changes.

The integrated LDOS images confirm that defects type D arise from VPt2. From the simulations, 4

× 4 triangular protrusions at positive and negative bias voltages (Figure 3.4d) are observed. The three Se atoms at the vertices of the triangle are vertically shifted upward by about 0.04 Å, which explains moderately bright protrusions at both positive and negative bias.

The observed STM images for defect type E agree with the integrated LDOS images of SePt1 defects (Figure 3.4e), although the effect of defect type E is quite subtle. Qualitative features such as 1 × 1 triangular protrusions at both negative and positive bias voltages and the surrounding depressions at positive bias are close to those of the experimental images.

The total DOS and PDOS onto all Pt and all Se atoms (Figure 4.10) are calculated here in order to further elucidate the comparison to the experimental STM/STS images (Figure 3.3). As shown in

Figure 4.10, significant DOS at the bias voltages is found where the theoretical LDOS and experimental STM images are obtained. For defect types A, C, E, both Pt and Se contribute significantly to DOS, while for defect types B and D, Se contributes more to the DOS than Pt, at the bias voltages marked by the arrows.

3.3. DFT calculations of defect formation energies

For a better understanding of stability of different defect types, we calculated the formation energies of all the defect types we considered in this work, as shown in Figure 3.5. The formation energy values at the extreme Se-rich and Pt-rich conditions for all defect types are listed in Table

4.1 in the Supplementary Information. Since the formation energies for a PtSe2 bilayer with inversion symmetry were calculated, Pt1 and Pt2 atoms are equivalent to each other and the formation energies of VPt1 and VPt2 are the same in our calculations. The formation energies of

63 some defect types are not shown in Figure 3.5 but listed in Table 4.1, because their formation energies are much higher than the other observed defects. Our calculated formation energies agree with the STM experimental densities of defects listed in Table 3.1, although the experimental sample flakes are thicker than a bilayer. For instance, in a Se-rich condition, the formation energy of SePt1 defect alone is well below the formation energies of other defects, becoming negative in the extreme Se rich case. In our sample grown under a Se-rich condition, defect type E turns out to have the highest density as observed in experiments (Table 3.1), and that the integrated LDOS images (Figure 3.4e) suggest that defect type E arises from the SePt antisite defect. In addition,

Table 3.1 shows that the density of defect type A is higher than that of defect type C. This agrees with our result that the formation energy of defect type A is noticeably lower than that of defect type C (Figure 3.5).

Figure 3.5. Calculated defect formation energies. adSept1 and adSe1a indicate Se adatoms at the hollow site above Pt atoms and the top site above Se1a atoms, respectively. The case of Se adatom

64 at the hollow site above Se1b atoms gives a very similar result to the adSe1a case and not shown here. VPt1 and VPt2 have the same formation energies.

Some defect types shown in Figure 3.5 and Table 4.1 have low formation energies but they have not been observed in the STM experiment. For example, Se adatoms (at the hollow Se site, hollow

Pt site, and on top site) have not been observed, although their formation energies are significantly lower than those of the observed defect types. This could be due to the annealing process done before transferring into the STM analysis chamber.

3.4. STS analysis

To characterize the electronic structures near the defects, we performed STS measurements on both defect-free and defect-rich areas. Figure 3.6 shows dI/dV spectra of pristine areas and defect- rich areas with types A-E with a thickness of six monolayers, in the voltage range of  0.8 V to

0.8 V. For the defect-free areas (see Figure 3.1c) the V-like shaped dI/dV spectrum has much higher density of states (DOS) at empty states than at filled states with a rather wide region of low

DOS near the Fermi level. This feature indicates that pristine PtSe2 is semi-metallic at the thickness down to six layers, which is consistent with the reported experimental data [212]. The dI/dV spectra of the defects were measured at the center for defect type A and at the corner protrusions of defect types B, C, D and E (see Figures 4.8 and 4.9 in the Supplementary Information), respectively. The STS at the centers of the defects was also measured, and found less prominent features compared with those measured at the protrusions, especially for VPt2 defects. Each dI/dV curve was obtained by averaging over 15 spectra. Due to the metallic nature of the PtSe2 flakes, the dI/dV peaks for the defect-rich regions are not as prominent as those for typical semiconducting layers with defects.

The direct voltage-by-voltage comparison between the experimental STS and the calculated

DOS/PDOS would be challenging due to the fact that the experimental samples are in metallic regime and the simulated films are in semiconducting regime. Note that 1T-PtSe2 undergoes a phase transition from semimetallic to semiconducting phase as thickness decreases. However, our theoretical results discussed earlier are still relevant to experiment because of the following reasons: (i) Total DOS of the pristine film of 2 MLs agrees with that of pristine 6 MLs (Figure

4.5); (ii) Our study of the simulated defects suggest that the most dominant defect type is type E in a Se-rich growth condition (Figure 3.5), which agrees well with experimental data (Table 3.1);

(iii) calculated LDOS images agree well with the experimental STM images.

Figure 3.6. STS of six-layer PtSe2 with and without defects. The top five panels are for the layer with defects, while the bottommost panel is for the pristine layer.

3.5. CONCLUSION

Intrinsic point defects in ultrathin PtSe2 layers grown via the CVT method were investigated using

STM/STS and first-principles calculations. Five dominant types of point defects were observed and identified, such as VSe1a, VPt1, VSe1b, VPt2 and SePt1. The formation energies of these defect types were calculated and compared with the densities of the defects observed in experiments. The relative densities of the dominant defect types are in good agreement with the calculated formation

67 energies. The experimental data and theoretical results suggest that SePt1 antisite defects are the most abundant with the lowest formation energy in the Se-rich condition. Our findings elucidate the modification of electronic structures from the point defects, which would be crucial for optimizing the growth of ultrathin PtSe2 layers and designing future electronic and spintronic devices.

ACKNOWLEDGMENTS

C.T. and H.Z. acknowledge the financial support provided for this work by the US Army Research

Office under the grant W911NF-15-1-0414. L.J. and D. H. acknowledge National Natural Science

Foundation of China (No.51372134, No.21573125) and Beijing Municipal Science & Technology

Commission (No.Z161100002116030). Y.C. was supported by the Virginia Tech Institute for

Critical Technology and Applied Science (ICTAS) fellowship. The computational support was provided by San Diego Supercomputer Center (SDSC) under DMR060009N and Virginia Tech

Advanced Research Computing (ARC).

