Exploring Two-Dimensional Graphene and Silicene in Digital and Rf Applications

EXPLORING TWO-DIMENSIONAL GRAPHENE AND SILICENE IN DIGITAL AND RF APPLICATIONS

A proposal submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy

ZHONGHANG JI M.S.EG., Wright State University, 2015 B.E., Changchun Institute of Technology, 2011

2019 Wright State University

ZHONGHANG JI

2019

WRIGHT STATE UNIVERSITY GRADUATE SCHOOL 11/20/2019

I HEREBY RECOMMEND THAT THE DISSERTATION PREPARED UNDER MY SUPERVISION BY Zhonghang Ji ENTITLED Exploring Two-Dimensional Graphene and Silicene in Digital and RF Applications BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy.

______Yan Zhuang, Ph.D. Dissertation Director

______Fred Garber, Ph.D. Interim Chair, Department of Electrical Engineering

______Barry Milligan, Ph.D. Interim Dean of the Graduate School Committee on Final Examination:

______Henry Chen, Ph.D.

______Lok C. Lew Yan Voon, Ph.D.

______Marian K. Kazimierczuk, Ph.D.

______Saiyu Ren, Ph.D.

ABSTRACT Ji, Zhonghang. Ph.D., Department of Electrical Engineering, Wright State University, 2019. Exploring Two-Dimensional Graphene and Silicene in Digital and RF Applications

Since the discovery of graphene, two-dimensional (2D) materials have attracted intensive interests in the past 15 years and there has been a growing interest in exploring new materials beyond graphene, such as silicene, germanene, etc. Numerous papers have been published to demonstrate their extraordinary electronic, optical, biological, and thermal properties which render broad applications in various fields. However, the absence of band gap in graphene and silicene prohibits their uses in digital applications. This dissertation reviews recent progress on band gap opening based on mono- and bilayer silicene and presents a new silicon atomic structure which exhibits a 0.17 eV bandgap. In addition, a feasible approach was first demonstrated and proposed to potentially achieve the industrial- scale production of our simulated structure. More broadly, this approach suggests a new path for growing any materials on different substrates without forming chemical bond between the interaction layers.

Although the gapless character of graphene prohibits its use in digital applications, it is not a concern for Radio Frequency (RF) applications. This work also investigated the impact of defects to RF electronic properties of the 2D materials. Chemical vapor deposited

Graphene (CVDG) was selected as an example and was measured using scanning

iv microwave microscopy (SMM). In order to analyze the result, a numerical model of SMM was first developed using Electromagnetic Professional (EMPro). From the results, both conductivity and permittivity of defective graphene exhibit the frequency-dependency properties. Additionally, the model we proposed in this work can precisely characterize the correlation between conductivity and permittivity of any materials in nanoscale at RF level.

Contents

Chapter 1 Introduction ...... 1

1.1 Background ...... 1

1.2 2-D materials ...... 2

1.2.1 Graphene ...... 5

1.2.2 Silicene ...... 7

1.3 Electronic properties of mono and bilayer silicene...... 9

1.3.1 Single layer silicene ...... 9

1.3.2 Bilayer silicene...... 12

1.4 Electric properties at RF of graphene...... 17

1.5 The scope of current research ...... 24

Chapter 2 Electronic properties of strained single- and bi-layered silicene ...... 26

2.1 Introduction ...... 26

2.2 The electronic properties of a free-standing monolayer silicene ...... 27

2.2.1 Simulation method ...... 27

2.2.2 Construction and optimization of monolayer silicene ...... 30

2.3 The electronic properties of strained monolayer silicene ...... 34

2.4 Biaxial strain induced on free-standing bi-layered silicene ...... 46

Chapter 3 Theoretical simulation of bilayer silicene on diverse substrates ...... 64

3.1 Introduction ...... 64

3.2 Selection of substrates ...... 66

3.3 Structural optimization on bi-layered silicene on selected substrates ...... 67

3.4 The realization of extraction of bilayer silicene from substrate ...... 73

Chapter 4 Theoretical simulations and experimental measurements on defective graphene...... 84

4.1 Introduction ...... 84

4.2 Experimental measurements ...... 86

4.3 Results and discussion ...... 94

4.4 Numerical simulation of SMM ...... 98

4.5 Summary...... 109

Chapter 5 Conclusion and Future work ...... 111

5.1 Conclusion ...... 111

5.2 Future work ...... 114

Reference ...... 115

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List of Figures

Figure 1.1 Moore’s Law – The number of transistors on integrated circuit chips in the past

50 years...... 2

Figure 1.2 Carbon nanostructure from 0D to 3D ...... 3

Figure 1.3 Atomic structure of graphene arranged in a honeycomb lattice ...... 5

Figure 1.4 Electronic dispersion of graphene and zoom in the dispersion ...... 6

Figure 1.5 Top- and side view of silicene[24] ...... 7

Figure 1.6 Simulated STM image (left) and experimental STM image (right) of silicene on

Ag (111) surface ...... 8

Figure 1.7 Band diagram of silicene. The Dirac cone can be observed near the Fermi energy level formed by conduction band and valence band...... 9

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Figure 1.10 Atomic structure of asymmetric bilayer silicene, top view (top) and side view

(bottom)...... 14

Figure 1.11 AB (left) and AA (right) band structures after applying an electric field. 60 meV and 67 meV bandgap opening have been observed from AB and AA respectively. 15

Figure 1.12 AB (left) and AA (right) band structures after applying an electric field. The band gap can be up to 0.27 eV and 0.25 eV with uniaxial- and biaxial strain respectively.

...... 16

Figure 1.13 Band structure (left) and band structure (right). The 0.43 eV band gap appears after adding the cation of potassium...... 16

Figure 1.14 Overview of standards in radio telecommunication technologies...... 18

Figure 1.15 Cut-off frequency versus gate length for different types of transistors.

Graphene MOSFET, as a young age material, can reach to 300 GHz...... 19

Figure 1.16 The real part (left) and the imaginary part (right) of graphene permittivity.

Permittivity exhibits a significant reduction as the frequency increases...... 20

Figure 1.17 Conductivity and resistance of CVD graphene. The conductivity of graphene is inversely proportional to the frequency...... 20

Figure 1.18 The general components consist by Atomic Force Microscopy ...... 22

Figure 1.19 Scanning a microwave microscope with AFM interface connected with a vector network analyzer...... 24

Figure 2.1 Atomic silicene side view, top view and supercell 3 by 3 (left to right). The buckling 0.51 Å has been observed by measuring the vertical distance along the c direction.

The honeycomb structure has a good agreement with published work and has a 3.866 Å lattice constant of the unit cell...... 31

Figure 2.2 Band structure of silicene. Dirac point occurs at Fermi energy level, where the crossing happens between conduction band and valence band...... 32

Figure 2.3 High-symmetry points of primitive hexagonal...... 33

Figure 2.4 Transmission spectrum of silicene. The Dirac cone shows in this figure with zero transmission efficiency...... 33

Figure 2.5 I-V curve of silicene. The current is proportional to the voltage...... 34

Figure 2.6 Buckling height of the silicene with compressive (left) and tensile (right) strain.

The observed buckling height decreases monotonically by the increasing of lattice constant until the tensile strain is up to 5.1%. And it becomes saturated when the lattice constant goes beyond 5.1% ...... 36

Figure 2.7 Si-Si bond length on the induced strain. The left region shows the bond length with a different compressive strain. The right region shows the bond length with a different tensile strain. The bond length increases monotonically as lattice constant increases in the entire testing range of lattice constant...... 38

Figure 2.8 variation of buckling height under different strain. The buckling height starts to increase after 10% tensile strain which has a good agreement with our simulation result shows in Figure. 2.6...... 39

Figure 2.9 A – I show band diagrams by giving the lattice constant from 3.566 Å from

4.366. The red line is indicating the Fermi energy level and the blue lines depict the offset of Dirac cone. E is showing the band diagram of freestanding silicene. As the induced compressive strain is small (Figs. 2.9 B and C), there is no noticeable shift of the Fermi energy level. Further enlarging the compressive strain (Fig. 2.9 A), the silicene structure shows the feature of an indirect semiconductor material. Contrary to the compressive strain, a tensile strain leads to a lowering of the Fermi energy level (Figs. 2.9 G-I). In Figures 2.9

E and F, the silicene structure retains the direct semiconductor feature...... 40

Figure 2.10 Band structures of silicene under 8 % compressive (left) and 10 % tensile (right) strain. The Dirac cone was observed to move upwards above the Fermi energy and result in p-type doping (right). And A n-type doping can be observed when a biaxial compressive strain induced which lead a downwards moving of Dirac cone from Fermi energy(left). 42

Further increasing of compressive and tensile strain will lead a deviation of transmission efficiency from zero at the Fermi energy level...... 43

Figure 2.12 I-V curves of silicene structure under compressive in-plane strain. Silicene still shows a slight change on transport property due to the direct semiconductor feature for strain as less than 5.17%. And a larger strain will lead to crossing of the L1/L2 and Fermi energy level, consequently increasing the hole current...... 45

Figure 2.13 I-V curves of silicene structure under tensile in-plane strain. Silicene still shows a slight change on transport property due to the direct semiconductor feature for strain as less than 5.17%. And a larger strain will lead to crossing of the L3 and Fermi energy level, consequently increasing the electron current...... 46

Figure 2.14 (a) Side views of a unit cell of AA-P and AA-NP with unit vectors ‘‘A’’, ‘‘B’’ and ‘‘C’’, and the top view of a 3 by 3 supercell of AA-P and AA-NP with lattice constant a = 3.866 A˚. The top views of AA-P and AA-NP are identical. (b) Side views and top view of AB-P, AB-NP and AB- Hybrid. A1, A2, A3 and A4 are the four silicon atoms with their coordinates listed in Table 2...... 48

Figure 2.15 A) Buckling height of AA-P and AA-NP with induced strain. B) Buckling height of AB-P, AB-NP AND AB-Hybrid with induced strain. The buckling height monotonically decreases as the in-plane strain increases from compressive (negative in- plane strain) to tensile (positive strain). However, that the buckling height approaches zero when the tensile strain is above 7% for AA-NP and 5% for AA-P shows in A and the non- coplanar structures tend to saturate at 0.38 Å for the AB-P and the AB-Hybrid, and at 0.65

Å for AB-NP once the tensile strain is above 5%...... 50

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Figure 2.16 A – I shows band diagrams of AA-P by giving the lattice constant from 3.566

Å to 4.366 Å. Fermi energy level is denoted with the red line. The blue lines show the energy offset of Dirac point, energy bands L1 and L2 in (I). Fig. D is the band diagram of freestanding AA-P configuration. And a 0.11 eV bandgap opening has been observed when the tensile strain reaches is up to 12.9%...... 52

Figure 2.17 A – I shows band diagrams of AA-NP by giving the lattice constant from 3.566

Figure 2.18 A – L shows band diagrams of AA-P and AA-NP by giving the lattice constant from 4.28 Å to 4.50 Å. Fermi energy level is denoted with the red line. The blue lines show the energy offset of Dirac point. The band gap can be observed from Fig.B to Fig.K. For strain in the range between 10.7% (Fig. 2.18 A) and 13.8% (Fig. 2.18 G), the energy band gap opening is almost linearly dependent on the in-plane strain. The energy band gap is given by the energy difference between the L1 and L2 energy bands. The energy band gap reaches a maximum of 0.168 eV when the strain equals to 14.3%...... 56

Figure 2.19 Band gap opening of AA-P and AA-NP for different tensile strains. he energy band gap reaches a maximum of 0.168 eV when the strain equals to 14.3% ...... 57

Figure 2.20 Transmission spectrum of bi-layered silicon film with tensile strain...... 60

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Figure 2.21 A) I-V curve of bi-layered silicon film with maximum band gap opening. B)

Differential I-V of bi-layered silicon film with maximum band gap opening. a plateau of zero current intensity in the vicinity of zero has been observed due to the existing of bandgap in Figure 2.21 A...... 60

Figure 2.22 Electron density of bilayer silicene with maximum band gap opening.

Comparing to the electron density of AA-P and AA-NP bilayer silicene shown in Figure

2.23, the coupling between two layers’ silicon is much stronger...... 61

Figure 2.23 Electron density of free standing bilayer silicene AA-P (left) and AA-NP

(right)...... 61

Figure 2.24 Atomic structure of asymmetric bilayer silicene side view (left) and top view

(right) ...... 62

Figure 2.25 Band gap opening under both compressive and tensile strain of asymmetric bilayer silicene ...... 62

Figure 3.1 Zinc Blende structure in the hexagonal orientation. It consists of three bi-layers, namely layers A, B and C. Each bilayer includes two atomic layers, forming an

ABCABC… structure. The duplicated top view shown in right side...... 66

Figure 3.2 In-plane strain provided by various substrates ...... 67

Figure 3.3 AA-P (left) and AA-NP (right) of bilayer silicene on the substrate ...... 68

Figure 3.4 optimized atomic structure of bilayer silicene on substrate. A: top view of unit cell. B: side view of unit cell. C: top view of duplicated unit cell...... 69

xiv

Figure 3.5 band diagram of bilayer silicene on InAs substrate. There is no band gap showing up due to the breaking of periodicity along c axis and the formation of chemical bond which make it difficult to decouple the band diagrams of substrate and bilayer silicene.

...... 70

Figure 3.6 Band structure of bilayer silicene after removing InAs substrate. A in direct band gap was observed with 0.08 eV...... 71

Figure 3.7 Band gap opening of bilayer silicene with/without substrate. the band gap of bilayer silicene with substrate was larger comparing to those of free-standing bilayer silicene...... 72

Figure 3.8 electron density of bilayer silicene on different substrate. As the lattice constant increases, the chemical bond between the bottom layer of bilayer silicene and top layer substrates get weaker. Meanwhile, the chemical bond between two layers of silicene become stronger...... 73

Figure 3.9 AA-P (left) and AA-NP (right) bilayer silicene on the substrate by inserting a monolayer graphene in between...... 74

Figure 3.10 Optimized atomic structure of Bilayer silicene on substrate and monolayer silicene. The bilayer silicene formed a ‘flat’ structure and moves away from monolayer graphene. In addition, the obtained atomic structure was similar to those of free-standing.

...... 75

Figure 3.11 Band gap opening of bilayer silicene with substrate, without substrate, and with substrate and graphene. The band gap was dramatically reduced after inserting the

xv monolayer silicene depicted by Blue Square in Figure 3.11. In addition, the blue square is perfectly following the curve of free-standing cases shown in Figure 3.11with the black dot...... 76

Figure 3.12 Band structures of bilayer silicene with the absence of substrate and graphene

...... 77

Figure 3.13 Electron density of bilayer silicene on substrates and monolayer graphene. The electron density between bilayer silicene and graphene is much lower compared to it between bilayer silicene. Moreover, comparing to bilayer silicene on substrate only, the coupling between bilayer silicene is slightly higher than in Figure 3.9 due to the weaker impact from substrates...... 77

Figure 3.14 Atomic structure of optimized bilayer silicene after removing substrates and graphene (if applicable). Side view(left) and top view (right)...... 80

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Additionally, the presence of the G- and 2D peaks for samples #A and #B prove that etching did not completely remove the graphene monolayer...... 90

Figure 4.3 SMM system combined by Agilent 5420 AFM, PNA N5230C and a special nose cone adapter...... 91

Figure 4.4 Block diagram of VNA, SMM sample holder and cables. A 1.5-meter coaxial cable is connected to one port of PNA, and the other end of the cable is connecting to the

24 cm coaxial cable...... 91

Figure 4.5 Schematic model of SMM probe with 3 cm resonator. The red triangle is the

SMM tip which shows in Figure 4.7...... 92

Figure 4.6 Equivalent circuit of the SMM system ...... 92

Figure 4.7 SMM images of sample #A measured at various half-wavelength harmonic resonances: amplitude (a) and phase angle (b) at 1st harmonic resonance (f = 4.2 GHz ); amplitude (c) and phase (d) at 2nd harmonic resonance (f = 4.2 GHz); amplitude (e) and phase (f) at 9th harmonic resonance (s). The imaging contrast of phase at f = 2.1 GHz (b) is reversed from (d) and (f) recorded at f = 4.2 GHz and f = 17.9 GHz, respectively...... 97

Figure 4.8 SMM probe modeling in EMPro. The tip is formed as a cone with a base diameter of 10 um and an end diameter of 50 nm. The sample was a 100 um × 100 um × 2 nm block with the tip placed at the center with 1 nm depth into the sample. The calculations were based on the finite element method (FEM) using a commercial software EMPro

(Keysight) ...... 99

Figure 4.9 Equivalent transmission line model of SMM system...... 100

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Figure 4.10 Simulated the amplitude modification (a) and phase shift (b) of the Γin versus the electrical conductivity ( σ) and the relative permittivity ( εr) of the etched graphene respect to the pristine graphene at f=2.1 GHz. The solid circles and squares are used to schematically represent the measurements carried out at f=2.1 GHz, and f=17.9 GHz, respectively, as the greater capacitive effect at higher frequencies is modeled by an increase of the permittivity. The shifts from the solid circles to the solid squares demonstrate the magnitude modifications in (a), and the phase shifts in (b) as frequency increases. The dashed lines mark the region where is in the range of 80 S/m to 3000S/m...... 104

Figure 4.11 Comparison of the magnitude modification  in (a), and the phase shift  in

(b) of the complex input reflection coefficient Γin of samples #A and #B at f = 2.1 GHz .

...... 107

Figure 4.12 Comparison of the magnitude modification (a), and the phase shift

(b) of the complex input reflection coefficient Γin of samples #A and #B at f =17.9 GHz .

