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

materials Article InSe/Te van der Waals Heterostructure as a High-Efficiency Solar Cell from Computational Screening Zechen Ma 1,, Ruifeng Li 1,, Rui Xiong 1, Yinggan Zhang 2, Chao Xu 3, Cuilian Wen 1, * and Baisheng Sa 1, * 1 Multiscale Computational Materials Facility, and Key Laboratory Eco-Materials Advanced Technology, College Materials Science and Engineering, Fuzhou University, Fuzhou 350100, China; mazc666@163.com (Z.M.); liruifeng1603@126.com (R.L.); 201810004@fzu.edu.cn (R.X.) 2 College Materials, Xiamen University, Xiamen 361005, China; ygzhang@xmu.edu.cn 3 Xiamen Talentmats New Materials Science & Technology Co., Ltd., Xiamen 361015, China; xuchao@talentmats.com * Correspondence: clwen@fzu.edu.cn (C.W.); bssa@fzu.edu.cn (B.S.) These authors equally contributed to this work. Citation: Ma, Z.; Li, R.; Xiong, R.; Zhang, Y.; Xu, C.; Wen, C.; Sa, B. InSe/Te van der Waals Heterostructure as a High-Efficiency Solar Cell from Computational Screening. Materials 2021, 14, 3768. https://doi.org/10.3390/ma14143768 Academic Editor: Haobin Wu Received: 26 May 2021 Accepted: 1 July 2021 Published: 6 July 2021 Publisher s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: 2021 by authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under terms and conditions Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Abstract: Designing electronic structures van der Waals (vdw) heterostructures to obtain high-efficiency solar cells showed a fascinating prospect. In this work, we screened potential vdw heterostructures for solar cell application by combining group III VI MX A (M = Al, Ga, In and X A = S, Se, Te) and elementary group VI X B (X B = Se, Te) monolayers based on first-principle calculations. The results highlight that InSe/Te vdw heterostructure presents type-ii electronic structure feature with a gap 0.88 ev, where tellurene and InSe monolayer are as absorber and window layer, respectively. Interestingly, tellurene has a 1.14 ev direct gap to produce photoexcited electron easily. Furrmore, 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. Keywords: van der Waals heterostructure; InSe; tellurene; first-principle calculations; solar cell 1. Introduction Van der Waals (vdw) heterostructures are stacked by two or more two-dimensional (2D) materials with only vdw interaction in ir 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 7], light-emitting devices (LEDs) [8], and so on. Because vdw force in interlayer is a long-range weak interaction, heterostructures can be formed under existence large lattice mismatch among monolayers [9]. Furrmore, vdw heterostructures can combine excellent properties monolayers [10]. Under interlayer coupling in vdw heterostructures, y can also exhibit novel characteristics that ir components do not possess [7,11 13]. Designing type-ii vdw heterostructures for solar cells through -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 two parts: a absorption layer with a small gap (~1.2 1.6 ev [16]) and strong light absorption capacity, and a window layer with a large gap and high transparency for incident light [17,18]. Besides, high carrier mobility and direct gap absorption layer that generates photo-generated electrons are also beneficial for improving efficiency solar cells [14,15]. Due to thickness and atomically sharp interfaces, light-generated carriers can be effectively separated in vdw heterostructures. Therefore, probability electron-hole recombination is very low, and efficiency is high [17]. For instance, a 2D WSe 2 -MoS 2 lateral p-n heterojunction with Materials 2021, 14, 3768. https://doi.org/10.3390/ma14143768 https://www.mdpi.com/journal/materials

Materials 2021, 14, 3768 2 10 a power conversion efficiency (PCE) 2.56% under AM1.5G illumination was designed, which can help develop next-generation photovoltaics [19]. Hence, finding vdw heterostructures with suitable gaps and light absorption abilities to obtain high solar energy efficiency is great interest and importance. On or hand, group III VI compounds represented by InSe are a kind layered hexagonal lattice semiconductor [20 22]. The layers m 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, 2D InSe related vdw heterostructures combined with anor 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, 1T-MoS 2 -like phase T-Se and α-te were successfully obtained in 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, selenene and tellurene are evaluated as indirect gaps 1.16 and 1.11 ev [30], respectively, which may be converted to direct gaps after formation 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 absorption layers for solar cell application. In this work, we established 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 electronic structure each monolayer and heterostructure. Then, according to energy requirement solar cells, InSe/Te vdw heterostructure was screened out for furr study. Our results demonstrated that InSe/Te vdw heterostructure shows type-ii electronic structure feature whose tellurene as absorber layer exhibits 1.14 ev direct HSE gap, exhibiting distinguished light absorption capacities. Moreover, corresponding maximum PCE can reach up to 13.39%, which indicates that InSe/Te vdw heterostructure has great potential for highefficiency solar cells. 