SUPPLEMENTARY INFORMATION FOR “VISUALIZATION OF POINT DEFECTS IN ULTRATHIN LAYERED 1T-PtSe2”

4.1. EXTRA EXPERIMENTAL DATA

PtSe2 layers were synthesized on mica substrates, with a triangular or hexagonal shape, shown in light color in Figure 4.1a. Figure 4.1b is a zoom-in image of the marked area in Figure 4.1a, indicating the thickness of the flake is 9 PtSe2 layers. As shown in Figure 4.2, PtSe2 flakes are with various thickness, since there is a height difference between the layers (part 1 versus part 2 in

Figures 4.2a and 4.2b). The step height on the mentioned area of PtSe2 flakes shows 1.55 nm height difference between two areas of PtSe2 which means the left (part1) part is about 3 layers of PtSe2 higher than the right part (part2). Figures 4.2c and 4.2d are atomically resolved STM images of part 1 and part 2, clearly showing that the crystallographic orientations of these two parts are with an 180˚ rotation. In the following images, we try to provide additional information about the position of defects and the nature of them. Figure 4.3a shows an STM image of the surface of an

1T-PtSe2 flake, and Figure 4.3b is the same image with an atomic model of PtSe2 overlapped on it for determine the atomic position of the defects. Note that Figure 4.3 was obtained at room temperature and all the rest of STM or STS data were at 77K. There is a high resolution electron microscopy image (Figure 4.4). As shown in this image, there are some defects marked by green circles being attributed to defects type A and C, and also those marked by yellow circles are attributed to defects type B and D. As defects of type A and C are both at Se sites, those could be either VSe1a or VSe1b. Similarly both defects of type B and D are at Pt sites. However, we did not see the effect of defect type E in the STEM image. It is mainly due to the thickness of the flake, 5 layers, used for taking the electron microscopy image. Defect formation energies of the considered

69 defect types are tabulated in the ascending order of the formation energy in the Se rich condition

(Table 4.1), which is relevant to the growth condition of our sample. Total density of states of the pristine bilayer and six-monolayer PtSe2 from the LDA-optimized geometries are shown in Figure

4.5. PDOS from Pt and Se atoms for the DFT-optimized pristine PtSe2 bilayer are shown in Figure

4.6. Additional DFT-calculated integrated LDOS is provided for each type of the defects at different bias voltages in Figure 4.7. Figures 4.8 and 4.9 show STS obtained at different positions.

The total DOS and PDOS onto all Pt and all Se atoms for each kind of defect are presented in

Figure 4.10.

Figure 4.1. (a) Optical image of a flake with similar color to the higher part shown in Figure 4.1b.

(b) AFM image of the area marked by the square in (a). Inset: line profile along the marked line.

Figure 4.2. (a) Optical image of flakes with thickness of 9 and 6 layers, labeled as 2 and 1, respectively. (b) STM image of the area marked by the circle in (a) (Vs = 2.0 V, I = 0.3 nA). Inset: line profile along the marked yellow line. (c) and (d) Atomically resolved STM images of the higher part (Vs = 0.7 V, I = 0.7 nA) and the lower part in (b) (Vs = 0.3 V, I = 0.5 nA). The defects in the higher part show opposite orientation compared with those in the lower part.

Figure 4.3. (a) STM image and (b) the same image with atomic model overlaid on it (Vs = − 0.4

V, I = 0.5 nA).

Figure 4.4. High resolution transmission electron microscopy image of a 5-layer 1T-PtSe2.

4.2. DFT CALCULATIONS OF FORMATION ENERGIES

Defect formation energy was calculated using the following formula [229]:

Ef = Edefect – Epristine – Σi niμi (1)

where Edefect and Epristine are total energies with and without a defect, respectively, μi is a chemical

th th potential of the i atomic species, and ni is the number of added i atoms by the defect (ni < 0 if the atoms are removed). The chemical potential of each atomic species depends on materials growth conditions. The bounds of the chemical potentials are determined from the following conditions:

μPt + 2μSe = μPtSe2,

bulk μi ≤ μi , (2)

bulk where μPtSe2 is the energy of pristine PtSe2 per formula unit, and μi is the bulk chemical potential of the ith species. The second inequality gives the upper bound of the chemical potential and indicates that the chemical potential of each atomic species during the synthesis cannot be greater than the chemical potential of the corresponding stable bulk state, since otherwise elemental bulk would be grown rather than desired PtSe2. Now combining the first equation (which is from the law of mass action) with the inequality, the lower bound of the chemical potential is set. Thus, the chemical potentials are confined within a specific range and the two extreme cases are Se rich (μSe

bulk bulk = μSe ) and Pt rich (μPt = μPt ) conditions. The LDA-calculated formation energies of defects that we considered are shown in Table 4.1.

Table 4.1. Defect formation energies of the considered defect types are tabulated in the ascending order of the formation energy in the Se rich condition, which is relevant to the growth condition of our sample. Except for adatom cases (which might be removed due to annealing), all defect types up to Se1b vacancy are observed in the STM experiment, and other defects with higher formation energies are not observed. Se adatom at bridge site is also simulated. However, in this case, the Se adatom moves toward a hollow site upon relaxation, which indicates that hollow sites are more stable than the bridge site. For the defect types marked by an asterisk, a 331 k-mesh is used. Other computational details are explained in the main text.

Defect Se rich Pt rich

Se antisite at Pt site − 0.064 eV 1.668 eV

Se adatom hollow Se1b site* 0.566 eV 1.144 eV

Se adatom top site* 0.570 eV 1.148 eV

Se adatom hollow Pt site* 1.294 eV 1.872 eV

Pt1 vacancy 1.353 eV 2.508 eV

Se1a vacancy 1.464 eV 0.877 eV

Se1b vacancy 1.884 eV 1.307 eV

Pt antisite at Se1b site 1.916 eV 0.184 eV

Se intercalation 2.983 eV 3.561 eV

Pt antisite at Se1a site* 3.593 eV 1.861 eV

Three Pt vacancy* 4.230 eV 7.693 eV

Pt intercalation 21.636 eV 20.481 eV

Figure 4.5. Total density of states of the pristine bilayer and six-monolayer PtSe2 from the LDA- optimized geometries. The density of states for the bilayer was scaled by a factor of three for comparison.

Total DOS PDOS from Se 8 PDOS from Pt

DOS (a.u.)

0 -4 -2 0 2 Energy - EF (eV)

Figure 4.6. Calculated PDOS from Pt and Se atoms for the DFT-optimized pristine PtSe2 bilayer.

Figure 4.7. Additional DFT-calculated integrated local density of states (LDOS) for the five types of defects at different bias voltages from the experimental data shown in Figure 3.3 and the simulated LDOS in Figure 3.4. Top panel: Empty-state images. (a) Type A at 0.4 eV. (b) Type B at 0.4 eV. (c) Type C at 0.1 eV. (d) Type D at 0.2 eV. (e) Type E at 0.4 eV. Bottom panel: Filled- state images. (a) Type A at − 0.1 eV. (b) Type B at − 0.2 eV. (c) Type C at − 0.3 eV. (d) Type D at – 0.1 eV. (e) Type E at − 0.4 eV.

Figure 4.8. STS obtained from different positions. (a) Atomically resolved STM image of a clean

1T-PtSe2 surface (Vs = 0.3 V, I = 0.6 nA). (b) STS obtained at three different areas similar to (a).

(c) STM image showing an isolated defect type B (Vs = 0.3 V, I = 0.7 nA). (d) STS obtained from the center and the protrusion.

Figure 4.9. STS obtained from different defects of type B defects. (a) STM image showing an isolated type B defect (Vs = 0.3 V, I = 0.7 nA). (b) A type B defect from another area (Vs = 0.3 V,

I = 0.7 nA). (c) STS taken from the 6 protruding Se atoms marked in (a) and (b).

Figure 4.10. Calculated total DOS and PDOS onto all Pt and all Se atoms for defect type A (a), type B (b), type C (c), type D (d), and type E (e), where the arrows indicate the bias voltages used for the calculated LDOS (Figure 3.4 in the main text).

