Interface Engineering of Band Evolution and Transport Properties of

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Interface Engineering of Band Evolution and Transport Properties of Bilayer WSe under Different Electric Fields 2

Zhe Zhang, Jiling Li, Guowei Yang, and Gang Ouyang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b06828 • Publication Date (Web): 22 Jul 2019 Downloaded from pubs.acs.org on July 25, 2019

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The Journal of Physical Chemistry

Interface Engineering of Band Evolution and Transport Properties of Bilayer WSe2 under Different Electric Fields Zhe Zhang,† Jiling Li,‡ Guowei Yang‡ and Gang Ouyang*,† † Key

Laboratory of Low-Dimensional Quantum Structures and Quantum Control of

Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Hunan Normal University, Changsha 410081, China ‡

State Key Laboratory of Optoelectronic Materials and Technologies, Institute of

Optoelectronic and Functional Composite Materials, Nanotechnology Research Center, School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, Guangdong, China

Abstract The van der Waals (vdW) coupling modulation is a crucial method for the designing of the physical performance in bilayer transition metal dichalcogenides (TMDs). Here we report the band evolution and quantum transport properties of twisted bilayer WSe2 under the approach of vertical electric fields by utilizing first-principles calculations. We find that the bandgap type of bilayer WSe2 can be transformed from indirect-to-direct by twisting two monolayers. The external electric field can enable the bilayer WSe2 under six twist angles to achieve a semiconductor-to-metal transition. Especially, the stacking structures of 0° and 60° show transport anisotropy, and the transport performance in the zigzag (ZZ) direction is slightly better than that in the armchair (AC) direction. Moreover, the transport performance of the case with twisted 60° is better than that of 0° regardless of edge direction when external electric field is applied. Our results are conducive to the design and application of future WSe2-based microelectronics and optoelectronic devices. 1

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* Corresponding author: [email protected]

1. Introduction Since graphene has been proved to be stable by mechanical exfoliation,1 two-dimensional (2D) materials have attracted extensive attention and research with their unique properties. In general, the atomic layers of 2D materials are combined by vdW coupling and can be made into monolayer or few-layers by molten salts method,2 chemical vapor deposition,3-4 scalable salt-templated synthesis5, and liquid exfoliation,6-7 etc. The maturity of 2D material preparation technology facilitates its in-depth and systematic research, which opens a way for the application of band engineering by utilizing alloying,8 strain,9 thickness,10 formation of superlattice,11 external electric field (E),12 and interface twist,13-17 etc. Among these modulation strategies, the methods through twist and external E have greatly promoted for the breakthrough of exploration of novel physical phenomena. For example, the intrinsic unconventional superconductivity,18 correlated insulating behavior,19 atomic scale reconstruction,20 and transport through the network of topological channels20-21 can be achieved by twisting two graphene sheets at a small angle. Also, ultraflatbands and shear solitons caused by the structural reconstruction in moiré pattern have been found in twisted bilayer MoS2.22 Moreover, E can not only open a bandgap of bilayer graphene,23-24 but also transform bilayer TMDs from semiconductor-to-metal.25 Whether in fundamental physical properties or microelectronic applications, WSe2 is favored as an emerging 2D material with superior performance, such as spin-layer locking effects,26 Shubnikov-de Haas oscillations,27 and piezoelectricity.28 Moreover, the non-volatile programmable vertical stacked p-n junction displays a rectification ratio of up to 104 and the power conversion efficiency (PCE) is as high as 2


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4.1%.29 The BP/WSe2 p-n junction diode shows an external quantum efficiency of 23%, an open-circuit voltage of 0.35 V, and the PCE can reach 1.7%.30 However, even though the interface twist and external field play the crucial role for the electronic/optoelectronic properties of 2D systems, the related modulation mechanism for the bilayer WSe2 has not been systematically explored. The in-depth investigation and exploration of bilayer WSe2 will afford a fundamental understanding of the vdW interaction of stacked 2D structures, which is of great significance for the application of WSe2-based devices. Therefore, in this work, we study the band evolution and quantum transport of twisted bilayer WSe2 under external E in terms of first-principles calculations. Our results indicate that the band offset of twisted bilayer WSe2 can be affected by the interface engineering and external stimulus, which provide some useful methods to design the new type of electronic nanodevices.

