# Tuning Electronic Properties of GaSe/Silicane Van der Waals Heterostructure by External Electric Field and Strain: A First-Principle Study

Authors: Gang Xu; Hao Lei
Journal: Advances in Condensed Matter Physics
 (2021)

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## Abstract

The electronic structure of GaSe/silicane (GaSe/SiH) van der Waals (vdW) heterostructure in response to a vertical electric field and strain was studied via first-principle calculations. The heterostructure had indirect band gap characteristics in the range [−1.0, −0.4] V/Å and direct band gap features in the range [−0.3, 0.2] V/Å. Furthermore, a type-II to type-I band alignment transition appeared at −0.7 and −0.3 V/Å. Additionally, the GaSe/SiH vdW heterostructure had a type-II band alignment under strain, but an indirect to direct band gap semiconductor transition occurred at −3%. These results indicated that the GaSe/SiH vdW heterostructure may have applications in novel nanoelectronic and optoelectronic devices.


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## Body

## 1. Introduction

Since the successful exfoliation of graphene by Novoselov et al. in 2004, there has been intense research interest in two-dimensional (2D) materials in the field of condensed matter physics [1]. A large number of 2D materials such as silicene [2–5], germanane [6], transition metal halides [7], transition metal chalcogenides [8–10], transition metal dichalcogenides (TMDs) [11–15], and the lesser known family of semiconducting monolayer metal monochalcogenides (MX, M = Ga, X = S, Se) [11–19] have been reported. However, each 2D material has its own advantages and disadvantages; hence, one material cannot be broadly applied to all fields. For example, the zero-band gap characteristics of graphene limit its applications in switching devices; in contrast, BN is a typical insulator with a very large band gap [20–22]. To overcome this issue, recent studies have reported that two different 2D materials can be stacked vertically to construct a van der Waals (vdW) heterostructure that not only retains the excellent characteristics of the original 2D materials but may also present novel physical properties because of the vdW forces between the two layers [23–26]. This approach has opened up new ways to study nanoelectronics and optoelectronic devices; hence, it has become a field of intense research interest.Monolayer GaSe is a member of the 2D MX family that has successfully been fabricated via chemical vapor deposition [27], pulsed laser deposition [28], and micromechanical cleavage techniques [29], and it has subsequently been widely studied [30–33]. Reports have theoretically demonstrated that the electronic structures, transport, and optical properties of GaSe monolayer are sensitive to applied electric fields and strains [30–32]. Furthermore, a number of nanoelectronic and optoelectronic devices based on monolayer GaSe with high photoresponse and on/off ratios have been successfully fabricated [31, 32]. These theoretical and experimental studies predicted that monolayer GaSe is a promising candidate for nanoelectronic and optoelectronic applications. Silicane (SiH), a fully hydrogenated silicene, has the same structure as silicene, but has a large band gap of ∼2.93 eV [34–36]. Numerous studies have demonstrated that the electronic band structure of SiH can be tuned via a uniform tensile strain and applied electric field [36–38]. Moreover, Low et al. [39] found that a SiH n-MOSFET offers a relatively better ON-current performance than transistors made of germanane and 2D TMD materials. These characteristics make SiH a promising candidate for electronic and optoelectronic devices.In addition, a large number of vdW heterostructures have been experimentally synthesized and theoretically proposed in recent years, including BN/graphene [23], WS2/MoS2 [40], and MoS2/GaN [41]. In particular, the combinations between SiH and GaSe with other 2D materials, including GaSe/MoS2 [17], GaSe/graphene, SiH/graphane, and SiH/hydrogenated hexagonal boron nitride have also received significant interest because of the preservation of their intriguing electronic properties and enhancement of their optical properties [42, 43]. For example, Jiang et al. [42] theoretically found that the band gaps of the SiH/graphane and SiH/hydrogenated hexagonal boron nitride could be tuned from a semiconductor to a metal under an applied electric field. Meanwhile, Pham et al. [44] demonstrated that the GaSe/MoS2 vdW heterostructure is an indirect band gap semiconductor with a band gap of 1.91 eV and a type-II band alignment. Furthermore, many research groups have successfully synthesized atomic layer GaSe/MoS2 van der Waals heterostructures and applied them for photoresponse modulation and as photodiodes [45, 46]. These reports indicate that GaSe- and SiH-based vdW heterostructures are promising 2D semiconductors with a high potential for novel applications in electronic and optoelectronic nanodevices. However, to date, there have been no reports focusing on the combination of GaSe with SiH monolayers and its electronic structure, as well as the electric field and strain effects. Therefore, this work investigated the design of GaSe/SiH vdW heterostructures and studied their electronic structures via first-principle calculations. The electric field and strain effects on the electronic structures of GaSe/SiH vdW heterostructures were also considered.