...... 108

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List of Tables

Table 2.1Buckling height and Bond length under different compressive and tensile strains.

...... 37

Table 2.2Coordinates of 5 different stackings of bi-layered silicene ...... 49

Table 3.1 Coordinates of four silicon atoms of bilayer silicene with/without graphene on different substrates ...... 79

Table 3.2 Related parameters of bilayer silicene after removing substrates and graphene (if applicable) ...... 81

Table 4.1Etching parameters of samples #A and #B, and the intensity ratio of the 2D- and

G- peaks (I2D/IG) in the corresponding Raman spectra, where D peak is representing in defective carbon materials, and G peaks is a result of in-plane vibrations of SP2 bonded atoms...... 88

   Table 4.2 Comparison of in and in between #A and #B measured at and ...... 106

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ACKNOWLEDGEMENTS

Foremost, I would like to express my deepest appreciation to my advisor Dr. Yan Zhuang for the continuous support of my Ph.D. study and research, for his patience, expertise, motivation, and enthusiasm. Without his guidance and persistent help, this dissertation would not have been possible.

I would like to thank my committee members, Dr. Lok C. Lew Yan Voon, Dr. Henry Chen,

Dr. Saiyu Ren, and Dr. Marian K. Kazimierczuk, for their encouragement, insightful comments, and challenging questions. And thank Dr. Ulas Sunar for serving as my External observer.

I would like also sincerely thank all my lab mates, Sheena Hussaini, Joshua Myers, Kathy

Brockdorf, Pradyumna Aditya, Hyung Min Jeon, and Kumar Vishal, for their selfless support.

Last but not the least, I would like to thank my family: my parents, my wife, and my kids for supporting me. You are the reason why I keep pushing and facing all the struggles, pains and hardships.

Chapter 1 Introduction

1.1 Background

Integrated circuits (ICs) have been playing a significant role in the semiconductor industry.

Billions of transistors have been integrated into a small chip to improve performance and lower the power consumption. For instance, a commercial microprocessor, which integrated 19.2 billion transistors, has been released by AMD named Zen-based Epyc in

2017. Later, NVidia company reported their graphics processing unit (GPU) with 21.1 billion metal-oxide-semiconductor field-effect transistors (MOSFETS) integrated, manufactured using 12 nm fin field-effect-transistor (FinFET) technique. Traditionally, the

IC technology has been following the trend, known as Moore’s Law, which predicts that the number of transistors on a chip would be double every two years[1], shown in Figure

1.1. Over the years, the size of a transistor has reduced, down to 10 nanometers in early

2017 and the tendency continues. However, the transistors will stop shrinking in the next five years after more than 50 years of miniaturization, predicted by International

Technology Roadmap for semiconductors (ITRS) in 2015. Therefore, it is imperative to find out a solution to continuously increase the density of transistors on one single chip.

The appearance of two dimensional materials has been considered as the most promising materials to extend Moore’s law, thus, improving the hardware performance for years to

1 come due to their extraordinary properties[2]. For instance, the short channel effects can be largely suppressed due to their atomic thickness of two-dimensional (2D) materials, which will be the excellent candidates to replace and supplement silicon-based CMOS[3].

Thus, 2D materials can potentially play a critical role in the future to continue scaling down of transistors.

Figure 1.1 Moore’s Law – The number of transistors on integrated circuit chips in the past 50 years. 1.2 2-D materials

2D materials are crystalline materials consisting of a single or a few layers of atoms. Figure

1.2 depicts the nanostructures of Carbon from 0D to 3D. In the early 20th century, 2D materials were believed to be non-existent in nature due to their unstable thermodynamic

2 property[4][5]. Later on, this argument was further supported by Mermin’s work[6].

However, this statement was proved incorrect by Andre Geim and Kostya Novoselov at the University of Manchester in 2004[7]. They demonstrated thermally stable single-atom- thick crystallites by peeling from bulk graphite, for which they were awarded a Nobel Prize in Physics in 2010[7].

Fullerenes (C60) 0D Carbon Nanotubes 1D

Graphene 2D Graphite 3D

Figure 1.2 Carbon nanostructure from 0D to 3D

So far, mechanical exfoliation is still the most effective method to obtain the highest quality graphene among the techniques of graphene production such as epitaxy, chemical vapor deposition and supersonic spray.

Encouraged by the discovery of graphene, many efforts have been devoted to study other forms of 2D materials, including silicene, Molybdenite[8], Borophene[9], Germanene[10],

Stanene[11], and Phosphorene[12]. For instance, 2D MoS2 is also considered as a promising material, which has achieved significant progress in energy conversion, storage and hydrogen evolution reaction (HER)[13]. The direct band gap was observed from monolayer flake of MoS2 in 2010 by Kin’s group. However, applications at the industrial- scale with high quality MoS2 are still challenging[13]. On the other hand, stanene, one of the group-IV monolayers, also attracts considerable attention. The stanene film was experimentally grown in 2015[11] and the band gap was observed on stanene by elemental mono-doping(B,N) and co-doping (B-N) by Priyanka’s group in 2017[14]. However, the incapability with the current silicon technique hinders stanene’s way from large-scale applications. Another promising 2D material is germanene. Pure germanene has no band gap, but hydrogenated germanene exhibits a sizeable band gap of 0.5 eV, and such structure is slightly n-type[15]. However, the quality of the germanene is difficult to control during the production. Therefore, an appropriate 2D material should not only exhibit a sizable band gap, but also be compatible with existing well-established silicon technologies. By considering this, graphene and silicene are the most suitable candidates and can potentially

4 be used in future electronics. In present work, one of the key jobs will be focusing on the investigations of opening a band gap on graphene and silicene.

1.2.1 Graphene

Graphene is a single layer of carbon atoms arranged in a honeycomb lattice, shown in

Figure 1.3. Technically, graphene is a crystalline allotrope of carbon with properties of two-dimensional materials. The carbon atoms and the sp2 bonds form the hexagonal structure. The distance between the nearest 2 carbon atoms is 0.142 nm[16]. At first, graphene was used to describe a single sheet of graphite as a constituent of

Figure 1.3 Atomic structure of graphene arranged in a honeycomb lattice graphite intercalation compounds (GICs) in 1987[17], while the actual ‘Graphene’ was named by Mouras’ group. Later, in 2004, graphene was re-discovered by Geim and

Novoselov by peeling layers from highly oriented pyrolytic graphite (HOPG). This discovery attracted tremendous attention and triggered massive theoretical and experimental research on graphene and its potential applications.

Graphene is undoubtedly one of the most promising nanomaterials because of its unique combination of superb properties, which open a way for a wider spectrum of application including electronics, thermo-electronics, mechanics, optics, etc. Graphene is a zero-gap semiconductor due to the contact between its valence and conduction bands at Dirac point.

Figure 1.4 shows the electronic structure of graphene[18]. As a result, the intrinsic graphene exhibits remarkable electron and hole mobilities at room temperature, with reported values of 320,000 cm2*V-1*S-1 and 351,000 cm2*V-1*S-1 , respectively[19].

Thermal transport of graphene is another charming area

Figure 1.4 Electronic dispersion of graphene and zoom in the dispersion of research. The thermal conductivity is reported in the range between 3000 – 5000

W·m−1·K−1[20]. Monolayer graphene is also considered as the strongest material ever tested, which is 200 times greater than steel. The intrinsic strength of graphene can reach up to 130 GPa[21]. The unique optical property produced by monolayer graphene is high opacity. In addition, one-atom-thick graphene can be seen by the naked eye due to its 2.3 % absorption of white light[22].

1.2.2 Silicene

Silicene, a silicon analogue of graphene, has been attracting much attention over the past few years. It was named by Guzmán-Verri and Lew Yan Voon in 2007[23]. Contrary to graphene, silicene shows a nonplanar honeycomb lattice, with a buckled height in the range of 0.49 - 0.51 Å[24]. Figure 1.5 shows the atomic structure of silicene.

Figure 1.5 Top- and side view of silicene[24] The basal plane of the silicene is not flat, because the electrons of silicon atoms try to form the tetrahedral sp3 hybridization and the buckled structure seems to be more stable[25].

Contrary to graphene, mechanical exfoliation does not work on silicene due to the lack of silicon allotrope with a graphite-like layered structure in nature. To date, epitaxial growth on metal substrates is still the main method for synthesizing silicene. The first large-area silicene sheet was synthesized epitaxially on Ag (111) by Vogt’s group in 2012[26]. In their work, both Density Functional Theory (DFT) calculations and experimental observations have a good agreement with theoretical prediction of silicene monolayer.

Figure 1.6 shows the simulated and experimental images of silicene on Ag (111) surface.

The two adjacent dark centers are separated by 1.14 nm distance, which corresponds to 4 times lattice constant of Ag (111).

Si 1.14 nm

Figure 1.6 Simulated STM image (left) and experimental STM image (right) of silicene on Ag (111) surface Due to the unique structure, silicene exhibits extraordinary properties in many aspects. Like graphene, the band structure of silicene has a zero-energy gap at the fermi energy level, forming the so-called Dirac cone at K and K’ points (Figure 1.7).

Figure 1.7 Band diagram of silicene. The Dirac cone can be observed near the Fermi energy level formed by conduction band and valence band. The intrinsic carrier mobility of silicene has been calculated by Shao’s group in 2013. The electron and hole mobilities are 257,000 cm2*V-1*S-1 and 222,000 cm2*V-1*S-1, respectively, which are much higher than those in bulk silicon (1400 cm2*V-1*S-1 for hole’s and 450 cm2*V-1*S-1 for electron’s)[19]. The thermal conductivity is 20 W·m−1·K−1 studied by Li’s group in 2012[27]. Comparing to graphene, silicene is much more favorable for thermoelectric devices. The thermo-electronic effect of silicene has been discussed in many works[28]–[30]. Moreover, silicene is also holding promises for different applications such as the chemical sensor[31], hydrogen storage[32] and electrode material for Li battery[33].

1.3 Electronic properties of mono and bilayer silicene

1.3.1 Single layer silicene

To date, tremendous works have been performed theoretically and experimentally on silicene [34], [35], [44]–[51], [36]–[43]. However, the zero-gap character impedes its

9 applications in electronics. Therefore, opening a sizable band gap without degrading its electronic properties is still an urgent issue.

The band gap opening was first obtained by Lu and Drummond group independently in

2012. In their work, a perpendicular electric field was utilized to break the sublattice symmetry. The maximum band gap can reach up to 0.15 eV with 1 V/Å applied in a freestanding silicene structure[34], [35] shown in Figure 1.8. However, the required electrical field exceeds the dielectric strength of most of the dielectric materials except diamond, which makes this method impractical.

Figure 1.8 Band gap dependency of silicene sandwiched by BN and freestanding silicene on electric field. 0.15 eV bandgap opening can be observed under 1 V/Å on freestanding silicene. A higher band gap 0.25 eV shows up on the h-BN-sandwiched silicene configuration under 1V/Å. Metal intercalation and adsorption were also proved to be a feasible way to obtain band gap opening on silicene without degrading the electric properties.[36]–[38]. Moreover, hydrogenation and oxidization are easy to apply on silicene due to its chemically active

10 surface[40], [41]. The band gap is about 2 eV on a completely hydrogenated silicene sheet and is about 0.7 eV of oxidized silicene theoretically. Those predictions of first-principle calculations were experimentally proved by Qin’s and Du’s groups in 2015 and 2014 [42],

[43].

Strain engineering, has been widely used as a mean of tailoring the electronic structure in order to bring more astonishing effects [52][53][54]. It is well known that certain strain is mainly generated by mismatch of a lattice constant between grown sheets and substrates.

In general, inducing strain will result in a shift in the energy levels of conduction and valence bands due to the breaks of symmetry of original structures. An n-type metal-oxide- field-effect-transistor (nMOSFET) was built using this principle by J.Welser and J.

Hoyt[55]. In their work, the effective mobility of silicon has a 70% enhancement compared to unstrained silicon. Moreover, the mobility in p-channel MOSFETs was discussed under biaxial strain by Oberhuber and Fischetti[56]. The enhancement of mobility was observed by applying both compressive and tensile strain. Triggered by the huge improvement of strain engineering on 3D materials under strain, several theoretical calculations have been done to investigate the electronic properties of silicene. Zhao reported that the maximum band gap of silicene is 0.08 eV under tension along ZZ direction and 0.04 eV under tension along AC direction in 2012[57]. Similar work was also proved by Mohan’s group in

2014[58]. However, other groups [59]–[63] only observed the energy bands shifting near the fermi energy level. In 2015, Voon et al further proved that both in-plane uniaxial and

11 perpendicular strain cannot open a gap for monolayer silicene by using symmetry-based k- p theory [12].

1.3.2 Bilayer silicene

Beyond the monolayer silicene, different groups [64]–[68] reported that bilayer silicon films have also exhibited appealing properties.. Several theoretical calculations have been performed on bilayer silicene using first-principle methods including stacking constructions, electronic properties and interlayer interactions [19]. Different from bilayer graphene, bilayer silicene can form diverse stacking geometries due to its low-buckle structure. Morishita et al. [69] reported AA and AB stacking with 2 by 2 reconstructed structure in 2011. Later on, Fu et al.[65] reported a bilayer silicene named Slide-2AA, which is named as AB’ studied by Padilha’s group[66]. The DFT-optimized bilayer structures are shown in Figure.1.9.

Figure 1.9 Optimized structure of bilayer silicene. There are 6 different bilayer silicene configurations have been simulated and AAp (a) turns to be the most stable structure due to lower total energy. However, free standing of bilayer silicene has been exhibiting a gapless band structure until an asymmetric structure was essentially identical as reported in 2013 by Ni and Lian[68].

The atomic structure has a small gap of 0.23 eV without strain shown in Figure 1.10.

Particularly, the smallest unit cell to obtain this asymmetric structure is 2 by 2, while other symmetric structures can be found in 1 by 1-unit cell. However, the strain/stress impacts on the energy band diagram and charge transport properties have not been discussed, which will be presented in this work. To better understand bilayer silicene, extensive efforts have been devoted to investigating its electronic properties. Band gap was also obtained by

Mohan’s group [64] in 2013. In the work, external electric field is induced on AA and AB- stacked bilayer silicene; the maximum band gap was observed as 67 meV and 60 meV respectively, shown in Figure 1.11. Another particular type named bilayer penta-silicene is

13 reported by Aierken’s group in the same year [70]. This structure is predicted to possess a lower energy than the most stable bilayer hexagonal silicene structures. Additionally, the band gap of this structure is up to 0.27 eV with uniaxial and 0.25 eV with biaxial respectively, which paves the way towards the electronics application on bilayer silicene.

Figure.1.12 depicts the band gap opening from the variation of the uniaxial and biaxial strains. However, pentagonal atomic structures are very difficult to be achieved in their fabrication.

Figure 1.10 Atomic structure of asymmetric bilayer silicene, top view (top) and side view (bottom)

Figure 1.11 AB (left) and AA (right) band structures after applying an electric field. 60 meV and 67 meV bandgap opening have been observed from AB and AA respectively.

Recently, many groups also observed band gap opening on bilayer silicene by using first- principle calculations. Hydrogenation successfully achieved the goal of gap opening on silicene, which is named as silicane[40], [71], [72]. Later, hydrogenated bilayer silicene were studied by other groups[73], [74]. Huang’s group report that the band gap of bilayer silicene is in the range from 1 to 1.5 eV with low hydrogen concentration.[73]. At a high hydrogen concentration, a direct band gap is obtained on three well-ordered double-sided

SiHx. i.e., Si8H4, Si16H12 and Si12H10, which can be used as a promising material on optoelectronics. On the other hand, Liu et al.[74] performed the first-principles calculation to study the stacking effects on electronic properties and show that the band gap has an increased trend with a reduction of silicene layers.

Figure 1.12 AB (left) and AA (right) band structures after applying an electric field. The band gap can be up to 0.27 eV and 0.25 eV with uniaxial- and biaxial strain respectively. Metal adsorption is another way to open a gap on bilayer silicene. Liu et al[38] theoretically proposed intercalation of alkali metal atoms in bilayer silicene by using first-principles calculations in 2014. In their work, the interlayer interaction of bilayer silicene is reduced by intercalation of alkali metal such as Li, Na, K and Rb. The 0.43 eV band gap was observed when the cation of potassium was added, shown in Figure.1.13.

Figure 1.13 Band structure (left) and band structure (right). The 0.43 eV band gap appears after adding the cation of potassium.

1.4 Electric properties at RF of graphene.

Many of today’s electronic applications have been functioning at radio frequency

(RF) such as cell phones, Global Positioning System (GPS), broadcast radios, Wi-Fi devices, etc. Additionally, 4G is the fourth generation of broadband cellular network technology in use for a decade. The frequency range of the 4G network is from 700 MHz to 2.6 GHz[75]. Moreover, GPS signals were also designed to utilize two frequencies,

1.575 GHz (primary frequency) and 1.227 GHz (secondary frequency). For the Wi-Fi network, however, the frequency has been up to 60 GHz in 2012. The standards of telecommunication technologies are showing in Figure 1.14. It’s clear to see that from frequency-division multiple access (FDMA) and time-division multiple access (TDMA) to code-division multiple access (CDMA) and wideband code division multiple access

(WCDMA), the frequency bands for those standards are all working in the RF level.

Therefore, the performance of those devices under the RF level is becoming significant.

Currently, both silicon-based technologies (SOI) and III-V devices provided distinct performance at millimeter wave frequencies. The performance of those devices are mainly driven by the lithography dimensions, which have been shrinking with the drive to high frequency figures of merit, such as cut-off frequency and maximum frequency of oscillation reported by ITRS in 2013[76][77].