2. Materials and Methods The first-principles calculations were based on density functional ory (DFT) using Vienna ab initio simulation package (VASP) [32 35] in conjunction with projector augmented wave (PAW) pseudopotentials [32,36]. The calculation models and results were dealt with ALKEMIE platform [37]. The generalized gradient approximation (GGA) [38] Perdew Burke Ernzerh (PBE) [39] pseudopotentials were selected to descried exchange correlation interactions between electrons. Our work conducted by using van der Waals (vdw) interaction to form a heterostructure with two monolayers. Since weak interaction is difficult to be evaluated by traditional exchange and correlation potentials [40], optb86b-vdw functional [41] was used to include weak interaction in all calculations. For lattice optimization, cutf energy and 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 z-direction, and a proper distance (~3 Å) between two layers in order to ensure that re was only vdw interaction between different layers and no significant interaction among repeating units in vertical direction. In geometric optimizations and static self-consistent calculations, k-sampling was performed using 9 9 1 points by Monkhorst Pack [42] mesh. The Heyd Scuseria Ernzerh (HSE06) [41] hybrid functional was used to evaluate electronic gaps. 3. Results and Discussion 3.1. 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 positions elements in periodic table are shown in Figure 1a, are crystallized

Materials 2021, 14, x FOR PEER REVIEW 3 11 3. Results and Discussion Materials 2021, 14, 3768 3 10 3.1. Geometry and Stability The MXA (M = Al, Ga, In and XA = S, Se, Te) and XB (XB = Se, Te) monolayers, where positions elements in periodic table are shown in Figure 1a, are crystallized in in space space group group P63/mmc P63/mmc with with a honeycomb honeycomb hexagonal hexagonal structure structure [30,43]. [30,43]. Table Table S1 S1 lists lists optimized optimized lattice lattice constant, constant, bond bond length length and and gaps gaps for for monolayers, monolayers, where where results are in good agreement with previous reports [44,45]. The lattice constants results are in good agreement with previous reports [44,45]. The lattice constants most MX A and X B monolayers are close to each or; for instance, lattice most MXA and XB monolayers are close to each or; for instance, lattice differences between AlSe monolayer and selenene, InSe monolayer and tellurene, are 0.062 differences between AlSe monolayer and selenene, InSe monolayer and tellurene, are and 0.144 Å, respectively. The corresponding mismatches are 1.6% and 3.4%, respectively. 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 assembly van der Waals The well matched crystalline nature is beneficial for assembly van der Waals (vdw) heterostructures, as illustrated in Figure 1b,c. (vdw) heterostructures, as illustrated in Figure 1b,c. (a) Position in periodic table elements for MXA/XB (M = Al, Ga, In, XA = S, Se, Te and XB Figure 1. (a) Position in periodic table elements for = Se, Te) heterostructures. A /X B (M = Al, Ga, In, X A = S, Se, Te and X B = Se, Te) heterostructures. (b) top- and (c) side-views optimized structure MX A /X B (b) top- and (c) side-views optimized structure MXA/XB heterostructures. heterostructures. We established MXA/XB vdw by placing XB A /X B vdw heterostructures by placing Xmonolayers B on top top MXA MX monolayers. A monolayers. There There are six are possible six possible stacking stacking configurations configurations hetero- heterostructures [46], named [46], named configurations configurations (a) to (f) (a) in to Figure (f) in Figure 2. In configuration 2. In configuration (a), XA (a), atom X A atom MXA monolayer MX A monolayer is placed is placed below below bottom bottom XB atom. X B atom. While While in configurations in configurations (b) or (c), (b) or XA (c), atom X A is atom located is located in bottom in bottom middle middle or upper orxb upper atom. XAt B atom. same At time, same we can time, also weregard can also configurations regard configurations (b) and (c)(b) as and shifting (c) as shifting XB monolayer X B monolayer in configuration in configuration (a) along (a) [11 0] alongdirection [110] direction 1/3 and 2/3 1/3 a, and respectively. 2/3 a, respectively. Besides, Besides, configura- configurations (d), (e), and (d),(f) (e), can and be (f) obtained can be obtained by flip by flip XB monolayer X B monolayer (a), (b), (a), and (b), (c) and types (c) around types around horizontal horizontal plane plane with with an angle angle 180. 180After. After structural optimizations for for a a total 288 288 structures all MXA/XB A /X B heterostructures, energy differences between different configurations, interlayer distances, lattice constants, and bond lengths are listed in Tables S2 S4. The The energy difference ΔEi E refers i refers to to difference between between corresponding corresponding configuration and and most most stable stable configuration, which which can can be defined be defined as fol- as lows follows [47]: [47]: E i = E i E 0 (1) Ei Ei E0 (1) where E i is total energy each configuration, and E 0 is total energy most where Ei is total energy each configuration, and E0 stable configuration. The most stable configuration, which is has zero total E energy most i, is presented in stable configurations configuration. (b) and The (d). most Moreover, stable configuration, calculated total which energy has zero various ΔEi, is configurations