InSe/Te van der Waals Heterostructure as a High-Efficiency Solar Cell from Computational Screening

Designing the electronic structures of the van der Waals (vdW) heterostructures to obtain high-efficiency solar cells showed a fascinating prospect. In this work, we screened the potential of vdW heterostructures for solar cell application by combining the group III–VI MXA (M = Al, Ga, In and XA = S, Se, Te) and elementary group VI XB (XB = Se, Te) monolayers based on first-principle calculations. The results highlight that InSe/Te vdW heterostructure presents type-II electronic band structure feature with a band gap of 0.88 eV, where tellurene and InSe monolayer are as absorber and window layer, respectively. Interestingly, tellurene has a 1.14 eV direct band gap to produce the photoexcited electron easily. Furthermore, InSe/Te vdW heterostructure shows remarkably light absorption capacities and distinguished maximum power conversion efficiency (PCE) up to 13.39%. Our present study will inspire researchers to design vdW heterostructures for solar cell application in a purposeful way.


Introduction
Van der Waals (vdW) heterostructures are stacked by two or more two-dimensional (2D) materials with only vdW interaction in their interlayers but no surface dangling bonds [1], which were widely used in vertical field-effect transistors [2], wearable and biocompatible electronics [3], photodetectors [4], photovoltaics [5][6][7], light-emitting devices (LEDs) [8], and so on. Because vdW force in the interlayer is a long-range weak interaction, the heterostructures can be formed under the existence of large lattice mismatch among the monolayers [9]. Furthermore, vdW heterostructures can combine the excellent properties of the monolayers [10]. Under the interlayer coupling in vdW heterostructures, they can also exhibit novel characteristics that their components do not possess [7,[11][12][13]. Designing type-II vdW heterostructures for solar cells through band-structure engineering by using calculations is an efficient way, such as graphene/GaAs [5], Ti 2 CO 2 /Zr 2 CO 2 [14] and GaSe/GaTe heterostructures [15]. Generally, a vdW heterostructure based high-efficiency solar cell consists of two parts: a absorption layer with a small band gap (~1.2-1.6 eV [16]) and strong light absorption capacity, and a window layer with a large band gap and high transparency for the incident light [17,18]. Besides, the high carrier mobility and the direct band gap of the absorption layer that generates photo-generated electrons are also beneficial for improving the efficiency of solar cells [14,15]. Due to thickness and atomically sharp interfaces, light-generated carriers can be effectively separated in vdW heterostructures. Therefore, the probability of electron-hole recombination is very low, and the efficiency is high [17]. For instance, a 2D WSe 2 -MoS 2 lateral p-n heterojunction with a power conversion efficiency (PCE) of 2.56% under AM1.5G illumination was designed, which can help develop the next-generation photovoltaics [19]. Hence, finding vdW heterostructures with suitable band gaps and light absorption abilities to obtain high solar energy efficiency is of great interest and importance.
On the other hand, the group III-VI compounds represented by InSe are a kind of layered hexagonal lattice semiconductor [20][21][22]. The layers of them are connected by vdW force without dangling bonds. Excitingly, 2D InSe was successfully prepared experimentally, which exhibits high electron mobility, quantum Hall effect, and anomalous optical response [23]. Moreover, the 2D InSe related vdW heterostructures combined with another layers such as graphene [24], black phosphorus [25], C 3 N 4 [26], SiGe [7], or III-VI monolayers [15,27] attracted remarkable attention for high-performance electronic and optoelectronic devices. Recently, the 1T-MoS 2 -like phase T-Se and α-Te were successfully obtained in the laboratory [28,29]. The III-VI monolayers and T-Se, α-Te are all P63/mmc lattice semiconductors with great optical properties and high carrier mobility [15,30]. Theoretically, the selenene and tellurene are evaluated as indirect band gaps of 1.16 and 1.11 eV [30], respectively, which may be converted to direct band gaps after the formation of vdW heterostructures [31]. Therefore, it is highly desirable to build group III-VI/selenene and III-VI/tellurene vdW heterostructures, which are good candidates for the absorption layers for solar cell application.
In this work, we established the MX A /X B vdW heterostructures by combining MX A (M = Al, Ga, In and X A = S, Se, Te) and X B (X B = Se, Te) monolayers. Based on firstprinciples calculations, we unraveled the electronic structure of each monolayer and heterostructure. Then, according to the energy band requirement of solar cells, InSe/Te vdW heterostructure was screened out for the further study. Our results demonstrated that InSe/Te vdW heterostructure shows type-II electronic band structure feature whose tellurene as absorber layer exhibits 1.14 eV direct HSE band gap, exhibiting distinguished light absorption capacities. Moreover, the corresponding maximum PCE can reach up to 13.39%, which indicates that InSe/Te vdW heterostructure has great potential for highefficiency solar cells.