DEFECT STABILITY AND KINETICS IN TWO- DIMENSIONAL 1T-PtSe2 5.1. INTRODUCTION

Transition metal dichalcogenide monolayers are a class of two-dimensional materials that exhibit a variety of different point defects. These defects exhibit a significant influence on physical properties. For example, the electrical conductivity and magnetic behavior of two-dimensional

PtSe2 (consisting of two molecular layers of PtSe2) [230] depends upon the number of several possible types of vacancies and anti-site defects in the layer. In our recent study, five types of point defects in PtSe2 were observed [231]. These defects are mobile at intermediate temperatures and rearrange into self-organizing patterns [231]. While each type of defect has a characteristic formation energy, these energies can be expected to depend upon the stoichiometry of the film. In addition, the defects appear arrange in self-organizing patterns that suggest energetic interactions among them. While ground-state energies of different defects have been calculated with density functional theory [232], it is desirable to develop an approach that can predict the stability of defects with temperature, interactions among the defects, and how the defects arrange themselves into patterns over time. Toward this end, an energy landscape for 1T-PtSe2 is constructed as part of the Steepest Entropy Ascent Quantum Thermodynamics (SEAQT) framework [233] and the

SEAQT equation of motion applied to this landscape to predict stable configurations of interacting defects in 1T-PtSe2 and explore the kinetics with which arbitrary initial configurations of defects relax toward stable equilibrium. The SEAQT framework is a non-equilibrium thermodynamic- ensemble approach that was originally formulated to address a number of physical inconsistencies between quantum mechanics and thermodynamics [234-238], and it has computational advantages that have led to its application in variety of solid-state problems [239-242]. Here, an energy landscape is constructed that includes the number, type, and distribution of point defects in 1T-

PtSe2 and solve an SEAQT equation of motion through state space to find the kinetic path and corresponding microstructural evolution from a specified initial distribution of defects to stable equilibrium.

5.2. METHODS 5.2.1. SYNTHESIS AND IMAGING

1T-PtSe2 flakes were synthesized via chemical vapor transport on Mica. Figure 5.1 represents the structure of a perfect “monolayer” of 1T-PtSe2, which consists of two layers of the PtSe2 formula unit. A projection of the unit cell along the c-axis is shown in left portion of the Figure. As discussed in our previous work on 2D 1T-PtSe2, there are 5 different individual defects in 2D 1T-

PtSe2, namely VSe1a, VSe1b, Vpt1, VPt2, and SePt1 (Figure 3.3) which were detected by scanning tunneling microscopy (STM) [231]. A sixth “individual” defect was defined as the combination of

VSe1b and Vpt1 located within the same unit cell. This particular pair of defects was the only combination of defects observed by STM to occur within a unit cell. Defects were imaged in a

20×20 nm2 of area using customized Omicron LT STM/AFM at constant current mode.

C = 5.07 Å

a = 3.73 Å

Figure 5.1: Schematic crystal structure of a perfect bilayer of 1T-PtSe2: the left image is along c axis and the right image is along a axis (cross section).

Initially, heat treatment was done on the samples at 250°C (523 K) for 2.5 hours in ultra-high vacuum environment (preparation chamber of the STM instrument which is connected to the analysis chamber) with the base pressure of almost 10-10 mbar, and then samples were cooled to room temperature for STM analysis. Later, the STM analysis at low temperature was done in order to dynamically stabilize atoms of the 2D material, increase thermal and mechanical stability of the sample and STM tip and to reduce temperature drift. Hence, liquid nitrogen was injected around the STM chamber and the whole chamber including the sample were cooled down to 77K. The experiment at room temperature and low temperature was done several times and each time there was a heat treatment before imaging was started. Comparing results after the first period of annealing with results after the last period gave us very good evidence that defects are either migrating in the material or being produced, since defect configurations were changing after successive annealing steps (Figure 5.2).

a c

b d

Figure 5.2: STM images of 2D 1T-PtSe2 after annealing at 523K for 2.5 hours for a and b) one time b and c and d) 7 times.

First of all, we can compare densities of defects and see if those are changing. After measuring the average density of defects (calculated from 15 different images at each annealing condition) and comparing the defect densities from the first and last annealing periods, it was concluded that the density of each defect does not change significantly and the change in the configurations comes from defect movement across the 2D material. The movement of the defects introduces defect combinations into the structure.

A series of topography STM images representing new configurations (Figure 5.3) were analyzed to identify and tabulate combinations (table 5.1) of defects that appeared in close proximity.

Specific combinations of defects, or patterns, seemed to recur in the STM images, so it was assumed they appear because they are energetically favorable, Combinations of two or more individual defects were identified as interacting defects. Twenty unique combinations of interacting defects were identified in the STM images; they will be discussed them in detail in the next sections.

0.6 nm 0.6 nm a b

0.2 nm 0.2 nm 0 0

Figure 5.3: STM images of defect combinations of VSe1a which are a) 2VSe1a and b) 3VSe1a. Both imaging parameters are V= -0.05 V, I= 0.7 nA.

1 Å c d e

1 nm 1 nm 1 nm 0

Figure 5.3 (Continued): STM images of defect combinations of two VPt1 which are c) two adjacent

Pt1 vacancies (2VPt1 – 1) at V= 0.5 V, I= 0.5 nA, d) two vacancies of Pt1 having two in-plain lattice constants distant (2VPt1 – 2) at V= 0.5 V, I= 0.5 nA, e) two vacancies of Pt1 having three in-plain lattice constants distant (2VPt1 – 3) at V= 0.5 V, I= 0.5 nA.

1 Å f g

0.5 nm 1 nm 0

Figure 5.3 (Continued): STM images of defect combinations of two VSe1b which are: f) two adjacent Se1b vacancies (2VSe1b – 1) at V= 0.3 V, I= 0.7 nA, g) two VSe1b having three in-plain lattice constants distant (2VSe1b – 3) at V= 0.3 V, I= 0.7 nA.

1 Å h i j k

1 nm 1 nm 1 nm 1 nm 0

Figure 5.3 (Continued): STM images of defect combinations of two VPt2 which are: h) two Pt2 vacancies in two different Pt2 rows (2VPt2 – 2R) which R represent rows and 2 represent rows distant between defetcs at V= 0.2 V, I= 0.4 nA, i) two Pt2 vacancies in the same Pt2 rows having two in-plain lattice constants distant (2VPt2 – 2) at V= 0.2 V, I= 0.4 nA, j) two

Pt2 vacancies in the same Pt2 rows having 5 in-plain lattice constants distant (2VPt2 – 5) at V= 0.2 V, I= 0.4 nA and k) two Pt2 vacancies in two different Pt2 rows (2VPt2 – 6R).

0.8 Å 1 Å k l m n

2 nm 0.5 nm 0.5 nm 2 nm 0 0

Figure 5.3 (Continued): STM images of defect combinations of: l) two SePt1 in two different Pt2 rows (2SePt1 – 1R) which R represent rows and 1 represent rows distant between

defetcs at V= 0.6 V, I= 0.7 nA, m) two SePt1 in the same row having one in-plain lattice constants distant (2SePt1 – 1) at V= 0.6 V, I= 0.7 nA, n) two SePt1 in the same row having two

in-plain lattice constants distant (2SePt1 – 2) at V= 0.6 V, I= 0.7 nA and o) five SePt1 in four different rows (5SePt1 – 4R) at V= 0.6 V, I= 0.7 nA.