presented in configurations relies on interlayer (b) and distances (d). Moreover, and lattice calculated constants total [48]. energy Therefore, various configurations configurations (b) and relies (d) show on a lower interlayer interlayer distances distance. and Moreover, lattice constants Figure 2[48]. shows Therefore, that atom configurations in bottom (b) and X (d) show a lower interlayer distance. Moreover, Figure 2 shows that atom in B monolayer is not aligned with any atom in MX A monolayer. bottom XB monolayer is not aligned with any atom MXA To evaluate rmodynamic stability and interlayermonolayer. interaction, we calculated formation energy E f and binding energy E b for heterostructures according to following equations: E f = E total E MXA E XB (2) E b = E total E MXA +X B A where E total is total energy MX A /X B heterostructures. E MXA and E XB represent total energy pristine MX A and X B monolayers, respectively. In addition, E MXA +X B is sum total energy mutually independent MX A and X B monolayers fixed in corresponding heterostructure lattices, and A is interface area. Table 1 lists formation and binding energies and or related parameters most stable configuration MX A /X B heterostructures. In addition, most heterostructures have negative value (3)

Materials 2021, 14, 3768 4 10 formation energy, which indicates that reaction combining monolayers to form se heterostructures is energetically favorable [49]. For example, those AlTe/Te, GaTe/Te and InSe/Te heterostructures are 280.3, 300.8 and 278.7 mev, respectively. On Materials 2021, 14, x FOR PEER REVIEW or hand, all heterostructures have binding energy around ~20 mev/å 2, which 4 is 11 sign vdw interaction between two monolayers [50]. Figure 2. Top (a) and side (b) views MXA/XB Figure 2. Top (a) and side (b) views MX heterostructures with various configurations. Red, A /X B heterostructures with various configurations. Red, brown, blue balls indicate M, XA, XB atoms, respectively. brown, blue balls indicate M, X A, X B atoms, respectively. Table To 1. Most evaluate stable configurations, rmodynamic lattice stability constants and a (Å), interlayer formation interaction, energies Ewe f (mev), calculated binding energies formation E b (mev/å energy 2 Ef ), PBE, and and binding HSE energy gapseb Eg PBE for (ev) heterostructures and Eg HSE (ev), andaccording edge to alignment following forequations: MX A /X B vdw types heterostructures. System Configuration a E E E f total E f MX E b X E PBE Type (2) AlS-Se d 3.627 174.0 20.7 1.00 1.35 I AlS-Te d 3.822 492.3 E E 20.4 0.15 0.55 I total MX A+XB AlSe-Se d 3.744 E (3) b 246.9 20.9 0.76 1.20 I A AlSe-Te d 3.935 58.5 20.4 0.52 0.90 I where AlTe-Se Etotal is btotal energy 3.965 MXA/XB 67.9 heterostructures. 24.1 0.43 EMX A and 0.75 E X B represent V AlTe-Te d 4.129 280.3 20.5 0.83 1.18 I GaS-Se total energy d pristine MXA 3.660and XB 213.7 monolayers, 21.2respectively. 0.76 In addition, 1.21 EMX I A+X is B GaS-Te sum total d energy 3.863 mutually 328.0 independent 22.4 MXA and 0.00 XB monolayers 0.26 fixed II in GaSe-Se corresponding d heterostructure 3.764 lattices, 250.0 and A is 21.5 interface 0.60 area. 1.12 Table 1 lists I GaSe-Te d 3.963 24.3 21.8 0.20 0.64 II formation and binding energies and or related parameters most stable configuration GaTe-Te MXA/XB d heterostructures. 4.141 In 300.8 addition, most 21.4 heterostructures 0.58 1.09have I neg- GaTe-Se b 3.980 74.8 25.6 0.36 0.67 II ative InS-Se value formation b energy, 3.829 which indicates 206.7 that 21.4 reaction 0.60 combining 0.99 monolayers InS-Te to form se dheterostructures 4.024 is energetically 164.8 favorable 21.7 [49]. 0.16 For example, 0.50 those II I AlTe/Te, InSe-Se GaTe/Te InSe/Te 3.921 heterostructures 107.9 are 280.3, 22.7 300.8 0.44and 278.7 0.99 mev, respectively. On or hand, all heterostructures have binding energy around ~20 I InSe-Te d 4.112 278.7 21.5 0.39 0.88 II InTe-Se b 4.124 178.0 29.0 0.20 0.49 V mev/å 2, which is sign vdw interaction between two monolayers [50]. InTe-Te b 4.290 309.5 21.7 0.44 0.89 V Table 1. Most stable configurations, lattice constants a (Å ), formation energies Ef (mev), binding 3.2. energies Electronic Eb (mev/å Properties 2 ), PBE, and HSE gaps E PBE g (ev) and E HSE g (ev), and edge alignment types Afor high-efficiency MXA/XB vdw heterostructures. solar cell requires type-ii structure feature, and absorption layer has a lower edge than window layer, PBE preferably HSE with a System Configuration a Ef Eb direct gap 1.2 1.4 ev [16,17]. Figure S1 illustrates projected E g E structures g Type and edge AlS-Se alignments MX d A and X B monolayers 3.627 174.0 by using20.7 HSE06 1.00 hybrid functional, 1.35 while Ι TableAlS-Te S1 lists ir corresponding d PBE3.822 and HSE492.3 gaps. 20.4 For instance, 0.15 0.55 conduction Ι AlSe-Se minima (CBM) and d gap for3.744 InSe monolayer 246.9 are 20.9 4.460.76 and 2.321.20 ev, and CBM Ι and AlSe-Te gap for tellurene d are 4.49 3.935 and 1.09 ev, 58.5 respectively. 20.4 In 0.52 addition, 0.90 CBMΙ tellurene AlTe-Se located in Г pointb is only 0.073.965 ev higher 67.9 than 24.1 energy 0.43 point 0.75 where VBM V located AlTe-Te in valance. d 4.129 280.3 20.5 0.83 1.18 Ι GaS-Se d 3.660 213.7 21.2 0.76 1.21 Ι GaS-Te d 3.863 328.0 22.4 0.00 0.26 II GaSe-Se d 3.764 250.0 21.5 0.60 1.12 Ι GaSe-Te d 3.963 24.3 21.8 0.20 0.64 II A B g E HSE g