Figure 1.14 Overview of standards in radio telecommunication technologies. A 240 nm-gate length graphene transistor operating at 100 GHz was demonstrated in

2010[78]. This cut-off frequency is already higher than those Si MOSFET with similar gate length[79] shown in Figure 1.15. Moreover, graphene with a 300 GHz cut off frequency was reported with 140 nm gate length, comparable with the very top HEMTs with similar gate lengths[80], [81]. Recently, a cut-off frequency of 427 GHz was extracted from a 67 nm channel length graphene transistor[82]. Considering the young age of graphene, those results are competitive and impressive compared to those longer timescale devices. This is an indication that GFETs (graphene based field effect transistors) have the potential to pass the THz-border in the near future[77]. Therefore, investigating the electronic properties of

2D materials at the RF level is urgently necessary.

Figure 1.15 Cut-off frequency versus gate length for different types of transistors. Graphene MOSFET, as a young age material, can reach to 300 GHz. Producing structural defects is unavoidable during the devices’ manufacturing to the monolayer graphene due to its atomic-thin feature. Kanghyun’s group reported that the conductance of defective monolayer graphene decreases exponentially while increasing the defects in the frequency range below 1 MHz due to the reduction of mobility[83]. Figure

1.16 shows that both real and imaginary parts of permittivity of graphene have an order of six and four at low frequency, respectively[84]. Furthermore, both real and imaginary parts of permittivity exhibit frequency-dependence under 4 GHz. Also, a wider frequency range investigation on conductivity and permittivity of graphene was also reported by this group in 2016[85]. Both conductivity and permittivity decrease as the frequency increases shown in Figure 1.16 and 1.17.

Figure 1.16 The real part (left) and the imaginary part (right) of graphene permittivity. Permittivity exhibits a significant reduction as the frequency increases.

Figure 1.17 Conductivity and resistance of CVD graphene. The conductivity of graphene is inversely proportional to the frequency.

Near-field scanning optical microscopy (NSOM) is a microscopy technique for nanostructure investigation that breaks the far field resolution limit by exploiting the properties of evanescent waves. The idea of using a small aperture to image a sub- wavelength surface using optical light is proposed by E.H.Synge in 1928[86]. The first paper that suggested using visible radiation for near field scanning was published by Pohl in 1984[87]. Two years later, the super-resolution results were obtained experimentally by

Lewis’s group[88]. In NSOM, the excitation laser light is focused through an aperture with a diameter smaller than the excitation wavelength, resulting in a near field on the far side of the aperture. When the sample is scanned at a small distance below the aperture, the optical resolution of transmitted or reflected light is limited only by the diameter of the aperture. Different from NSOM, Atomic force microscopy (AFM) traces the topography of samples with extremely high atomic resolution by recording the interaction forces between the surface and a sharp tip mounted on a cantilever, shown in Figure 1.18.

Figure 1.18 The general components consist by Atomic Force Microscopy

Scanning microwave microscopy (SMM) technique is developed based on the AMF to measure electromagnetic interactions of the microwave with a sample under test on a scale that is significantly less than the wavelength of radiation. Typically, SMM uses a metal or metal-coated probe in-line with a coaxial resonator. Materials’ properties were obtained from the frequency shift and/or change of quality factor of resonance.

SMM consists of an AFM interfaced with a vector network analyzer (VNA) shown in

Figure 1.19. A microwave signal is sent directly from the network analyzer and transmitted through a resonant circuit to a conductive AFM probe linked to a sample being scanned.

The probe is served as a receiver to capture the reflected microwave from the contact point.

By directly measuring the complex reflection coefficient () from the network analyzer, the impedance of the sample at each scanned point can be mapped, simultaneously with the surface topography. A half wavelength impedance transformer was placed directly

22 across a 50 Ohms load to form a matched resonance circuit. The software, PicoView, controls data acquisition of all channels including topography from the AFM controller, amplitude and phase of the reflection coefficient from the network analyzer. The software saves data in 32 bits, which completely overcomes the limitation of data’s dynamic range and resolution for extremely delicate measurements. Therefore, in this work, SMM mode was utilized to investigate the electronic properties of micro-/nanostructure of graphene monolayer at RF/MW frequencies.

Figure 1.19 Scanning a microwave microscope with AFM interface connected with a vector network analyzer. 1.5 The scope of current research

This work mainly consists of two parts. Part one is focusing on the band gap opening on monolayer silicene and bilayer silicene, which includes a systematic study on structural and electronic properties of single and bi-layered silicon films under various in-plane biaxial strains and stress. The configurations were calculated using density functional theory (DFT) method. Both local-density approximations (LDA) and generalized gradient approximation (GGA) are employed to attain relatively precise results. Moreover, energy

24 band structure, electron transmission efficiency and charge transport property were also calculated to support our work. Additionally, in order to achieve massive production of our optimized structures, some proper substrates have been selected and discussed. Part 2 will concentrate on the investigation of electrical properties on micron/nano scale defective graphene in RF field. Both numerical and experimental results have been obtained using

SMM and EMPro, respectively.

Chapter 1: Introduction of 2D materials and literature reviews of graphene and silicene

Chapter 2: Electronic properties of strained single and bi-layered silicon layer and substrates inducing.

Chapter 3: Substrates selection and realization of growing bilayer silicene

Chapter 4: Theoretical simulations and experimental measurements on defective graphene

Chapter 5: Conclusion and future work.

Chapter 2 Electronic properties of strained single- and bi-layered

silicene

2.1 Introduction

Graphene has attracted tremendous attention in recent year due to its excellent electronic properties[89]–[93]. Graphene-based devices have also been fabricated and reported[80][94][95]. However, the low on/off current ratio is still the main challenge, which hinders graphene’s transition to electronic digital applications. Silicene, with a- single-atom-thick honeycomb structure, also exhibits charming properties as graphene does[19], [27], [63], [68]. Dirac cone occurs at Fermi energy level and forms a zero bandgap diagram. To date, tremendous works have been performed on silicene to open a band gap due to its compatibility with current mature silicon-based semiconductor technology[52]. Various methods have been reported to observe the band-gap opening on silicene such as applying electrical field[34], [35], metal intercalation and adsorption[36]–

[38] and hydrogenation and oxidization[40], [41]. Moreover, a silicene-based FET has been developed in 2015. However, both carrier mobility (~100 cm2V-1S-1) and current on/off ratio (~ 10) are still low[44]. In this chapter, both mono- and bilayer silicene were discussed under compressive and tensile strain to achieve the band gap opening.

2.2 The electronic properties of a free-standing monolayer silicene

2.2.1 Simulation method

In this work, the Atomistic Tool-kit (ATK) was employed to perform the first-principles calculations using density functional theory (DFT). DFT is nowadays the main tool of quantum mechanics, which allow to describe larger and larger systems as accurate as far the theory can go. The main idea of DFT is to describe an interacting system of fermions via its density and not via its many-body wave function. For N electrons in solid, which obey the Pauli principle and repulse each other via the Coulomb potential, which means that the basic variable of the system depends only on three spatial coordinates x, y, and z rather than 3N degrees of freedom.

The simplest approximation of this functional is local density approximation (LDA), which was proposed by Hohenberg and Kohn in 1964[96]. LDA locally substitutes the exchange- correlation energy density of an inhomogeneous system by that of an electron gas evaluated at the local density. The LDA approximation (shown below) assumes that the density is slowly varying and inhomogeneous density of a solid or molecule can be calculated using the homogeneous electron gas functional.

퐿퐷퐴 ℎ표푚 퐸푥푐 [푛(푟)] = ∫ 푑푟푛(푟) 휀푥푐 (푟, [푛(푟)]) 2.1

퐿퐷퐴 Where 휖푋퐶 is the exchange-correlation energy per particle of a uniform electron gas

(UEG). Because of this, LDA tends to underestimate the exchange energy and over- estimate the correlation energy[97], thus, underestimate the band gap[98]. Another approach is called generalized gradient approximation (GGA), which considers variations in the density by including the gradient of the density in the functional:

퐺퐺퐴 퐺퐺퐴 퐸푋퐶 = ∫ 푑푟휀푋퐶 (푛(푟), |∇푛(푟)|)

푢푛푖푓 ≡ ∫ 푑푟 휀푥푐 (푛(푟))퐹푥푐(푛(푟), |∇푛(푟)|) 2.2

Where 푓푋퐶 either fitted on experimental results or deduced from results of full CI quantum mechanics calculations, and serval of them have been developed. The most common versions are Perdew and Wang (PW91)[99] and Perdew, Burke and Enzerhof (PBE) [100], where the PBE is a simplification of PW91. Even though the gradient is taken into considered in GGA approach, the calculate band gap is still lower than the practical value.

This because the GGA only includes the first derivative of electron density in the exchange- correlation potential[98]. Spin-orbit interaction, also called spin-orbit coupling, is the interaction between the electron’s spin and its orbital motion around the nucleus. Taking spin-orbit coupling into consideration during the calculation will increase the accuracy of results[101]. However, this feature is still under development by QuantumWise (ATK provider). In this work, all the results were mainly performed using PBE, which can

28 provide relatively accurate results with simpler formula and derivation. The Quasi-Newton method was employed to optimize the atomic structure until the Hellmann-Feynman forces between each atom were smaller than 0.001 eV/Å[102]. The other method, fast inertial relaxation engine (FIRE), is also provided in the software. However, the Quasi-newton method is much more efficient compared to FIRE due to the lack of curvature information[103]. The force tolerance is used to determine the lowest energy during structural optimization, where the force is derivative of energy to distance. In addition, the stress tolerance was set to 0.001 eV/Å3(GPa). The stress tolerance is generally expressed as a fraction of the bulk modulus of the materials and determined when the optimization stops. The Brillion zone integration was calculated using Monkhorst-Pack of K-points mesh of 21 × 21 × 1. A 40 Å, which is much higher than the bond length of Si-Si[34][104], spatial distance was given to sufficiently avoid the interaction from adjacent layers along c-axis shown in Figure 2.1. Γ, M and K are the highly symmetric points in the 1st Brillion zone of a primitive hexagonal unit cell in reciprocal space. Monkhorst-Pack describes how many points will be used in performing integrals over the Brillouin zone. Generally, more points will bring more accurate results and more time consumption. In addition, the original

Monkhorst-Pack procedure assumes that the odd k-point grid includes Γ point while even k-point grids avoid the Γ point[105]. Moreover, as the important part of the Brillouin zone in silicene is K where the position of Dirac cone is, the k-points should be the multiple of

3, which only happens in special cases like graphene and silicene (provided by ATK experts). For instance, the k-points for the semiconductor is about 20 and here, we picked

21. The stability of atomic structures was verified by adding perturbation to each atom under 2 × 2, and 3× 3-unit cells by considering the periodic boundary conditions. The density mesh cutoff energy and electron temperature were chosen to be 75 Hartree and

300K (absolute zero in DFT), respectively. The mesh cut-off is an energy that corresponds to the fineness of the real-space grid. It can be expressed as dx = pi / sqrt (E), where dx is the fineness or grid point spacing and E is in Rydberg. A higher value of the mesh cut-off gives a finer real-space grid and, hence, better accuracy. Hartree is the atomic unit of energy, usually used in atomic physics. The electronic transport properties have been performed by using DFT with Non-Equilibrium Green’s Function (NEGF) method[106], which is used to calculate current and charge densities under finite bias in nanometer electronic devices[107][106].

2.2.2 Construction and optimization of monolayer silicene

The optimized atomic structure of monolayer silicene is shown in Figure 2.1. The initial buckling height was given as 0 Å, 0.3 Å and 0.6 Å before optimization. After optimization, an in-plane lattice constant 3.866 Å is obtained, shown in Figure 2.1 C from my calculation, which has a good agreement with reported works[23][108]. Similarly, monolayer silicene also forms a honeycomb structure as graphene does, shown in Figure 2.1 C. However, a buckling height with 0.51 Å was observed, which is different from the flat structure of graphene. The buckling height was measured along the c axis. So far, the reported lattice

30 constant is in the range from 3.83 Å to 3.88 Å[35][109], with the buckling height varying in between 0.42 Å to 0.53 Å[110][111].

0.51Å B C A b 3.866 Å

0.51Å 40 Å c c

b a

Figure 2.1 Atomic silicene side view, top view and supercell 3 by 3 (left to right). The buckling 0.51 Å has been observed by measuring the vertical distance along the c direction. The honeycomb structure has a good agreement with published work and has a 3.866 Å lattice constant of the unit cell. The energy band diagram is shown in Figure 2.2. The Dirac cone is clearly observed by the avoided crossing between conduction bands and valence bands at K-points, where K is depicting the middle of edge, joining two rectangular faces shown in Figure 2.3. M is the center of a rectangular face and Γ is the center of the Brillouin zone. Figure 2.4 and 2.5 exhibit the transmission spectrum, which in principle is a sum over the available modes in

Figure 2.2 Band structure of silicene. Dirac point occurs at Fermi energy level, where the crossing happens between conduction band and valence band. the band structure at each energy, and I-V curves monolayer silicene by integrating the transmission spectrum shown below:

2푒 +∞ 퐼(푉 ) = ∫ {푇(퐸, 푉 )[푓(퐸 − 휇 ) − 푓(퐸 − 휇 )]} 푑퐸 2.3 푏 ℎ −∞ 푏 퐿 푅

Where T(E,Vb) is the transmission probability and f (E) is the distribution function of

Fermi-Dirac, the μL and μR are the electrochemical potential of left and right electrodes.

The Dirac cone, located at Fermi energy shown in Figure 2.2, is manifested by the zero- transmission efficiency close to the Fermi energy level.

Figure 2.3 High-symmetry points of primitive hexagonal

ɛF

Figure 2.4 Transmission spectrum of silicene. The Dirac cone shows in this figure with zero transmission efficiency.

Figure 2.5 I-V curve of silicene. The current is proportional to the voltage. 2.3 The electronic properties of strained monolayer silicene

As mentioned in Chapter I, inducing strain can be an effective method to vary the electronic properties of materials. An in-plane uniaxial strain can only lead to a shift of Dirac point and a change of dispersion at K points of monolayer silicene[19][12][52]. Additionally, silicene under biaxial strain was also investigated and a change on both lattice constant and internal atom[52] was observed. However, the dependency of band gap opening on mono- and bi-layer silicene under biaxial strain is still missing and will be discussed in this chapter.

The strain was applied by the variation of the relaxed lattice constant 3.866 Å of silicene.

The induced in-plane strain of the atomic structure of monolayer silicene can be expressed using the equation below:

푞 − 푞 푃 = 0 2.4 푞0

Where P is the percentage of induced strain, q is the lattice constant of a new atomic structure and the q0 is the original lattice constant, equating to 3.866 Å. The tensile strain was induced by increasing the lattice constant, wherein the compressive strain is induced by decreasing the lattice constant. In this work, both the compressive and tensile strain were applied to investigate the electronic properties of monolayer silicene. The lattice constant was varied from 3.566 Å (compressive strain with 7.8%) to 4.366 Å (tensile strain with 12.9%). Different bond length and buckling height were observed and discussed in this work.

Figure 2.6 exhibits the variation of buckling height with a different lattice constant. The observed buckling height decreases monotonically by the increasing of lattice constant until the tensile strain is up to 5.1%. In the compressive strain region, the buckling height displays a strong linear dependency of strain and the largest buckling height was observed when the lattice constant equated to 3.566 Å (7.8%). However, in the tensile strain region, the buckling height decreases after applying tensile strain and becomes saturated when the lattice constant goes beyond 5.1%.

Figure 2.6 Buckling height of the silicene with compressive (left) and tensile (right) strain. The observed buckling height decreases monotonically by the increasing of lattice constant until the tensile strain is up to 5.1%. And it becomes saturated when the lattice constant goes beyond 5.1% The Dependency of Si-Si bond length on the induced strain is shown in figure 2.7. The bond length increases monotonically as lattice constant increases. Different from buckling height in Figure 2.6, the Si-Si bond length was showing a strong strain dependency in both the compressive and tensile region in the lattice constant span discussed in this work. The largest Si-Si bond length was observed when the 12.9 % tensile strain was applied. Table

1 shows the variation of specific value of buckling height and Si-Si bond length under different compressive and tensile strain.

Lattice Buckling constant Bond length(Å) Strain % distance(Å) (Å) 3.566 0.796 2.205 7.76 3.666 0.7 2.227 5.17 3.766 0.61 2.258 2.59 3.866 0.51 2.288 0 3.966 0.451 2.336 2.59 4.066 0.415 2.384 5.17 4.166 0.414 2.437 7.76 4.266 0.416 2.494 10.3 4.366 0.421 2.563 12.9 Table 2.1Buckling height and Bond length under different compressive and tensile strains.

The results exhibit a good agreement with published work performed by Peng’s group in

2013[110]. In their work, the buckling height was decreasing initially with the increasing of biaxial strain, and then was found to increase again after strain goes beyond 10 % displayed by black curve in Figure 2.8. Our strain span is selected from 3.566 Å

(compressive strain with 7.8%) to 4.366 Å (tensile strain with 12.9%) with 2.5 % increment.