## 2. Computational Methods

The optimized structures and electronic structures of GaSe/SiH vdW heterostructures were obtained via first-principles calculations based on the density functional theory. The generalized gradient approximation of the Perdew–Burke–Ernzerhof functional [47, 48] was used for crystal structure relaxation, which was a part of the SIESTA code [49, 50]. The norm-conserving pseudopotentials were used to solve the Kohn–Sham equations. The cutoff energy was set at 100 Hatree, and a Brillouin zone sampling K-mesh of 9 × 9 × 1 was chosen. To obtain more accurate results, a K-mesh of 11 × 11 × 1 was adopted for the energy band structure calculations. For relaxation, the energy criterion was set as 10−4 eV, and the residual force was smaller than −0.05 eV/Å. The vacuum layer thickness was set to 20 Å to avoid other interactions with neighboring layers. Importantly, the long-ranged vdW interaction was required to hold the vdW heterostructure together. Here, the vdW-DF3 functional was chosen to describe long-range electron correlation effects [51].


## 3. Results and Discussion

### 3.1. Optimized Structures and Formation Energy

First, we optimized the original monolayer SiH and GaSe. The optimized lattice constants of SiH and GaSe were 3.889 and 3.847 Å, which are consistent with pre-existing theoretical and experimental values [35, 37, 38, 52–54]. Therefore, we built the GaSe/SiH vdW heterostructure using one unit cell of SiH and GaSe. The lattice mismatch was defined as(1)2×a1−a2a1+a2×100%,where a1 and a2 represent the lattice constants of SiH and GaSe, respectively. The calculated result was only ∼1.1%, indicating that the GaSe/SiH vdW heterostructure could be easily fabricated with very little interfacial stress. Hence, we built six possible heterostructure stacking configurations to find the ground structure, as shown in Figures 1(a)–1(f)) and labeled as model I to model VI.Figure 1
The lattice structure of GaSe/SiH vdW heterostructure: (a) model I, (b) model II, (c) model III, (d) model IV, (e) model V, and (f) model VI. The upper part is for top view, and the lower part is for side view. The Ga, Se, Si, and H atoms are represented by brown, yellow, golden yellow, and white balls, respectively.To analyze the vdW interactions between SiH and the GaSe layers, the formation energy (Ef) was defined as(2)Ef=ESiH/GaSe−ESiH−EGaSe,where Ef represents the formation energy of the GaSe/SiH vdW heterostructures and ESiH/GaSe, ESiH, and EGaSe represent the total energy of the GaSe/SiH vdW heterostructures, SiH, and GaSe monolayer, respectively. The calculated values of Ef are listed in Table 1. All the calculated Ef values were negative, indicating that all the six stacking configurations were stable from an energy perspective. Among them, the conformation model V was the ground structure because it had the lowest formation energy. In addition, we listed the interface distance (Δ, as shown in Figure 1(f)) in Table 1. The conformation model V has the smallest distance, indicating that the conformation model V was the ground structure. Therefore, in the following section, we only focused on conformation model V.Table 1
The formation energy (Ef) and interface distance (Δ) for the six stacking conformations.
ModelIIIIIIIVVVIEf/eV−0.855−0.838−0.838−0.856−0.857−0.856Δ/Å3.2173.2333.2183.2333.1643.189Next, we calculated the band structures of SiH, GaSe, and the GaSe/SiH vdW heterostructures, as shown in Figure2. The conduction band minimum (CBM) of SiH was located at the M point of the two-dimensional hexagonal Brillouin zone, while the valence band maximum (VBM) was located at the Γ point; this indicated that the pristine SiH is an indirect band gap semiconductor, with a corresponding band gap of 2.184 eV, which is in line with the results of the papers by Wang et al. and Guzmán-Verri et al. [38, 55, 56]. The CBM of GaSe was located at the Γ points, while the VBM was on the line of Γ-M and was close to the Γ points; this indicated the formation of an indirect semiconductor with a band gap of 1.871 eV. The calculated band gap value was similar to the theoretical values of 1.60 and 1.77 eV obtained from the