Cataloguing MoSi$_2$N$_4$ and WSi$_2$N$_4$ van der Waals Heterostructures: An Exceptional Material Platform for Excitonic Solar Cell Applications

Two-dimensional (2D) materials van der Waals heterostructures (vdWHs) provides a revolutionary route towards high-performance solar energy conversion devices beyond the conventional silicon-based pn junction solar cells. Despite tremendous research progress accomplished in recent years, the searches of vdWHs with exceptional excitonic solar cell conversion efficiency and optical properties remain an open theoretical and experimental quest. Here we show that the vdWH family composed of MoSi$_2$N$_4$ and WSi$_2$N$_4$ monolayers provides a compelling material platform for developing high-performance ultrathin excitonic solar cells and photonics devices. Using first-principle calculations, we construct and classify 51 types of MoSi$_2$N$_4$ and WSi$_2$N$_4$-based [(Mo,W)Si$_2$N$_4$] vdWHs composed of various metallic, semimetallic, semiconducting, insulating and topological 2D materials. Intriguingly, MoSi$_2$N$_4$/(InSe, WSe$_2$) are identified as Type-II vdWHs with exceptional excitonic solar cell power conversion efficiency reaching well over 20%, which are competitive to state-of-art silicon solar cells. The (Mo,W)Si$_2$N$_4$ vdWH family exhibits strong optical absorption in both the visible and ultraviolet regimes. Exceedingly large peak ultraviolet absorptions over 40%, approaching the maximum absorption limit of a free-standing 2D material, can be achieved in (Mo,W)Si$_2$N$_4$/$\alpha_2$-(Mo,W)Ge$_2$P$_4$ vdWHs. Our findings unravel the enormous potential of (Mo,W)Si$_2$N$_4$ vdWHs in designing ultimately compact excitonic solar cell device technology.