2. Methods The bulk WSe2 belongs to the space group 194 with a hexagonal structure and each conventional unit cell has 6 atoms. First, we calculate the lattice parameters of bulk WSe2 are ab  bb  3.282 Å and cb  12.96 Å, which are consistent with the theoretical values10 and experimental measurement.31 The structures of the bilayer WSe2 with different rotation angles are obtained by twisting two monolayer WSe2 films. Simultaneously, the supercells at different rotation angles are geometrically optimized to obtain the corresponding lattice constants, which is to search for the equilibrium structure between finding the minimum lattice mismatch and the minimum number supercell atoms. Figure 1 shows the bilayer WSe2 supercell with different twist angles. Notably, we define the configuration in Figure 1a (the stack 3



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structure is the same as the 2H bulk WSe2) as the initial structure with the twist angle of zero. The lattice parameters of initial unit supercell of bilayer WSe2 are abg1  bbg1  3.323 Å , abg 3  bbg 3  8.796 Å ,

the

lattice

constants

abg 4  bbg 4  8.797 Å ,

including

abg 2  bbg 2  14.492 Å ,

abg 5  bbg 5  14.492 Å ,

and

abg 6  bbg 6  3.325 Å correspond to the twist angles of 13.17°, 21.79°, 38.21°, 46.83°

and 60°, respectively (see Figure 1b, 1c, 1d, 1e, and 1f, respectively). Our calculations of electronic band structure and transport properties in bilayer WSe2 are enforced by density functional theory (DFT) coupled with non-equilibrium Green’s

functions

(NEGF),32

which

is

accomplished

in

the

Virtual

NanoLab-Atomistic ToolKit (VNL-ATK) package. The VNL-ATK package in conjunction with linear combination of atomic orbitals (LCAO) method within the generalized gradient approximations (GGA) of Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional is used.33 The electron wave function is expanded using the SG1534-36 pseudopotential and the basis set is chosen to high accuracy. The density mesh cutoff energy was set to be 360 Ry for all calculations. The Monkhorst-Pack κ-point grid37 of 16 16 1 , 4  4 1 , 6  6 1 , 6  6 1 , 4  4 1 , and 16 16 1 are applied to the calculations for different twist angles of 0°, 13.17°, 21.79°, 38.21°, 46.83°, and 60°, respectively, which can ensure the bilayer WSe2 having same sampling density under different twist angles in the reciprocal space. In the process of obtaining six rotation angles by twisting two monolayers, the strain caused by lattice mismatch is all zero. The long-range vdW coupling will be comprised through the semi-empirical Grimme38 correction which does not attempt to delineate the actual source of the interaction (fluctuating dipoles) but rather its impact on the DFT mean-field effective potential. The DFT-D2 functional exploited by Grimme38 augments an extra portion to the DFT total energy for purpose of 4


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accounting for vdW coupling, or dispersion forces. However, if we employ the Grimme correction but do not take basis set superposition error (BSSE) into consideration, the interlayer distance between two monolayers is not sufficiently accurate owning to incompleteness of the LCAO basis set. Therefore, to consider the vdW coupling in the bilayer WSe2, we have merged Grimme DFT-D2 semi-empirical correction38 as established in the ATK informix in association with counterpoise correction39 to process the BSSE of LCAO basis sets. The unit cell with periodic boundary condition was applied to simulate bilayer WSe2. The layered structures are positioned in the x-y plane, and a vacuum thickness of 16 Å is employed to suppress interaction between periodic images of slabs in the z direction. The geometric structures are optimized by the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm.40 All atoms of optimized structure are relaxed and the final forced exerted on each atom is less than 0.01 eV/Å for each ionic step and maximum stress tolerance smaller than 0.001 eV/Å3. In the calculations of band structure, we collected 100 points along each high-symmetry line in reciprocal space. Only 20 (or 10) points are taken as a demonstration in diagrams and the Fermi level is set as zero.