tures and edge alignments MXA and XB monolayers by using HSE06 hybrid functional, while Table S1 lists ir corresponding PBE and HSE gaps. For instance, conduction minima (CBM) and gap for InSe monolayer are 4.46 and 2.32 ev, and CBM and gap for tellurene are 4.49 and 1.09 ev, respectively. In addition, Materials 2021, 14, 3768 tellurene located in Г point is only 0.07 ev higher than energy point 5 10 CBM where VBM located in valance. Figure 3 illustrates HSE structures all MXA/XB heterostructures. GaS/Te, GaSe/Te, InS/Te and InSe/Te are type-ii with tellurene as Figure 3 illustrates all HSE heterostructures structures all MX A /XB heterostructures. GaS/Te, GaSe/Te, and InSe/Te are all type-ii heterostructures tellurene absorption layer. The black shortins/te lines mark corresponding positions with CBM and as absorption layer. The black short lines mark corresponding positions CBM and VBM tellurene. In structures GaSe/Te, InS/Te, and InSe/Te, re are two VBM tellurene. In structures GaSe/Te, InS/Te, and InSe/Te, re lines in valence s because ir energy levels are similar. The overlap structures are two lines in valence s because ir energy levels are similar. The overlap structures mutually independent monolayers fixed in InSe/Te heterostructure and projected mutually independent monolayers fixed in InSe/Te heterostructure and projected HSE structure InSe/Te vdw heterostructure are illustrated in Figure 4. Tellurene HSE structure InSe/Te vdw heterostructure are illustrated in Figure 4. Tellurene exhibits direct gapdirect 1.14 ev.gap And re 0.36re ev conduction fset (CBO) exhibits 1.14 ev.isand is 0.36 ev conduction fset (CBO) between InSe monolayer and tellurene to separate charges [51]. Therefore, InSe/Te vdw vdw between InSe monolayer and tellurene to separate charges [51]. Therefore, InSe/Te heterostructure heterostructure has suitable structure forstructure solar cells. has suitable for solar cells. terials 2021, 14, x Figure FOR PEER REVIEW 11 circles 3. Projected structures MXA/XB heterostructures byfunctional HSE hybrid functional 3.Figure Projected structures MXA /XB heterostructures by HSE hybrid method. Red and6method. blue and blue circles represent weight MXA and XB monolayers, respectively. representred projected weight MX monolayers, respectively. A and XBprojected Figure 4. (a)structures Overlap structures mutually independent fixed in InSe/Te heterofigure 4. (a) Overlap mutually independent monolayers fixed monolayers in InSe/Te heterostructure and (b) projected (b) projectedvia structure functional InSe/Te heterostructure via HSE06 hybrid functional structure structure InSe/Teand heterostructure HSE06 hybrid method. method. 3.3. Solar Cell Applications To furr evaluate light absorption capacity and reflectivity InSe/Te vdw heterostructure, we calculated absorption coefficient and reflectivity by following formula [52]: n( ) 1 2 1 12 2 2 (4)

Materials 2021, 14, 3768 6 10 3.3. Solar Cell Applications To furr evaluate light absorption capacity and reflectivity InSe/Te vdw heterostructure, we calculated absorption coefficient and reflectivity by following formula [52]: n(λ) = 1 ε 1 (λ) + ε 2 1 (λ) + ε 2 2 (λ) (4) 2 κ(λ) = 1 ε 1 (λ) + ε 2 1 (λ) + ε 2 2 (λ) (5) 2 α(λ) = 2πε 2 λ R(λ) = (n 1)2 + κ 2 (n + 1) 2 + κ 2 (7) where λ is photon wavelength, ε 1 and ε 2 are real and imaginary parts dielectric function, respectively, and n(λ), κ(λ) are refractive index and extinction coefficient, respectively. α(λ) and R(λ) are absorption coefficient and reflectivity, respectively. The absorption coefficients and reflectivity curves InSe/Te heterostructure, InSe monolayer and tellurene are shown in Figure 5. Herein, tellurene as absorption layer exhibits high absorption coefficient about 10 5 to 10 6 cm 1 in visible light, which can be comparable with that bulk WS 2 and WSe 2 used in efficient single junction solar cell [53]. The InSe monolayer as window layer is required high transparency for incident light, which means low absorption coefficient and reflectivity [17,54]. The InSe monolayer has an absorption coefficient about one order magnitude lower than that 2021, 14, x FOR PEER REVIEW tellurene, and reflectivity it is about 0.13 to 0.34 in range 0 7 to 411 ev photon energy. This result can be compared with that Janus WSeTe monolayer used as buffer layer [54]. (6) Figure 5. (a) Figure Calculated 5. (a) Calculated optical absorption optical absorption coefficients coefficients as well as (b) as well reflectivity as (b) reflectivity InSe/Te heterostructure, InSe/Te heterostructure, tellurene. InSe Curvemonolayer, in bottom indicates and tellurene. reference Curve solarin spectral bottom irradiance, indicates and reference colorful solar background spectral represents irra- InSe monolayer, and visible lightdiance, area [55]. and colorful background represents visible light area [55]. To more intuitively To more evaluate intuitively solar evaluate energy conversion solar energyability conversion InSe/Te ability vdw InSe/Te heterostructure, we heterostructure, evaluated wepower evaluated conversion power efficiency conversion (PCE) efficiency η in (PCE) limit η in 100% limit 100% vdw external quantum external efficiency quantum (EQE) efficiency by (EQE) following by equation following [6,51]: equation [6,51]: P( ) 0.65( Eg Ec 0.3) d( ) Eg η = 0.65(E g E c 0.3) P(ħω) E g ħω d(ħω) (8) P( ) d( 0 ) P(ħω)d(ħω) (8) 0 where 0.65 is -fill factor, P(ħω) is AM1.5 solar energy flux at value ħω for where 0.65 is photon -fill energy, factor, E P(ћω) is AM1.5 solar energy flux at value ћω g is gap donor, E c is conduction fset between for photon energy, donor Eg is and acceptor, gap and donor, (E ΔEc g E c is 0.3) term conduction is an estimation fset between donor and acceptor, and (Eg ΔEc 0.3) term is an estimation maxi- maximum mum open circuit voltage. For this formula, smaller ΔEc means greater value PCE. Additionally, it requires a suitable Eg, because if gap donor is higher, open circuit voltage will be better. However, higher gap will reduce

