The interlayer coupling modulation of a g-C3N4/WTe2 heterostructure for solar cell applications

Constructing van der Waals (vdW) heterostructures has been proved to be an excellent strategy to design or modulate the physical and chemical properties of 2D materials. Here, we investigated the electronic structures and solar cell performances of the g-C3N4/WTe2 heterostructure via first-principles calculations. It is highlighted that the g-C3N4/WTe2 heterostructure presents a type-II band edge alignment with a band gap of 1.24 eV and a corresponding visible light absorption coefficient of ∼106 cm−1 scale. Interestingly, the band gap of the g-C3N4/WTe2 heterostructure could increase to 1.44 eV by enlarging the vdW gap to harvest more visible light energy. It is worth noting that the decreased band alignment difference resulting from tuning the vdW gap, leads to a promotion of the power conversion efficiency up to 17.68%. This work may provide theoretical insights into g-C3N4/WTe2 heterostructure-based next-generation solar cells, as well as a guide for tuning properties of vdW heterostructures.


Introduction
From graphene, two-dimensional (2D) materials open a new gate to the material society and provide us with unprecedented insight to understanding and exploring materials. 1,2 Generally speaking, 2D materials could show distinguished physical and chemical properties due to their giant specic surface areas. 3 For example, as the rst discovered two-dimensional material, graphene has been demonstrated to be an outstanding candidate in tremendous applications such as Li-ion batteries, supercapacitors, and beyond. [4][5][6] So far, the applications of various typical 2D materials have been investigated, involved in MXene, graphene-based materials, transition metal oxides, and so on. [7][8][9][10] Besides, 2D materials present high performance not only in energy storages but also in catalysts, thermoelectric devices, electronic devices, and optoelectronic devices. [11][12][13][14] Especially, many 2D semiconducting materials show dramatic light harvesting properties, inspiring global researchers to explore their applications in solar cells. 15 Currently, the 2D transition metal dichalcogenides materials (TMDs) have been a research hotspot. 16,17 TMDs are a class of materials with the formula MX 2 , where M is a transition metal element, and X presents for S, Se, and Te. These materials form layered structures with the X-M-X stacking conguration, where the chalcogens in two hexagonal planes are separated by a plane of transition metal atoms. 18 The bulk TMDs have various properties ranging from insulators, semiconductors, semi-metals, and metals; meanwhile, their corresponding monolayers or few layers essentially preserve these properties. 19 Multitudinous researches illustrated that TMDs could be a class of excellent materials in applications of photovoltaics and solar cells. 20 On the other hand, the g-C 3 N 4 and its isomers have been widely explored aiming at solar energy converting because of their high surface activities and easily modulated surface chemistry by means of surface engineerings. 21,22 Monolayer g-C 3 N 4 presents a suitable band gap leading to its favorable absorption properties in the visible light spectrum. 23,24 However, the high recombination rate of electrons and holes in these individual 2D materials limits their performance in photocatalysts and solar cells. 25,26 Hence, promoting the efficiency of carrier separations in 2D materials is of great interest and importance. 27,28 Constructing van der Waals (vdW) heterostructures with different types of 2D materials stacking in a vertical direction has been proved an accessible approach to tune the properties and performance of 2D materials, [29][30][31][32] which have been proved to be one of the most efficient categories to enhance the performance of TMDs and g-C 3 N 4 . It is noted that heterostructure solar cells, considered as next-generation solar cell technology, have attracted great attention because of their fascinating properties in solar cell application. 33,34 For example, compared to single-layer structures, the optical properties under visible-light irradiation of Blue_P/TMDs vdW heterostructures are signicantly improved combined, which achieves higher efficiency in solar energy conversions. 35 Similarly, the g-C 3 N 4 based heterostructures have tunable electric properties, stronger optical properties as well as higher catalytic activity. 36,37 Especially, g-C 3 N 4 /WTe 2 vdW heterostructure has been proved to be a potential electrocatalyst for hydrogen evolution reaction. 38 At the same time, challenges and opportunities for exploring advanced g-C 3 N 4 based heterostructure are still ongoing.
In this work, we investigated the interlayer interactions, electronic structures, and optical properties of an articial g-C 3 N 4 /WTe 2 vdW heterostructure. It is worth noting that vertical strains can modify the band gap and further result in a better light harvest with a light absorption coefficient up to $10 6 cm À1 in the process. The decreased band alignment difference caused by the increased vdW gap gives rise to the promotion of power conversion efficiency are unraveled. Our ndings provide signicant guidance to design and modulate the performance of 2D materials applied in next-generation optoelectronic devices.