Materials and Methods
The first-principles calculations were based on density functional theory (DFT) using the Vienna ab initio simulation package (VASP) [32][33][34][35] in conjunction with the projector augmented wave (PAW) pseudopotentials [32,36]. The calculation models and results were dealt with the ALKEMIE platform [37]. The generalized gradient approximation (GGA) [38] of Perdew-Burke-Ernzerhof (PBE) [39] pseudopotentials were selected to descried the exchange correlation interactions between electrons. Our work conducted by using van der Waals (vdW) interaction to form a heterostructure with two monolayers. Since the weak interaction is difficult to be evaluated by traditional exchange and correlation potentials [40], the optB86b-vdW functional [41] was used to include the weak interaction in all the calculations. For the lattice optimization, the cutoff energy and the convergence criteria for energy were set to 500 eV and 10 −5 eV·atom −1 , respectively. We maintained a sufficiently large vacuum space (~20 Å vacuum for each layer) in the z-direction, and a proper distance (~3 Å) between the two layers in order to ensure that there was only vdW interaction between the different layers and no significant interaction among the repeating units in the vertical direction. In geometric optimizations and static self-consistent calculations, k-sampling was performed using 9 × 9 × 1 points by the Monkhorst-Pack [42] mesh. The Heyd-Scuseria-Ernzerhof (HSE06) [41] hybrid functional was used to evaluate the electronic band gaps.

Geometry and Stability
The MX A (M = Al, Ga, In and X A = S, Se, Te) and X B (X B = Se, Te) monolayers, where the positions of the elements in the periodic table are shown in Figure 1a, are crystallized in the space group of P63/mmc with a honeycomb hexagonal structure [30,43]. Table S1 lists the optimized lattice constant, bond length and band gaps for the monolayers, where the results are in good agreement with the previous reports [44,45]. The lattice constants of most of the MX A and X B monolayers are close to each other; for instance, the lattice differences between AlSe monolayer and selenene, InSe monolayer and tellurene, are 0.062 and 0.144 Å, respectively. The corresponding mismatches are 1.6% and 3.4%, respectively. The well matched crystalline nature is beneficial for the assembly of van der Waals (vdW) heterostructures, as illustrated in Figure 1b