PBE method [52–54]. The band structures for the GaSe/SiH vdW heterostructure are shown in Figure 2(c). Both the VBM and CBM of the GaSe/SiH vdW heterostructure are situated at the Γ points, indicating a direct semiconductor with a band gap of 0.558 eV. Furthermore, the VBM was predominantly derived from the SiH layer, and the CBM had a contribution from the GaSe layer, i.e., a representative type-II band alignment [57–60]. To understand the electronic structures of the GaSe/SiH vdW heterostructures in detail, we plotted the energy band alignment of the GaSe/SiH vdW heterostructure, as shown in Figure 2(d). The band edges of SiH and GaSe were (1.875, −0.313) eV and (0.245, −1.319) eV, respectively. The CBM and VBM of the GaSe were lower than those of the SiH, which further verified the type-II band alignment of the GaSe/SiH vdW heterostructure. In addition, we found that there was a small discrepancy between our study and previous studies because we used a different software package. Furthermore, we also found that these band gaps were smaller than the values obtained via the HSE method because the PBE method underestimated the band gap. The standard PBE functional enabled the prediction of the correct trend for the band structures, properly demonstrating their physical mechanisms. Hence, to save on computational load, we used the PBE method to perform electronic structure calculations for the GaSe/SiH vdW heterostructures under an applied electric field and strain.Figure 2
The band structures of (a) SiH, (b) GaSe, and (c) GaSe/SiH vdW heterostructure. The blue lines represent the GaSe, while the red lines represent the SiH. (d) The band offset of the GaSe/SiH vdW heterostructure.
(a)(b)(c)(d)


### 3.2. External Electric Field Effect

Previously reported theoretical and experimental results showed that an applied electric field can significantly affect the band structures of the vdW heterostructure, so we studied the electronic structures of the GaSe/SiH vdW heterostructure under a vertical electric field [38, 61–66]. The electric field was perpendicular to the GaSe/SiH vdW heterostructure, and the positive direction of the electric field was from SiH towards GaSe. The range for the external electric field was [−1.0, 1.0] V/Å, and the step length was 0.1 V/Å. The influence of the electric field on the band edges, band gap, and band structures of the GaSe/SiH vdW heterostructure is shown in Figure 3 and Figure S1. The VBM derived from GaSe and the CBM derived from SiH were in the range of [−1.0, −0.7] V/Å, both the VBM and CBM derived from GaSe were in the range of [−0.6, −0.4] V/Å, and the VBM derived from SiH and the CBM derived from GaSe were in the range of [−0.3, 0.2] V/Å. These results indicated that the GaSe/SiH vdW heterostructure had a type-II band alignment in the range of [−1.0, −0.7] and [−0.3, 0.2] V/Å, while it had a type-I band alignment in the range of [−0.6, −0.4] V/Å. Moreover, the VBM lay on the Γ-M line and was close to the Γ point in the range of [−1.0, −0.4] V/Å and was located at the Γ points in the range of [−0.3, 0.2] V/Å. The CBM was located at the M points in the range of [−1.0, −0.6] V/Å and was located at the Γ points in the range of [−0.5, 0.2] V/Å. These numerical results demonstrated that the GaSe/SiH vdW heterostructure was an indirect band gap semiconductor in the range of [−1.0, −0.4] V/Å, while it was a direct band gap semiconductor in the range of [−0.3, 0.2] V/Å. Furthermore, a metal-semiconductor phase transition occurred at 0.3 V/Å. In summary, the GaSe/SiH vdW heterostructure was an indirect band gap semiconductor with a type-II band alignment in the range of [−1.0, −0.7] V/Å, an indirect band gap semic\onductor with a type-I band alignment in the range of [−0.6, −0.4] V/Å, a direct band gap semiconductor with a type-II band alignment in the range of [−0.3, 0.2] V/Å, and it then changed to the metallic state. These results indicated that the GaSe/SiH vdW heterostructure had a variable band structure under an applied electric field.Figure 3
The (a) band edge and (b) band gap as a function of the external external field strength in the GaSe/SiH vdW heterostructure.
(a)(b)