Materials 2021, 14, 3768 7 10 open circuit voltage. For this formula, smaller E c means greater value PCE. Additionally, it requires a suitable E g, because if gap donor is higher, open circuit voltage will be better. However, higher gap will reduce amount photons that can be absorbed, which will reflect in decrease short circuit current. Here, maximum PCE InSe/Te vdw heterostructure is calculated to 13.39%, which is highlighted as red star in Figure 6. To show uniqueness InSe/Te vdw heterostructure, Materials 2021, 14, x FOR PEER REVIEW PCE calculated by same method for or 2D heterostructure solar cells are 8 listed 11 in Table 2. Therefore, we infer that InSe/Te vdw heterostructure is a potential candidate for high-efficiency solar cell application. Figure Figure 6. Simulated 6. Simulated solar cell solar power cellconversion power conversion efficiency efficiency (PCE) η for (PCE) InSe/Te η for heterostructure InSe/Te heterostructure (marked (marked as as red star). red star). 4. Conclusions Table 2. Calculated maximum power conversion efficiency (PCE) (%) some recently reported 2D heterostructure solar cells. In summary, we established vdw heterostructures by combining MXA (M = Al, Ga, In and XA = S, Se, Te) and XB (XB System = Se, Te) monolayers. PCE Based on first-principles References calculations, stability and interlayer force se heterostructures were demonstrated by InSe/Te 13.39 This work formation GaTe/InS, and binding GaTe/GaSe energy. From screening, 11.52, 18.39 InSe/Te vdw heterostructure [15] shows type-ii Tielectronic 2 CO 2 /Zr 2 CO 2 structure feature with 22.74 a gap 0.88 ev, where [14] tellurene as absorber phosphorene/mos layer with 2 a direct gap about 16 18 1.14 ev could produce [56] photoexcited electron easily. PCBM/CBN In addition, tellurene and 10 20 InSe monolayer respectively exhibit [6] high absorption coefficient and low reflectivity. Furrmore, maximum power conversion efficiency 4. Conclusions (PCE) InSe/Te vdw heterostructure can reach up to 13.39%. Very recently, multilayer In InSe/Te summary, vdw we heterostructure established was vdw experimentally heterostructures observed by combining and showed MX potential application Ga, In andin X electronic and optoelectronic devices [57]. We believed that monolayer A = S, Se, Te) and X B (X B = Se, Te) monolayers. Based on first-principles calcula- A (M = Al, InSe/Te tions, vdw heterostructure stability and interlayer can be force experimentally se heterostructures realized and were show demonstrated better perfor-bmance. formation Our present and research binding energy. not only From finds screening, a novel type-ii InSe/Te heterostructure vdw heterostructure for high-effi- shows ciency type-ii solar cell, electronic but also furr structure guides feature design with a more gap2d vdw 0.88 ev, semiconductors where tellurene for as photovoltaic absorber materials. layer with a direct gap about 1.14 ev could produce photoexcited electron easily. In addition, tellurene and InSe monolayer respectively exhibit high absorption Supplementary coefficient Materials: and low The reflectivity. following Furrmore, are available online maximum at www.mdpi.com/xxx/s1, power conversion Figure efficiency S1: Projected structures (a) AlS, (b) AlSe, (c) AlTe, (d) GaS, (e) GaSe, (f) GaTe, (g) InS, (h) InSe, (PCE) InSe/Te vdw heterostructure can reach up to 13.39%. Very recently, multilayer (i) InTe, (j) Se and (k) Te monolayers by HSE06 hybrid functional method. The red, brown, blue InSe/Te vdw heterostructure was experimentally observed and showed potential application circles represent projected specific gravity M, XA, XB atoms, respectively. The first Brillouin zone with high-symmetry in electronic and points optoelectronic are shown in devices inset [57]. (a). We (l) believed The that edge monolayer alignments InSe/Te se vdw monolayers, heterostructure Table S1: canlattice be experimentally constants a (Å ), realized M-M, and show M-XA and better XB-XB (M performance. = Al, Ga, In, Our XA = present S, Se, Te research and XB = Se, notte) only bond finds lengths a novel LM-M type-ii (Å ), LM-XA heterostructure (Å ) and LXB-XB for (Å ), high-efficiency PBE and HSE solar cell, gaps but also E PBE g (ev), furr E HSE g guides (ev) for design MXA and XB more monolayers, 2D vdwtable semiconductors S2: energy for differences photovoltaic ΔE (mev) materials. and interlayer distances d (Å ) as well as lattice constants a (Å ) and bond lengths L (Å ) various configurations for AlXA/XB vdw heterostructures, Table S3: energy differences ΔE (mev) and interlayer distances d (Å ) as well as lattice constants a (Å ) and bond lengths L (Å ) various configurations for GaXA/XB vdw heterostructures, Table S4: energy differences ΔE (mev) and interlayer distances d (Å ) as well as lattice constants a (Å ) and bond lengths L (Å ) various configurations for InXA/XB vdw heterostructures.