Introduction
Solar-to-electricity conversion offers a promising clean energy source to power a more sustainable technology landscape in the future. Despite the widespread deployment of conventional silicon-based solar cell, the continual improvement of the solar-to-electricity conversion efficiency remains a formidable challenge. Conventional crystalline silicon pn junction solar cell is plagued by nonradiative recombination of photogenerated electron-hole pairs, 1 which severely limits its solar-to-electricity conversion efficiency. 2 Silicon solar cells also entails the use of thicker layers to achieve longer optical path for better light absorption, which fundamentally limits their deployment in ultracompact and low-mass solar cell design. 3 The search of novel nanomaterials and device architectures beyond the conventional silicon pn junction solar cell remain an open research challenge that urgently needs to be addressed.
Excitonic solar cell has recently emerged as a compelling candidate for high-efficiency solar-to-electricity conversion. In contrast to conventional semiconductor-based pn junction solar cell where light-to-electricity conversion occurs exclusively within the same bulk material, excitonic solar energy conversion is an interfacial effect that arises from the band discontinuity across a heterojunction. 4, 5 Unlike the pn junction solar cell in which a built-in potential is needed to separate the photogenerated electron-hole pairs in the bulk, electrons and hole are spontaneously dissociated onto the two sides of the interface in an excitonic solar cell. The interfacial band alignment thus provides an exothermic pathway for exciton dissociation even though they do not possess sufficient energy to dissociate in the bulk. The huge chemical potential gradient created across the interface significantly increases the open-circuit voltage beyond the built-in potential. 6 Recent advances of two-dimensional (2D) materials and their van der Waals heterostructures (vdWHs) 7-9 unravel an exciting route towards advanced excitonic solar cell technology. 10,11 The vertical coupling of different 2D materials via weak van der Waals (vdW) forces results in 'designer' heterostructures with physical properties not easily found in the nature, thus enabling myriads of high-performance nanoelectronics, optoelectronics, photonics and neuromorphic devices to be realized. 4,5,[12][13][14][15][16][17][18][19][20][21][22][23] The optical absorption, band alignment and band gap of vdWHs can be custom made with ease. Together with the long exciton lifetime and the capability of efficient charge harvesting at ultrafast timescales 13-15 , vdWH has become a compelling and potentially disruptive platform for the development of ultimately compact excitonic solar cell technology. 5,24,25 Designing high-performance vdWH excitonic solar cell is, however, a complex technological challenge both theoretically and experimentally.
Computationally, the design space of vdWHs is enormously large due to nearly unlimited material combinations and the continual discovery of new 2D materials. The maximum power conversion efficiency (PCE) of vdWHs is predicted to lie within the range of 10% to 20%, with only a minority of vdWHs 20, 21, 26 (e.g. GaAs/InAs, HfSe2/GeO2 and BAs/BP) capable of achieving large PCE over 20%. Experimentally, the PCE of fabricated devices are only a small fraction of the theoretical limit 10 due to material defects and carrier recombination losses. 5 Furthermore, the experimentally realizable material combinations of vdWHs are constrained by the material synthesis and assembly processes. 27,28 The limited availability of high-PCE vdWHs and the formidable challenges of fabricating high-quality vdWHs highlight the urgency and importance of continual computationally searching for high-PCE vdWH, so to further expand the ground for the experimental realization of high-performance excitonic solar cell technology.
In this work, we show that the vdWH family composed of septuple-layered MoSi2N4 and WSi2N4 monolayers 29the recently discovered archetypes of the emerging MA2Z4 monolayer familyoffers a versatile material platform towards high-efficiency solar energy harvesting, optoelectronics and photonics applications. Using first-principle density functional theory (DFT) simulations, we constructed 51 types of (Mo,W)Si2N4-based vdWHs and characterized their electronic and optical properties. The vdWHs are systematically classified according to their contact types and band alignments. 30 Remarkably, we found that MoSi2N4/(ZnO, WGe2N4) and MoSi2N4/(InSe, WSe2) are Type-II vdWHs with PCE reaching well over 15% and 20% respectively, which are comparable to many state-of-art solar cells composed of silicon and perovskite 31 as well as vdWHs. 20, 26 Furthermore, majority of the 51 types vdWHs exhibit substantial optical absorption in the visible and ultraviolet (UV) spectrum.
Nearly all vdWHs exhibit peak optical absorption in the UV regime, thus suggesting their potential in UV photonics applications. Our work unravels the enormous potential of (Mo,W)Si2N4-based vdWHs in UV photonics, optoelectronics and solar energy harvesting applications, and call for a more comprehensive computational and experimental search of vdWHs with exceptional physical properties in the expansive MA2Z4 material family.

Computational Methods
QuantumATK 32 is used to construct the heterostructures with lattice mismatch of less than 5% 33, 34 between monolayers using supercell structure and applying the appropriate rotation. A vacuum layer of thickness ~25 Å is inserted between adjacent bilayer unit cell to eliminate the interactions from periodic images. We used the Vienna Ab initio Simulation Package (VASP) 35 for structural optimization, energy and charge calculation, and VASPKIT 36 for optical properties calculation. For structural optimization and self-consistent field calculations, a Gamma-centered Brillouin zone k-point sampling grid of 11 x 11 x 1 with Monkhorst-Pack method is used. In the structural optimization step, the supercell volume is kept constant while the cell shape and ion positions are allowed to change. The break condition for each ionic relaxation loop is set to 10 -3 eV Å -1 such that the forces acting on the unit cell after convergence is less than this value and the break condition for each electronic relaxation loop is set to 10 -6 eV. To take into account the weak van der Waals interactions between the monolayers, we adopted the DFT-D3 method with the Grimme scheme. We chose the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) form for the exchange correlation functional in the calculations for all our heterostructures, since MoSi2N4 band gap obtained from PBE (i.e. 1.73 eV and 1.78 eV) 37, 38 is closer to the experimental value of 1.94 eV, 29 as compared to the Heyd-Scuseria-Ernzerhof hybrid functional form (HSE06) with bandgap of 2.30 eV. 29 Moreover, it has been demonstrated that the band alignment typesone of the key results of this workpredicted using PBE is in good agreement with that obtained using HSE06. 30 The supercells of the vdWHs are shown in Figures S1-S6. The electronic band structures, plane-averaged electrostatic potential profiles, plane-averaged differential charge density profiles, dielectric constants, optical absorption spectra and the general calculation data of all 51 types of vdWHs are compiled and systematically presented in Figures S7-S13, S14-S19, S20-S25, S26-S31, Tables S1 and S2 of the Supporting Information respectively.