0.8Å r p q s t

0.5 nm 0.5 nm 2 nm 0.5 nm 0.5 nm 0

Figure 5.3 (Continued): STM images of defect combinations of: p) adjacent VSe1b and VPt1 (VSe1bVPt1) at V= 0.3 V, I= 0.7 nA, q) VSe1b and VPt1 (VSe1bVPt1 - 1) at V= 0.3 V, I= 0.7 nA

(1 at the end of the name is to differentiate this configuration with the next one), r) VSe1b and VPt1 (VSe1bVPt1 - 2) at V= 0.3 V, I= 0.7 nA, s) VSe1a and VPt1 (VSe1aVPt1 ) at V= 0.6 V, I=

0.7 nA (as there is only one defect of this type, we do not allocate a number to it), and t) VPt1 and VPt2 (VPt1VPt2) at V = 0.5 V, I = 0.5 nA (as there is only one defect it, we do not allocate a number to it).

5.2.2. DFT CALCULATION

DFT calculation including spin-orbit coupling was performed in order to calculate the formation energy of these new configurations of interacting defects. As the local density approximation

(LDA) [243] gives more accurate in-plane and out-of-plane lattice constants that are close experimental values [207, 244, 245], LDA was selected as the exchange-correlation functional and the Projected-Augmented Wave (PAW) Pseudopotential [205] was used. An ultra-thin layer of two 1T-PtSe2 was the geometry used for DFT calculation. As there are different defect combinations, different supercell sizes (Table 5.1) were selected to relax the geometry and find the whole system energy. A vacuum layer of 25 Å was added to the layers to prevent layers from interaction. The energy cutoff was set to 280eV and relaxation was done on all supercells until the residual forces were less than 0.01eV/Å. For supercells larger than 5×5×1, spin-orbit coupling was turned off and the energy cutoff was reduced to 230eV. K-meshes for each supercell are in table

5.1 as well.

Table 5.1: Defects combinations, their corresponding supercell and K-mesh sizes for DFT calculation, and their formation energies at synthesis condition and stoichiometric condition.

Formation energy at synthesis Formation energy at Stoichiometric

Defect # Combination Supercell size K-mesh Condition (eV) Condition (eV)

Se Rich Pt Rich (Thermodynamic Model)

1 (a) 2VSe1a 5×5 5×5×1 2.4865 2.1759 1.5674

2 (b) 3VSe1a 5×5 5×5×1 3.987 3.3896 2.231

3 (c) 2VPt1 - 1 5×5 5×5×1 2.598 3.4016 5.076

4 (d) 2VPt1 - 2 5×5 5×5×1 2.531 3.4218 5.278

5 (e) 2VPt1 - 3 5×5 5×5×1 2.387 3.1919 4.869

6 (f) 2VSe1b - 1 5×5 5×5×1 3.387 3.1524 2.693

7 (g) 2VSe1b - 3 7×7 3×3×1 3.381 3.1349 2.653

8 (h) 2VPt2 – 2R 9×9 3×3×1 2.563 3.4628 5.291

9 (i) 2VPt2 - 2 9×9 3×3×1 2.570 3.4694 5.297

10 (j) 2VPt2 - 5 11×11 3×3×1 2.671 3.4747 5.115

11 (k) 2VPt2 – 6R 11×11 3×3×1 2.708 3.5143 5.146

12 (l) 2SePt1 – 1R 5×5 5×5×1 -0.155 0.94036 3.268

13 (m) 2SePt1 - 1 5×5 5×5×1 -0.133 0.9947 3.391

14 (n) 2SePt1 - 2 5×5 5×5×1 -0.139 0.9224 3.178

15 (o) 5SePt1- 4R 11×11 3×3×1 -0.368 2.8525 9.802

16 (p) VSe1bVPt1 5×5 5×5×1 2.811 2.9486 3.227

17 (q) VSe1bVPt1 - 1 5×5 5×5×1 2.981 3.2412 3.767

18 (r) VSe1bVPt1 - 2 5×5 5×5×1 2.835 3.1647 3.831

19 (s) SePt1VSe1a 5×5 5×5×1 1.327 1.7485 2.637

20 (t) VPt1VPt2 7×7 3×3×1 2.715 3.4931 5.103

The formation energies are in table 5.1. These formation energies are for the synthesis conditions which could be either Se rich or Pt rich. However, when heat treating the material, defects migrate and make new configurations under the stoichiometric condition and the Se-rich or Pt-rich synthesis conditions no longer exist. Therefore, a different method is needed to calculate the formation energies of defect combinations at the stoichiometric ratio of Se to Pt and any concentration between Se-rich or Pt-rich conditions. To do so, the thermodynamic model in the next section was developed.

5.2.3. THERMODYNAMIC MODEL

A film of 1T-PtSe2 is currently being modeled as a thermodynamic system 30a×30a in size (where a is the in-plane 1T-PtSe2 lattice constant). To demonstrate the ability of the SEAQT framework to identify realistic equilibrium states and their corresponding microstructures and predict the associated kinetics, results for a thermodynamic system 12a×12a in size are presented in this dissertation.

In this model, each unit cell contains two Pt atoms and four Se atoms. According to our findings in Figure 5.3, annealing in a vacuum at temperatures up to 523 K makes defects move across the materials and create new configurations. One of the new configurations corresponds to a Pt vacancy (VPt1) in the top layer and a Se vacancy in the bottom Se plane (VSe1b) of the top layer with the two types of vacancies aligned within the same unit cell (VSe1bVPt1). Since, the location of defects is specified by unit cell coordinates and this combination is the only combination within the same unit cell, from now on this particular combination will be treated as an additional individual defect. Therefore, in addition to the defects detected by Zheng et.al. [231] which are: Pt vacancies in the top layer and bottom layer (VPt1 and VPt2), Se vacancies in the two Se planes in the top layer (VSe1a and VSe1b), and an anti-site defect corresponding to a Se atom sitting on a Pt

96 site of the top layer (SePt1), the VSe1bVPt1 combination is added as the sixth individual defect. After heat treatment and the formation of new defect configurations, the total extensive energy of a film of PtSe2 is taken to be the sum of (i) the energy of a perfect (defect-free) film, (ii) the formation energy of the defects, and (iii) the interaction energy among the various defects associated with their configuration or their relative locations within the film. These contributions are represented in the following expression:

푓 퐸푡표푡 = 푁0퐸푐푒푙푙 + ∑푗 푛푗 퐸푗 + 퐸푐표푛푓푖푔 (1)

푓 where 푛푗 is the number of j-type defects (the sum is taken over the six defect types in the film), 퐸푗 is the formation energy of the j-type defect, and 퐸푐표푛푓푖푔 represents the configurational energy resulting from the arrangement of defects in the film. This expression provides a way to calculate the energy landscape of the extensive, ground-state energy for a defective sheet of 1T-PtSe2 of specified dimensions. The first term of Equation 1, the energy of a perfect sheet of 1T-PtSe2, is simply the total number of unit cells times the energy of a unit cell. The ground state energy of a single unit cell of 1T-PtSe2 (containing two molecules of stoichiometric PtSe2) was calculated with

DFT to be 퐸푐푒푙푙 = −29.30 푒푉. The defect formation energies in Equation 1 also can be estimated

푓 with DFT, but since each defect alters the film concentration, the 퐸푗 values are concentration- dependent and, thus, their values change with the film composition. Their dependence on concentration is related to the chemical potentials of Se and Pt through the following relationship, which applies to each defect type:

푓 퐸푗 = 퐸푗 − 퐸푝푒푟푓푒푐푡 − (푛푆푒μ푆푒 + 푛푃푡μ푃푡) (2)

Where 퐸푗 and 퐸푝푒푟푓푒푐푡 are DFT-calculated energies of 5×5 supercells containing a particular type of defect and the perfect (defect-free) lattice, respectively. The factors 푛푆푒 and 푛푃푡 are the number of Se and Pt atoms added to (or removed from) the sheet by the creation of the defect (see Table 97

5.2), and 휇푆푒 and 휇푃푡 are the concentration-dependent chemical potentials for Se and Pt. The procedure for calculating the chemical potentials is detailed in Appendix A. The interaction energy in Equation 1 arises from the proximity of defects to each other. A defect configuration, or arrangement of defects in the monolayer, is represented by two pieces of information: a list of 2D coordinates of the unit cells that contain a defect, and the Potts model (see the following section) spin (an integer from 0 to 6) that identifies the type of defect in each of the defective unit cells.