The buckling height at 12.9 % strain was found to have a slight increasing shown in Figure

2.5 A.

ɛF

Figure 2.9 A – I show band diagrams by giving the lattice constant from 3.566 Å from 4.366. The red line is indicating the Fermi energy level and the blue lines depict the offset of Dirac cone. E is showing the band diagram of freestanding silicene. As the induced compressive strain is small (Figs. 2.9 B and C), there is no noticeable shift of the Fermi energy level. Further enlarging the compressive strain (Fig. 2.9 A), the silicene structure shows the feature of an indirect semiconductor material. Contrary to the compressive strain, a tensile strain leads to a lowering of the Fermi energy level (Figs. 2.9 G-I). In Figures 2.9 E and F, the silicene structure retains the direct semiconductor feature.

Figure 2.9 shows the band structures of silicene under different compressive and tensile strain. Silicene with the reference lattice 3.866 Å, exhibits a direct semiconductor material feature in Fig. 2.9 D. Additionally, the Dirac cone appears at K-point and is coincident with

Fermi energy level. When the induced compressive is small (Figs. B and C), the Dirac cone doesn’t shift noticeably from Fermi energy level. However, further increasing the compressive strain will lead a downward shift of Dirac cone, and the silicene structure shows an indirect semiconductor material feature shows in Fig.2.9 A. Additionally, energy bands L1 and L2 moved upwards and crossed with Fermi energy level. Contrary to the impact of compressive strain, a lager tensile strain will lead an upward shift shows in Figs.

2.9 G, H and I. A small tensile strain will not lead a noticeable change of Dirac cone and the silicene structure exhibits a direct semiconductor feature shows in Figs. 2.9 E and F.

However, as the tensile strain increases, energy band L3 starts to move downwards and

Dirac cone starts to shift upwards shows in Figs. H and I, and the silicene structure shows a feature of indirect semiconductor material.

These results exhibit a perfect matching with other groups’ work[59]–[61], [63]. In their work, the Dirac cone was observed to move upwards above the Fermi energy and result in p-type doping[60]. In addition, the conduction band was lowered at Γ point (G point in our results) when the tensile strain is larger than 7 %, which lead to a semimetal-metal transition. A n-type doping can be observed when a biaxial compressive strain induced which lead a downward moving of Dirac cone from Fermi energy[60]. Figure 2.10 is showing the band diagrams of silicene under compressive and tensile strain performed by

Wang and Ding[61].

Figure 2.11 The transmission spectrum of silicene under various in-plane strains. The minimum transmission efficiency was located at the Fermi energy level, which coincides with the position of the Dirac cone shown in B-F in Figures 2.11 and 2.9, respectively. Further increasing of compressive and tensile strain will lead a deviation of transmission efficiency from zero at the Fermi energy level. Figure 2.11 displays the transmission properties under both compressive and tensile strain.

The transmission spectrums exhibit the good agreement with band structures shown in

Figure 2.9. The minimum transmission efficiency was located at the Fermi energy level, which coincides with the position of the Dirac cone shown in B-F in Figures 2.11 and 2.9,

43 respectively. As outlined in Figure 2.11 A, B and C, when the structure is under compressive strain, the transmission efficiency increases due to the upward shifting of L1 and L2 in Figure 2.9 A-C. In addition, any further increase in the compressive strain will observe a deviation of transmission efficiency from zero at the Fermi energy level shown in Figure 2.11 A. In the tensile strain region, an increase of transmission efficiency is observed due to the downward shifting of the L3 band. Further increasing the tensile strain will lead a non-zero transmission efficiency shown in Figure H and I due to the crossing of L3 and Fermi energy level. The Current-voltage (I-V) curves have also been calculated under compressive (Fig.2.12) and tensile (Fig.2.13) strains. When the strain is below

±5.17%, there is no significant enhancement on I-V curves due to the feature of direct semiconductor material. In this case, the transmission property of silicene structure is mainly determined by the position of Dirac cone. However, as the strains increase (>

±5.17%), energy bands L1/L2 and L3 start crossing with Fermi energy level and lead an increasing of hole current and electron current, respectively.

In conclusion, the free-standing monolayer silicene doesn’t exhibit a band gap opening.

The Dirac cone was observed at the Fermi energy level at the hexagonal Brillion zone K point. In addition, both compressive and tensile biaxial strains were applied to monolayer silicene. However, the induced strain can only lead to a shift of Dirac cone in band energies.

The Dirac cone will move below the Fermi energy level under compressive strain but move upwards above the Fermi energy level under tensile strain. Moreover, the transmission

44 spectrum and I-V curves under both compressive and tensile strain were first calculated and reported in this work, which exhibit a good agreement with band structures.

2.4 Biaxial strain induced on free-standing bi-layered silicene

The lattice constant of bi-layered silicene is 3.866 Å, which remains the same value as it is in silicene. Bi-layered silicene consists of four silicon atoms, which are fully relaxed during the optimization by using DFT-GGA method. There are five energetically stable structures obtained from our simulations. In general, the stable structures can be divided into two categories: AA and AB showing in Figure 2.14. The stability of both AA and AB structures have been proved by adding a small perturbation during the optimization. The simulation results turn to be identical with prior cases. Both AA and AB structures are reaching the

46 minimum energy by giving the same force and stress optimized condition. However, comparing the two categories, the total energies of AA structures are lower than that of AB types. In order to obtain the AA structures, the initial position of silicon atom should be assigned to be very close to the optimized one. In AA category, it includes coplanar parallel

(AA-P) and coplanar non-parallel (AA-NP) structures shown in Figure 2.14 (a). The AB category includes three configurations named non-coplanar parallel (AB-P), non-coplanar non-parallel (AB-NP) and AB-hybrid structures shown in Figure 2.14 (b). The coordinates of all five structures, buckling height D1(first layer) &D2(second layer), and the distance between two layers D3 are listed in table 2.2.

Figure 2.15 shows the buckling height of AA and AB structures under both compressive and tensile strain. Buckling heights of AA-P and AA-NP are shown in Fig. 2.15 A. In the region of compressive strain, as the strain increases, the buckling height increases accordingly. However, in the region of tensile strain, the buckling height reduces when the

Coordinates(Å) A1(Å) A2(Å) A3(Å) A4(Å) D1&D2(Å) D3(Å)

x 0 -0.001 1.933 1.932 AA-P y 0 -0.009 -1.113 -1.127 0.85 1.888 z 0 2.738 0.85 3.589 x 0 0 1.933 1.933 AA- y 0 -0.007 -1.115 -1.123 0.67 2.447 NP z 0 2.447 -0.67 3.118 x 0 -0.001 1.935 1.935 AB-P y 0 -0.025 1.117 -1.139 0.708 2.16 z 0 2.867 0.708 3.65 x 0 0 1.932 1.932 AB- y 0 -0.01 1.116 -1.126 0.676 2.501 NP z 0 2.501 -0.676 3.177 x 0 0 1.931 1.93 AB- y 0 -0.008 1.114 -1.125 0.526 1.573 Hybrid z 0 2.611 0.526 2.099

Table 2.2Coordinates of 5 different stackings of bi-layered silicene strain increases. Additionally, the buckling height approaches zero when the tensile strain is above 7% for AA-NP and 5% for AA-P. Figure 2.15 B shows the buckling heights of

AB-P, AB-NP and AB-Hybrid. Like the coplanar structure, the buckling height of all AB structures increases as the strain increases in the compressive region. In the tensile strain region, the buckling height will decrease as the strain increases. However, instead of approaching zero for the coplanar structure, the non-coplanar structures tend to saturate at

0.38 Å for the AB-P and the AB-Hybrid, and at 0.65 Å for AB-NP once the tensile strain is above 5%. Later, systematic band diagrams have been calculated on both AA and AB

49 structures. As the band gap was only observed in AA structures, the following calculations are focused on the AA-P and AA-NP structures.

A B Figure 2.15 A) Buckling height of AA-P and AA-NP with induced strain. B) Buckling height of AB-P, AB-NP AND AB-Hybrid with induced strain. The buckling height monotonically decreases as the in-plane strain increases from compressive (negative in- plane strain) to tensile (positive strain). However, that the buckling height approaches zero when the tensile strain is above 7% for AA-NP and 5% for AA-P shows in A and the non-coplanar structures tend to saturate at 0.38 Å for the AB-P and the AB-Hybrid, and at 0.65 Å for AB-NP once the tensile strain is above 5%.

The band diagrams of AA-P and AA-NP structures are shown in Figures 2.16 (AA-P) and

2.17(AA-NP) under the same range of strain as described in Figure 2.15. the band diagrams exhibit a dramatic change in both AA-P and AA-NP structures under compressive and tensile strain. As mentioned before, for AA-P structure, the buckling height has a rapid drop when the tensile is above 5% and will approach to zero by further increasing the strain.

Such changes can also be observed in Figure 2.16 F, G, H, and I, which indicate that the

50 buckling height has a significant impact on the energy band diagrams in bi-layered silicene.

Similarly, the buckling height of AA-NP structure also approaches zero when the tensile strain is above 7%, at which point the buckling height is dropping dramatically. By analyzing the configuration of AA-P and AA-Np shown in Figure 2.14 (a). the only difference between two structures is the position of silicon atom A3 along the c-axis. When the tensile strain is above 7%, the buckling height of both AA-P and AA-NP structures approach to zero and their atomic structures become identical, which are also verified by the energy band diagrams shown in Figure 2.16. G, H, and I and 2.17. G, H and I. The energy band diagrams of those zero-buckling-height bi-layered silicene structures show indirect semiconductor features. When the in-plane strain is less than 10%, the bi-layered silicene is electrically conductive. As the strain reaches above 12.9%, bi-layered silicene becomes an indirect semiconductor, which shows a 0.11 eV energy bandgap opening in figs. 2.16 (I) and 2.17 (I).

ɛF

0% strain ɛF

ɛF

Figure 2.16 A – I shows band diagrams of AA-P by giving the lattice constant from 3.566 Å to 4.366 Å. Fermi energy level is denoted with the red line. The blue lines show the energy offset of Dirac point, energy bands L1 and L2 in (I). Fig. D is the band diagram of freestanding AA-P configuration. And a 0.11 eV bandgap opening has been observed when the tensile strain reaches is up to 12.9%.

ɛF

ɛF 0% strain

ɛF

Figure 2.17 A – I shows band diagrams of AA-NP by giving the lattice constant from 3.566 Å to 4.366 Å. Fermi energy level is denoted with the red line. The blue lines show the energy offset of Dirac point, energy bands L1 and L2 in (I). Fig. D is the band diagram of freestanding AA-P configuration. And a 0.11 eV bandgap opening has been observed when the tensile strain reaches is up to 12.9%.

Figure 2.18 shows the energy band diagrams of bi-layered silicene under the in-plane strain from 10.7% up to 15.4%. When the strain is below 13.8% (Fig. 2.18 G), the energy band

53 gap is almost linearly dependent on the in-plane strain shows in Figure 2.19. The band gap is given by the energy difference between L1 and L2 energy bands. A maximum band gap

0.17 eV was obtained when the strain equals to 14.3% shows in Figure 2.18 H. Interestingly, the maximum band gap is counted from L3 to L2 due to the lower energy level of L3 comparing to it of L1. Further increases of strain will lead a drop of band gap which is caused by the lowering of the energy band L3 shown in Figure 2.18 (I to L). The energy band gap becomes zero when the L3 energy band crosses with Fermi energy level shown in Figure 2.18 L.

ɛF

Figure 2.19 Band gap opening of AA-P and AA-NP for different tensile strains. he energy band gap reaches a maximum of 0.168 eV when the strain equals to 14.3%

The transmission spectrum of flat bi-layered silicene (buckling height is zero) are calculated and shown in Figure 2.20. The range of tensile strain is corresponding to it of

Figure 2.19. The band gap opening can be observed from figures 2.20 B–I, manifested by the zero-transmission efficiency close to the Fermi energy level, which has a good agreement with the results shown in Figures 2.18 and 2.19. Additionally, the I-V curve and the differential I-V curve are calculated when the energy band gap reaches its maximum and shown in Figure 2.21 A. A plateau of zero current intensity is observed in the vicinity of zero applied voltage due to the existence of energy band gap shown in Figure 2.21 B. In

57 addition, the electron density is calculated, shown in Figure 2.22. Comparing to the electron density of free-standing AA-P and AA-NP bilayer silicene shown in Figure 2.23, the coupling between two layers’ silicon is much stronger.

ɛF ɛF

Figure 2.20 Transmission spectrum of bi-layered silicon film with tensile strain.

A B Figure 2.21 A) I-V curve of bi-layered silicon film with maximum band gap opening. B) Differential I-V of bi-layered silicon film with maximum band gap opening. a plateau of zero current intensity in the vicinity of zero has been observed due to the existing of bandgap in Figure 2.21 A.

Silicon

Figure 2.22 Electron density of bilayer silicene with maximum band gap opening. Comparing to the electron density of AA-P and AA-NP bilayer silicene shown in Figure 2.23, the coupling between two layers’ silicon is much stronger.

Silicon

Figure 2.23 Electron density of free standing bilayer silicene AA-P (left) and AA-NP (right). It is worthy of mentioning that an asymmetric bilayer structure is obtained in a 2 × 2 super cell[68], which cannot be obtained in 1 × 1 configuration. The same structure was also discussed in this work, shown in Figure 2.24. The external strain is applied to the structure and the maximum 0.15 eV band gap was observed shown in Figure 2.25. Both compressive and tensile strain were applied, and the band gap can be only observed in a very tiny strain span. Both transmission efficiency and I-V curve were also attached in the graph in Figure

2.25.

Figure 2.24 Atomic structure of asymmetric bilayer silicene side view (left) and top view (right)

Figure 2.25 Band gap opening under both compressive and tensile strain of asymmetric bilayer silicene In conclusion, the structural and electronic transport properties of Bi-layered silicene were investigated. Five energetically favorable triangular lattice structures of Bi-layered silicene with AA- and AB- stacking configurations have been obtained. The buckling height of AA-

62 stacked Bi-layered silicene decreases to zero as the applied in-plane strain exceeds 5.17% for AA-P and 7.76% for AA-NP structures. Upon further increase of the strain, AA-P and

AA-NP converge to a single structure and start to have an energy band gap. A correlation has been observed between the strain-induced buckling height reduction and the band gap appearing. It turns out that the range of strain to open the band gap is 10.7% ~ 15.4%, and the maximum energy band gap opening is about 0.17 eV. Therefore, our theoretical results pave a new way to the utility of 2D bilayer silicene, which goes further to the silicene based transistors and potentially enables numerous novel nonelectronic applications.

Chapter 3 Theoretical simulation of bilayer silicene on diverse

substrates

3.1 Introduction

So far, the work related to band gap opening on bilayer silicene has been reported theoretically. However, realizing it in the real applications is still challenging. It is well known that silicene sheets need to be placed on semiconducting or insulating substrate in nano electronic devices. Therefore, how substrates affect the electronic properties of bilayer silicene is becoming a significant topic. Silver, a promising substrate of silicene, has been investigated systematically using Ab initio density functional theory. As reported, growing silicene on Ag substrate can exhibit many different structural phases[112]. A band gap in the range 0.1-0.4eV was obtained from those configurations due to the strong interaction between silicene atoms and silver atoms. However, although the value of band gap is attractive, the Ag substrate is still difficult to be applied in the experimental synthesis due to some co-existence of several superstructures and smaller domain size of monolayer silicene. More recently, ZrB2 substrate and Ir substrate have also been reported. For instance, silicene was deposited on an Ir(111) surface and annealed the sample to

670k[113]. The paper showed that the silicon ad-layer presents a LEED pattern. Also, the honeycomb feature of the system is obtained from a STM. However, the gapless problem is still pending a solution. Recent reports proposed that the hetero-structure formed by

64 silicene and CaF2 shows a very strong p-type self-doping feature[112]. A small band gap was obtained between π and π*cones when the CaF2 was induced to silicene in [111] direction. Also, GaS was demonstrated to be a proper substrate, which can form heterosheets with silicene[104]. In their work, a sizable band gap is observed at the Dirac point because of the interlayer charge redistribution. However, GaS substrate can only be obtained by mechanical exfoliation, hindering its applications into the silicon-based mainstream semiconductor industry. Since then, researchers have been trying to investigate other semiconductor substrates, especially focusing on Group II-VI and Group III-V, e.g.

AlAs (111), AlP (111), GaAs (111), GaP (111), ZnS (111) and ZnSe (111)[114]. The paper demonstrates that the properties and stability of the silicene overplayed really depends on whether the interacting top layer of the substrate shows the metallic or nonmetallic property.

In this chapter, based on density functional theory (DFT) calculations, we investigated the structural and electronic properties of bilayer silicene on various substrates. A few substrates were tested to be appropriate to provide enough biaxial strain on bilayer silicene.

A sizeable band gap was observed from bilayer silicene with the absence of substrate.

Additionally, a feasible way was demonstrated to get rid of the chemical bond formed between bilayer silicene and substrate. A systematic calculations of electron density were first proposed in this work. In this configuration, a weaker coupling between graphene and bilayer silicene was observed, while the coupling between bilayer silicene was stronger, which steps forward to physical exfoliation of bilayer silicene and potentially activate the silicene based Nano-electronic applications.

3.2 Selection of substrates

As discussed previously, inducing a 10% to 15% tensile strain will lead to a bandgap opening on bilayer silicene. Our work will focus on the investigation of proper substrates, which can provide enough strain, and its realization based on current technique. Systematic calculations on diverse substrates will be demonstrated by using the DFT method.

Considering the symmetry of bilayer silicene, substrates with a hexagonal structure will be more favorable to match with it. Figure 3.1 shows the atomic structure of Zincblende (ZB) and its top view, respectively.

Figure 3.1 Zinc Blende structure in the hexagonal orientation. It consists of three bilayers, namely layers A, B and C. Each bilayer includes two atomic layers, forming an ABCABC… structure. The duplicated top view shown in right side.