### 3.3. Strain Effect

Strain is known to also affect the electronic structures of the vdW heterostructure [38, 63–68]. Here, we studied the effect of inplane biaxial strain on the electronic structures of the GaSe/SiH vdW heterostructure. The inplane biaxial strain on the GaSe/SiH vdW heterostructure was emulated by changing the crystal lattice parameters and then calculating in accordance with the following formula:(3)Θ=a−a0/a0×100%,where a0 and a are the crystal lattice parameters under the unstrained and strained conditions, respectively. The external strain was applied in the range of −5% to 5% in steps of 1%. The strain effects on the band edges, band gap, and electronic structures of the GaSe/SiH vdW heterostructure are shown in Figure 4 and Figure S2. The band gap increased with an increasing strain in the range of [−5%, −4%] and then decreased with increasing strain in the range of [−3%, 5%]. The VBM was located at the Γ points over the whole range, while the CBM was located at the M points in the range of [−5%, −4%] and at the Γ points in the range of [−3%, 5%]. Furthermore, the VBM was derived from SiH, and the CBM was derived from GaSe. Therefore, the GaSe/SiH vdW heterostructure had a type-II band alignment under strain. The above results demonstrated that the GaSe/SiH vdW heterostructure is an indirect band gap semiconductor with a type-II band alignment in the range of [−5%, −4%], while it is a direct band gap semiconductor with a type-II band alignment in the range of [−3%, 5%]. The results of this work indicate that the electronic structures of the GaSe/SiH vdW heterostructure can be effectively regulated by strain.Figure 4
The (a) band edge and (b) band gap as a function of the strain strength in the GaSe/SiH vdW heterostructure.
(a)(b)


