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

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1 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 , China; mazc666@163.com (Z.M.); liruifeng1603@126.com (R.L.); @fzu.edu.cn (R.X.) 2 College Materials, Xiamen University, Xiamen , China; ygzhang@xmu.edu.cn 3 Xiamen Talentmats New Materials Science & Technology Co., Ltd., Xiamen , 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, 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 ( 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 (~ 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,

2 Materials 2021, 14, 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 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

3 Materials 2021, 14, x FOR PEER REVIEW Results and Discussion Materials 2021, 14, 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 differences between AlSe monolayer and selenene, InSe monolayer and tellurene, are and Å, respectively. The corresponding mismatches are 1.6% and 3.4%, respectively and 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 After. After structural optimizations for for a a total 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)

4 Materials 2021, 14, 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, and 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 I AlS-Te d E E I total MX A+XB AlSe-Se d E (3) b I A AlSe-Te d I where AlTe-Se Etotal is btotal energy MXA/XB 67.9 heterostructures EMX A and 0.75 E X B represent V AlTe-Te d I GaS-Se total energy d pristine MXA 3.660and XB monolayers, 21.2respectively In addition, 1.21 EMX I A+X is B GaS-Te sum total d energy mutually independent 22.4 MXA and 0.00 XB monolayers 0.26 fixed II in GaSe-Se corresponding d heterostructure lattices, and A is 21.5 interface 0.60 area Table 1 lists I GaSe-Te d II formation and binding energies and or related parameters most stable configuration GaTe-Te MXA/XB d heterostructures In addition, most 21.4 heterostructures have I neg- GaTe-Se b II ative InS-Se value formation b energy, which indicates that 21.4 reaction 0.60 combining 0.99 monolayers InS-Te to form se dheterostructures is energetically favorable 21.7 [49] For example, 0.50 those II I AlTe/Te, InSe-Se GaTe/Te InSe/Te heterostructures are 280.3, and mev, respectively. On or hand, all heterostructures have binding energy around ~20 I InSe-Te d II InTe-Se b V mev/å 2, which is sign vdw interaction between two monolayers [50]. InTe-Te b 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 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 by using20.7 HSE hybrid functional, 1.35 while Ι TableAlS-Te S1 lists ir corresponding d PBE3.822 and HSE492.3 gaps For instance, conduction Ι AlSe-Se minima (CBM) and d gap for3.744 InSe monolayer are and ev, and CBM Ι and AlSe-Te gap for tellurene d are and 1.09 ev, 58.5 respectively In 0.52 addition, 0.90 CBMΙ tellurene AlTe-Se located in Г pointb is only ev higher 67.9 than 24.1 energy 0.43 point 0.75 where VBM V located AlTe-Te in valance. d Ι GaS-Se d Ι GaS-Te d II GaSe-Se d Ι GaSe-Te d II A B g E HSE g

5 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 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( ) (4)

6 Materials 2021, 14, 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

7 Materials 2021, 14, 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 This work formation GaTe/InS, and binding GaTe/GaSe energy. From screening, 11.52, InSe/Te vdw heterostructure [15] shows type-ii Tielectronic 2 CO 2 /Zr 2 CO 2 structure feature with a gap 0.88 ev, where [14] tellurene as absorber phosphorene/mos layer with 2 a direct gap about ev could produce [56] photoexcited electron easily. PCBM/CBN In addition, tellurene and 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 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.

8 Materials 2021, 14, References Supplementary Materials: The following are available online at /ma /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.2017YFB ), National Natural Science Foundation China (No ), Natural Science Foundation Fujian Province (Nos. 2020J01351, 2020J01474), Scientific Research Project Jinjiang Science and Education Park Fuzhou University (Nos 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, Liu, Y.; Weiss, N.O.; Duan, X.; Cheng, H.-C.; Huang, Y.; Duan, X. Van der Waals heterostructures and devices. Nat. Rev. Mater 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, Wang, X.; Xia, F. Van der Waals heterostructures: Stacked 2D materials shed light. Nat. Mater. 2015, 14, 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, Bernardi, M.; Palummo, M.; Grossman, J.C. Semiconducting Monolayer Materials as a Tunable Platform for Excitonic Solar Cells. ACS Nano 2012, 6, 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, 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, [PubMed] 9. Koma, A. Van der Waals epitaxy A new epitaxial growth method for a highly lattice-mismatched system. Thin Solid Films 1992, 216, 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, 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, [PubMed]

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