In this work, AABBCC stacking substrates were employed to induce tensile strain to bilayer silicene. Figure 3.2 exhibits the amplitude of in-plane strain provided by different substrates, which forms a lattice constant mismatching to the free-standing bilayer silicene.

Figure 3.2 In-plane strain provided by various substrates

3.3 Structural optimization on bi-layered silicene on selected substrates

According to Fig 3.2, five types of materials have been selected in our calculations: CdSe,

InAs, GaSb, AlSb and InSb. During the structural optimization, the bottom atomic layer is fixed to stand for multiple solid layers of substrate while the other three atomic layers can

67 relax along the x-, y- and z- axes. The side- views of bilayer silicene on the substrate are shown in figure 3.3. As simulated before, the AA structure consists of two different types of structure, AA-P and AA-NP. Both structures were simulated in this work. Due to the large mismatching of lattice constant, both AA-P and AA-NP turn to zero-buckling height structures after optimization.

Figure 3.3 AA-P (left) and AA-NP (right) of bilayer silicene on the substrate

The same computational method was utilized in the calculations. The lattice constant along the c-axis is set to 40 Å to avoid inter-layer interaction. In the calculations, a periodic boundary condition was chosen to allow self-consistent solving of the Poisson equation using the fast Fourier transform solver. The atomic structures have been optimized using the generalized gradient approximation (GGA). It’s important to point out that the Van Der

Walls interaction effect is not considered in our simulations in order to explore the pure

68 effects provided by substrates. After the optimization, a perturbation was applied to further verify the stability of the structures.

A B C

Figure 3.4 optimized atomic structure of bilayer silicene on substrate. A: top view of unit cell. B: side view of unit cell. C: top view of duplicated unit cell. Structural optimization of the bi-layered silicon has gone through the complete list of the materials shown in figure 3.4. The silicon layer on all these substrates exhibits hexagonal

69 symmetry. Bilayer silicene with InAs substrate was selected as an example for the further discussion. Figure 3.5 shows the band diagram of bilayer silicene on InAs substrate. There is no band gap showing up due to the breaking of periodicity along c axis and the formation of chemical bond which make it difficult to decouple the band diagrams of substrate and bilayer silicene. However, interestingly, the bilayer silicene was forming a flat layer in each

Figure 2.12 B in chapter 2. Therefore, the band structure of bilayer silicene after removing the InAs substrate was calculated shown in Figure 3.6. An indirect band gap was observed with 0.08 eV. After that, the same simulations were carried out on other four substrates.

Figure 3.7 shows the band gap opening of bilayer silicene after removing substrates and the band gap opening under manual strain in free-standing cases. The graph exhibits that the band gap of bilayer silicene with substrate was larger comparing to those of free- standing bilayer silicene, which is suspiciously caused by the effects of substrates. The chemical bond was observed between the top layer of substrate and bottom layer of bilayer silicene. Although the band gap can be obtained from bilayer silicene after removing substrate, the bilayer silicene is very difficult to peel off physically due to the chemical bond impact.

Figure 3.6 Band structure of bilayer silicene after removing InAs substrate. A in direct band gap was observed with 0.08 eV.

Figure 3.7 Band gap opening of bilayer silicene with/without substrate. the band gap of bilayer silicene with substrate was larger comparing to those of free-standing bilayer silicene. To further verify our assumption, the electron density calculations of the entire system

(bilayer silicene and substrates) were performed. Figure 3.8 shows the electron density of bilayer silicene on different substrates: CdSe, InAs, GaSb, AlSb and InSb. InP was selected as a reference. The electron density of bilayer silicene with InP was shown in Figure 3.8

A. As the lattice constant increases, the chemical bond between the bottom layer of bilayer silicene and top

A B1 B2 B3 B4 B5 Figure 3.8 electron density of bilayer silicene on different substrate. As the lattice constant increases, the chemical bond between the bottom layer of bilayer silicene and top layer substrates get weaker. Meanwhile, the chemical bond between two layers of silicene become stronger.

layer substrates get weaker. Meanwhile, the chemical bond between two layers of silicene become stronger. However, the chemical bond between substrate and silicene still have substantial influence to make difficulties on peeling bilayer silicene off.

3.4 The realization of extraction of bilayer silicene from substrate

It has been reported by Kim’s group [115] that monolayer graphene can be served as an intermediate in between the epilayer and substrates. The Van der Waals will be formed between monolayer graphene and the epilayer. Meanwhile, the interaction between the substrate and epilayer is still dominant during the optimization. Theoretical work has been

73 demonstrated on GaAs, InP and GaP and confirmed the predictions. The simulation was performed by inserting the monolayer graphene into a bilayer silicene – substrate system shown in Figure 3.9. Both AA-P and AA-NP were calculated in this work. The distance along c axis between graphene and substrate is set to 1.5 Å, and distance between bilayer silicene and graphene is 2.3 Å. The total distance between bilayer silicene and substrates is 3.8 Å, in which bilayer silicene can still experience the effect of substrates

Figure 3.9 AA-P (left) and AA-NP (right) bilayer silicene on the substrate by inserting a monolayer graphene in between.

Figure 3.10 shows the optimized atomic structure of bilayer silicene on the substrate and monolayer graphene. During the optimization, the substrate and monolayer graphene were constrained. The bilayer silicene formed a ‘flat’ structure and has a 3.4 Å distance

74 between the bottom layer silicene and graphene. Once the buckling height approach to zero, AA-P and AA-NP become identical structures which are similar to those of free- standing.

Figure 3.10 exhibits the band gap opening of bilayer silicene in free-standing, substrates and substrate with graphene cases. The band gap was dramatically reduced after inserting the monolayer silicene depicted by Blue Square in Figure 3.11. In addition, the blue square is perfectly following the curve of free-standing cases shown in Figure 3.11with the black dot. Also, the band

Figure 3.11 Band gap opening of bilayer silicene with substrate, without substrate, and with substrate and graphene. The band gap was dramatically reduced after inserting the monolayer silicene depicted by Blue Square in Figure 3.11. In addition, the blue square is perfectly following the curve of free-standing cases shown in Figure 3.11with the black dot.

diagrams of bilayer both with/without graphene on different substrates were shown in

Figure 3.12. This observation could be caused by the formation of Van Der Waals force.

The electron density of the atomic structures was simulated to further verify the hypothesis shown in Figure 3.13. The electron density between bilayer silicene and graphene is much lower compared to it between bilayer silicene. Moreover, comparing to bilayer silicene on substrate only, the coupling between bilayer silicene is slightly higher than in Figure 3.9 due to the weaker impact from substrates.

Substrate with graphene

Substrate without graphene Figure 3.12 Band structures of bilayer silicene with the absence of substrate and graphene

In order to further understand the effect of substrates, the atomic structures of bilayer silicene with/without graphene on substrates (InAs, GaSb, and AlSb) were discussed. Table

3.1 shows the coordinates of four atoms of bilayer silicene.

InAs without graphene x y z

A1 0 0 0

A2 2.13889 1.236748 -0.0053

B1 -0.00347 0.001899 2.4045

B2 2.14263 1.241728 2.4003

InAs with graphene

A1 0 0 0

A2 2.14042 1.237015 0.0113

B1 0.00472 -0.00305 2.3665

B2 2.1464 1.233205 2.3726

GaSb without graphene x y z

A1 0 0 0

A2 2.16219 1.247455 -0.0118

B1 -0.01173 -0.00386 2.4032

B2 2.15329 1.24597 2.3968

GaSb with graphene

A1 0 0 0

A2 2.1627 1.247331 -0.0454

B1 0.01499 -0.00791 2.3846

B2 2.17866 1.240514 2.3438

AlSb without graphene x y z

A1 0 0 0

A2 2.1682 1.251759 -0.0085

B1 0.00129 0.000829 2.4031

B2 2.1716 1.253486 2.3972

AlSb with graphene

A1 0 0 0

A2 2.17021 1.249731 -0.0105

B1 0.03134 -0.0153 2.3739

B2 2.19962 1.23815 2.3626

Table 3.1 Coordinates of four silicon atoms of bilayer silicene with/without graphene on different substrates The atomic structure of bilayer silicene is shown in Figure 3.14. A1, A2, B1 and B2 denote the four silicon atoms. A1 and A2 are at bottom layer named layer A, and B1, B2 are at top layer named layer B. D1 is distance between A1 and B1 and D2 is distance between A2 and B2. D1 and D2 are measured vertically along c axis. Buckling height of layer A (BHA) and buckling height of layer B (BHB) are very close to zero due to the induced tensile

79 strain. The bond length between A1 and A2 is name as BLA, and the bond length between

B1 and B2 is named as BLB. Table 3.2 shows all the parameters related to the atomic structure of bilayer silicene.

Figure 3.14 Atomic structure of optimized bilayer silicene after removing substrates and graphene (if applicable). Side view(left) and top view (right).

BLA (Å) BHA(Å BLB(Å) BHB(Å D1(Å) D2(Å)

) )

InAs with 2.4707 0.0053 2.4784 0.0042 2.4045 2.4056

graphene

InAs without 2.4721 0.0113 2.4728 0.0061 2.3665 2.3613

graphene

GaSb with 2.4962 0.0118 2.4998 0.0064 2.4032 2.4086

graphene

GaSb without 2.497 0.0454 2.4983 0.0408 2.3846 2.3892

graphene

AlSb with 2.5036 0.0085 2.50587 0.0059 2.4031 2.4057

graphene

AlSb without 2.5043 0.0105 2.5045 0 2.3739 2.3731

graphene

Table 3.2 Related parameters of bilayer silicene after removing substrates and graphene (if applicable)

According to the data in table 3.2, for example, the BLA has 0.0014 Å difference between bilayer silicene with graphene and bilayer silicene without graphene on InAs substrates.

Such small difference can be summarized as numerical error of the simulation software.

Similarly, the BLB of bilayer silicene between two different configurations are also nearly the same. Such feature was also observed on GaSb and AlSb substrate due to the identical setting of lattice constant during the simulation. However, the distance between layer A and layer B (D1&D2) exhibit a larger difference comparing with other parameters. For example, D1 is 2.4045 Å when bilayer silicene is grown on InAs substrate with graphene inserted, while it is down to 2.3665 Å by taking the graphene out (labelled blue). Similar reduction also observed on GaSb (Labelled green) and AlSb (Labelled yellow) cases. The differences between D1&D2 are in the range of 0.02 Å ~ 0.04 Å, which is more than 10

81 times larger than other difference of parameters (BLA. BLB. BHA. BHB). Therefore, we suspect that the distance between two layers of bilayer silicene exhibits a significant impact to its band structure. It’s worthy to point out that BHA&BHB of bilayer silicene on GaSb also shows a larger difference between graphene case and non-graphene case (labelled red).

Such difference may also lead a variation of bandgap opening which can be explained in

Figure 3.11. We assume that band gap of bilayer silicene on different substrates (InAs,

GaSb, and AlSb) without graphene should also follow a linear trend by experiencing the same effect of substrates. However, the band gap of bilayer silicene on GaSb without graphene (red triangle) has a lower band gap opening than our expectation, which is not following the same trend as InAs and AlSb (red triangle). This feature could be caused by the non-zero buckling height (BHA&BHB).

In conclusion, in this Chapter, the electronic properties of bilayer silicene on various substrates were discussed. The atomic structures of bilayer silicene exhibited a sizeable band gap with absence of substrate after optimization. The maximum band gap can reach up to 0.145 eV on AlSb substrate. Later calculations were performed by inserting one monolayer silicene in between bilayer silicene and substrates. The band gap of bilayer silicene after removing substrate and graphene displayed a decrease and follow the curve of free-standing case obtained in Chapter II. This result is first demonstrated in this work, and further verified that monolayer graphene as an intermediate can prevent the formation of chemical bond between substrates and epilayer. Additionally, the distance between two silicene layer and buckling height of each layer were found to have a significant impact on

82 bandgap opening. In the future work, Van Der Waals interaction need to be considered to further understand this observation. In this work, bilayer silicene with a sizeable band gap can be potentially grown and peeled off, which paves a way towards the silicene-based nanoelectronics.

Chapter 4 Theoretical simulations and experimental measurements

on defective graphene.

4.1 Introduction

It’s well known that the low on/off current ratio character of graphene hinders its way on digital applications[116]. The on/off current ratio usually characterizes how much the difference between the on state current and off state current. Typically, the on/off current ratio is silicon field-effect transistors (FET) should be in the range of 104 to 105, and can be reaching to 107 in SiGe technique[117], while graphene based field-effect transistors

(FET) possesses a low on/off ratio around 5 due to its gapless property[118]. Although some breakthroughs have been made and enhanced the on/off current ratio up to 2000, such value is still not enough to be implemented in digital circuits. However, this character does not rule out the graphene applications in Radio frequency (RF) and microwave (MW) field

[78], [79], [124]–[131], [80], [81], [94], [119]–[123] due to its high electron mobility and high saturation velocity[81][78][132][133] which is owing to its Dirac points where conduction band and valence band reach together. In addition, RF/MW application does not require high on/off ratio because RF and analog circuits are essentially always conducting and prefer to modulate the amplitude of signals rather than turn them on or off digitally. So far, graphene with lowest density of defects can be obtained from mechanical exfoliation. However, this method is only useful for lab-scale investigations as it’s

84 impossible to scale-up the process[134]. for which prevents it from industrial-scale production. Up to now, many techniques of graphene production have been reported such as epitaxy, nanotube slicing and so on. Chemical vapor deposition (CVD) is one of the common methods of epitaxy. CVD can produce high quality and large-scale thin films in semiconductor industry by using vacuum deposition method. However, the structural imperfections so called “grain boundaries” are ineluctably produced and significantly impact on the electronic properties of graphene by lowering the electrical and thermal conductivity of the materials [135].

So far, many works have reported the impact of induced defects on the electronic properties of graphene[84], [136]–[138]. It has been reported by Seunghyun and Zhaohui’s that the minimum conductivity of graphene is affected by defects and impurities in 2014[139].

Also, Leonardo’s group reported the electrical transport properties of graphene nanostructures is strongly depends on the structural defects[138]. In addition, a dramatic decrease of the conductivity of graphene was observed at low frequency by Kim’s group[136] in 2009. Furthermore, the permittivity of graphene also exhibits the frequency dependency from 1 GHz to 5 GHz[84]. So far, although effects of frequency on conductivity and permittivity on graphene have been observed and reported, the systematic search for correlation between graphene micro-structure and RF permittivity is still lacking.

There are many methods to characterize graphene properties such as scanning tunneling microscopy (STM), transmission electron microscopy (TEM) and scanning electron microscopy (SEM). STM possesses excellent resolution which can be down to 0.1 nm in lateral and 0.01 nm in depth. While TEM also has extradentary resolution on recording atomic structures. The SEM with lower 1 nm resolution is also capable to obtain the thickness, roughness, and edge contrast of materials. However, none of above methods can be used for investigating the RF performance under nanoscale.

As mentioned before, scanning microwave microscope (SMM) has the unique ability to measure electronic properties at micro- and nanoscale spatial resolutions. Although near field scanning optical microscope (SNOM) is also a well-known technique to perform nanostructure investigation, SMM still has advantages over SNOM. For instance, first,

SMM can observe the noninvasive images because the energy of microwave photons is on the order 10 μeV. Secondly, SMM has higher sensitivity to dielectric permittivity over frequencies[140]. Therefore, SMM is utilized in this dissertation to explore the graphene

RF properties on defective chemical vapor deposition (CVD) graphene. In addition, the

SMM was modeled by using finite element method in EMPro, the results further supported our experimental works.

4.2 Experimental measurements

CVD is considered as one of the most promising techniques to grow large scale graphene sheets and possess the capability with current mature silicon technology. In details, the

86 graphene sheets were deposited on both sides of a Cu foil with 100 µm thickness. Then, the CVDG sheet was transferred onto a Si (550 µm)/SiO2 (300 nm) substrate. Briefly, a

200 nm thick PMMA was coated on one side of CVDG and the other side of graphene and

Cu were removed by using Fe(NO3)3 wet chemical etching and oxygen plasma etching.

Subsequently, the remaining CVDG and PMMA layers were placed on SiO2/Si substrate after rinsing by the Deionized (DI) water. Later, the PMMA was removed in acetone to form a CVDG/substrate film. The conductivity  of monolayer graphene was estimated at around 106 S / m by considering the thickness of 1 nm[141]. The grating structure was added to the surface of CVDG with photoresist by using photolithography techniques and structured using oxygen plasma etching. Furthermore, the photoresist was rinsed by using an acetone/isopropyl alcohol (IPA).

In this work, in order to investigate the effect of electrical properties affected by defects, two samples, prepared by Kathy Brockdorf[142], were intentionally etched which is convenient to locate the defects position shown in Table 4.1. In addition, those two samples have different etching time for comparison and verification. Figure 4.1 outlines the topography and friction of sample A and B. The un-etched graphene (bright region) exhibits higher surface topography than in etched graphene (dark region) shown in Fig 4.1

A. In addition, inducing etching will lead a rougher surface comparing to pristine graphene shown in Fig 4.1 B. Both samples were also verified by using Raman spectroscopy to identify the induced etching shown in Table 4.1 and Figure 4.12. In Figure 4.2, Peak D is referred to defective carbon structure. Peak G is referred to graphitic structure like carbon.

And Peak 2D is referred to the stacking order of graphene layers. The ratio between intensities of 2D band and G band is a measure of induced defects depending on the etching time. The higher I2D/IG ratio indicates less induced defects (#A, 10s etching time) shown in Table 4.1.