3. Results and discussion Table 1 lists the interlayer spacing dSe (the average distance from the nearest Se atom) and d W (the average distance from the nearest W atom) under different twist angles. Evidently, the twist angle of 0° has the minimum interlayer spacing, while the 60° corresponds to the largest interlayer spacing. The distance between interlayers reflects the sensitivity to outfield action.25 Large interlayer spacing means high sensitivity. In the light of average energy at 0° angle, the relative average energy of other twist angles can be defined as 5



E 

E E0  N N 0

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(1)

where E ( N ) stands for the total energy (total atomic number of supercell) as the twist angle is  . Thus, the case of 0° angle corresponds to the most stable structure. Also, the average binding energy can be defined as

Eb  ( EB  EMT  EMB ) N

(2)

where EB represents the total energy of bilayer WSe2, EMT ( EMB ) stands for the total energy at the top (bottom) monolayer, and N is the total atomic number of bilayer WSe2 supercell. It can be obtained from Table 1 that the average binding energy is the lowest when the twist angle is 0°, which is consistent with the relative average energy and it means that the 0° twist angle structure has the highest stability. Note that the bandgaps under different twist angles are also listed in Table 1. Figure 2 shows the projected band structure (PBS) and related projected density of states (PDOS) of bilayer WSe2 under different twist angles. Specifically, the bandgaps are 1.4423, 1.5170, 1.5215, 1.5269, 1.5199, and 1.5172 eV at twist angles of 0°, 13.17°, 21.79°, 38.21°, 46.83°, and 60°, respectively (see Figure 2a, 2b, 2c, 2d, 2e, and 2f, respectively). No matter how the bilayer WSe2 films are relatively twisted, the conduction band minimum (CBM) and valence band maximum (VBM) are principally determined by the d-orbitals of W atoms and p-orbitals of Se atoms, respectively. Specifically, for the 0° twist angle, the CBM is basically contributed by the d xy and d x2  y 2 states of W atoms, while the VBM is mostly composed of d z 2 state of W atoms and p z state of Se atoms. For the cases of 13.17° and 46.83°, the CBM is primarily occupied by the d z 2 and d xy states of W atoms, while the VBM is largely taken up by d xy and d x2  y 2 states of W atoms. In addition, for the cases of 6


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21.79° and 38.21°, the main contribution of CBM comes from d z 2 state of W atoms. and the prime contribution of VBM comes from d xy and d x2  y 2 states of W atoms. As for the 60° twist angle, the CBM and VBM are primarily composed of

d xy and

d x2  y 2 states of W atoms. Interestingly, except for the initial bilayer WSe2 of 0°, the PBSs of other five twist angles show direct bandgap. The relative twisting of the two monolayers increases the interlayer spacing, which causes the bandgap to transform from indirect-to-direct. This phenomenon has not been found when twisting other TMDs.13, 15-16, 41 However, some researchers have reported that there will be a direct bandgap in the process of twisting bilayer blue phosphorus.42 When two monolayers are twisted to form five twist angles, the strain caused by the lattice mismatch is all zero, hence, it is the effect of vdW coupling that leads to the change of bandgap type from indirect-to-direct. Especially, the interlayer spacing plays a crucial role in vdW coupling. In order to verify our predictions, we have approached two related issues: first, we enhance the interlayer spacing at 0° twist angle and find the change of bandgap type from indirect-to-direct when the interlayer spacing increases to dSe=4.00 Å (dW=7.36 Å); second, we reduce the interlayer spacing at interface twist of 60° and find the change of bandgap type from direct-to-indirect when the interlayer spacing decreases to dSe=3.80 Å (dW=7.16 Å). This means that the electronic orbital coupling in bilayer WSe2 is largely decided by the interlayer spacing and does not depend particularly on the horizontal matching of the two monolayers. Long et al.43 also indicated that the interlayer spacing of bilayer MoS2 is greater than 6.9 Å, the bandgap will change from indirect-to-direct, which is consistent with our calculations. Moreover, the bandgap is proportional to the interlayer spacing for the same structure, and the larger the interlayer spacing, the larger the bandgap. Interestingly, agreement 7



