Type-II van der Waals heterostructures constructed by V-V binary monolayers for ultra-thin solar cells

The development of solar cells holds great importance in the field of renewable energy and sustainability. Type-II van der Waals heterostructures, constructed from V-V binary monolayers, which exhibit easily-tunable electronic and optical properties, represent promising materials. In this work, we constructed and screened type-II van der Waals heterostructures using V-V binary monolayers for ultra-thin solar cells, and predicted their solar cell performance based on first-principles study. Five stable type-II van der Waals heterostructures were selected from forty-five heterostructures. The results showed that BiP/SbAs and BiP/BiAs heterostructures are promising candidates for solar cells with the power conversion efficiency as high as 17% and well light absorption performance. It will provide insights into the development and refinement of ultra-thin photovoltaic cells utilizing type-II van der Waals heterostructures composed of V-V binary monolayers.


Introduction
In response to the environmental crisis, developing clean energy has become an effective means.Solar energy stands out in clean energy due to its abundance, low cost, and negligible pollution [1][2][3].It offers numerous benefits, including environmental protection, sustainability, low maintenance, long lifespan, and wide adaptability.Consequently, researchers have widely adopted it as a key area of study.Solar cells have been developed since the early 1950s, with Chapin being the first to produce them using silicon materials.However, the power conversion efficiency (PCE) at the time was only around 6% [4].Since then, researchers have primarily focused on using silicon as the main material in solar cells, despite its limited ability to absorb solar energy [5][6][7].However, as a result of this, researchers have recently started exploring the use of high-efficiency novel materials fo Abstract.The development of solar cells holds great importance in the field of renewable energy and sustainability.Type-Ⅱ van der Waals heterostructures, constructed from V-V binary monolayers, which exhibit easily-tunable electronic and optical properties, represent promising materials.In this work, we constructed and screened type-Ⅱ van der Waals heterostructures using V-V binary monolayers for ultra-thin solar cells, and predicted their solar cell performance based on first-principles study.Five stable type-Ⅱ van der Waals heterostructures were selected from forty-five heterostructures.The results showed that BiP/SbAs and BiP/BiAs heterostructures are promising candidates for solar cells with the power conversion efficiency as high as 17% and well light absorption performance.It will provide insights into the development and refinement of ultra-thin photovoltaic cells utilizing type-II van der Waals heterostructures composed of V-V binary monolayers.r solar cells [8].Two-dimensional (2D) group-VA materials have attractive characteristics, and can be applied in many fields such as electronics, optoelectronics, and energy equipment [9,10].2D V-V binary materials (AB) (A doped to semiconductor B), as the internal combination of group-VA materials, have also been widely studied.The research shows that V-V binary materials have quite large band gap and high carrier mobility, and have easily-tunable electronic and optical properties [11,12].They are potential materials for the next generation of optoelectronic devices.Among them, β-SbN, AsN, SbP and SbAs monolayers have been predicted to the candidate materials for solar cell [13].The assembly of van der Waals (vdWs) heterostructures presents a highly efficient approach for enhancing the properties of two-dimensional monolayers, unveiling unique phenomena, and devising advanced-performance materials.Recent studies have shown that V-V binary materials can achieve high efficiencies in solar cells.For example, a record efficiency of 13% for blue-AsP/CdSe (13%) and 16% for GeSe/AsP [14].Although many studies have reported the structure, properties and applications of 2D V-V binary monolayers and their heterostructures, no systematic research has been carried out on the vdWs heterostructures composed of AB (A, B =N, P, As, Sb, Bi) in the field of solar cells.
In this work, we predicted the vdWs heterostructures that could be 1:1 constructed by 2D V-V binary materials as solar cells.We started to screen the vdWs heterostructures with lattice mismatch less than 5% among 45 heterostructures that may be constructed by two-layer V-V binary monolayers combination.Then, from the 6 selected vdWs heterostructures, we explored the type-II heterostructures through the contribution of energy band, and analysed their electronic properties.In addition, their potential applications in solar cells are predicted by calculating the PCE.Finally, we calculated their optical absorption to prove the feasibility of them as solar cells.Our research will provide theoretical basis for the application of 2D V-V binary materials in the field of solar cells.