Geometry and Stability
The MXA (M = Al, Ga, In and XA = S, Se, Te) and XB (XB = Se, Te) monolayers, where the positions of the elements in the periodic table are shown in Figure 1a, are crystallized in the space group of P63/mmc with a honeycomb hexagonal structure [30,43]. Table S1 lists the optimized lattice constant, bond length and band gaps for the monolayers, where the results are in good agreement with the previous reports [44,45]. The lattice constants of most of the MXA and XB monolayers are close to each other; for instance, the lattice differences between AlSe monolayer and selenene, InSe monolayer and tellurene, are 0.062 and 0.144 Å , respectively. The corresponding mismatches are 1.6% and 3.4%, respectively. The well matched crystalline nature is beneficial for the assembly of van der Waals (vdW) heterostructures, as illustrated in Figure 1b,c.  Tables S2-S4. The energy difference ΔEi refers to the difference between the corresponding configuration and the most stable configuration, which can be defined as follows [47]: where Ei is the total energy of each configuration, and E0 is the total energy of the most stable configuration. The most stable configuration, which has zero ΔEi, is presented in configurations (b) and (d). Moreover, the calculated total energy of various configurations relies on the interlayer distances and lattice constants [48]. Therefore, configurations (b) and (d) show a lower interlayer distance. Moreover, Figure 2 shows that the atom in the bottom of XB monolayer is not aligned with any atom in MXA monolayer. We established the MX A /X B vdW heterostructures by placing the X B monolayers on the top of MX A monolayers. There are six possible stacking configurations of the heterostructures [46], named configurations (a) to (f) in Figure 2. In configuration (a), X A atom of the MX A monolayer is placed below the bottom X B atom. While in configurations (b) or (c), X A atom is located in the bottom of the middle or upper X B atom. At the same time, we can also regard configurations (b) and (c) as the shifting of the X B monolayer in configuration (a) along the [110] direction of 1/3 and 2/3 a, respectively. Besides, the configurations (d), (e), and (f) can be obtained by flip the X B monolayer of (a), (b), and (c) types around the horizontal plane with an angle of 180 • . After structural optimizations for a total of 288 structures of all the MX A /X B heterostructures, the energy differences between different configurations, the interlayer distances, lattice constants, and bond lengths are listed in Tables S2-S4. The energy difference ∆E i refers to the difference between the corresponding configuration and the most stable configuration, which can be defined as follows [47]: where E i is the total energy of each configuration, and E 0 is the total energy of the most stable configuration. The most stable configuration, which has zero ∆E i , is presented in configurations (b) and (d). Moreover, the calculated total energy of various configurations relies on the interlayer distances and lattice constants [48]. Therefore, configurations (b) and (d) show a lower interlayer distance. Moreover, Figure 2 shows that the atom in the bottom of X B monolayer is not aligned with any atom in MX A monolayer.
To evaluate the thermodynamic stability and interlayer interaction, we calculated the formation energy E f and binding energy E b for the heterostructures according to the following equations: where E total is the total energy of the MX A /X B heterostructures. E MX A and E X B represent the total energy of pristine MX A and X B monolayers, respectively. In addition, E MX A +X B is the sum of the total energy of the mutually independent MX A and X B monolayers fixed in the corresponding heterostructure lattices, and A is the interface area. Table 1 lists the formation and binding energies and other related parameters of the most stable configuration of the MX A /X B heterostructures. In addition, most of heterostructures have the negative value of formation energy, which indicates that the reaction of combining monolayers to form these heterostructures is energetically favorable [49]. For example, those of AlTe/Te, GaTe/Te and InSe/Te heterostructures are −280.3, −300.8 and −278.7 meV, respectively. On the other hand, all the heterostructures have the binding energy around~20 meV/Å 2 , which is the sign of vdW interaction between two monolayers [50]. To evaluate the thermodynamic stability and interlayer interaction, we calculated the formation energy Ef and binding energy Eb for the heterostructures according to the following equations: where Etotal is the total energy of the MXA/XB heterostructures. E is the sum of the total energy of the mutually independent MXA and XB monolayers fixed in the corresponding heterostructure lattices, and A is the interface area. Table 1 lists the formation and binding energies and other related parameters of the most stable configuration of the MXA/XB heterostructures. In addition, most of heterostructures have the negative value of formation energy, which indicates that the reaction of combining monolayers to form these heterostructures is energetically favorable [49]. For example, those of AlTe/Te, GaTe/Te and InSe/Te heterostructures are −280.3, −300.8 and −278.7 meV, respectively. On the other hand, all the heterostructures have the binding energy around ~20 meV/Å 2 , which is the sign of vdW interaction between two monolayers [50].