results have also been found in the bilayer MoS215 and InSe.44 In general, the external E has an important regulatory effect on the band structure of semiconductors. For example, the external vertical E can open the bandgap of the bilayer graphene,23-24,

45

and also reduce the bandgap of bilayer InSe,44 or bilayer

MoS2.25, 46 In addition, by applying E in different directions, the bandgap of bilayer BP/MoS2 can be increased or decreased to achieve the semiconductor-to-metal transformation.12, 47 Therefore, we investigated the influence of a vertical external E on the electronic band structures of bilayer WSe2 with different twist angles. Figure 3 shows the evolution of bandgaps as a function of E with six different twist angles. Clearly, it reveals that the bandgaps of bilayer WSe2 can be modified by E. Under the condition of E, the bandgap evolution has similar variation trend regardless of different twist angles, which can be summarized by the primary impact of the E on the space charge distribution of the lowest energy electrons and holes pairs. The potential difference between two monolayers can be caused by an external vertical E. Consequently, the energy bands belonging to different WSe2 layers are completely separated from each other. In the WSe2 bilayer, as the E strength increases, the band splitting enlarges, eventually resulting in a smaller bandgap. Specifically, when applying E on the bilayer WSe2, the bandgap has undergone linear and slow reduction, and then gradually realizes the transition from semiconductor-to-metallization. For the intra-layer WSe2, the holes move in the direction of the electric field while the electrons run the opposite directions, they are highly localized on both sides, which causes the conduction band bottom and the valence band top of the bilayer WSe2 to approach each other. As the electric field strength increases, the transition from semiconductor-to-metal will be realized eventually. Similarly, at larger E, the bandgap of BN nanoribbons will also gradually close, which is induced by the 8


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near-free electron state motion under the strong E.48 Interestingly, at 0° twist angle, the bandgap experiences a slow decrease before linear reduction and similar phenomena have been found in other bilayer TMDs.25 The reason is that the bandgap type is indirect during the process. No such change was found in the other twist angles of bilayer WSe2, it is the twist angle that causes an increase of interlayer spacing between two monolayers, which makes the twisted bilayer WSe2 show a direct bandgap type. For the linear reduction of bandgap at a slightly larger E strength, the relationship among the slope of the curve, the bandgap, and E strength can be expressed as

dEg dE

 eS

(3)

where S is the linear coefficient of giant Stark effect25, 49 and e is the electron charge. Meanwhile, the potential difference can be described as46

U  eE*d

(4)

where d is the interlayer spacing and E* represents the effective E (internal E that caused by charge redistribution plus external E). Here, the external E plays a leading role. Hence, the variation of bandgap can be approximately expressed as

Eg  eE  z  cb  eE  z  vb

(5)

where  z  vb ( z  cb ) is the center of valence (conduction) band along the direction of E. This is basically equivalent to a hypothetical two-band model where the conduction band and the valence band experience a rigid displacement (in the opposite direction) in respond to the external vertical E. The slopes S obtained by fitting the linearly decreasing parts of the six twist angles (0°, 13.17°, 21.79°, 38.21°, 46.83°, and 60°, respectively) are 1.45, 1.86, 1.85, 1.74, 1.86, and 2.35 Å, respectively. As can be seen 9