Table 5.2: Defect types and designations in 1T-PtSe2.

Defect label Defect type Defect notation Effect on concentration

st VSe1a A(Potts spin = 1) Top Se vacancy in 1 layer Removes one Se atom

st VPt1 B(Potts spin = 2) Pt vacancy in 1 layer Removes one Pt atom

Bottom Se vacancy in 1st VSe1b C(Potts spin = 3) Removes one Se atom layer

nd VPt2 D(Potts spin = 4) Pt vacancy in 2 layer Removes one Pt atom

Se on 1st layer Pt site (anti- Removes one Pt atom, adds SePt1 E(Potts spin = 5) site) one Se atom

Pt vacancy in 1st layer and Removes one Pt atom, st VSe1aVPt1 F(Potts spin = 6) Bottom Se vacancy in 1 removes one Se atom layer

5.2.4. ENERGY LANDSCAPE

The SEAQT framework is implemented by applying an equation of motion to an energy landscape that represents all the possible energy levels the system can occupy together with their respective degeneracies [246]. The energy levels and degeneracies along with the probability distribution predicted by the SEAQT equation of motion at each instant of time are used to directly calculate the system entropy at each state of the system as it evolves. Equation 1 provides a means of calculating the energy of any possible arrangement of the six types of individual defects in a 1T-

PtSe2 sheet. To determine the multiplicity (or degeneracy) of each energy level, one could resort to a permutation formula to determine the number of possible permutations the system has.

However, such formulas are impractical for systems larger than a few tens of atoms. For larger systems, the energy levels and degeneracies can be estimated numerically using the Replica-

Exchange-Wang-Landau (REWL) method [247-249].

An in-plain (two dimensional) set of pixels describe the microstructure of the system. The energy of this system is defined by a q-state Potts model. The integer q (Potts spin) varies from 0 (a perfect unit cell) to 6 (1≤q≤6 is for defects types A-F) and captures the configuration of atoms in different unit cells. Each unit cell has an associated q number, which reflects either that the unit cell is perfect or defective.

The sum of the energies of all the perfect and defective unit cells is a system eigen energy, E, of the energy landscape and is given by the Potts model interaction Hamiltonian [250]which is as follows:

1 퐸 = ∑푁 ∑푛 퐽(1 − 훿(푞 , 푞 ) (3) 2 푖=1 푗=1 푖 푗

The sum is over the number of unit cells (in this case, N2 = 144) and the number of neighbors to each unit cell. The interaction energy, J, which the Potts coupling constant switches between a

99 perfect unit cell and a defective unit cell, depending on qi and qj. The Kronecker delta, 훿, is 1 if qi

= qj and is 0 if qi ≠ qj. Equation 3 provides the energy of any arbitrary configuration of the system.

All possible system configurations are associated with the various eigenenergies of the energy landscape or energy eigenstructure. It is demonstrated that many of these possible configurations have the same eigenenergy, which means that the eigenenergies are degenerate. To calculate the

2D material properties like the entropy, it is necessary to accurately predict the degeneracy of each eigenenergy (or energy level), and this is commonly described by the density of states for the energy level. The density of states for the 2D material can be found using the Wang-Landau method [247, 248], which uses a non-Marcovian Monte Carlo walk through all the possible energy levels. The replica exchange [251] variant of the Wang-Landau method greatly accelerates the algorithm by subdividing the energy spectrum into multiple windows, utilizing multiple Monte

Carlo walkers over the energy windows and passing information among between the overlapping regions of any two windows.

The density of states for the energy landscape of a 12 x 12 lattice of Pt2Se4 12x12 is shown in

Figure 5.4. The discrete energy levels, ε, are plotted along the horizontal axis, and the vertical axis represents the logarithm of g(ε) where g represents the degeneracy corresponding to the energy levels.

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Figure 5.4: Density of states (DOS) corresponding to the energy landscape of the 12x12 lattice.

5.2.5. KINETIC MODEL AND TEMPERATURE

The application of the SEAQT framework to solid-state problems is described in detail in reference

[246]. The framework relies on an equation of motion that finds the path of steepest-entropy ascent in a system described by energy and entropy state variables. For the case when quantum correlations can be neglected (e.g., in a classical system), the equation of motion is given by [252-

254]:

푑푝 1 푗 = 퐷 (풑) (4) 푑푡 휏(풑) 푗

th where 푝푗 represents the occupation probability of the j energy eigenlevel, εj, 푝 denotes the vector of all the 푝푗 at a given instant of time, 퐷푗(푝) is the dissipation term, and 휏(푝) is a relaxation parameter.

For the special case of a system interacting with a heat reservoir (which enables us to consider systems that are heated or cooled), the equation of motion can be simplified to yield [246]:

푑푝 푗 = 푝 [푠 − 〈푠〉 − 푗 − 〈푒〉βR] (5) 푑푡 푗 푗

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푡 푡∗ (= ) is the dimensionless time, 푠 the entropy of the 푗푡ℎ eigenlevel, 〈∙〉 the expectation value 휏(푝) 푗

푅 1 of a property, and 훽 = . In this last expression, 푘 퐵 is Boltzmann’s constant and 푇푅 the 푘퐵푇푅 temperature of the reservoir. Equation 5 for all the j represents a system of first-order differential equations, the solution of which gives the time-dependent occupation probabilities, 푝푗, that describe the system’s kinetic path through state space from an initial state to stable equilibrium.

The entropy and energy terms can be calculated explicitly from the energy landscape, and the system of differential equations can be solved given an initial condition represented by the set of probabilities, 푝푗, for the initial state of the system (estimated from the defect densities observed with STM).

The final stable equilibrium state is checked by comparing with a canonical distribution given by

푔 exp (−훽푠푆푒Ɛ ) 푠푆푒 푗 푗 1 푠푆푒 푝푗 = 푠푆푒 = 푠푆푒 푔푗exp (−훽 Ɛ푗) ∑푖 푔푖exp (− 훽 Ɛ푖) 푍

푠푆푒 푠푆푒 1 Here the se superscript denotes stable equilibrium, 푍 is the partition function, and 훽 = 푆푒. 푘퐵푇

The time-dependent occupation probability distributions determined from the SEAQT equation of motion provide all the information needed to characterize the state of the system as the system evolves in time.

To relate the occupation probabilities to actual defect configurations, a set of parameters are needed to link the energy levels (eigenenergies) to representative defect configurations. The descriptors chosen were the arithmetic-average defect densities. That is, for each energy level visited by the Monte Carlo walkers of the replica exchange Wang-Landau algorithm, the arithmetic-average density of each type of individual defect was calculated. These averages are

102 shown in Figure 5.5. Thus, each energy level has an associated arithmetic-average density of A,

B, C, D, E, and F defects.