MoSi2N4 and WSi2N4: An Overview of their van der Waals Heterostructures
The discovery of MoSi2N4 and WSi2N4 open an exciting avenue towards the development of remains valid for most of the metallic TMDC, graphene, InSe, hBN and MA2Z4 family due to their weak coupling nature. In contrast, the disagreement between AR and direct DFT calculations is rather severe for semiconducting and Janus TMDC monolayers as well as the honeycomb semiconducting monolayers of GaN, BP and ZnO. This disagreement highlights the importance of direct DFT calculations for contact type and band alignment determination.

Metal/Semiconductor (MS) Contacts
We first consider (Mo,W)Si2N4-based vdWHs of MS contact type. In this case, either Ohmic or Schottky contacts can be formed at the interface. 78,79 For an Ohmic contact, the absence of a Schottky barrier greatly facilitate charge injection across an MS contact and is much sought after for creating energy-efficient electrical contacts. 80 MS vdWH contacts are particularly attractive due to the strong suppression of the Fermi level pinning effect, a detrimental effect that severely impedes the engineering of energy-efficient electrical contacts. 81, 82 Here we identify 4 species of p-type Ohmic contacts formed by MoSi2N4 and WSi2N4 in contact with NbS2 and NbSe2 [see Figure 3(A-D)]. The formation of these p-type Ohmic vdWHs can be readily understood from the band alignment diagram in Figure 2(A), where the relatively larger work functions of NbS2 (6.06 eV) and NbSe2 (5.35 eV) align with the valence band maximum (VBM) energies of MoSi2N4 (5.30 eV) and WSi2N4 (5.14 eV) to yield p-type Ohmic contact by virtue of AR. We note that the MoSi2N4/NbS2 contact is predicted to be an p-type Schottky contact with ultralow Schottky barrier height (SBH) 38 where the strain arising from lattice mismatch upon forming the vdWH is entirely distributed on the NbS2 monolayer only. In contrary, strain is distributed evenly between the two monolayers in our calculations, which yields a p-type Ohmic contact instead. Although SBH is absent in Ohmic vdWH contact, a van der Waals gap is present between the two contacting monolayers that may impede charge ejection efficiency. 83 The tunneling potential barrier Φ and the barrier width can be extracted from the plane- where ℏ, e, is the Planck's constant, charge magnitude and mass of the free electron respectively. The calculated lies in the order of 10 -9 which are comparable to those of metal/MoSi2N4 and metal/WSi2N4 contacts (i.e. from 0.1 × 10 −9 to 3.85 × 10 −9 Ω 2 ) 37 and that in the semimetal contact of Bi/MoS2 contact ( 1.81 × 10 −9 Ω 2 ). 85 Finally, when

Band Alignment Types
The band gap values, the direct or indirect nature of the band gap, and the band alignment types (i.e. Type-I, II and H) are summarized in Figure 5(A). We identify 19 species of Type-I vdWHs a band alignment type that is useful for photoluminescence applications, such as lightemitting diodes and lasers, due to the localization of CBM and VBM states within the same sub-monolayer. Among these Type-I vdWHs, 15 species possess direct band gap that is highly beneficial for engineering efficient excited electron-hole pair recombination. 90 The electronic band structure of a representative Type-I vdWH, MoSi2N4/hBN is shown in Figure 5(  impede the potential of Type-H vdWHs for optoelectronics applications. We further note that to verify these unusual band structures, we employ the HSE06 exchange correlation functional in the electronic band structure calculations of these heterostructures. The Gamma-centered Brillouin zone k-point sampling grid of 6 x 6 x 1 is used due to computational resources constraint. Interestingly, the VBM hybridization is removed in MoSi2N4/2H-MoS2 and MoSi2N4/ 2 -WGe2P4 under the HSE06 calculations [see Figure S13].