from Table 1, the slope is related to the interlayer spacing and the relationship can be approximated as S  d 2 . The larger the interlayer spacing, the greater the slope, the more sensitive it is to the external vertical E, and the larger interlayer spacing means a faster bandgap reduction. In order to systematically investigated the impact of E on the band structure, we calculate the PDOS and PBS with different twist angles and different E strengths. However, we only choose 0° twist angle to illustrate. There are two main reasons: first, the 0° twist angle experiences the most complex changes under an external E. For example, no nonlinear reduction in weak E intensity is found at other twist angles of the bilayer WSe2. Second, the lattice structure of 0° twist angle is the same as that of the most stable bulk structure (2H) WSe2, which can be easily verified by experiments and applied in related microelectronic fields. Figure 4 shows the PBS and PDOS of the 0° twist angle bilayer WSe2 at different E. In detail, Figure 4a reveals the PBS and PDOS at zero E strength, where the CBM located at midpoint D between Γ and K, and the VBM situated at point V. Meanwhile, there is an indirect bandgap of 1.44 eV. Our results for the band structure and bandgap are the same as related studies.10 When a weak E (E < 0.1 V/Å) is applied in Figure 4b, the energy level at point C decreases while the bandgap is still indirect. Until the E reaches 0.1 V/Å (see Figure 4c), point C gains an advantage in competing with the energy level of point D, becoming a new CBM. At the same time, the bandgap has changed from indirect-to-direct. In the process of enhancement of E to 1 V/Å is described in Figure 4d, we can see that the bandgap decreases linearly. Figure 4e and 4f show the gradual conversion from semiconductor-to-metal at 1.125 and 1.15 V/Å, respectively. Importantly, the clarification of modulation mechanism on the bandgap engineering in bilayer WSe2 is beneficial to meet the various applications in the field of 10


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optoelectronics Due to its excellent performance, WSe2 has broad prospects in the fields of optoelectronics and microelectronics. For example, electrostatically doped bipolar monolayer WSe2 can be made into p-n junction,50-51 light-emitting diode, and photovoltaic solar cell.52 However, the electronic transport characteristics in bilayer WSe2, which are directly concerned with the capability of electronic equipment, have not been systematically researched. In order to facilitate the application of bilayer WSe2 for the high-performance equipment, detailed research on the stacking and anisotropic electron transport of bilayer WSe2 is required. Figure 5a shows that a dual-gated bilayer WSe2 field effect transistor combined with SiO2 dielectric layer. The dual-gate strategy has the advantage of controlling electrostatic doping level and vertical E compared to a single-gate field effect transistor. Vb and Vt represent the bottom and top gate voltages, respectively. The height between the two gates is set to

d h  39.5 Å . The dielectric constant of SiO2,   3.9 and its thickness is set to d d  9.75 Å . Thus, the total doping level Vg and vertical E can be written as follows: Vg  Vt  Vb E

(6)

Vt  Vb d h  2d d  2d d / 

(7)

where the bias voltage and total doping level are set to zero. In our consideration, the transport performance of bilayer WSe2 is studied by calculating the orthorhombic structure (blue dotted box in Figure 5a) rather than the whole device. This avoids errors that Fermi level shifts and possible Schottky barriers (or ohmic contact resistance) due to the contact between metal electrodes and semiconductor. Figure 5b depicts the top and side views of the orthorhombic unit cell at 0° twist angle. Since WSe2 is anisotropic,53-54 the transport properties in AC and ZZ directions have been 11