Sample Etching Power (W) Etching time (s) I2D/IG A 5.0 10 0.48 B 5.0 30 0.21 Table 4.1Etching parameters of samples #A and #B, and the intensity ratio of the 2D- and G- peaks (I2D/IG) in the corresponding Raman spectra, where D peak is representing in defective carbon materials, and G peaks is a result of in-plane vibrations of SP2 bonded atoms.

Figure 4.1 Surface topography (a) and friction (b) of sample #A. Topography is consist of two areas, etched graphene (dark region) and un-etched ribbon (bright region). The etched graphene displays a lower topology after etching process. Image b shows the friction of etch (bright region) and un-etched graphene (dark region). The etched graphene exhibits higher roughness after etching process. Further verification has been performed on sample # A and # B by using Raman spectroscopy technique. The experimental results were provided by Nick Engel[143]. The etched graphene exhibits a significant rise of D-peak shows in Figure 4.2, which indicates the structural disorders induced by oxygen plasma etching. Comparing to sample # A, the higher density of defects in sample # B is depicted with lower ratio between the 2D- and

G- peaks.[144]. Additionally, due to the existing of the G- and 2D peaks, after the etching procedure, the monolayer graphene hasn’t been removed completely.

Figure 4.2 Raman spectrum of #A and #B. Compared to the un-etched graphene, the etched samples #A and #B present a raised D-peak and a reduced ratio between the 2D- and G- peaks, thereby, indicating that defects have been induced during oxygen plasma etching. Additionally, the presence of the G- and 2D peaks for samples #A and #B prove that etching did not completely remove the graphene monolayer.

Figure 4.3 is showing the equipment we are using in this work. SMM is basically an upgraded atomic force microscope (AFM, Agilent 5420) connecting with a vector network analyzer (Agilent PNA-N5230C). A 1.5-meter coaxial cable is connected to one port of PNA shows in Figure 4.4. The other end of the cable is connected to a 24 mm coaxial cable which directly mounted to the sample holder. The other end of the 24 mm cable is connecting with transmission line resonator which directly transmits the signal to the SMM cantilever and probe shows in Figure 4.5.

Figure 4.3 SMM system combined by Agilent 5420 AFM, PNA N5230C and a special nose cone adapter.

Figure 4.4 Block diagram of VNA, SMM sample holder and cables. A 1.5-meter coaxial cable is connected to one port of PNA, and the other end of the cable is connecting to the 24 cm coaxial cable.

Figure 4.5 Schematic model of SMM probe with 3 cm resonator. The red triangle is the SMM tip which shows in Figure 4.7.

The equivalent circuit of SMM is shown in Figure 4.6. The dielectric property and conductive property are represented by the shunt capacitive and resistive components respectively. According to the transmission line theory, both amplitude gamma Γ and phase

θ can be obtained using equation 4.3 and 4.4.

Figure 4.6 Equivalent circuit of the SMM system

The SMM measurement were performed after one-port calibration at the end of 1.5 m coaxial cable, which means the impact from 1.5 m cable has been calibrated out. The VNA data will be totally reflecting the performance of the component connected to the end of the 1.5 cable. The procedure has been done manually by calibrate Open, Short, and Match calibration kit and verifies by using those kits. The calibration has been performed at the end of 1.5 mm coaxial cable resulting in a shifting of resonating frequency due to the 24 mm uncalibrated trace. The more details are discussed in next part. Since all the components have calibrated and matched shunted 50 Ω source, the SMM imaging will be mainly reflecting the properties of measured materials at their resonant frequencies.

The complex input reflection coefficient Γ can be written as

푍 + 푗푍 tan(훽휄 ) Γ = − 0 퐿 0 4.1 (푍0 + 2푍퐿) + 푗(2푍0 + 푍퐿) tan 훽휄0

Where β is the wave number and 푍퐿 is shown below:

1 푍퐿 = 1 4.2 +푗휔퐶 푅

휆 When the wavelength = , the 4.1 can be simplified as: 2

푍 Γ = − 0 4.3 푍0 + 2푍퐿

Bring the 4.2 into this equation, the amplitude |Γ| and phase angle θ can be expressed as:

푍 1 Γ ≈ 0 ∙ √ + 휔2퐶2 4.4 2 푅2

휃 ≈ tan−1(휔푅퐶) 4.5

1 The above equations were calculated by considering R 푅 ≫ 푍0, and ⁄휔퐶 ≫ 푍0.

4.3 Results and discussion

The half wavelength λ / 2 resonator can be obtained by varying the operating frequency. The first resonance frequency appears at 2.1 GHz designed with 24 mm

휋 resonator. In order to identify the λ / 2 resonances, the phase with ± was selected as the 2 criterion[145]. In this work, three different λ / 2 resonance frequency have been selected:

2.1 GHz, 4.2 GHz, and 17.9 GHz. The 17.9 GHz is the measured frequency for the 9th harmonic resonance due to the calibration limit.

SMM images of sample #A were recorded at a series of half-wavelength (  2 ) harmonic resonances shown in Figure 4.7: 1st harmonic resonance ( f = 2.1 GHz ) (Fig. 4.7

(a), (b)); 2nd harmonic resonance ( f = 4.2 GHz ) (Fig. 4.7 (c), (d)); and 9th harmonic resonance ( f =17.9 GHz ) (Fig. 4.7 (e), (f)). As the Γin is a complex number at RF/MW

frequencies, both its amplitude ( in ) (Figs. 4.7 (a), (c) and (e)) and phase angle (in ) (Figs.

4.7 (b), (d) and (f)) were recorded. In measurements, the cantilever and tip of the AFM behave as a transmission line to conduct the RF signal to the sample. As mentioned before, the integrated VNA is only used to provide RF signal and simultaneously collecting the reflection coefficient. The contrast of amplitude shows in Figure 4.7 is indicating the

et difference performance contributed by etched graphene ( in−A ) and the un-etched graphene

unet et ( in−A ). And phase contrast was formed by etched graphene ( in−A ) and the un-etched

unet graphene ( in−A ).

As mentioned before, the impact from the 1.5 m cable has been calibrated out, while the impact from the 24.0 cm cable remained in the measured results (Fig. 4.7 a in ref. 103).

Ideally, if the first resonating frequency happens at 2.1 GHz, the 9th harmonic of 2.1 GHz should be 18.9 GHz. In the real measurement, our 9th harmonic resonance is obtained at

17.9 GHz due to the un-calibrated 24 mm cable. The appearance of oscillation induced by the 24.0 cm long cable causes about ±0.1 GHz uncertainty in determining the half- and quarter- wavelength resonances.

Thus, based on the 1st ( f = 2.1 GHz ) and 2nd ( f = 4.2 GHz ) harmonic resonant frequencies, the period of harmonic resonance is Δf=2.1±0.2 GHz. At  2 harmonic

resonances, the un-etched graphene exhibits a greater amplitude in over the etched graphene strips at all three frequencies. Imaging contrast reversion has been observed in the SMM phase images as frequency increased from 2.1 GHz to 4.2 GHz and 17.9 GHz

unet et (Fig. 4.7 (b), (d) and (f)): in−A > in−A at , < at and f =17.9 GHz .

4.4 Numerical simulation of SMM

The numerical model employed in the simulations is optimized from previous work[146].Although the relative conductivity and permittivity of materials can be estimated by using SMM technique, the quantitative values of those properties is still under investigation. Therefore, numerical simulation can help us efficiently test our model and provide support to our experimental results. The main challenge in this work is the simulation accuracy. The completed model is including 1.5 mm cable, 24 mm cable, a cantilever and SMM probe. However, it’s extremely difficult to simulate the entire model due to the higher time consumption. Moreover, the meshing point need to be down to 1 nm to obtain the precise results and the true performance of the materials.

The model only consists of SMM tip, graphene sample and substrate shown in Figure

4.8. The tip is formed as a cone with a base diameter of 10 um and an end diameter of

50 nm. The sample was a 100 um × 100 um × 2 nm block with the tip placed at the center with 1 nm depth into the sample. The calculations were based on the finite element method (FEM), which divides the full problem space into many small elements, generate governing equations for those elements, relate all of elements, and solve the resultant system of equations[147]. This technique is supported by commercial software EMPro

(Keysight).

Figure 4.9 exhibits the SMM system with arbitrary resonator length. The complex ZLSim can be obtained from EMPro simulations by solving the electro-magnetic field distribution. S-parameters were the main output obtained from simulations.

Input impedance Zin and compare to the experimental measurements. Where ZL =

ZLSim, phase constant 훽 = 2π / λ, ℓ is the length of transmission line resonator. Γin can

Zinfinal−Z0 be obtained by using the equation , where Zinfianl = Zin // 50 Ω. Zinfinal+Z0

Figure 4.9 Equivalent transmission line model of SMM system.

In the model, the graphene sheet was considered as a three-dimensional (3D) material with 3D conductivity and permittivity because graphene exhibits anisotropic electric properties due to the low dimensionality, i.e. the conductivity and permittivity along the vertical direction (normal to the surface) are different from their in-plane counterparts

(parallel to the surface)[148]. This difference might result in significant impact on the measurements at DC or low frequencies, such as contact resistance. In this case, the conductivity of graphene in the vertical direction is dominated. However, at RF and microwave frequencies, the capacitive effect around the SMM tip starts to play a role.

The capacitive effect can be described as that when a current flow through a capacitor, it is restricted by the internal impedance of the capacitor written as XC, called Capacitive reactance. In general, the capacitive effect is inversely proportional to film thickness and is proportional to frequency[149][148]. The reason can be explained by the equation below:

1 푋푐 = 4.6 2휋푓퐶

100 where f is the frequency and C is the capacitance. Therefore, due to the atomic layer feature of graphene, the distance between two plates is very narrow leading a high capacitance. In addition, as the frequency increases, the denominator is getting even smaller. According to the equation above, the capacitive reactance XC turns to be extremely small and the capacitive effect becomes extremely large along the vertical direction. As a result, the admittance Y = 1⁄ of graphene along the vertical direction 푍퐿 is further enhanced by the high frequency, consequently causing graphene sheets to become a “short circuit” at RF and microwave frequencies. In this case, the major impact on the SMM measurements is the in-plane conductivity and permittivity of the graphene sheets. Neglecting the impact by graphene’s vertical conductivity and permittivity allows us to use 3D conductivity and permittivity to model 2D graphene sheets. The simulations were performed at single frequency (f=2.1 GHz) by varying the conductivity (from 1 to

106 S/m) and the permittivity (from 1 to 105) with 100.25 increment (Fig. 4.10). The input reflection coefficient Γin is the main output obtained from our simulations. Both relative

amplitude  in and phase  in were defined with respect to the pristine graphene by

6 5 assuming its 휎 = 10 푆/푚 and 휀푟 = 10 . The conductivity  of the pristine graphene monolayer is estimated from the measured sheet resistance by taking the thickness 1.0 nm[150] due to zero-overlap semimetal with electrons and holes as charge carriers. The reported permittivity of graphene monolayer shows an exceedingly large value in a range

5 6 5 10 ~10 at RF/MW frequencies[84]. In my work, the 휀푟 = 10 is selected. However,

101 it worthy to mention that the reason of extremely high permittivity of graphene is remaining undiscovered.

As mentioned before, the impacts generated by the capacitive effects on Γin are indeed determined by an admittance (휔퐶), where 휔 is the angular frequency and C is the sample induced capacitance. Hence, the increase of frequency will have the same impacts on the capacitive effects as the increase of materials’ permittivity (i.e. capacitance), if the admittance keeps consistent. Based upon the above arguments, the capacitive effects at higher frequency in this work will be interpreted by performing simulations at lower frequencies while taking a larger value of permittivity into account. The location marks

(solid circles and squares) in Fig. 4.10 are used to schematically represent the measurements at different frequencies. In this region, both conductivity and permittivity exhibit significant changes comparing to it in pristine graphene. It’s worth to mention that the simulation is also very sensitive to tip diameter. The results by varying the diameter of tip from 20 nm to 50 nm exhibited relative changes of reflection coefficient. In this work, 50 nm has been chosen to display the “worst” scenario without losing generality.

Future reducing the diameter will be leading a relative enhancement of Γin.

Figure 4.10 is displaying the relative amplitude  in and phase  in of etched graphene. The negative in Figure 4.10 (a) implies the weaker amplitude due to the reduction of conductivity or permittivity. However, the phase in Figure 4.10 (b)

102 possesses two different regions labeled in different colors. In addition, there is a transition observed from in our simulation. According to our experimental results, for #

A at 2.1 GHz, the conductivity and permittivity of etched graphene decreases depicted

with smaller in in Figure 4.7 (a). Observed from Figure 4.7 (b), the phase of etched

et unet graphene in−A is less then phase of pristine graphene in−A , leading a negative value  in shows in Figure 4.10 (b) grey region, which also exhibits lower conductivity and permittivity. However, due to the higher capacitive effect at higher frequencies, the phase contrast has been reversed in the SMM images obtained at 4.2 GHz and 17.9 GHz shown in Figure 4.7 (d) and 4.7 (f). In this case, the relative phase should be in the green region shows in Figure 4.10 (b). As the frequency increases, the relative phase of etched graphene experienced a transition described by red arrow in Figure 4.10 (b). In

addition, the  in is reduced (less negative) from -0.4dB at f = 2.1 GHz to -0.1 dB at

f =17.9 GHz due to the increase of permittivity shows in Figure 4.10 (a). The results have a good agreement with our experimental tests shown in Table 4.2.

103

104

increases. The dashed lines mark the region where is in the range of 80 S/m to 3000S/m.

Further experimental testes have been performed on sample #B with longer etching time to investigate the impact of the defects on electrical properties of graphene. The SMM measurements show similar imaging contrast between etched and un-etched graphene at three different resonating frequencies as #A. Figure 4.11 and 4.12 depict the comparison

of  in and  in between #A and #B at 2.1 GHz and 17.9 GHz, and the results are summarized in Table 4.2. At 2.1 GHz, the relative amplitude reduces 0.4 dB and relative phase increases 3 degree over #A. As shown in Figure 4.10 (a), the lower

implies the further reduction of conductivity and permittivity comparing to #A due to the longer etching time. However, in order to achieve an increase of of #B over #A, the conductivity of #A and #B should be in the range from 80 S/m to 3000S/m shows in

Figure 4.10 (b). Only in this region, the can be increased which conductivity and permittivity are decreasing.

At 17.9 GHz, the relative amplitude of # B shows a 0.5 dB decrease over #

A, and the relative phase of # B is 4.5 degree higher than it of # A. The results have a very good agreement with our numerical simulations. First, comparing to # A, # B shows a lower due to the further reduction of conductivity and permittivity. Second, both #

105

A and # B show a positive  in due to the higher capacitive effect at higher frequency depicted in Figure 4.10 (b). Third, the higher of # B over # A is also observed in our simulation shows in Figure 4.10 (b). The lower conductivity and permittivity of # B could be caused by more induced defects due to longer etching time. It worth to mention that the conductivity of # A and # B should be in the range from 80 S/m to 3000S/m, which is more than 3 orders of magnitude reduction compared to the pristine graphene.

Sample f = 2.1 GHz f =17.9 GHz

 in (dB) (degree) (dB) (degree) A -0.4 -6.8 -0.1 0.8 B -0.8 -3.7 -0.6 5.3

Table 4.2 Comparison of and between #A and #B measured at and

106

Figure 4.11 Comparison of the magnitude modification  in (a), and the phase shift

 in (b) of the complex input reflection coefficient Γin of samples #A and #B at f = 2.1 GHz .

Figure 4.11. Comparison of the magnitude modification (a), and the phase shift

(b) of the complex input reflection coefficient Γin of samples #A and #B at .

107

Figure 4.12 Comparison of the magnitude modification  in (a), and the phase shift

 in (b) of the complex input reflection coefficient Γin of samples #A and #B at f =17.9 GHz .

108

Figure 4.12. Comparison of the magnitude modification  in (a), and the phase shift  in

(b) of the complex input reflection coefficient Γin of samples #A and #B at f =17.9 GHz .

4.5 Summary

It’s extremely important to understand the correlation between the structural- and electrical properties of 2D materials such as graphene in their application field. The impact of etched- induced defects on electrical properties of graphene have been measured using SMM and further verified by numerical simulation software EMPro. The SMM image contrast between etched and un-etched graphene clearly exhibit the significant changes of surface impedance, leading to a variation of conductivity and permittivity. Moreover, by comparing two samples with different etching time, results reveal that more defects will cause more variation on graphene’s electrical properties. In addition, the reversion of the

SMM contrast have been observed between low and high frequencies, indicating that the capacitive effect is not negligible at RF frequency. Comparing to most of the electrical characterizations of graphene sheets performed at DC level, such as atomic force microscope, and Hall measurements, SMM can overcome the uncontrollable contact resistances due to the tip-sample effect at RF/MW frequency. In addition, SMM possesses its unique capability to estimate the range of conductivity and permittivity of measured materials. However, the reason of extremely high permittivity is still lacking, which need

109 more precious calibration and quantitative simulation model to perform further investigations.