Materials 2021, 14, 3768 8 10 References Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/ma14143768/s1, Figure S1: Projected structures (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 projected specific gravity M, X A, X B atoms, respectively. The first Brillouin zone with high-symmetry points are shown in inset (a). (l) The edge alignments se monolayers, Table S1: lattice constants a (Å), 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), PBE and HSE gaps E PBE g (ev), E HSE g (ev) for MX A and X B monolayers, Table S2: energy differences E (mev) and interlayer distances d (Å) as well as lattice constants a (Å) and bond lengths L (Å) various configurations for AlX A /X B vdw heterostructures, Table S3: energy differences E (mev) and interlayer distances d (Å) as well as lattice constants a (Å) and bond lengths L (Å) various configurations for GaX A /X B vdw heterostructures, Table S4: energy differences E (mev) and interlayer distances d (Å) as well as lattice constants a (Å) and bond lengths L (Å) various configurations for InX A /X B vdw heterostructures. Author Contributions: Conceptualization, R.L. and B.S.; methodology, Y.Z.; stware, Y.Z. and B.S.; validation, R.X., Y.Z. and C.X.; formal analysis, R.L. and B.S.; investigation, Z.M., R.L.; resources, Y.Z. and B.S.; data curation, Z.M., R.L. and R.X.; writing original draft preparation, Z.M. and R.L.; writing review and editing, C.W. and B.S.; supervision, B.S.; project administration, B.S.; funding acquisition, C.W. and B.S. All authors have read and agreed to published version manuscript. Funding: This work was supported by National Key Research and Development Program China (No.2017YFB0701701), National Natural Science Foundation China (No. 21973012), Natural Science Foundation Fujian Province (Nos. 2020J01351, 2020J01474), Scientific Research Project Jinjiang Science and Education Park Fuzhou University (Nos. 2019-JJFDKY-01 and 2019-JJFDKY-02), and Qishan Scholar Scientific Research Startup Project Fuzhou University. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from corresponding authors. Conflicts Interest: The authors declare no conflict interest. 1. Geim, A.K.; Grigorieva, I.V. Van der Waals heterostructures. Nature 2013, 499, 419 425. 2. Liu, Y.; Weiss, N.O.; Duan, X.; Cheng, H.-C.; Huang, Y.; Duan, X. Van der Waals heterostructures and devices. Nat. Rev. Mater. 2016. 3. Cheng, W.; Zhou, Z.; Pan, M.; Yang, H.; Xie, Y.; Wang, B.; Zhan, Q.; Li, R.-W. Stretchable spin valve with strain-engineered wrinkles grown on elastomeric polydimethylsiloxane. J. Phys. D Appl. Phys. 2019, 52. 4. Wang, X.; Xia, F. Van der Waals heterostructures: Stacked 2D materials shed light. Nat. Mater. 2015, 14, 264 265. 5. Li, X.; Chen, W.; Zhang, S.; Wu, Z.; Wang, P.; Xu, Z.; Chen, H.; Yin, W.; Zhong, H.; Lin, S. 18.5% efficient graphene/gaas van der Waals heterostructure solar cell. Nano Energy 2015, 16, 310 319. 6. Bernardi, M.; Palummo, M.; Grossman, J.C. Semiconducting Monolayer Materials as a Tunable Platform for Excitonic Solar Cells. ACS Nano 2012, 6, 10082 10089. 7. Eren, I.; Ozen, S.; Sozen, Y.; Yagmurcukardes, M.; Sahin, H. Vertical van der Waals Heterostructure Single Layer InSe and SiGe. J. Phys. Chem. C 2019, 123, 31232 31237. 8. Wirs, F.; Pozo-Zamudio, O.D.; Mishchenko, A.; Rooney, A.P.; Gholinia, A.; Watanabe, K.; Taniguchi, T.; Haigh, S.J.; Geim, A.K.; Tartakovskii, A.I. Light-emitting diodes by -structure engineering in van der Waals heterostructures. Nat. Mater. 2015, 14, 301 306. [PubMed] 9. Koma, A. Van der Waals epitaxy A new epitaxial growth method for a highly lattice-mismatched system. Thin Solid Films 1992, 216, 72 76. 10. Pierucci, D.; Henck, H.; Avila, J.; Balan, A.; Naylor, C.H.; Patriarche, G.; Dappe, Y.J.; Silly, M.G.; Sirotti, F.; Johnson, A.T.; et al. Band alignment and minigaps in monolayer MoS 2 -graphene van der Waals heterostructures. Nano Lett. 2016, 16, 4054 4061. 11. Jin, C.; Ma, E.Y.; Karni, O.; Regan, E.C.; Wang, F.; Heinz, T.F. Ultrafast dynamics in van der Waals heterostructures. Nat. Nanotechnol. 2018, 13, 994 1003. [PubMed]