studied. The top and side views of Figure 5c correspond to 60° twist angle. Figure 5d shows the transmission spectra of bilayer WSe2 stacked at 0° and 60° in the AC direction. In the absence of E, the difference between transmission gaps (TGs) of 0° (1.45 eV) and 60° (1.55 eV) stacked structures is very small, where the TG corresponds to the bandgap. The transmission coefficients at negative energies are also similar. However, when an E strength of 0.4 V/Å is applied as shown in Figure 5d, the 60° stacked structure has higher transmission coefficient and smaller TG at the same energy (-1.0 ~ 0.66 eV), which means better transport performance. The inserts in Figure 5d shows the variation of TG as a function of E. Larger slope means that the 60° twist angle is more sensitive to E and easier to be modulated. A similar conclusion can be found in Figure 5e, which shows the transmission spectrum of the bilayer WSe2 of 0° and 60° stacked structures in the ZZ direction. Therefore, the 0° stacked structure has slightly better transmission characteristics in both AC and ZZ directions when the E strength is 0. However, the 60° stacked structure exhibits better transmission performance under E due to the greater interlayer spacing and the sensitivity of vdW interaction. Figure 5f shows the anisotropy of the transmission spectrum along the AC and ZZ directions when the bilayer WSe2 is stacked at 0°. Whether there is an E or not, the ZZ direction has a slightly smaller TG and a larger transmission coefficient at each energy. This reflects that the transport property in the ZZ direction is superior to that in the AC direction. The illustration in Figure 5f depicts that the TG along the ZZ direction is always smaller than that along the AC direction regardless of E intensity. It happens that there is a similar case in Figure 5g, which exhibits the anisotropy of the transmission spectrum along the AC and ZZ directions when the bilayer WSe2 is stacked at 60°. Therefore, our results provide a better understanding of transport performance of bilayer WSe2-based electronic 12


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devices and facilitate the design of optimal structures that meet expected functions.

4. Conclusions In the light of DFT and NEGF, we study the electronic and transport properties of bilayer WSe2. We find that the interface twisting of two monolayers can increase the bandgap of bilayer WSe2 and change the bandgap type from indirect-to-direct, which is caused by the different vdW coupling determined by the interlayer spacing. The external E linearly reduces the bandgap of bilayer WSe2, and then gradually changes to 0, which realizes the transition from semiconductor-to-metal. In addition, the application of E can also transform the bandgap type of bilayer WSe2 from indirect-to-direct. The effect of external E on the band structure is realized by changing the lowest energy electron and hole pairs. Whether in the AC or ZZ direction, the 0° stacked structure has slightly better transmission characteristics when the E strength is 0, while the 60° stacked structure shows better transmission performance under E modulation due to the greater interlayer spacing and the sensitivity of the vdW interaction to the external E. Moreover, the stacking structures of 0° and 60° show the transport anisotropy, and the transport performance in the ZZ direction is slightly better than that in the AC direction. Therefore, our work provides a reliable and useful guidance for the understanding of the fundamental properties of bilayer WSe2.

Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 11574080 and 91833302).

13



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Table 1. The twist angle θ, interlayer spacing dSe , d W , relative average energy E , average binding energy Eb , and bandgap Eg of bilayer WSe2 under different twist angles.

θ

dSe (Å)

dW (Å)

∆E (meV)

Eb (meV)

Eg (eV)

0°

3.41

6.77

0

-98.66

1.4423

13.17°

3.73

7.09

7.28

-90.74

1.5170

21.79°

3.72

7.08

7.11

-90.58

1.5215

38.21°

3.63

6.99

5.52

-92.17

1.5269

46.83°

3.73

7.09

7.32

-90.69

1.5199

60°

4.10

7.46

11.85

-86.73

1.5172

14


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(c)

(b)

(a)

(d)

(e)

15


(f)


Figure 1. Top and side view of bilayer WSe2 under different twist angles of (a) 0°, (b) 13.17°, (c) 21.79°, (d) 38.21°, (e) 46.83°, and (f) 60°, respectively.