110

Chapter 5 Conclusion and Future work

5.1 Conclusion

In this work, the main effort concentrated on monolayer silicene and bilayer silicene simulations to achieve band gap opening by inducing biaxial strain. In addition, a feasible way to industrially grow bilayer silicene was proposed and tested. Specifically speaking, this work is including three sections. In section I, both compressive and tensile biaxial strains were applied to monolayer silicene. However, the induced strain can only lead to a shift of Dirac cone in band energies. The Dirac cone will move below the Fermi energy level under compressive strain but move upwards above the Fermi energy level under tensile strain. Moreover, compressive and tensile strain will lead to an increase of current monotonously. In section II, the structural and electronic transport properties of Bi-layered silicene were investigated. Five energetically favorable triangular lattice structures of Bi- layered silicene with AA- and AB- stacking configurations have been obtained. The bucking height of AA-stacked Bi-layered silicene decreases to zero as the applied in-plane strain exceeds 5.17% for AA-P and 7.76% for AA-NP structures. Upon further increase of the strain, AA-P and AA-NP converge to a single structure and start to have an energy band gap. A correlation has been observed between the strain-induced buckling height reduction and the band gap appearing. It turns out that the range of strain to open the band gap is

10.7% ~ 15.4%, and the maximum energy band gap opening is about 0.17 eV. In section

III, the structural and electronic properties of bilayer silicene on various substrates were

111 investigated. A few substrates were tested to be appropriate to induce enough biaxial strain on bilayer silicene. A sizeable band gap was observed from bilayer silicene with the absence of substrate. However, the formation of chemical bond between bilayer silicene and substrate were inevitable and make bilayer silicene difficult to be isolated. Further attempt was performed by inducing a monolayer graphene to separate bilayer silicene and substrate without screening the potential filed of substrates. A systematic calculations of electron density were first proposed in this work. In this configuration, a weaker coupling between graphene and substrate was observed, while the coupling between bilayer silicene was stronger, which steps forward to physical exfoliation of bilayer silicene and potentially activate the silicene based nano-electronic applications.

It’s well known that the low on/off current ratio character of graphene hinders its way on digital applications. However, this character does not rule out the graphene applications in Radio frequency (RF) and microwave (MW) field. However, the ineluctable surface imperfections will be produced during the large-scale growth of graphene by using chemical vapor deposition (CVD), which will have significant impact on electronic properties of graphene. In the part II of this dissertation, experimental measurements were performed on defective graphene samples at RF level. Briefly, the electronic properties between etched and un-etched graphene were observed by analyzing the SMM imaging contrast at different harmonic resonances. The SMM imaging contrast turns out to be determined by the difference of the permittivity and the conductivity between the etched

112 and un-etched graphene. At the higher frequency, the impact of capacitive effect is not negligible supported by numerical simulations.

The main contributions are listed below: • I-V curve of monolayer silicene under both compressive and tensile strain were performed. The systematical calculations were first proposed in this work and revealed that electronic properties of monolayer silicene exhibit a strong strain- dependency. • The dependency and tunability of an energy band gap opening versus strain have been first discussed in this work. A sizeable band gap was obtained on bilayer silicene under tensile strain. Considering the feasibility of synthesis, the atomic structure with band gap proposed in this work is more favored to current technique of growth comparing to other reported work. • Remote epitaxy was tested to experimentally grow silicene from appropriate substrates, which is potentially solving the synthesis problem of 2D materials and paves the way to silicene-based nano-electronic devices. • The impact of imperfections of CVDG to its electronic properties was experimentally observed using SMM. By using this technology, we were able to investigate the RF performance of materials under nano-scale resolution, while so far, reported work either performed in a large area or in a lower frequency. • A numerical model of SMM was first developed. Both conductivity and permittivity of measured materials can be characterized at RF level preciously. Using this model, the correlation between conductivity and permittivity of any materials can be obtained. Moreover, it can also investigate the dependency of frequency which is much more significant in the future RF nano-electronics.

113

5.2 Future work

Future work will include further investigation on the band gap opening on bilayer silicene by considering the spin-orbit coupling to obtain more accurate result. This will allow us to further understand the electrical properties of silicene and bilayer silicene under both tensile and compressive strain. According to our observation, the effect of substrates has a significant impact to grown 2D materials. In the future simulation, Van Der Waals interaction need to be considered to further explore its impact to the bilayer silicene grown on substrates by having the remote epitaxy graphene.

Future work will also focus on the improvement of SMM technique and simulation model.

An end-to-end calibration need to be experimentally done in order to clearly observed half- and quarter-wavelength results. Additionally, a quantitative model is more meaningful to preciously extract the conductivity and permittivity of measured materials, thus, further help to improve the performance of RF electronics.

114

Reference

[1] Gordon E. Moore, “Progress In Digital Integrated Electronics,” IEDM Tech. Dig.,

pp. 11–13, 1975.

[2] K. Xu et al., “Sub-10 nm Nanopattern Architecture for 2D Material Field-Effect

Transistors,” Nano Lett., vol. 17, no. 2, pp. 1065–1070, 2017.

[3] L. Liu, Y. Lu, and J. Guo, “On Monolayer MoS2 Field-Effect Transistors at the

Scaling Limit,” IEEE Trans. Electron Devices, vol. 60, no. 12, pp. 4133–4139,

Dec. 2013.

[4] R. E. Peierls, “Quelques proprietes typiques des corpses solides,” vol. 3, pp. 177–

222, 1935.

[5] L. D. Landau, “Zur Theorie der phasenumwandlungen II,” 1937.

[6] D. Mermint, “DECEMBER 1968 Crystalline Order,” vol. 176, no. 1, 1968.

[7] K. S. K. S. Novoselov et al., “Electric field effect in atomically thin carbon films.,”

Science (80-. )., vol. 306, no. October, pp. 666–669, 2004.

[8] K. S. Novoselov et al., “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci.,

vol. 102, no. 30, pp. 10451–10453, 2005.

[9] Z. A. Piazza, H. S. Hu, W. L. Li, Y. F. Zhao, J. Li, and L. S. Wang, “Planar

115

hexagonal B 36 as a potential basis for extended single-atom layer boron sheets,”

Nat. Commun., vol. 5, pp. 1–6, 2014.

[10] N. J. Roome and J. D. Carey, “Beyond graphene: Stable elemental monolayers of

silicene and germanene,” ACS Appl. Mater. Interfaces, vol. 6, no. 10, pp. 7743–

7750, 2014.

[11] F. F. Zhu et al., “Epitaxial growth of two-dimensional stanene,” Nat. Mater., vol.

14, no. 10, pp. 1020–1025, 2015.

[12] L. C. Lew Yan Voon, A. Lopez-Bezanilla, J. Wang, Y. Zhang, and M. Willatzen,

“Effective Hamiltonians for phosphorene and silicene,” New J. Phys., vol. 17,

2015.

[13] X. Li and H. Zhu, “Two-dimensional MoS2: Properties, preparation, and

applications,” J. Mater., vol. 1, no. 1, pp. 33–44, 2015.

[14] P. Garg, I. Choudhuri, A. Mahata, and B. Pathak, “Band gap opening in stanene

induced by patterned B-N doping,” Phys. Chem. Chem. Phys., vol. 19, no. 5, pp.

3660–3669, 2017.

[15] Q. Yao et al., “Bandgap opening in hydrogenated germanene,” Appl. Phys. Lett.,

vol. 112, no. 17, p. 171607, Apr. 2018.

[16] D. R. Cooper et al., “Experimental Review of Graphene,” vol. 2012, 2012.

[17] S. MOURAS, A. HAMWI, D. DJURADO, and J. COUSSEINS, “Systhesis of first

116

stage graphite intercalation compounds with fluorides,” Rev. Chim. Min., pp. 572–

582, 1987.

[18] A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The

electronic properties of graphene,” vol. 81, no. March, 2007.

[19] J. Zhao et al., “Rise of silicene: A competitive 2D material,” Prog. Mater. Sci.,

vol. 83, pp. 24–151, 2016.

[20] A. A. Balandin et al., “Superior Thermal Conductivity of Single-Layer Graphene,”

Nano Lett., 2008.

[21] C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the Elastic Properties

and Intrinsic Strength of Monolayer Graphene,” Science (80-. )., vol. 321, no. July,

pp. 385–388, 2008.

[22] A. B. Kuzmenko, E. Van Heumen, F. Carbone, and D. Van Der Marel, “Universal

Optical Conductance of Graphite,” vol. 117401, no. March, pp. 2–5, 2008.

[23] G. G. Guzmán-Verri and L. C. Lew Yan Voon, “Electronic structure of silicon-

based nanostructures,” Phys. Rev. B - Condens. Matter Mater. Phys., vol. 76, no. 7,

2007.

[24] S. Mehdi Aghaei and I. Calizo, “Band gap tuning of armchair silicene nanoribbons

using periodic hexagonal holes,” J. Appl. Phys., vol. 118, no. 10, 2015.

[25] S. Huang, W. Kang, and L. Yang, “Electronic structure and quasiparticle bandgap

117

of silicene structures,” Appl. Phys. Lett., vol. 133106, no. 2013, pp. 2–7, 2013.

[26] P. Vogt et al., “Silicene: Compelling experimental evidence for graphenelike two-

dimensional silicon,” Phys. Rev. Lett., vol. 108, no. 15, pp. 1–5, 2012.

[27] H. P. Li and R. Q. Zhang, “Vacancy-defect-induced diminution of thermal

conductivity in silicene,” Epl, vol. 99, no. 3, pp. 1–6, 2012.

[28] K. Yang, S. Cahangirov, A. Cantarero, A. Rubio, and R. D’Agosta,

“Thermoelectric properties of atomically thin silicene and germanene

nanostructures,” Phys. Rev. B - Condens. Matter Mater. Phys., vol. 89, no. 12, pp.

1–13, 2014.

[29] M. Wierzbicki, J. Barnas̈ , and R. Swirkowicz, “Zigzag nanoribbons of two-

dimensional silicene-like crystals: Magnetic, topological and thermoelectric

properties,” J. Phys. Condens. Matter, vol. 27, no. 48, 2015.

[30] W. Zhao, Z. X. Guo, Y. Zhang, J. W. Ding, and X. J. Zheng, “Enhanced

thermoelectric performance of defected silicene nanoribbons,” Solid State

Commun., vol. 227, pp. 1–8, 2016.

[31] W. Hu, N. Xia, X. Wu, Z. Li, and J. Yang, “Silicene as a highly sensitive molecule

sensor for NH3, NO and NO2,” Phys. Chem. Chem. Phys., vol. 16, no. 15, pp.

6957–6962, 2014.

[32] Y. Wang et al., “Metal adatoms-decorated silicene as hydrogen storage media,”

118

Int. J. Hydrogen Energy, vol. 39, no. 26, pp. 14027–14032, 2014.

[33] X. Tan, C. R. Cabrera, and Z. Chen, “Metallic BSi3 Silicene: A Promising High

Capacity Anode Material for Lithium-Ion Batteries,” J. Phys. Chem. C, vol. 118,

no. 45, pp. 25836–25843, 2014.

[34] Z. Ni et al., “Tunable bandgap in silicene and germanene,” Nano Lett., vol. 12, no.

1, pp. 113–118, 2012.

[35] N. D. Drummond, V. Zólyomi, and V. I. Fal’Ko, “Electrically tunable band gap in

silicene,” Phys. Rev. B - Condens. Matter Mater. Phys., vol. 85, no. 7, pp. 1–7,

2012.

[36] Z. Ni et al., “Tunable band gap and doping type in silicene by surface adsorption:

towards tunneling transistors,” Nanoscale, vol. 6, no. 13, pp. 7609–7618, 2014.

[37] R. Quhe et al., “Tunable and sizable band gap in silicene by surface adsorption,”

Sci. Rep., vol. 2, 2012.

[38] H. Liu, N. Han, and J. Zhao, “Band gap opening in bilayer silicene by alkali metal

intercalation,” J. Phys. Condens. Matter, vol. 26, no. 47, 2014.

[39] M. Houssa, G. Pourtois, V. V. Afanas’Ev, and A. Stesmans, “Can silicon behave

like graphene? A first-principles study,” Appl. Phys. Lett., vol. 97, no. 11, 2010.

[40] L. C. Lew Yan Voon, E. Sandberg, R. S. Aga, and A. A. Farajian, “Hydrogen

compounds of group-IV nanosheets,” Appl. Phys. Lett., vol. 97, no. 16, pp. 1–4,

119

2010.

[41] R. Wang et al., “Silicene oxides: Formation, structures and electronic properties,”

Sci. Rep., vol. 3, pp. 1–6, 2013.

[42] J. Qiu et al., “Ordered and reversible hydrogenation of silicene,” Phys. Rev. Lett.,

vol. 114, no. 12, pp. 1–5, 2015.

[43] Y. Du et al., “Tuning the band gap in silicene by oxidation,” ACS Nano, vol. 8, no.

10, pp. 10019–10025, 2014.

[44] L. Tao et al., “Silicene field-effect transistors operating at room temperature,” Nat.

Nanotechnol., vol. 10, no. 3, pp. 227–231, 2015.

[45] Y. Ding and J. Ni, “Electronic structures of silicon nanoribbons,” Appl. Phys. Lett.,

vol. 95, no. 8, p. 083115, 2009.

[46] C. C. Liu, H. Jiang, and Y. Yao, “Low-energy effective Hamiltonian involving

spin-orbit coupling in silicene and two-dimensional germanium and tin,” Phys.

Rev. B - Condens. Matter Mater. Phys., vol. 84, no. 19, pp. 1–11, 2011.

[47] L. Chen, B. Feng, and K. Wu, “Observation of a possible superconducting gap in

silicene on Ag(111) surface,” Appl. Phys. Lett., vol. 102, no. 8, 2013.

[48] A. Kara et al., “A review on silicene - New candidate for electronics,” Surf. Sci.

Rep., vol. 67, no. 1, pp. 1–18, 2012.

120

[49] P. De Padova, P. Perfetti, B. Olivieri, C. Quaresima, C. Ottaviani, and G. Le Lay,

“1D graphene-like silicon systems: Silicene nano-ribbons,” J. Phys. Condens.

Matter, vol. 24, no. 22, 2012.

[50] A. Dimoulas, “Silicene and germanene: Silicon and germanium in the ‘flatland,’”

Microelectron. Eng., vol. 131, pp. 68–78, 2015.

[51] L. C. L. Yan Voon and G. G. Guzmán-Verri, “Is silicene the next graphene?,”

MRS Bull., vol. 39, no. 04, pp. 366–373, Apr. 2014.

[52] L. C. Lew Yan Voon, J. Zhu, and U. Schwingenschlögl, “Silicene: Recent

theoretical advances,” Appl. Phys. Rev., vol. 3, no. 4, 2016.

[53] H. H. Hall, J. Bardeen, and G. L. Pearson, “The Effects of Pressure and

Temperature on the Resistance of P-N Junctions in Germanium,” Phys. Rev., vol.

84, no. 1, pp. 129–132, Oct. 1951.

[54] C. S. Smith, “Piezoresistance Effect in Germanium and Silicon,” Phys. Rev., vol.

94, no. 1, pp. 42–49, Apr. 1954.

[55] Welser, Hoyt, and Gibbons, “NMOS and PMOS transistors fabricated in strained

silicon/relaxed silicon-germanium structures,” in International Technical Digest

on Electron Devices Meeting, 1992, pp. 1000–1002.

[56] Y. Sun, S. E. Thompson, and T. Nishida, “Physics of strain effects in

semiconductors and metal-oxide-semiconductor field-effect transistors,” J. Appl.

121

Phys., vol. 101, no. 10, p. 104503, May 2007.

[57] H. Zhao, “Strain and chirality effects on the mechanical and electronic properties

of silicene and silicane under uniaxial tension,” Phys. Lett. Sect. A Gen. At. Solid

State Phys., vol. 376, no. 46, pp. 3546–3550, 2012.

[58] B. Mohan, A. Kumar, and P. K. Ahluwalia, “Electronic and optical properties of

silicene under uni-axial and bi-axial mechanical strains: A first principle study,”

Phys. E Low-Dimensional Syst. Nanostructures, vol. 61, pp. 40–47, 2014.

[59] G. Liu, M. S. Wu, C. Y. Ouyang, and B. Xu, “Strain-induced semimetal-metal

transition in silicene,” Epl, vol. 99, no. 1, 2012.

[60] T. P. Kaloni, Y. C. Cheng, and U. Schwingenschlögl, “Hole doped Dirac states in

silicene by biaxial tensile strain,” J. Appl. Phys., vol. 113, no. 10, pp. 3–7, 2013.

[61] Y. Wang and Y. Ding, “Strain-induced self-doping in silicene and germanene from

first-principles,” Solid State Commun., vol. 155, pp. 6–11, 2013.

[62] R. Qin, W. Zhu, Y. Zhang, and X. Deng, “Uniaxial strain-induced mechanical and

electronic property modulation of silicene,” Nanoscale Res. Lett., vol. 9, no. 1, pp.

1–7, 2014.

[63] R. Qin, C. H. Wang, W. Zhu, and Y. Zhang, “First-principles calculations of

mechanical and electronic properties of silicene under strain,” AIP Adv., vol. 2, no.

2, 2012.

122

[64] B. Mohan, A. Kumar, and P. K. Ahluwalia, “A first principle calculation of

electronic and dielectric properties of electrically gated low-buckled mono and

bilayer silicene,” Phys. E Low-Dimensional Syst. Nanostructures, vol. 53, pp. 233–

239, 2013.

[65] H. Fu, J. Zhang, Z. Ding, H. Li, and S. Meng, “Stacking-dependent electronic

structure of bilayer silicene,” Appl. Phys. Lett., vol. 104, no. 13, 2014.

[66] J. E. Padilha and R. B. Pontes, “Free-standing bilayer silicene: The effect of

stacking order on the structural, electronic, and transport properties,” J. Phys.

Chem. C, vol. 119, no. 7, pp. 3818–3825, 2015.