## 3.1. Optimized Structures and Formation Energy

First, we optimized the original monolayer SiH and GaSe. The optimized lattice constants of SiH and GaSe were 3.889 and 3.847 Å, which are consistent with pre-existing theoretical and experimental values [35, 37, 38, 52–54]. Therefore, we built the GaSe/SiH vdW heterostructure using one unit cell of SiH and GaSe. The lattice mismatch was defined as(1)2×a1−a2a1+a2×100%,where a1 and a2 represent the lattice constants of SiH and GaSe, respectively. The calculated result was only ∼1.1%, indicating that the GaSe/SiH vdW heterostructure could be easily fabricated with very little interfacial stress. Hence, we built six possible heterostructure stacking configurations to find the ground structure, as shown in Figures 1(a)–1(f)) and labeled as model I to model VI.Figure 1
The lattice structure of GaSe/SiH vdW heterostructure: (a) model I, (b) model II, (c) model III, (d) model IV, (e) model V, and (f) model VI. The upper part is for top view, and the lower part is for side view. The Ga, Se, Si, and H atoms are represented by brown, yellow, golden yellow, and white balls, respectively.To analyze the vdW interactions between SiH and the GaSe layers, the formation energy (Ef) was defined as(2)Ef=ESiH/GaSe−ESiH−EGaSe,where Ef represents the formation energy of the GaSe/SiH vdW heterostructures and ESiH/GaSe, ESiH, and EGaSe represent the total energy of the GaSe/SiH vdW heterostructures, SiH, and GaSe monolayer, respectively. The calculated values of Ef are listed in Table 1. All the calculated Ef values were negative, indicating that all the six stacking configurations were stable from an energy perspective. Among them, the conformation model V was the ground structure because it had the lowest formation energy. In addition, we listed the interface distance (Δ, as shown in Figure 1(f)) in Table 1. The conformation model V has the smallest distance, indicating that the conformation model V was the ground structure. Therefore, in the following section, we only focused on conformation model V.Table 1
The formation energy (Ef) and interface distance (Δ) for the six stacking conformations.
ModelIIIIIIIVVVIEf/eV−0.855−0.838−0.838−0.856−0.857−0.856Δ/Å3.2173.2333.2183.2333.1643.189Next, we calculated the band structures of SiH, GaSe, and the GaSe/SiH vdW heterostructures, as shown in Figure2. The conduction band minimum (CBM) of SiH was located at the M point of the two-dimensional hexagonal Brillouin zone, while the valence band maximum (VBM) was located at the Γ point; this indicated that the pristine SiH is an indirect band gap semiconductor, with a corresponding band gap of 2.184 eV, which is in line with the results of the papers by Wang et al. and Guzmán-Verri et al. [38, 55, 56]. The CBM of GaSe was located at the Γ points, while the VBM was on the line of Γ-M and was close to the Γ points; this indicated the formation of an indirect semiconductor with a band gap of 1.871 eV. The calculated band gap value was similar to the theoretical values of 1.60 and 1.77 eV obtained from the PBE method [52–54]. The band structures for the GaSe/SiH vdW heterostructure are shown in Figure 2(c). Both the VBM and CBM of the GaSe/SiH vdW heterostructure are situated at the Γ points, indicating a direct semiconductor with a band gap of 0.558 eV. Furthermore, the VBM was predominantly derived from the SiH layer, and the CBM had a contribution from the GaSe layer, i.e., a representative type-II band alignment [57–60]. To understand the electronic structures of the GaSe/SiH vdW heterostructures in detail, we plotted the energy band alignment of the GaSe/SiH vdW heterostructure, as shown in Figure 2(d). The band edges of SiH and GaSe were (1.875, −0.313) eV and (0.245, −1.319) eV, respectively. The CBM and VBM of the GaSe were lower than those of the SiH, which further verified the type-II band alignment of the GaSe/SiH vdW heterostructure. In addition, we found that there was a small discrepancy between our study and previous studies because we used a different software package. Furthermore, we also found that these band gaps were smaller than the values obtained via the HSE method because the PBE method underestimated the band gap. The standard PBE functional enabled the prediction of the correct trend for the band structures, properly demonstrating their physical mechanisms. Hence, to save on computational load, we used the PBE method to perform electronic structure calculations for the GaSe/SiH vdW heterostructures under an applied electric field and strain.Figure 2
The band structures of (a) SiH, (b) GaSe, and (c) GaSe/SiH vdW heterostructure. The blue lines represent the GaSe, while the red lines represent the SiH. (d) The band offset of the GaSe/SiH vdW heterostructure.
(a)(b)(c)(d)