5.3. RESULT AND DISCUSSION

Combining the arithmetic average defect densities associated with each energy level (Figure 5.5) with the occupation probabilities of the energy levels provides a time-dependent description of the weighted-average density of defects predicted by the SEAQT equation of motion. Two kinetic paths are shown in Figure 5.6: the left side of the diagram represents isothermal annealing, and the right side of the diagram reflects heating from 77 K to the annealing temperature. In both diagrams, the horizontal axis is dimensionless time, and the vertical axis is the weighted-average density of each defect (the expected value of the defect density from the equation of motion). The left side of each plot represents the initial configuration of defects, and the right side of the plot represents stable equilibrium. During isothermal annealing, the density of all six defects remain relatively constant. This is unsurprising since the system is maintained at constant energy. The entropy does increase, however, as the defects rearrange. In the heating case, energy increases as heat is transferred from the thermal reservoir to the material so the relative densities of the defects change more noticeably: the density of defect E increases, the density of defect A remains constant, and all the others decrease with time. Nevertheless, the final stable equilibrium state for both the isothermal and heating cases are the same, as they must be at a common final temperature. Figures

5.7 and 5.8 show representative configurations for a series of times along the isothermal annealing path and along a heating path to the final annealing temperature. The time, t0, represents the initial configuration (defect densities obtained from STM images). These configurations in these images represent the same densities shown in Figure 5.6, but they also provide insight into the way the defects rearrange as they move toward stable equilibrium. These results from the test lattice of 12

103 x 12 unit cells represent an area that is too small to compare directly with the defect patterns observed with STM (the STM images covered an area of roughly 30 x 30 unit cells). However, the test lattice is sufficiently large to demonstrate the efficacy of the SEAQT approach in modeling defect migration and pattern formation during annealing, and it is a straightforward process to scale the calculations completed to the size of the experimental STM images.

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Figure 5.5: Arithmetic-average defect density versus the energy levels.

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Figure 5.6: Weighted-average defect densities versus time for the a) isothermal condition (at annealing temperature) and b) during heating.

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t t 0 3

t t9 10

Figure 5.7: Microstructure evolution vs time during the heating process.

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t t0 4

t t 6 9

Figure 5.8: Microstructure evolution vs time at isothermal condition (annealing).

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APPENDIX A A.1 CHEMICAL POTENTIALS

Expressions for the chemical potentials required in Equation 2 are obtained as follows. Both μPt and μSe are composition-dependent, and since defects alter the com position of the sheet, these chemical potentials change with the numbers of defects. Considering first the perfect stoichiometric compound, the total energy for a formula unit of PtSe2, which is equal to its chemical potential, is constructed from the chemical potentials of its component species via

μ푃푡푆푒2 = E푃푡푆푒2 = μ푃푡 + 2μ푆푒 (A.1)

From DFT calculations, the energy of formation of stoichiometric PtSe2 is:

푒푉 E = −14.650 푃푡푆푒2 푓표푟푚푢푙푎 푢푛푖푡

(Half the value of 퐸푐푒푙푙 = −29.30 푒푉).

Film growth takes place under Se-rich conditions, and the chemical potential of Se is fixed at the

푒푉 lattice energy of Se. That is, μ = 퐸 = −3.475 . From these calculated values for μ and 푆푒 푆푒 푎푡표푚 푆푒

E푃푡푆푒2, Equation A.1 can be rearranged to yield the chemical potential of Pt in a Se-rich film:

푒푉 μ푆푒−푟푖푐ℎ = E − 2퐸 = −7.700 (A.2) 푃푡 푃푡푆푒2 푆푒 푎푡표푚

Similarly, for a Pt-rich film, the chemical potential of pure Pt can be taken to be the calculated

푒푉 lattice energy of Pt, that is, μ = 퐸 = −6.036 . Using this value and E , Equation A.1 푃푡 푃푡 푎푡표푚 푃푡푆푒2 can be rearranged to provide an expression for the chemical potential of Se (in a Pt-rich film):

1 푒푉 μ푃푡−푟푖푐ℎ = (E − 퐸 ) = −4.307 (A.3) 푆푒 2 푃푡푆푒2 푃푡 푎푡표푚

These values for the chemical potentials of Pt and Se in films with the extremes of the composition range (Se-rich and Pt-rich) are listed in Table 6.A.1. The chemical potentials needed to calculate

109 the defect formation energies in Equation 2 for any film composition between these concentration limits is calculated from linear interpolation:

푁푆푒 푆푒−푟푖푐ℎ 푁푃푡 푃푡−푟푖푐ℎ μ푆푒 = ( )μ푆푒 + ( )μ푆푒 (A.4) 푁푆푒+푁푃푡 푁푆푒+푁푃푡

푁푆푒 푆푒−푟푖푐ℎ 푁푃푡 푃푡−푟푖푐ℎ μ푃푡 = ( )μ푃푡 + ( )μ푃푡 (A.5) 푁푆푒+푁푃푡 푁푆푒+푁푃푡 where 푁푆푒 and 푁푃푡 are the total numbers of Se and Pt atoms in the film, respectively, and values for the Se-rich and Pt-rich μ푖’s are taken from Table 6.A.1.

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VIBRATIONAL PROPERTIES OF TWO DIMENSIONAL 2M-WS2 FILMS

6.1. ABSTRACT

The layer dependence of vibrational modes of 2M-WS2 is investigated using Raman spectroscopy and first principle calculations. Raman spectroscopy and density- functional theory (DFT) calculation demonstrate that all Raman active modes have a downshift when material is thinned to few layers (less than 5 layers). It is shown that due to the strong interaction between layers, downshift in Raman active modes is mostly for the ones which belong to the out-of-plane atomic movements and the most

2 downshift is for the Ag . Also, I investigated the effect of number of layers on the band structure and electronic properties of this material. As the number of layers decreases, the band gap does not change until the material is thinned down to only a single monolayer. For a single monolayer of 2M-WS2, the band gap is 0.05eV; however, with applying in-plane strain to this monolayer, the material takes a metallic behavior as the strain goes beyond ±1%.

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6.2. INTRODUCTION

Two dimensional (2D) materials have been recently used vastly in optoelectronic, spintronic, electronic, and energy storage application-oriented researches [255, 256]. Main reasons why these materials are interesting for researchers are that power consumption and performance improvement are of main demands of electronic industry [257]. One of the 2D material families is transition metal dichalcogenides (TMDCs) which has a variety of phases depending on the stacking of layers [46, 255, 258]. These phases have been described in chapter 1. However, depending on the stacking order, there could be different structures [259]. The most recent discovered monoclinic structure consists of 1T’ monolayers which stack in AA fashion along c axis with c/2 stacking distance as shown in Figure 6.1. and as there must be at least two similar monolayers in a unit cell to have monoclinic structure, it is called 2M [260, 261]. 2M-WS2 is the material which was synthesized firstly with this structure. This material was shown to have superconducting properties [260]. Two-dimensional TMDCs have layer-dependent properties. For example, vibrational modes, conductivity, and electronic properties change as the number of layers change [262, 263]. Therefore, in this study we investigate the layer dependence of vibrational modes, band structure and electronic properties of 2M-WS2. In addition, I investigated the effect of in-plain (along a, b, or both axes) strain on the band structure and electronic properties of 2M-

WS2.

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Figure 6.1: 2M-WS2 structure stacked along c axis with c/2 interlayer stacking distance.