[67] Z. Ji, R. Zhou, L. C. Lew Yan Voon, and Y. Zhuang, “Strain-Induced Energy

Band Gap Opening in Two-Dimensional Bilayered Silicon Film,” J. Electron.

Mater., vol. 45, no. 10, pp. 5040–5047, 2016.

[68] C. Lian and J. Ni, “Strain induced phase transitions in silicene bilayers: A first

principles and tight-binding study,” AIP Adv., vol. 3, no. 5, 2013.

[69] T. Morishita, M. J. S. Spencer, S. P. Russo, I. K. Snook, and M. Mikami, “Surface

reconstruction of ultrathin silicon nanosheets,” Chem. Phys. Lett., vol. 506, no. 4–

6, pp. 221–225, 2011.

[70] Y. Aierken, O. Leenaerts, and F. M. Peeters, “A first-principles study of stable

few-layer penta-silicene,” Phys. Chem. Chem. Phys., vol. 18, no. 27, pp. 18486–

123

18492, 2016.

[71] P. Zhang, X. D. Li, C. H. Hu, S. Q. Wu, and Z. Z. Zhu, “First-principles studies of

the hydrogenation effects in silicene sheets,” Phys. Lett. Sect. A Gen. At. Solid

State Phys., vol. 376, no. 14, pp. 1230–1233, 2012.

[72] M. Houssa, E. Scalise, K. Sankaran, G. Pourtois, V. V. Afanas’Ev, and A.

Stesmans, “Electronic properties of hydrogenated silicene and germanene,” Appl.

Phys. Lett., vol. 98, no. 22, pp. 96–99, 2011.

[73] B. Huang et al., “Exceptional optoelectronic properties of hydrogenated bilayer

silicene,” Phys. Rev. X, vol. 4, no. 2, pp. 1–12, 2014.

[74] Y. Liu, H. Shu, P. Liang, D. Cao, X. Chen, and W. Lu, “Structural, electronic, and

optical properties of hydrogenated few-layer silicene: Size and stacking effects,” J.

Appl. Phys., vol. 114, no. 9, 2013.

[75] “Telstra 4G (LTE) on the Next G® network.” [Online]. Available:

http://web.archive.org/web/20120207145300/http://www.telstra.com.au/mobile-

phones/coverage-networks/network-information/4g/.

[76] ITRS, “Radio Frequency and Analog/Mixed Signal Technologies,” Int. Technol.

Roadmap Semicond., p. 38, 2013.

[77] A. C. Ferrari et al., “Science and technology roadmap for graphene, related two-

dimensional crystals, and hybrid systems,” Nanoscale, vol. 7, no. 11, pp. 4598–

124

4810, 2015.

[78] Y. M. Lin et al., “100-GHz transistors from wafer-scale epitaxial graphene,”

Science (80-. )., vol. 327, no. 5966, p. 662, 2010.

[79] F. Schwierz, “Graphene transistors,” Nat. Nanotechnol., vol. 5, no. 7, pp. 487–496,

Jul. 2010.

[80] Y. Wu et al., “State-of-the-art graphene high-frequency electronics,” Nano Lett.,

vol. 12, no. 6, pp. 3062–3067, 2012.

[81] L. Liao et al., “High-speed graphene transistors with a self-aligned nanowire gate,”

Nature, vol. 467, no. 7313, pp. 305–308, 2010.

[82] R. Cheng et al., “High-frequency self-aligned graphene transistors with transferred

gate stacks,” Proc. Natl. Acad. Sci., vol. 109, no. 29, pp. 11588–11592, Jul. 2012.

[83] K. Kanghyun, J. P. Hyung, B. C. Woo, J. K. Kook, T. K. Gyu, and S. Y. Wan,

“Electric property evolution of structurally defected multilayer grapheme,” Nano

Lett., vol. 8, no. 10, pp. 3092–3096, 2008.

[84] Y. Wu et al., “Microwave transmission properties of chemical vapor deposition

graphene,” Appl. Phys. Lett., vol. 101, no. 5, pp. 99–102, 2012.

[85] Y. Wu et al., “Characterization of CVD graphene permittivity and conductivity in

micro-/millimeter wave frequency range,” AIP Adv., vol. 6, no. 9, 2016.

125

[86] E. H. Synge, “A suggested method for extending microscopic resolution into the

ultra-microscopic region,” London, Edinburgh, Dublin Philos. Mag. J. Sci., vol. 6,

no. 35, pp. 356–362, Aug. 1928.

[87] D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with

resolution λ/20,” Appl. Phys. Lett., vol. 44, no. 7, pp. 651–653, Apr. 1984.

[88] A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 Å

spatial resolution light microscope,” Ultramicroscopy, vol. 13, no. 3, pp. 227–231,

Jan. 1984.

[89] K. S. K. S. Novoselov, “Electric Field Effect in Atomically Thin Carbon Films,”

Science (80-. )., vol. 306, 2004.

[90] A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The

electronic properties of graphene,” vol. 81, no. March, 2007.

[91] E. V. Castro et al., “Limits on charge carrier mobility in suspended graphene due

to flexural phonons,” Phys. Rev. Lett., vol. 105, no. 26, pp. 16–18, 2010.

[92] K. S. K. S. Novoselov and A. K. a. K. Geim, “The rise of graphene,” Nat. Mater.,

vol. 6, no. 3, pp. 183–191, 2007.

[93] D. C. Elias et al., “Dirac cones reshaped by interaction effects in suspended

graphene,” Nat. Phys., vol. 7, no. 9, pp. 701–704, 2011.

[94] Yu-Ming Lin, Hsin-Ying Chiu, K. a. Jenkins, D. B. Farmer, P. Avouris, and A.

126

Valdes-Garcia, “Dual-Gate Graphene FETs With fT of 50 GHz,” IEEE Electron

Device Lett., vol. 31, no. 1, pp. 68–70, 2010.

[95] F. Xia, D. B. Farmer, Y. M. Lin, and P. Avouris, “Graphene field-effect transistors

with high on/off current ratio and large transport band gap at room temperature,”

Nano Lett., vol. 10, no. 2, pp. 715–718, 2010.

[96] P. Hohenberg and W. Kohn, “Inhomogeneous Electron Gas,” Phys. Rev., vol. 136,

no. 3B, pp. B864–B871, Nov. 1964.

[97] A. D. Becke, “Perspective: Fifty years of density-functional theory in chemical

physics,” J. Chem. Phys., vol. 140, no. 18, p. 18A301, May 2014.

[98] J. P. Perdew, S. Kurth, A. Zupan, and P. Blaha, “Accurate Density Functional with

Correct Formal Properties: A Step Beyond the Generalized Gradient

Approximation,” Phys. Rev. Lett., vol. 82, no. 12, pp. 2544–2547, Mar. 1999.

[99] J. P. Perdew and Y. Wang, “Accurate and simple analytic representation of the

electron-gas correlation energy,” Phys. Rev. B, vol. 45, no. 23, pp. 13244–13249,

Jun. 1992.

[100] J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized Gradient Approximation

Made Simple,” Phys. Rev. Lett., vol. 77, no. 18, pp. 3865–3868, Oct. 1996.

[101] M. Gmitra and J. Fabian, “First-principles studies of orbital and spin-orbit

properties of GaAs, GaSb, InAs, and InSb zinc-blende and wurtzite

127

semiconductors,” Phys. Rev. B, vol. 94, no. 16, 2016.

[102] G. Henkelman, G. Jóhannesson, and H. Jónsson, “Methods for Finding Saddle

Points and Minimum Energy Paths,” in Theoretical Methods in Condensed Phase

Chemistry, Dordrecht: Kluwer Academic Publishers, pp. 269–302.

[103] B. Schaefer, S. Alireza Ghasemi, S. Roy, and S. Goedecker, “Stabilized quasi-

Newton optimization of noisy potential energy surfaces,” J. Chem. Phys., vol. 142,

no. 3, pp. 1–11, 2015.

[104] Y. Ding and Y. Wang, “Electronic structures of silicene/GaS heterosheets,” Appl.

Phys. Lett., vol. 103, no. 4, 2013.

[105] H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,”

Phys. Rev. B, vol. 13, no. 12, pp. 5188–5192, Jun. 1976.

[106] M. Brandbyge, J.-L. Mozos, P. Ordejón, J. Taylor, and K. Stokbro, “Density-

functional method for nonequilibrium electron transport,” Phys. Rev. B, vol. 65,

no. 16, p. 165401, Mar. 2002.

[107] D. Stradi, U. Martinez, A. Blom, M. Brandbyge, and K. Stokbro, “General

atomistic approach for modeling metal-semiconductor interfaces using density

functional theory and nonequilibrium Green’s function,” Phys. Rev. B, vol. 93, no.

15, p. 155302, Apr. 2016.

[108] B. Lalmi et al., “Epitaxial growth of a silicene sheet,” Appl. Phys. Lett., vol. 97,

128

no. 22, pp. 223107–223109, 2010.

[109] S. Cahangirov, M. Topsakal, E. Aktürk, H. Šahin, and S. Ciraci, “Two- and one-

dimensional honeycomb structures of silicon and germanium,” Phys. Rev. Lett.,

vol. 102, no. 23, pp. 1–4, 2009.

[110] Q. Peng, X. Wen, and S. De, “Mechanical stabilities of silicene,” RSC Adv., vol. 3,

no. 33, p. 13772, 2013.

[111] N. B. Le, T. D. Huan, and L. M. Woods, “Tunable Spin-Dependent Properties of

Zigzag Silicene Nanoribbons,” Phys. Rev. Appl., vol. 1, no. 5, pp. 1–6, 2014.

[112] S. Kokott, P. Pflugradt, L. Matthes, and F. Bechstedt, “Nonmetallic substrates for

growth of silicene: An ab initio prediction,” J. Phys. Condens. Matter, vol. 26, no.

18, 2014.

[113] L. Meng et al., “Buckled silicene formation on Ir(111),” Nano Lett., vol. 13, no. 2,

pp. 685–690, 2013.

[114] A. Bhattacharya, S. Bhattacharya, and G. P. Das, “Exploring semiconductor

substrates for silicene epitaxy,” Appl. Phys. Lett., vol. 103, no. 12, 2013.

[115] Y. Kim et al., “Remote epitaxy through graphene enables two-dimensional

material-based layer transfer,” Nature, vol. 544, no. 7650, pp. 340–343, 2017.

[116] J. Chauhan, L. Liu, Y. Lu, and J. Guo, “A computational study of high-frequency

behavior of graphene field-effect transistors,” J. Appl. Phys., vol. 111, no. 9, 2012.

129

[117] C.-W. Chen, C.-T. Chung, J.-C. Lin, G.-L. Luo, and C.-H. Chien, “High On/Off

Ratio and Very Low Leakage in p + /n and n + /p Germanium/Silicon

Heterojunction Diodes,” Appl. Phys. Express, vol. 6, no. 2, p. 024001, Feb. 2013.

[118] F. Xia, D. B. Farmer, Y. Lin, and P. Avouris, “Graphene Field-Effect Transistors

with High On/Off Current Ratio and Large Transport Band Gap at Room

Temperature,” Nano Lett., vol. 10, no. 2, pp. 715–718, Feb. 2010.

[119] J. Lee et al., “RF Performance of Pre-patterned Locally-embedded-Back-Gate

Graphene Device,” vol. 2, no. c, pp. 568–571, 2010.

[120] Y. Wu et al., “High-frequency, scaled graphene transistors on diamond-like

carbon,” Nature, vol. 472, no. 7341, pp. 74–78, 2011.

[121] I. Meric, N. Baklitskaya, P. Kim, and K. L. Shepard, “RF performance of top-

gated, zero-bandgap graphene field-effect transistors,” Tech. Dig. - Int. Electron

Devices Meet. IEDM, no. c, pp. 2–5, 2008.

[122] Y.-M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P.

Avouris, “Operation of Graphene Transistors at Gigahertz Frequencies,” Nano

Lett., vol. 9, no. 1, pp. 422–426, 2009.

[123] J. S. Moon et al., “Epitaxial-graphene RF field-effect transistors on Si-face 6H-SiC

substrates,” IEEE Electron Device Lett., vol. 30, no. 6, pp. 650–652, 2009.

[124] J. S. Bunch et al., “Electromechanical resonators from Graphene Sheets,” Science

130

(80-. )., vol. 315, pp. 490–493, 2007.

[125] Y. Xu et al., “Radio frequency electrical transduction of graphene mechanical

resonators,” Appl. Phys. Lett., vol. 97, no. 24, 2010.

[126] K. M. Milaninia, M. A. Baldo, A. Reina, and J. Kong, “All graphene

electromechanical switch fabricated by chemical vapor deposition,” Appl. Phys.

Lett., vol. 95, no. 18, pp. 2007–2010, 2009.

[127] L. Liao et al., “Scalable fabrication of self-aligned graphene transistors and circuits

on glass,” Nano Lett., vol. 12, no. 6, pp. 2653–2657, 2012.

[128] Y. M. Lin et al., “Wafer-scale graphene integrated circuit,” Science (80-. )., vol.

332, no. 6035, pp. 1294–1297, 2011.

[129] D.-Y. Jeon et al., “Radio-Frequency Electrical Characteristics of Single Layer

Graphene,” Jpn. J. Appl. Phys., vol. 48, no. 9, p. 091601, 2009.

[130] H. J. Lee, E. Kim, J. G. Yook, and J. Jung, “Intrinsic characteristics of

transmission line of graphenes at microwave frequencies,” Appl. Phys. Lett., vol.

100, no. 22, pp. 1–4, 2012.

[131] H. J. Lee et al., “Radio-frequency characteristics of graphene monolayer via nitric

acid doping,” Carbon N. Y., vol. 78, pp. 532–539, 2014.

[132] I. Meric, M. Y. Han, A. F. Young, B. Ozyilmaz, P. Kim, and K. L. Shepard,

“Current saturation in zero-bandgap, top-gated graphene field-effect transistors,”

131

Nat. Nanotechnol., vol. 3, no. 11, pp. 654–659, 2008.

[133] K. S. Novoselov, V. I. Fal’Ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K.

Kim, “A roadmap for graphene,” Nature, vol. 490, no. 7419, pp. 192–200, 2012.

[134] D. G. Papageorgiou, I. A. Kinloch, and R. J. Young, “Progress in Materials

Science Mechanical properties of graphene and graphene-based nanocomposites,”

Prog. Mater. Sci., vol. 90, pp. 75–127, 2017.

[135] X. Fan et al., “Direct observation of grain boundaries in graphene through vapor

hydrofluoric acid ( VHF ) exposure,” pp. 1–10, 2018.

[136] D. C. Kim, D. Y. Jeon, H. J. Chung, Y. Woo, J. K. Shin, and S. Seo, “The

structural and electrical evolution of graphene by oxygen plasma-induced

disorder,” Nanotechnology, vol. 20, no. 37, 2009.

[137] F. Banhart, J. Kotakoski, and A. V. Krasheninnikov, “Structural Defects in

Graphene,” ACS Nano, vol. 5, no. 1, pp. 26–41, Jan. 2011.

[138] L. Vicarelli, S. J. Heerema, C. Dekker, and H. W. Zandbergen, “Controlling

Defects in Graphene for Optimizing the Electrical Properties of Graphene

Nanodevices,” ACS Nano, vol. 9, no. 4, pp. 3428–3435, Apr. 2015.

[139] S. Lee and Z. Zhong, “Nanoelectronic circuits based on two-dimensional atomic

layer crystals,” Nanoscale, vol. 6, no. 22, pp. 13283–13300, 2014.

[140] M. Farina et al., “Inverted scanning microwave microscope for in vitro imaging

132

and characterization of biological cells,” Appl. Phys. Lett., vol. 114, no. 9, p.

093703, Mar. 2019.

[141] Z. E. Al I, Peter Nemes Osvath, “Anomalies in thickness measurements of

graphene and FLG crystals by tapping mode AFM,” Carbon N. Y., vol. 46, no. 11,

pp. 1435–42, 2008.

[142] K. Brockdorf et al., “Imaging of edge inactive layer in micro-patterned graphene

monolayer,” Mater. Lett., vol. 211, pp. 183–186, 2018.

[143] N. A. Engel, “Functionalization and Characterization of Chemical Vapor

Deposited Graphene Sheets Towards Application in Chemical Vapor Sensing,”

2018.

[144] I. Childres, L. A. Jauregui, J. Tian, and Y. P. Chen, “Effect of oxygen plasma

etching on graphene studied using Raman spectroscopy and electronic transport

measurements,” New J. Phys., vol. 13, 2011.

[145] Y. Xing, J. Myers, O. Obi, N. X. Sun, and Y. Zhuang, “Scanning microwave

microscopy characterization of spin-spray-deposited ferrite/nonmagnetic films,” J.

Electron. Mater., vol. 41, no. 3, pp. 530–534, 2012.

[146] J. Myers, S. Mou, K.-H. Chen, and Y. Zhuang, “Scanning microwave microscope

imaging of micro-patterned monolayer graphene grown by chemical vapor

deposition,” Appl. Phys. Lett., vol. 108, no. 5, p. 053101, 2016.

133

[147] M. Sadiku, Numerical Techniques in Electromagnetics. 2000.

[148] Z. Ji et al., “Microwave imaging of etching-induced surface impedance

modulation of graphene monolayer.”

[149] S. M. Levy, Construction Calculations Manual. Elsevier, 2012.

[150] P. Nemes-Incze, Z. Osváth, K. Kamarás, and L. P. Biró, “Anomalies in thickness

measurements of graphene and few layer graphite crystals by tapping mode atomic

force microscopy,” Carbon N. Y., vol. 46, no. 11, pp. 1435–1442, 2008.

134