Excitonic Solar Cell Maximum Conversion Efficiency of Type-II vdWHs
Optically excited electron-hole pairs are spatially well-separated in Type-II vdWHs, which enables the efficient dissociation of these carriers to form conduction current. Such vdWHs are thus practically useful for applications where long-live and/or delocalized electron-hole pairs are needed, such as photodetector, excitonic solar cell and photocatalytic water splitting. 87 We calculated the maximum solar cell PCE of these Type-II vdWHs, which represents the theoretical upper limit of solar-to-electricity conversion in a heterostructure device. The PCE is calculated as: 86, 94 where is the bandgap of the donor monolayer, is the conduction band offset (CBO) between the two monolayers, ( ℏ ) is the solar spectral irradiance as a function of photon frequency , and the 0.3 eV term in Equation (

Optical Properties
The We compiled the peak absorbance for photon energies up to 5 eV for all vdWHs as shown in Figure 7. Intriguingly, almost all vdWHs exhibit peak absorbance in the UV regime, except for MoSi2N4/2H-WS2 vdWH which has a peak absorbance at the visible photon energy of 3.2 eV. The peak absorbance of the isolated MoSi2N4 and WSi2N4 monolayers [see Figure 6(G) and 6(H) for the optical absorption spectra of MoSi2N4 and WSi2N4 monolayers] is 20% at 4.0 eV and 17% at 4.4 eV respectively, which are comparable to some of the strongest mid-UVabsorbing 2D materials (e.g. SnS2 and SnSe2). 102 More importantly, the peak absorbance is significantly enhanced upon forming the vdWHs, with many vdWHs reaching a peak absorbance of over 30% in the UV regime. In general, the WSi2N4 vdWHs exhibit peak absorbance at higher photon energies as compared to that of MoSi2N4 counterpart in the energy range being studied, owing to the slightly higher peak absorbance photon energies of 4.4 eV of the WSi2N4 monolayer, as compared to that of monolayer MoSi2N4 at 4.0 eV [see Figure 6(G) and 6(H)]. We grouped the vdWHs into the sub-groups of near-UV (3.5 eV to 4.0 eV), mid-UV (4.1 eV to 4.4 eV) and deep-UV (>4.5 eV) according to the peak absorbance photon energies. Intriguingly for the vdWHs composed of entirely MA2Z4, (i.e. (Mo,W)Si2N4/α2-(Mo,W)Ge2P4) the vdWHs exhibit exceptionally strong UV absorption of over 40%, which approaches the optical absorption limit of a free-standing monolayer, and a broadband strong absorption shoulder between 3 eV and 5 eV [see Figure S29 and S31]. These findings suggest the potential strength of MA2Z4-based vdWHs in photonics device applications.

Conclusion
In summary, we investigated 51 types of MoSi2N4 and WSi2N4 vdWHs and categorized these heterostructures based on their contact and band alignment types. For MS Ohmic contacts, the tunnelling-specific resistivities are comparable or lower than many of the previously reported 2D semiconductor electrical contacts. Multiple Type-II heterostructures are identified.
Particularly, MoSi2N4/InSe and MoSi2N4/WSe2 exhibit excellent solar cell energy conversion efficiency greater than 20% and substantial optical absorption in the visible light regime, making them potential candidates for photovoltaic applications. In terms of optical absorption, the family of (Mo,W)Si2N4-based bilayer van der Waals heterostructures generally exhibit much enhanced ultraviolet optical absorption when compared to their isolated counterparts.
The (Mo,W)Si2N4/(α2-MoGe2P4,α2-WGe2P4) heterostructures have an exceedingly high ultraviolet peak absorbance of over 40% that approaches the theoretical maximum absorption limit of a free-standing monolayer, thus revealing their strength in ultraviolet photonics applications. Our findings reveal the promising role of (Mo,W)Si2N4-based van der Waals heterostructures as a versatile platform for designing novel optoelectronics and photonics applications, and call for a more comprehensive screening of the expansive MA2Z4 vdWH family to fully unlock their potential as building blocks of high-performance nanodevice technology.

Supporting Information
Supporting Information is available from the Wiley Online Library.