6.3. METHODS

6.3.1. SAMPLE PREPARATION

2M-WS2 crystals were prepared by the topochemical method [264]. The precursor K0.7WS2 crystals were synthesized through high-temperature solid state reactions [265]. The reactants

K2S2 (prepared via liquid ammo nia), W (99.9%, Alfa Aesar) and S (99.99%, Alfa Aesar) were mixed by the stoichiometric ratios and ground in an argon-filled glove box. The mixtures were sealed in an evacuated silica tube, which was heated at 850 °C for 2000 minutes and slowly cooled down to 550 °C at a rate of 0.1°C /min. For deintercalation of potassium ions, the

−1 synthesized K0.7WS2 (0.1 g) was oxidized chemically by K2Cr2O7 (0.01 mole L ) in aqueous

−1 H2SO4 (50 ml, 0.02 mole L ) at room temperature for 1h. Finally, after wishing 2M-WS2 crystals in distilled water for several times, those are dried in vacuum oven at room temperature. There are a verity of methods to exfoliate layered materials and make two dimensional form of them [266]; however, in order to exfoliate layered materials, researchers normally use liquid or mechanical exfoliation [267, 268]. In mechanical exfoliation, the material is exfoliated using a scotch tape for several times, and then is transferred onto a substrate (e.g.

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Si/SiO2 or gold) [5, 268, 269]; however, the problem is that this method will leave a lot of residue which contaminates the substrate and also two dimensional materials. In order to resolve this issue, a thermal release tape (TRT) can be used instead of scotch tape [270]. In this research,

Revalpha TRT was used, flakes were transferred onto it, exfoliation was done for several times, then in order to transfer the thinned material onto a substrate, the tape was put on a Si wafer coated with 300 nm SiO2 and finally all of them were heated up to 120 °C on a hotplate. After few seconds at this temperature, the tape loses its stickiness and thinned materials attached to it are released. Therefore, flakes are on the substrate now; nonetheless, these flakes are still thin films and don’t have the thickness of the 2D materials. Hence, the sample was sonicated in acetone for few seconds. This process removed most of the layers and left at least a single monolayer on the substrate (Fig. 2 & 3). By doing this process we transferred the 2D forms of

2M-WS2 onto a Si/SiO2 substrate.

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Figure 6.2: optical microscopy image of 2M-WS2 flakes on Si/SiO2 substrate. Arrows show 2D forms of the material having 1-5 2M-WS2 layers.

115

Figure 6.3: Atomic force microscopy (AFM) image of 2M-WS2 flakes showing a trilayer system.

6.3.2. MEASUREMENT METHODS

WITec alpha 500 Raman confocal atomic force microscope (AFM) with the spectral resolution of

0.5 cm−1 in Raman measurement was used to measure the thicknesses of layers first and then do

Raman spectroscopy. The laser light of λ = 634 nm with the power of 10 mW was used as the excitation source and the reference was the Si band at 520 cm−1. Each measurement was done 10 times and results are average of the 10 measurements. After scanning the slabs with AFM, we found that there are 6 kinds of slabs including monolayers (half a 2M-WS2 layer), bilayers (a full layer of 2M-WS2), trilayers (one and a half 2M-WS2 layers), four-layer (two 2M-WS2 layers), five-layer (two and a half 2M-WS2 layers) and the bulk 2M-WS2. Hence, this is why we did not measure Raman spectroscopy for slabs having more than 5 layers and directly measured the Raman active modes for the bulk 2M-WS2.

116

6.3.3. COMPUTATIONAL DETAILS

Density functional theory (DFT) [271], was used to calculate band structure (BS), density of states

(DOS), and vibrational frequencies of the 2M-WS2 slabs. As Perdew Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA) [272] gives more accurate bond length [273], GGA-

PBE exchange correlation functional and projector-augmented wave (PAW) pseudopotentials

[274] were used in VASP [202] for DFT calculations. It should be noted that there was not much difference between four-layer and bulk 2M-WS2 in terms of BS, DOS, and Vibrational modes; hence, calculation on the 2D 2M-WS2 structure was done for up to the four-layer system (two 2M-

WS2 layers). To remove the interaction between successive slabs of 2M-WS2, a vacuum layer of

15 Å was added between them. All calculations were done with spin-orbit-coupling. In order to relax the geometry and calculate DOS, K-meshes of 11 × 11 × 1 and 11 × 11 × 11 were used for slabs and bulk 2M-WS2, respectively. Geometry relaxation was done until the residual force on each atom was less than 0.001 eV/Å. The energy cutoff was set at 400 eV for all calculations.

Later, in order to see the influence of strain on the band structure of a single monolayer system

(half a 2M-WS2 layer), different sets of uniaxial strains along b and c axes were applied to the material. There are 12 strain combinations (steps) being from -6% to 6% (strain change equal to 1 percent per step and zero means no strain).The highest internal energy for a single layer of 2M-

WS2 under strain belongs to the = −6% which is F = -4.15E+1 eV. As it has the highest ground state internal energy and if the layer is dynamically stable under such a strain, it means the rest of the strain combinations do not change the dynamical stability of the material [275, 276]. To investigate the dynamic stability of the strained and unstrained monolayer 2M-WS2, phonon dispersion frequencies of the bulk was calculated which shows no imaginary mode (Figure 6.4a).

Also, phonon dispersion frequencies (Figure 6.4b) of a monolayer of 2M-WS2 strained -6% along

117 each a and b directions were calculated. Density functional perturbation theory (DFPT) [277, 278] was used in order to determine the Hessian matrix. Finally, phonopy package [279] was used to calculate phonon band structure of the material. As it is seen, there is no imaginary mode in its phonon dispersion frequencies and therefore, this material is dynamically stable under the mentioned strains (-6%) and in unstrained situation [280, 281].

Figure 6.4: phonon dispersion frequencies (band structure) of a) perfect 2M-WS2 and b) strained -

6% along a and b directions which both of the diagrams show that there is no imaginary mode and the material is dynamically stable under both conditions.

This material belongs to P2/m (C2/m) space group and C2h (2/m) point group [260]. There are 18 normal vibrational modes which mechanical representation of them at Gamma point of the

Brillouin zone is as follows:

M = 6Ag + 3Au + 3Bg + 6Bu

M includes Acoustic and Optic modes which are ΓAcoustic = Au + 2Bu and ΓOptic = 6Ag + 2Au +

3Bg + 4Bu. ΓOptic is decomposed into Raman and Infrared active modes being 6Ag + 3Bg and 2Au

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+ 4Bu, respectively. Hence, this material has 9 Raman active modes. To calculate only zone centered frequencies (Γ−point) finite difference method was used [282].

6.4. MEASURED VIBRATIONAL MODES

Figure 6.5 shows that all 9 Raman active modes exist in Raman spectroscopy of the bulk 2M-

WS2. When the material becomes thinner, especially from 5 layers to a single monolayer, Raman

2 peaks downshift and look mostly asymmetric. Despite other Raman active modes, Bg does not

4 1 2 6 change much and Ag disappears for the 2D forms of the material. Ag , Ag , and Ag Peaks have

1 the most downshift. However, Bg frequency decreases from bulk to 3 layers and then it stays almost the same with a slight increase from the trilayer to bilayer and monolayer. The reason is because for the bulk, 5-layer, and 4-layer 2M-WS2, this peak is under the influence of three

2 things. The first reason is that the adjacent Raman active mode which is Ag makes it be asymmetric even for the bulk. The second is once laser beam is exciting the 5-layer and 4-layer

2M-WS2, It also hits and excite a bulk area next to the 2D slabs. The last reason is because of

1 2 the peak which exists between Bg and Ag for bulk, 5-layer and 4-layer 2M-WS2 and this peak

1 2 6 is for the tape we used for mechanical exfoliation. Downshifts in Ag , Ag , and Ag modes are 7,

−1 12 and 22 cm , respectively. Compared to Ag Raman active modes, Bg active modes do not have much downshifts and it will be discussed in details in the discussion part. As the number of layers decreases, the intensity of Raman active modes decreases for all the peaks (active modes). The reason is because excitation in the bulk material happens for a lot of layers and the intensity of the shifted (scattered) light will be much more than that of when the scattering happens due to few layers of a layered material interaction with the incoming laser light.