Details of Computational Methods
The Vienna Ab initio simulation package (VASP) [15] was performed.And the projector augmented wave (PAW) method [16] was employed in all calculations.To prevent interaction between adjacent layers, a vacuum layer surpassing 20 Å was included in all simulations [17].For the optimization of geometric structures, electronic and optical properties, the Generalized Gradient Approximation (GGA) in the framework of the Perdew-Burke-Ernzerhof (PBE) functional was utilized [18].A Monkhorst-Pack mesh of 8 × 8 × 1 was employed.Simultaneously, the energy cutoff of plane-wave basis was set to 450 eV.The energy convergence criteria were determined at 10 -5 eV.And the force was established at 0.01 eV/Å.Grimme's D3 correction was implemented to consider the interlayer interaction in all heterostructures.Geometric optimization was conducted while constraining the lattice cell shapes and volumes.Additionally, the Heyd-Scuseria-Erenzerhof (HSE06) hybrid functional was employed to derive more precise energy bandgaps and position levels [20].

Structure construction and preliminary screening
The 2D V-V binary materials AB (A and B=N, P, As, Sb, Bi) is composed of group-VA materials, as shown in Figure 1 (a).There are 10 possible compounds in total.Five possible configurations of V-V binary compounds have been proposed in previous studies(α-, β-, γ-, δ-, and θ-) [21].It found that V-V binary compounds in β phase are more stable than other four phases.Therefore, we chose β phase V-V binary compound for further study.The structure is shown in Fig. 1 (b), which is graphene-like hexagonal buckled structure.Previous investigations have demonstrated their dynamic stability [21].The optimized lattice constants of each compound have been marked in Fig. 1 (a), which are aligned with prior studies [21].The large lattice mismatch will lead to the increase of stress on the interface, which may cause the interface instability and performance decline when preparation in the experiment.When constructing heterostructures, the lattice mismatch is generally controlled less than 5%.In this case, the stress on the interface can be considered tolerable, and the heterostructures are relatively stable.To save computing resources, we only consider the heterostructures whose ratios of primitive cell are 1:1.According to the different combination of ten V-V binary compounds, as shown in Table 1, forty-five heterostructures could be constructed.The lattice mismatch of these possible A 1 B 1 /A 2 B 2 heterostructures are shown in Table 1.Six heterostructures with lattice mismatch less than 5% were selected, named BiN/AsP (0%), SbP/BiP (4.02%), SbAs/SbP (3.75%), BiP/SbAs (0.26%), BiP/BiAs (3.09%), SbAs/BiAs (3.36%) heterostructures.2. The interface binding energy, which represents structural stability, was defined as follows [22]: in which the  .,  and  are the energies of the heterostructures, individual A 1/2 B 1/2 monolayers, respectively.The calculated results are all negative, ranging from -323.29 to -208.42 meV.
Among them, BiP/BiAs heterostructure is the most stable in these six heterostructure.

Electronic properties and type-II heterostructures screening
Type-II heterostructures which profit to separate photogenerated electrons and holes (e-h) might be effectively improve the mobility of carriers, and are widely used in solar cells, photodetectors, lightemitting diodes (LEDs) and other devices.The distinguishable band of the above six heterostructures were calculated in Figure 3.The red and blue circles represent different layers which are represented by chemical formula in the same colour.The results show that they are all indirect-bandgap semiconductors.Except that SbAs/BiAs is type-I heterostructure, others are type-II heterostructures.Taking the most stable BiP/BiAs heterostructure as an example, the valence band maximum (VBM) is at the point between K-Γ, which is mainly from the BiP monolayer.The conduction band minimum (CBM) is located at the points between Γ-M, mainly contributed by BiAs monolayer.In the interface of BiP/BiAs heterostructure, the electrons from the BiP layer will flow to the BiAs layer.On the contrary, the holes will transfer from the BiAs layer to the BiP layer.It will achieve the separation of electrons and holes and extend the carrier lifetime.