Computational methods
In our work, we adopted the ALKEMIE platform 39 together with the Vienna ab initio simulation package (VASP) based on density functional theory (DFT) to perform the rst-principles calculations. 40 The projection-augmented wave (PAW) exchange and correlation effects potential was used in the term of generalized gradient approximation (GGA) Perdew-Burke-Ernzerhof (PBE). [41][42][43] We introduced the DFT-D3 method 44 to correct the vdW interactions. A vacuum space of 20Å along the z-direction was built to avoid periodic interactions. Energy cutoff of 500 eV was set, and 8 Â 8 Â 1 G-centered k-mesh was used for Brillouin zone (BZ) integrations. To overcome the underestimation of the band gap by the standard semilocal DFT functionals, we introduced the Heyd-Scuseria-Ernzerhof (HSE06) function 45 for the electronic structure calculations. The relaxation convergence for electrons and ions were 1 Â 10 À6 eV and 1 Â 10 À5 eV, respectively. To obtain accurate dielectric functions comparable to the experimental results, time-dependent Hartree-Fock calculation (TDHF) was introduced to calculate the response functions by including the excitonic effects based on the HSE06 wavefunctions.

Results and discussion
Geometry and electronic structure Firstly, we analyzed the geometry and electronic structures of monolayer g-C 3 N 4 and WTe 2 . As shown in Fig. 1(a) and (b), g-C 3 N 4 consists of N and C atoms in a staggered fashion similar to graphene with the optimized constant lattice of 6.95Å, while monolayer WTe 2 shows 2H phase with the optimized constant lattice of 3.52Å, which agree well with previous works. 46,47 We, therefore, built a g-C 3 N 4 /WTe 2 heterostructure by stacking a 2 Â 2 Â 1 supercell of WTe 2 upon the unit cell of g-C 3 N 4 together with a lattice constant mismatch of 1.3%. Furthermore, we considered 6 possible stacking congurations by shiing g-C 3 N 4 in a certain direction to explore the energetically favorable structure of the heterostructure, as illustrated in Fig. 1(c-h). Herein, the formation energy E form was dened as where E total heterostructure , E free g-C 3 N4 and E free WTe2 are the total energy of the g-C 3 N 4 /WTe 2 heterostructure, freestanding g-C 3 N 4 and WTe 2 monolayer, respectively. On the other hand, the vdW binding energy E b was dened as 48 where A is the interface area of a heterostructure unit cell, E g-C 3 N 4 +WTe 2 is the sum of the total energies of the mutually independent g-C 3 N 4 and WTe 2 monolayers xed in the corresponding heterostructure lattice, respectively. The optimized lattice constant a, the calculated vdW gap d layer , formation energy E form and binding energy E b are listed in Table 1. It is interesting to note that the values of E form for all these 6 congurations are negative, indicating these heterostructures are energetic favorable. In addition, the calculated E b between the g-C 3 N 4 and WTe 2 monolayers is around 15 meVÅ À2 , which is close to the typical vdW binding energy. 49,50 Therefore, the g-C 3 N 4 /WTe 2 heterostructure can be dened as a vdW heterostructure. We chose conguration-I as the object to study in the subsequent work since stacking conguration-I exhibits the most favorable E form and smallest d layer .