Materials 2021, 14, 3768 9 10 12. Liu, K.; Zhang, L.; Cao, T.; Jin, C.; Qiu, D.; Zhou, Q.; Zettl, A.; Yang, P.; Louie, S.G.; Wang, F. Evolution interlayer coupling in twisted molybdenum disulfide bilayers. Nat. Commun. 2014, 5, 4966. 13. Duong, D.L.; Yun, S.J.; Lee, Y.H. Van der Waals Layered Materials: Opportunities and Challenges. ACS Nano 2017, 11, 11803 11830. 14. Zhang, Y.; Xiong, R.; Sa, B.; Zhou, J.; Sun, Z. MXenes: Promising donor and acceptor materials for high-efficiency heterostructure solar cells. Sustain. Energy Fuels 2021, 5, 135 143. 15. Chen, J.; He, X.; Sa, B.; Zhou, J.; Xu, C.; Wen, C.; Sun, Z. III VI van der Waals heterostructures for sustainable energy related applications. Nanoscale 2019, 11, 6431 6444. 16. Shockley, W.; Queisser, H.J. Detailed balance limit efficiency p-n junction solar cells. J. Appl. Phys. 1961, 32, 510 519. 17. Das, S.; Pandey, D.; Thomas, J.; Roy, T. The role graphene and or 2D materials in solar photovoltaics. Adv. Mater. 2019, 31, e1802722. 18. Fonash, S.J. Solar Cell Device Physics; Academic Press: Cambridge, MA, USA, 1981. 19. Tsai, M.L.; Li, M.Y.; Retamal, J.R.D.; Lam, K.T.; Lin, Y.C.; Suenaga, K.; Chen, L.J.; Liang, G.; Li, L.J.; He, J.H. Single atomically sharp lateral monolayer p-n heterojunction solar cells with extraordinarily high power conversion efficiency. Adv. Mater. 2017, 29. 20. Tan, C.; Cao, X.; Wu, X.J.; He, Q.; Yang, J.; Zhang, X.; Chen, J.; Zhao, W.; Han, S.; Nam, G.H.; et al. Recent advances in ultrathin two-dimensional nanomaterials. Chem. Rev. 2017, 117, 6225 6331. 21. Kuhn, A.; Chevy, A.; Chevalier, R. Crystal structure and interatomic distances in GaSe. Phys. Status Solidi 1975, 31, 469 475. 22. Gouskov, A.; Camassel, J.; Gouskov, L. Growth and characterization III VI layered crystals like GaSe, GaTe, InSe, GaSe 1 x Te x and Ga x In 1 x Se. Prog. Cryst. Growth Charact. 1982, 5, 323 413. 23. Bandurin, D.A.; Tyurnina, A.V.; Yu, G.L.; Mishchenko, A.; Zolyomi, V.; Morozov, S.V.; Kumar, R.K.; Gorbachev, R.V.; Kudrynskyi, Z.R.; Pezzini, S.; et al. High electron mobility, quantum Hall effect and anomalous optical response in atomically thin InSe. Nat. Nanotechnol. 2017, 12, 223 227. 24. Mudd, G.W.; Svatek, S.A.; Hague, L.; Makarovsky, O.; Kudrynskyi, Z.R.; Mellor, C.J.; Beton, P.H.; Eaves, L.; Novoselov, K.S.; Kovalyuk, Z.D.; et al. High broad- photoresponsivity mechanically formed InSe-graphene van der Waals heterostructures. Adv. Mater. 2015, 27, 3760 3766. 25. Zhao, S.; Wu, J.; Jin, K.; Ding, H.; Li, T.; Wu, C.; Pan, N.; Wang, X. Highly polarized and fast photoresponse black phosphorus- InSe vertical p-n heterojunctions. Adv. Funct. Mater. 2018, 28. 26. He, C.; Zhang, J.H.; Zhang, W.X.; Li, T.T. Type-II InSe/g-C 3 N 4 heterostructure as a high-efficiency oxygen evolution reaction catalyst for photoelectrochemical water splitting. J. Phys. Chem. Lett. 2019, 10, 3122 3128. 27. Yan, F.; Zhao, L.; Patane, A.; Hu, P.; Wei, X.; Luo, W.; Zhang, D.; Lv, Q.; Feng, Q.; Shen, C.; et al. Fast, multicolor photodetection with graphene-contacted p-gase/n-inse van der Waals heterostructures. Nanotechnology 2017, 28, 27LT01. 28. Apte, A.; Bianco, E.; Krishnamoorthy, A.; Yazdi, S.; Rao, R.; Glavin, N.; Kumazoe, H.; Varshney, V.; Roy, A.; Shimojo, F.; et al. Polytypism in ultrathin tellurium. 2D Mater. 2018, 6. 29. Xing, C.; Xie, Z.; Liang, Z.; Liang, W.; Fan, T.; Ponraj, J.S.; Dhanabalan, S.C.; Fan, D.; Zhang, H. 2D nonlayered selenium nanosheets: Facile synsis, photoluminescence, and ultrafast photonics. Adv. Opt. Mater. 2017, 5. 30. Singh, J.; Jamdagni, P.; Jakhar, M.; Kumar, A. Stability, electronic and mechanical properties chalcogen (Se and Te) monolayers. Phys. Chem. Chem. Phys. 2020, 22, 5749 5755. 31. Peng, Q.; Guo, Z.; Sa, B.; Zhou, J.; Sun, Z. New gallium chalcogenides/arsenene van der Waals heterostructures promising for photocatalytic water splitting. Int. J. Hydrogen Energy 2018, 43, 15995 16004. 32. Kresse, G.G.; Furthmüller, J.J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B Condens. Matter 1996, 54, 11169. [PubMed] 33. Kresse, G.; Joubert, D. From ultrast pseudopotentials to projector augmented-wave method. Phys. Rev. B 1999, 59, 1758 1775. 34. Hafner, J. Ab-initio simulations materials using VASP: Density-functional ory and beyond. J. Comput. Chem. 2008, 29, 2044 2078. [PubMed] 35. Kresse, G.; Hafner, J. Ab initio molecular-dynamics simulation liquid-metal-amorphous-semiconductor transition in germanium. Phys. Rev. B Condens. Matter 1994, 49, 14251 14269. [PubMed] 36. Blochl, P.E. Projector augmented-wave method. Phys. Rev. B Condens. Matter 1994, 50, 17953 17979. [PubMed] 37. Wang, G.; Peng, L.; Li, K.; Zhu, L.; Zhou, J.; Miao, N.; Sun, Z. ALKEMIE: An intelligent computational platform for accelerating materials discovery and design. Comput. Mater. Sci. 2021, 186. 38. Perdew, J.P.; Wang, Y. Accurate and simple analytic representation electron-gas correlation energy. Phys. Rev. B Condens. Matter 1992, 45, 13244 13249. 39. Perdew, J.P.; Burke, K.; Ernzerh, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1998, 77, 3865 3868. 40. Yang, X.; Sa, B.; Zhan, H.; Sun, Z. Electric field-modulated data storage in bilayer InSe. J. Mater. Chem. C 2017, 5, 12228 12234.