Solar cell performance and optical properties
Power conversion efficiency (PCE) refers to the ability of solar cells to convert solar radiation into electrical energy.It is one of the most critical indicators to evaluate the performance of solar cells.In heterostructure solar cells, PCE might vary with the band arrangement of the two layers.They were calculated for five type-II heterostructures by the following [23]: In this expression, the fill factor  is set to 0.65,  ∆ 0.3 represents the maximum opencircuit voltage employed for estimating VOC, where  is the bandgap of the independent donor, and ∆ corresponds to the conduction band offset (CBO) between the two independent layers.The short circuit current  is calculated by integrating at the 100% external quantum efficiency limit.The result in Figure 4 shows that the PCE of BiN/AsP, SbP/BiP, SbAs/SbP, BiP/SbAs, BiP/BiAs heterostructures are about 9%, 10%, 11%, 17%, 15%, respectively.The light absorption coefficient is another important performance indicator of solar cells.The higher the light absorption coefficient, the more light-energy the solar cell can absorb.So, the light absorption coefficients of BiP/SbAs and BiP/BiAs heterostructures, as shown in Figure 5.For comparison, the light absorption coefficients of the other five heterostructures were also calculated.The results show that, in the visible light range, compared with the other heterostructures, the BiP/BiAs heterostructure has better light absorption performance.While the light absorption performance of BiP/SbAs heterostructure is slightly weaker than the BiP/BiAs heterostructure.Their maximum light absorption coefficients can all reach 5×10 5 cm -1 .Therefore, the BiP/SbAs and BiP/BiAs heterostructures with PCE over 15% and appreciable light absorption coefficient are the promising materials in the field of solar cell.

Conclusion
In conclusion, this study demonstrated that type-Ⅱ van der Waals heterostructures constructed by V-V binary monolayers can be promising candidates for ultra-thin solar cells.We systematically constructed possible heterostructures, screened type-Ⅱ van der Waals heterostructures, and then analyzed the electronic, optical properties and the performance of these heterostructures for solar cell.In particular, the BiP/SbAs and BiP/BiAs heterostructures showed the best performance for solar cell in power conversion efficiency, as high as 17%, which is higher than that of many conventional solar cell materials.Also, we found that they exhibited high light absorption coefficients.Overall, this study provides a new direction for the design and development of high-efficiency and low-cost solar cells using type-Ⅱ van der Waals heterostructures with V-V binary monolayers.

Figure 1 .
Figure 1.(a) The selected elements from V-V AB binary compounds.The lattice parameters (a = b) for the AB monolayers are indicated.(b) Top and side views of the atomic structures for the AB monolayers.The large lattice mismatch will lead to the increase of stress on the interface, which may cause the

Figure 2 .
Figure 2. The top and side views of the atomic structures for A 1 B 1 /A 2 B 2 heterostructures.Their interface binding energy ( ) were computed to confirm the stability of the heterostructures, as shown in Table2.The interface binding energy, which represents structural stability, was defined as follows[22]:

Figure 3 .
Figure 3.The band structures at the HSE06 level for these vdWs A 1 B 1 /A 2 B 2 heterostructures.The contributions from the A 1 B 1 layer and the A 2 B 2 layer are depicted by red and blue circles, respectively.

Figure 4 .
Figure 4.The power conversion efficiency (PCE) for five heterostructures.Distinct efficiencies are displayed with varying colour regions.The light absorption coefficient is another important performance indicator of solar cells.The higher the light absorption coefficient, the more light-energy the solar cell can absorb.So, the light absorption coefficients of BiP/SbAs and BiP/BiAs heterostructures, as shown in Figure5.For comparison, the light absorption coefficients of the other five heterostructures were also calculated.The results show that, in the visible light range, compared with the other heterostructures, the BiP/BiAs heterostructure has better light absorption performance.While the light absorption performance of BiP/SbAs heterostructure is slightly weaker than the BiP/BiAs heterostructure.Their maximum light absorption coefficients can all reach 5×10 5 cm -1 .Therefore, the BiP/SbAs and BiP/BiAs heterostructures with PCE over 15% and appreciable light absorption coefficient are the promising materials in the field of solar cell.

Figure 5 .
Figure 5.The absorption coefficient of five heterostructures marked in different lines.

Table 1 .
The lattice mismatch of forty-five possible A 1 B 1 /A 2 B 2 heterostructures according to the combination of ten V-V binary compounds.

Table 2 .
The lattice parameters (a = b), bond length (d), lattice mismatch, interface binding energy (E b ), band gaps at the HSE06 level (E g ), gap type and heterostructure type for the heterostructures.