Electronic Properties
A high-efficiency heterostructure solar cell requires the type-II band structure feature, and the absorption layer has a lower band edge than the window layer, preferably with a direct band gap of 1.2-1.4 eV [16,17]. Figure S1 illustrates the projected band structures and band edge alignments of MX A and X B monolayers by using HSE06 hybrid functional, while Table S1 lists their corresponding PBE and HSE band gaps. For instance, the conduction band minima (CBM) and band gap for InSe monolayer are −4.46 and 2.32 eV, and CBM and band gap for tellurene are −4.49 and 1.09 eV, respectively. In addition, the CBM of tellurene located in Г point is only 0.07 eV higher than the energy of the point where VBM located in valance band. Figure 3 illustrates the HSE band structures of all the MX A /X B heterostructures. GaS/Te, GaSe/Te, InS/Te and InSe/Te are all type-II heterostructures with tellurene as the absorption layer. The black short lines mark the corresponding positions of the CBM and VBM of tellurene. In the band structures of GaSe/Te, InS/Te, and InSe/Te, there are two lines in valence bands because their energy levels are similar. The overlap band structures of mutually independent monolayers fixed in InSe/Te heterostructure and the projected HSE band structure of InSe/Te vdW heterostructure are illustrated in Figure 4. Tellurene exhibits the direct band gap of 1.14 eV. And there is 0.36 eV conduction band offset (CBO) between InSe monolayer and tellurene to separate charges [51]. Therefore, InSe/Te vdW heterostructure has the suitable band structure for solar cells.
tures and band edge alignments of MXA and XB monolayers by using HSE06 hybrid functional, while Table S1 lists their corresponding PBE and HSE band gaps. For instance, the conduction band minima (CBM) and band gap for InSe monolayer are −4.46 and 2.32 eV, and CBM and band gap for tellurene are −4.49 and 1.09 eV, respectively. In addition, the CBM of tellurene located in Г point is only 0.07 eV higher than the energy of the point where VBM located in valance band. Figure 3 illustrates the HSE band structures of all the MXA/XB heterostructures. GaS/Te, GaSe/Te, InS/Te and InSe/Te are all type-II heterostructures with tellurene as the absorption layer. The black short lines mark the corresponding positions of the CBM and VBM of tellurene. In the band structures of GaSe/Te, InS/Te, and InSe/Te, there are two lines in valence bands because their energy levels are similar. The overlap band structures of mutually independent monolayers fixed in InSe/Te heterostructure and the projected HSE band structure of InSe/Te vdW heterostructure are illustrated in Figure 4. Tellurene exhibits the direct band gap of 1.14 eV. And there is 0.36 eV conduction band offset (CBO) between InSe monolayer and tellurene to separate charges [51]. Therefore, InSe/Te vdW heterostructure has the suitable band structure for solar cells.

Solar Cell Applications
To further evaluate the light absorption capacity and reflectivity of InSe/Te vdW heterostructure, we calculated the absorption coefficient and reflectivity by the following formula [52]:

Solar Cell Applications
To further evaluate the light absorption capacity and reflectivity of InSe/Te vdW heterostructure, we calculated the absorption coefficient and reflectivity by the following formula [52]: where λ is the photon wavelength, ε 1 and ε 2 are the real and imaginary parts of the dielectric function, respectively, and n(λ), κ(λ) are the refractive index and the extinction coefficient, respectively. α(λ) and R(λ) are the absorption coefficient and reflectivity, respectively. The absorption coefficients and reflectivity curves of InSe/Te heterostructure, InSe monolayer and tellurene are shown in Figure 5. Herein, tellurene as the absorption layer exhibits the high absorption coefficient about 10 5 to 10 6 cm −1 in the visible light, which can be comparable with that of bulk WS 2 and WSe 2 used in efficient single junction solar cell [53]. The InSe monolayer as the window layer is required high transparency for the incident light, which means low absorption coefficient and reflectivity [17,54]. The InSe monolayer has an absorption coefficient about one order of magnitude lower than that of tellurene, and the reflectivity of it is about 0.13 to 0.34 in the range of 0 to 4 eV photon energy. This result can be compared with that of the Janus WSeTe monolayer used as buffer layer [54]. To more intuitively evaluate the solar energy conversion ability of InSe/Te vdW heterostructure, we evaluated the power conversion efficiency (PCE) η in the limit of 100% external quantum efficiency (EQE) by the following equation [6,51]: where 0.65 is the band-fill factor, P(ћω) is the AM1.5 solar energy flux at the value of ћω for photon energy, Eg is the band gap of the donor, ΔEc is the conduction band offset between the donor and acceptor, and the (Eg − ΔEc − 0.3) term is an estimation of the maximum open circuit voltage. For this formula, the smaller ΔEc means the greater value of PCE. Additionally, it requires a suitable Eg, because if the band gap of the donor is higher, the open circuit voltage will be better. However, the higher band gap will reduce the To more intuitively evaluate the solar energy conversion ability of InSe/Te vdW heterostructure, we evaluated the power conversion efficiency (PCE) η in the limit of 100% external quantum efficiency (EQE) by the following equation [6,51]: where 0.65 is the band-fill factor, P( ω) is the AM1.5 solar energy flux at the value of ω for photon energy, E g is the band gap of the donor, ∆E c is the conduction band offset between the donor and acceptor, and the (E g − ∆E c − 0.3) term is an estimation of the maximum open circuit voltage. For this formula, the smaller ∆E c means the greater value of PCE. Additionally, it requires a suitable E g , because if the band gap of the donor is higher, the open circuit voltage will be better. However, the higher band gap will reduce the amount of photons that can be absorbed, which will reflect in the decrease of short circuit current. Here, the maximum PCE of InSe/Te vdW heterostructure is calculated to 13.39%, which is highlighted as red star in Figure 6. To show the uniqueness of InSe/Te vdW heterostructure, the PCE calculated by the same method for other 2D heterostructure solar cells are listed in Table 2. Therefore, we infer that the InSe/Te vdW heterostructure is a potential candidate for the high-efficiency solar cell application.