Materials 2021, 14, 3768 10 10 41. Klimes, J.; Bowler, D.R.; Michaelides, A. Chemical accuracy for van der Waals density functional. J. Phys. Condens. Matter 2010, 22, 022201. 42. Monkhorst, H.J.; Pack, J.D. Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13, 5188 5192. 43. Peng, Q.; Xiong, R.; Sa, B.; Zhou, J.; Wen, C.; Wu, B.; Anpo, M.; Sun, Z. Computational mining photocatalysts for water splitting hydrogen production: Two-dimensional InSe-family monolayers. Catal. Sci. Technol. 2017, 7, 2744 2752. 44. Demirci, S.; Avazlı, N.; Durgun, E.; Cahangirov, S. Structural and electronic properties monolayer group III monochalcogenides. Phys. Rev. B 2017, 95. 45. Zhuang, H.L.; Hennig, R.G. Single-layer group-iii monochalcogenide photocatalysts for water splitting. Chem. Mater. 2013, 25, 3232 3238. 46. Peng, Q.; Wang, Z.; Sa, B.; Wu, B.; Sun, Z. Blue phosphorene/ms 2 (M = Nb, Ta) heterostructures as promising flexible anodes for lithium-ion batteries. ACS Appl. Mater. Interfaces 2016, 8, 21. 47. Yang, X.; Sa, B.; Lin, P.; Xu, C.; Zhu, Q.; Zhan, H.; Sun, Z. Tunable contacts in graphene/inse van der Waals heterostructures. J. Phys. Chem. C 2020, 124, 23699 23706. 48. Chiu, M.H.; Zhang, C.; Shiu, H.W.; Chuu, C.P.; Chen, C.H.; Chang, C.Y.; Chen, C.H.; Chou, M.Y.; Shih, C.K.; Li, L.J. Determination alignment in single-layer MoS 2 /WSe 2 heterojunction. Nat. Commun. 2015, 6, 7666. [PubMed] 49. Liao, J.; Sa, B.; Zhou, J.; Ahuja, R.; Sun, Z. Design high-efficiency visible-light photocatalysts for water splitting: MoS 2 /AlN(GaN) heterostructures. J. Phys. Chem. C 2014, 118, 17594 17599. 50. Bjoerkman, T.; Gulans, A.; Krasheninnikov, A.V.; Nieminen, R.M. van der Waals bonding in layered compounds from advanced density-functional first-principles calculations. Phys. Rev. Lett. 2012, 108, 235502. [PubMed] 51. Scharber, M.C.; Mühlbacher, D.; Koppe, M.; Denk, P.; Waldauf, C.; Heeger, A.J.; Brabec, C.J. Design rules for donors in bulkheterojunction solar cells Towards 10 % energy-conversion efficiency. Adv. Mater. 2006, 18, 789 794. 52. Peng, Q.; Wang, Z.; Sa, B.; Wu, B.; Sun, Z. Electronic structures and enhanced optical properties blue phosphorene/transition metal dichalcogenides van der Waals heterostructures. Sci. Rep. 2016, 6, 31994. [PubMed] 53. Chaurasiya, R.; Gupta, G.K.; Dixit, A. Ultrathin Janus WSSe buffer layer for W(S/Se)2 absorber based solar cells: A hybrid, DFT and macroscopic, simulation studies. Sol. Energy Mater. Sol. Cells 2019, 201. 54. Chaurasiya, R.; Gupta, G.K.; Dixit, A. Heterostructure AZO/WSeTe/W(S/Se) 2 as an efficient single junction solar cell with ultrathin janus WSeTe buffer layer. J. Phys. Chem. C 2021, 125, 4355 4362. 55. A. G173-03, A.I. West Conshohocken, PA. 2012. Available online: www.astm.org (accessed on 17 May 2021). 56. Dai, J.; Zeng, X.C. Bilayer phosphorene: Effect stacking order on gap and its potential applications in thin-film solar cells. J. Phys. Chem. Lett. 2014, 5, 1289 1293. [PubMed] 57. Qin, F.; Gao, F.; Dai, M.; Hu, Y.; Yu, M.; Wang, L.; Feng, W.; Li, B.; Hu, P. Multilayer InSe-Te van der Waals Heterostructures with an Ultrahigh Rectification Ratio and Ultrasensitive Photoresponse. ACS Appl. Mater. Interfaces 2020, 12, 37313 37319. [PubMed]