To prove the thermodynamically stability, Born-Oppenheimer ab initio molecular dynamics (AIMD) simulations were adopted for the proposed g-C 3 N 4 /WTe 2 heterostructure at 300 K for 10 ps. A 2 Â 2 supercell has been constructed for the AIMD calculations. Fig. 1(i) displays the energy evolution and structure snapshots aer 300 K annealing for 10 ps of the g-C 3 N 4 / WTe 2 heterostructures. It is noted that the structure snapshots suggest that atoms just move near their equilibrium location during the simulations, and there is no structural reconstruction at 300 K. At the same time, the changes of the total energy are very small during the simulations from Fig. 1(i), indicating that the proposed g-C 3 N 4 /WTe 2 vdW heterostructure is thermodynamically stability at 300 K. Fig. 2(a) shows the band structures of freestanding g-C 3 N 4 and WTe 2 monolayers using HSE06 calculations. To compare clearly, the vacuum level was set to 0 eV as a baseline. It can be found that g-C 3 N 4 has an indirect band gap of 3.21 eV, where CBM and VBM locate at the K (1/3, 1/3, 0) and G (0, 0, 0) point, respectively. Meanwhile, the WTe 2 shows the direct gap feature with the band gap of 1.60 eV, where both CBM and VBM locate at the K (1/3, 1/3, 0) point. These results agree well with the previously published studies. 46,47 On the other hand, the projected band structure and partial density of states of g-C 3 N 4 / WTe 2 heterostructure is plotted in Fig. 2(b), in which the projected weight of g-C 3 N 4 and WTe 2 are distinguished by size and color. The pink and blue balls represent the contributions from g-C 3 N 4 and WTe 2 , respectively. For g-C 3 N 4 /WTe 2 heterostructure, both CBM and VBM locate at the K (1/3, 1/3, 0) point, showing the direct band gap feature, with the calculated HSE06 band gap of 1.24 eV. Interestingly, the g-C 3 N 4 /WTe 2 heterostructure shows the band structure feature of a type-II heterostructure, 51 where CBM is contributed by the g-C 3 N 4 layer and VBM is occupied by the WTe 2 layer. The band alignment diagrams for isolated g-C 3 N 4 , WTe 2 monolayer, and heterostructure interface are illustrated in Fig. 2(c). Obviously, the work function of the g-C 3 N 4 /WTe 2 heterostructure lies between the g-C 3 N 4 and WTe 2 monolayers. When g-C 3 N 4 and WTe 2 come into contact, the electrons ow from WTe 2 to g-C 3 N 4 due to the lower work function of WTe 2 and vice versa for the holes. As a result of the increased transfer of electrons, the Fermi level shis and nally reaches the same energy level. The Table 1 The calculated lattice constants a, the vdW gap d layer , formation energy E form and binding energy E b of g-C 3 N 4 /WTe 2 heterostructure with possible stacking configurations  differences between the band structure of g-C 3 N 4 /WTe 2 heterostructure and corresponding monolayers indicate that the vdW interactions play an essential role in the electronic structures.
To understand the vdW interlayer interaction between the different parts of the heterostructure, we further investigated g-C 3 N 4 /WTe 2 heterostructure with different interlayer distance d layer of the vdW gap. As shown in Fig. 3, both E form and ÀE b follow the Lenard-Jones type relation as a function of d layer , 52 and a lower value of ÀE b correspond to a stronger binding. Clearly, g-C 3 N 4 /WTe 2 heterostructure with the equilibrium d layer holds the most negative E form and ÀE b . As the d layer decreases, both E form and ÀE b increase dramatically. As the d layer increases, E form and ÀE b gradually increases towards zero. Herein, E form and ÀE b remain negative among an extensive range of d layer , indicating the possibility to tune the interlayer interaction by varying d layer . As mentioned before, there is the transfer of electrons within the vdW gap, which affects the electronic structure of the g-C 3 N 4 /WTe 2 heterostructure. Thereby, we calculated the planar-averaged charge density differences of g-C 3 N 4 /WTe 2 heterostructure with different d layer , as shown in Fig. 4. Here, the plane-averaged electron density difference Dr was calculated by where r g-C3N4/WTe2 is the charge density of the heterostructure, r g-C3N4 and r WTe2 are charge densities of the g-C 3 N 4 and WTe 2 parts in the heterostructure, respectively. The positive and negative values denote charge accumulation and depletion in the combined system comparing with the two isolated monolayers, respectively. Fig. 4 clear presents the charge redistribution in the vdW gap of g-C 3 N 4 /WTe 2 heterostructure: the charge depletion around the g-C 3 N 4 part and the charge accumulation around the WTe 2 region, indicating the charge transfer from g-C 3 N 4 to WTe 2 . As the d layer decreases, the stronger interlayer interaction results in the more obvious charge transfer. Oppositely, the charge transfer weakens when d layer increases. The similar shape of Dr for g-C 3 N 4 /WTe 2 heterostructure with different d layer indicates the excellent stability of the heterostructure from the electronic structure point of view. This phenomenon suggests a possible method to tune the band structure of the g-C 3 N 4 / WTe 2 heterostructure by modifying the interlayer interaction.