Energy (eV)

2 1 Eg = 1.4423 eV

0

M K

Γ

Eg = 1.5170 eV

Eg = 1.5215 eV

-1 -2

Γ

M K

Γ

(a)

4 8 12 DOS (states/eV) 0

Γ

M

K

Γ

800 400 DOS (states/eV)

Γ

M

K

(b)

Γ

40 80 120 DOS (states/eV)

(c)

2

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 Eg = 1.5269 eV

0

Eg = 1.5199 eV

Eg = 1.5172 eV

-1 -2

Γ

M K

Γ

100 200 Γ DOS (states/eV)

M K

Γ

(d)

400 800 DOS (states/eV)

(e)

Γ

M K

8 4 12 Γ DOS (states/eV)

(f)

Figure 2. The PBS and PDOS evolutions of bilayer WSe2 under different twist angles of (a) 0°, (b) 13.17°, (c) 21.79°, (d) 38.21°, (e) 46.83°, and (f) 60°, respectively.

16


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1.5

Eg [ eV ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 13.17 21.79 38.21 46.83 60

1.0

0.5

0.0 0.00

0.25

0.50

0.75

1.00

E [ V/Å ]

Figure 3. The bandgap variations of bilayer WSe2 with different twist angles under the approach of external electric fields.

17



Energy (eV)

2 1

C M K

Γ

0

-2

D Eg = 1.40 eV E = 0.075 V/Å

D Eg = 1.44 eV E = 0 V/Å

Γ

C

M K

Γ

(a)

4 8 12 DOS (states/eV) 0

Γ

Eg = 1.38 eV E = 0.1 V/Å

V

V

V

-1

M K

Γ

8 12 4 DOS (states/eV)

Γ

M K

(b)

Γ 5 10 15 20 DOS (states/eV)

(c)

2

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 0

-1 -2

Γ

M

K

Γ

(d)

2 4 6 8 Γ DOS (states/eV) 0

M K

Γ

2 4 6 8 DOS (states/eV)

(e)

Γ

M K

Γ 2 4 6 8 DOS (states/eV)

(f)

Figure 4. The PBS and PDOS evolutions of bilayer WSe2 at the twist angle of 0° when the electric field is 0 (a), 0.075 (b), 0.1 (c), 1 (d), 1.125 (e), and 1.15 V/Å (f), respectively.

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Gate Dielectric

Zigzag

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Armchair

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Gate

(a)

0 60

1.0

8

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0.5 E ( V/Å )

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AC 0 0 V/Å 60 0 V/Å 0 0.4 V/Å 60 0.4 V/Å

2

0 -2

(e)

0.5

Transmission

Transmission

4

(b)

-1

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TG (eV)

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TG (eV)

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6

0 60

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0.5 E ( V/Å ) ZZ 0 0 60 0 0 0.4 60 0.4

4

0

1

0 -2

2

-1

0.5 E ( V/Å )

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0 AC 0 V/Å ZZ 0 V/Å AC 0.6 V/Å ZZ 0.6 V/Å

4

2

0 -2

-1

(g)

0

0

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TG (eV)

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0.5 0.0 0.0

6

AC ZZ

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V/Å V/Å V/Å V/Å

1

2

1

2

E-Ef ( eV )

Transmission

(f)

TG (eV)

8

1.0

2

E-Ef ( eV )

Transmission

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


6

2

0 -2

E-Ef ( eV )

0.25 0.50 E ( V/Å ) 60 AC 0 V/Å ZZ 0 V/Å AC 0.2 V/Å ZZ 0.2 V/Å

2

1

0.5 0.0 0.00

4

AC ZZ

1.0

-1

0

E-Ef ( eV )

Figure 5. (a) Gate-modulated bilayer WSe2 homojunction, top and side views of bilayer WSe2 stacked at 0° (b) and 60°(c) with orthogonal structure. The transport properties of stack modes of 0° and 60° in the armchair (d) and zigzag (e) directions, and the anisotropy of transport properties of bilayer WSe2 with stack modes of 0° (f) 19



and 60° (g).

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TOC Graphic

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Gate Dielectric

Source

Drain Bottom

Dielectric

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Gate

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Interface Engineering of Band Evolution and Transport Properties of

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