Conclusions
In summary, we established the vdW heterostructures by combining MXA (M = Al, Ga, In and XA = S, Se, Te) and XB (XB = Se, Te) monolayers. Based on first-principles calculations, the stability and interlayer force of these heterostructures were demonstrated by the formation and binding energy. From screening, the InSe/Te vdW heterostructure shows type-II electronic band structure feature with a band gap of 0.88 eV, where the tellurene as absorber layer with a direct band gap about 1.14 eV could produce the photoexcited electron easily. In addition, tellurene and InSe monolayer respectively exhibit high absorption coefficient and low reflectivity. Furthermore, the maximum power conversion efficiency (PCE) of InSe/Te vdW heterostructure can reach up to 13.39%. Very recently, multilayer InSe/Te vdW heterostructure was experimentally observed and showed potential application in electronic and optoelectronic devices [57]. We believed that monolayer InSe/Te vdW heterostructure can be experimentally realized and show better performance. Our present research not only finds a novel type-II heterostructure for high-efficiency solar cell, but also further guides the design of more 2D vdW semiconductors for photovoltaic materials.

Conclusions
In summary, we established the vdW heterostructures by combining MX A (M = Al, Ga, In and X A = S, Se, Te) and X B (X B = Se, Te) monolayers. Based on first-principles calculations, the stability and interlayer force of these heterostructures were demonstrated by the formation and binding energy. From screening, the InSe/Te vdW heterostructure shows type-II electronic band structure feature with a band gap of 0.88 eV, where the tellurene as absorber layer with a direct band gap about 1.14 eV could produce the photoexcited electron easily. In addition, tellurene and InSe monolayer respectively exhibit high absorption coefficient and low reflectivity. Furthermore, the maximum power conversion efficiency (PCE) of InSe/Te vdW heterostructure can reach up to 13.39%. Very recently, multilayer InSe/Te vdW heterostructure was experimentally observed and showed potential application in electronic and optoelectronic devices [57]. We believed that monolayer InSe/Te vdW heterostructure can be experimentally realized and show better performance. Our present research not only finds a novel type-II heterostructure for high-efficiency solar cell, but also further guides the design of more 2D vdW semiconductors for photovoltaic materials.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/ma14143768/s1, Figure S1: Projected band structures of (a) AlS, (b) AlSe, (c) AlTe, (d) GaS, (e) GaSe, (f) GaTe, (g) InS, (h) InSe, (i) InTe, (j) Se and (k) Te monolayers by HSE06 hybrid functional method. The red, brown, blue circles represent the projected specific gravity of M, X A , X B atoms, respectively. The first Brillouin zone with high-symmetry points are shown in the inset of (a). (l) The band edge alignments of these monolayers, Table S1: the lattice constants a (Å), the M-M, M-X A and X B -X B (M = Al, Ga, In, X A = S, Se, Te and X B = Se, Te) bond lengths L M-M (Å), L M-XA (Å) and L XB-XB (Å), the PBE and HSE band gaps E PBE g (eV), E HSE g (eV) for the MX A and X B monolayers, Table S2: the energy differences ∆E (meV) and interlayer distances d (Å) as well as the lattice constants a (Å) and bond lengths L (Å) of various configurations for AlX A /X B vdW heterostructures, Table S3: the energy differences ∆E (meV) and interlayer distances d (Å) as well as the lattice constants a (Å) and bond lengths L (Å) of various configurations for GaX A /X B vdW heterostructures, Table S4: the energy differences ∆E (meV) and interlayer distances d (Å) as well as the lattice constants a (Å) and bond lengths L (Å) of various configurations for InX A /X B vdW heterostructures.

Data Availability Statement:
The data presented in this study are available on request from the corresponding authors.

Conflicts of Interest:
The authors declare no conflict of interest.