To further explore the inuence of the vdW interactions on the electronic structures of the g-C 3 N 4 /WTe 2 heterostructure, we plotted the band gap, band alignment, and work function of g-     Fig. 5(a). The PBE and HSE06 results show similar trends that the band gap decreases continuously as d layer decreases. Oppositely, as d layer increases, the band gap increases towards a balance value of 1.44 eV (HSE06). In addition, since the band alignment and work function are crucial in semiconductor heterostructurebased functional device designs, we plotted the band alignment and work function of the g-C 3 N 4 /WTe 2 heterostructure corresponding to the vacuum level, as shown in Fig. 5(b). Correspondingly, the band alignment and work function show similar trends of band gap with different d layer . As the d layer decreases, CBM shis downward continuously, and VBM shis upward continuously, which reduces the band gap. On the contrary, as d layer increases, CBM and VBM shi oppositely and towards convergent.
To explore the solar light-harvesting ability of the g-C 3 N 4 / WTe 2 heterostructure, we calculated the optical absorption coefficients with a series of d layer . As presented in Fig. 6, there are three absorption peaks in the visible light region for the equilibrium vdW gap d layer ¼ 3.07Å. The rst absorption peak locates at $1.9 eV, and the main peak covers the light energy region of 2.25-2.6 eV with an ultra-high light absorption coefficient up to 1.22 Â 10 6 cm À1 . And the third absorption peak locating at $2.8 eV presents the absorption coefficient of about $1 Â 10 6 cm À1 . It is worth noting that the lightharvesting ability in the entire visible solar spectrum is elevated when the d layer increases. Interestingly, the absorption peaks shi weakly towards the lower energy region as the d layer rises, and the absorption coefficient increases the maximum value up to 1.34 Â 10 6 cm À1 when d layer ¼ 3.47Å. Due to the direct band gap feature being benecial for separating photo-excited electron-hole pairs and strong light absorption, the g-C 3 N 4 /WTe 2 heterostructure could be a promising material for efficient photovoltaic solar cells and optoelectronic devices.
Furthermore, we estimated the power conversion efficiency (PCE) by the method proposed by Scharber et al., 53 which is widely used in efficiency estimation. The upper limited PCE of the g-C 3 N 4 /WTe 2 heterostructure is described by 54 where 0.65 is the ll factor (b FF ), P(ħu) is the AM1.5 solar energy ux at the photon energy ħu, E g and DE c are the band gaps of the donor and conduction band offset between donor and acceptor respectively. The (E opt,d g À DE c À0.3) term is an estimation of the open-circuit voltage (V oc ). The integral term in the numerator is the short-circuit current density (J sc ) assuming external quantum efficiency to be 100%, while the energy integral from 0 to innity in the denominator is the power of incident solar radiation. Fig. 7(a) illustrates the donor band gap Gap donor and conduction band offset DE c , which are critical to the maximum PCE, as well as simulated PCE of heterostructures with different d layer . Interestingly, due to a suitable band gap of about 1.4 eV with a Gap donor of about 1.65 eV, the g-C 3 N 4 /WTe 2 heterostructure shows an excellent solar spectrum absorption. Furthermore, the Gap donor hardly changes, but the DE c decreases about 70% in the process of compression and stretching. The reduced band offset differences in the stretching process lead to a higher PCE. Dramatically, the PCE improves considerably with a maximum value of 17.68% for the Fig. 6 Absorption coefficient of g-C 3 N 4 /WTe 2 with different vdW gap. g-C 3 N 4 /WTe 2 heterostructure. Fig. 7(b) depicts PCE variation with the Gap donor and DE c . Therefore, we concluded that the g-C 3 N 4 /WTe 2 heterostructure could show a better performance in solar cell applications by modifying the vdW gap.

Conclusion
To conclude, based on the rst-principle calculations, we have constructed the g-C 3 N 4 /WTe 2 heterostructure and systematically analyzed the corresponding electronic band structure, optical properties with different d layer . As the d layer increases, the band gap rises from 1.24 to 1.44 eV when the interlayer interactions become weaker, which brings an augmented light harvest in the visible range. Signicantly, the maximum optical absorption coefficient can reach $10 6 cm À1 level. Furthermore, the larger band gap and smaller band alignment difference make it better for light absorption and energy conversion. Finally, we found that the PCE of g-C 3 N 4 /WTe 2 heterostructure has been promoted obviously during vdW gap tuning. The optimized PCE can reach up to 17.68%. Our results show that the g-C 3 N 4 /WTe 2 heterostructure is favorable in solar cell applications. Here, we gave a tasteful way to realize the better performances of heterostructures, which is vital in the future study of vdW heterostructures.

Conflicts of interest
The authors declare no competing nancial interest.