119

2 Figure 6.5: a) Raman spectra of 5, 4, 3, 2, and 1 layers and bulk 2M-WS2, b-g) individual peaks in separated graphs except Bg which

4 does not change much and also and Ag which disappears.

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6.5. DENSITY-FUNCTIONAL THEORY CALCULATIONS

6.5.1. RAMAN ACTIVE MODES

Raman active modes of the bulk 2M-WS2 at Γ point were calculated and are depicted in Figure

6.6. As it is seen from the calculated eigenvectors, there are 6 out-of-plain (not purely) and 3 in- plain vibrational modes. Arrows show relative vibration direction and their length represents the

2 proportional amplitude. The strongest out of plain movement belongs to the Ag Raman active mode at 327.96 cm−1. In this Raman active mode, outmost sulfur atoms of each layer move out- of-plane in opposite directions and their movement is out-of-plane expansion and compression of

1 6 the layer. Also, the second and the third strongest out-of-plane movements belong to Ag , and Ag

Raman active modes and as the result, the out of-plane expansion and compression is less than

2 that of Ag . Also as the result of this kind of movement, vibrating atoms in this mode (out-of-plane movement) are to interact with atoms of other layers and hence, if layers are removed in order to make 2D form of the material, these interactions will decrease.

121

Figure 6.6: Eigenvectors of the Raman active modes of bulk 2M-WS2. Ag and Bg are seen along b and c directions,respectively. Arrows show relative vibration direction and their length represents the proportional amplitude.

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6.5.2. ELECTRONIC BAND STRUCTURE OF A SINGLE MONOLAYER OF 2M-WS2

UNDER STRAIN

The electronic band structure of the bulk and single monolayer of 2M-WS2 is shown in Figure 6.7.

It has been proven that bulk 2M-WS2 has semi-metalic behavior [260, 283] and local gaps in the band structure. The metallic behavior of the bulk is seen in Figure 6.8a; however, the single monolayer 2M-WS2 is now a semiconductor having Eg = 0.04 eV. As shown in Figure 6.7 and

6.8, both p orbitals of S atoms and d orbitals of W atoms have almost the same contribution to the conduction and valance bands of the monolayer 2M-WS2. Band structures of 2D 2M-WS2 thicker than a single monolayer were also calculated. However, as there was not much difference between their band structure and the band structure of the bulk 2M-WS2, those are not shown in this dissertation.

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Figure 6.7: Electronic band structure of a) bulk 2M-WS2 and single monolayer of 2M-WS2. b and d are projected band structure of a and c respectively.

124

Figure 6.8: Density of State calculation of a) bulk 2M-WS2 and b) single monolayer of 2M-WS2. Graph b shows semiconducting behavior in the single monolayer.

125

Uniaxial strain sets along a and b axes were applied to the single monolayer (half a 2M-WS2 layer) and the effect of strain on the band structure is shown in Figure 6.9. Projected band structure associated with the 12 strain sets is depicted in Figure 6.10. The band gap of the material is closed when the strain goes below -1% or above +1%. After applying uniaxial strain to the material, it is proven that the contribution of the Ss and dW orbitals to the band gap and conduction and valence bands do not change significantly.

126

127

Figure 6.9: Electronic band structure of single monolayer of 2M-WS2 under a) Ɛa = Ɛb = +1%, b) Ɛa = Ɛb = +2%, c) Ɛa = Ɛb = +3%, d) Ɛa = Ɛb = +4%, e) Ɛa = Ɛb = +5%, f) Ɛa = Ɛb = +6%, Ɛa = Ɛb = -1%, Ɛa = Ɛb = -2%, Ɛa = Ɛb = -3%, Ɛa = Ɛb = -4%, Ɛa = Ɛb = -

5%, Ɛa = Ɛb = -6%.

128

129

Figure 6.10: Projected electronic band structure of single monolayer of 2M-WS2 under a) Ɛa = Ɛb = +1%, b) Ɛa = Ɛb = +2%, c) Ɛa

= Ɛb = +3%, d) Ɛa = Ɛb = +4%, e) Ɛa = Ɛb = +5%, f) Ɛa = Ɛb = +6%, Ɛa = Ɛb = -1%, Ɛa = Ɛb = -2%, Ɛa = Ɛb = -3%, Ɛa = Ɛb = -

4%, Ɛa = Ɛb = -5%, Ɛa = Ɛb = -6%.

130

6.6. RAMAN SPECTROSCOPY: SIMULATION AND EXPERIMENT

Figure 6.11 shows the frequencies of Raman active modes as a function of number of layers. As it is seen, all the frequencies downshift in both experiment and DFT calculation. However,

1 2 6 2 downshifts for Ag , Ag , and Ag Raman modes are the highest. Ag is the strongest out-of-plain

6 mode and after that Ag is the second strongest out-of plain Raman active mode with the amount of downshifts of 12 and 22 cm−1, respectively. As it was discussed earlier, these atomic movements belong to the out-of plane expansion and compression of the layers. Hence, when there are a stack of a lot of layers, the out-of-plane movement is limited and as the result, the domain of vibration for atoms in these three modes will decreases. On the other hand, when the material becomes thinner and thinner, this limit is losing its strength and atoms can vibrate more easily than before, then the domain of movement will be higher and as the result, the frequency of the vibration will decrease. Therefore, it is concluded that there is a huge interaction between layers (interlayer interaction) such that by removing layers, vibrational frequencies are influenced. On the other hand, it is seen that by thinning the material, interalayer interaction is influenced but not as much as the interlayer interaction is impacted. Hence, it means there is a huge interlayer interaction and this interaction is much stronger than the intralayer interaction in

2M-WS2 layered material.

131

2 Figure 6.11: Raman active mode frequencies as a function of number of layers. All modes exist except for the Ag . Blue dots stand for the experimental measurement and the orange dots stand for the calculated Raman active modes.

132

6.7. CONCLUSION

In summary, we simulated the band structure of layered 2M-WS2 considering different number of layers of the material. As discussed above, by decreasing the number of stacking layers, the band structure of the material does not change much until it reaches to a single monolayer. At this point, there is a 0.05eV band gap. Applying 12 uniaxial in-plain strain sets (-6% to 6% with 1% step size) to the single monolayer of 2M-WS2 closes the band gap of the material when the uniaxial strain goes above 1% or below -1%. After closing the band gap with strain, the contribution of p orbitals of S atoms and d orbitals of W atoms are almost the same. Raman spectroscopy proved that there are 9 Raman active modes including 6 out-of-plain and 3 in-plain modes. Decreasing the number of layers change the out-of-plain modes significantly.

6.8. ACKNOWLEDGEMENT

We are grateful to Virginia Tech Advanced Research Computing for computational support

Institute of Critical Technology and Applied Science (ICTAS) at Virginia Tech for supporting our

Raman spectroscopy experiments.

133

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