## 3.2. External Electric Field Effect

Previously reported theoretical and experimental results showed that an applied electric field can significantly affect the band structures of the vdW heterostructure, so we studied the electronic structures of the GaSe/SiH vdW heterostructure under a vertical electric field [38, 61–66]. The electric field was perpendicular to the GaSe/SiH vdW heterostructure, and the positive direction of the electric field was from SiH towards GaSe. The range for the external electric field was [−1.0, 1.0] V/Å, and the step length was 0.1 V/Å. The influence of the electric field on the band edges, band gap, and band structures of the GaSe/SiH vdW heterostructure is shown in Figure 3 and Figure S1. The VBM derived from GaSe and the CBM derived from SiH were in the range of [−1.0, −0.7] V/Å, both the VBM and CBM derived from GaSe were in the range of [−0.6, −0.4] V/Å, and the VBM derived from SiH and the CBM derived from GaSe were in the range of [−0.3, 0.2] V/Å. These results indicated that the GaSe/SiH vdW heterostructure had a type-II band alignment in the range of [−1.0, −0.7] and [−0.3, 0.2] V/Å, while it had a type-I band alignment in the range of [−0.6, −0.4] V/Å. Moreover, the VBM lay on the Γ-M line and was close to the Γ point in the range of [−1.0, −0.4] V/Å and was located at the Γ points in the range of [−0.3, 0.2] V/Å. The CBM was located at the M points in the range of [−1.0, −0.6] V/Å and was located at the Γ points in the range of [−0.5, 0.2] V/Å. These numerical results demonstrated that the GaSe/SiH vdW heterostructure was an indirect band gap semiconductor in the range of [−1.0, −0.4] V/Å, while it was a direct band gap semiconductor in the range of [−0.3, 0.2] V/Å. Furthermore, a metal-semiconductor phase transition occurred at 0.3 V/Å. In summary, the GaSe/SiH vdW heterostructure was an indirect band gap semiconductor with a type-II band alignment in the range of [−1.0, −0.7] V/Å, an indirect band gap semic\onductor with a type-I band alignment in the range of [−0.6, −0.4] V/Å, a direct band gap semiconductor with a type-II band alignment in the range of [−0.3, 0.2] V/Å, and it then changed to the metallic state. These results indicated that the GaSe/SiH vdW heterostructure had a variable band structure under an applied electric field.Figure 3
The (a) band edge and (b) band gap as a function of the external external field strength in the GaSe/SiH vdW heterostructure.
(a)(b)


## 3.3. Strain Effect

Strain is known to also affect the electronic structures of the vdW heterostructure [38, 63–68]. Here, we studied the effect of inplane biaxial strain on the electronic structures of the GaSe/SiH vdW heterostructure. The inplane biaxial strain on the GaSe/SiH vdW heterostructure was emulated by changing the crystal lattice parameters and then calculating in accordance with the following formula:(3)Θ=a−a0/a0×100%,where a0 and a are the crystal lattice parameters under the unstrained and strained conditions, respectively. The external strain was applied in the range of −5% to 5% in steps of 1%. The strain effects on the band edges, band gap, and electronic structures of the GaSe/SiH vdW heterostructure are shown in Figure 4 and Figure S2. The band gap increased with an increasing strain in the range of [−5%, −4%] and then decreased with increasing strain in the range of [−3%, 5%]. The VBM was located at the Γ points over the whole range, while the CBM was located at the M points in the range of [−5%, −4%] and at the Γ points in the range of [−3%, 5%]. Furthermore, the VBM was derived from SiH, and the CBM was derived from GaSe. Therefore, the GaSe/SiH vdW heterostructure had a type-II band alignment under strain. The above results demonstrated that the GaSe/SiH vdW heterostructure is an indirect band gap semiconductor with a type-II band alignment in the range of [−5%, −4%], while it is a direct band gap semiconductor with a type-II band alignment in the range of [−3%, 5%]. The results of this work indicate that the electronic structures of the GaSe/SiH vdW heterostructure can be effectively regulated by strain.Figure 4
The (a) band edge and (b) band gap as a function of the strain strength in the GaSe/SiH vdW heterostructure.
(a)(b)


## 4. Conclusion

In summary, the electronic structures of the GaSe/SiH vdW heterostructure under an applied electric field and strain were determined via first-principles calculations. We observed that the GaSe/SiH vdW heterostructure was an indirect band gap semiconductor with a type-II band alignment in the range of [−1.0, −0.7] V/Å, an indirect band gap semiconductor with a type-I band alignment in the range of [−0.6, −0.4] V/Å, a direct band gap semiconductor with a type-II band alignment in the range of [−0.3, 0.2] V/Å, and it then transitioned to the metallic state. Furthermore, the GaSe/SiH vdW heterostructure was an indirect band gap semiconductor with a type-II band alignment in the range of [−5%, −4%], while it was a direct band gap semiconductor with a type-II band alignment in the range of [−3%, 5%]. The results indicated that the tunable band gap of the GaSe/SiH vdW heterostructures provides a promising avenue for the fabrication of novel nanoelectronic and optoelectronic devices.



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