1 Introduction

As the energy crisis is continuously increasing globally, the demand for sufficient energy is of high interest. The technique of using fossil fuels to harvest energy has led to very severe environmental issues, such as air pollution. The burning of fossil fuels releases greenhouse gases, such as carbon dioxide (CO2) [1], sulphur dioxide (SO2) [2], and others [3, 4]. Since fossil fuels are non-renewable resources, they will not be available in future, as they will be used up or fade out due to their toxic nature. This has led to the investigation of a photovoltaic (PV) cell as the ideal solution. The PV method has been a clean, eco-friendly, reliable and safe way of producing energy.

In the early years, titanium oxide (TiO2) monocrystalline was used in PV cells to harvest solar energy, where TiO2 had percentage conversion efficiency (PCE) of about 3.8% [5]. When TiO2 was later incorporated in the flat zinc oxide (ZnO) through the deposition process by aerosol spray pyrolysis, the large conversion efficiency of about 15.0% was observed [6, 7]. This shows its great potential as a new photovoltaic technology [6, 7]. Due to the above-mentioned improvement, more work has been done with PCE of over 22.0% [8,9,10] and they are cost-effective and cause no harm to the environment and human health.

Graphene, a single layer consisting of carbon atoms arranged in a hexagonal lattice form, has brought a lot of attention in energy production [11] because of its remarkable magnetic and electronic properties [12]. Two-dimensional (2D) materials have shown a wide application in the photovoltaic cell [13, 14] and photocatalysis [15]. With their promising physical and chemical properties for future applications in solar cells, nanoelectronic and nano-optoelectronics devices, and 2D transition metal dichalcogenides (TMDs) are gaining much attention [16,17,18]. Up to now, various 2D materials, such as g-C3N4, C2N, C3N4 and C6N6 [19,20,21], as well as dichalcogenides metals [22], phosphorus [23], silicene [23, 24] and others, have been broadly used in experimental and theoretical studies for application in photovoltaic cells [25], electronic devices [26] and others [27].

The carbon nitride (C2N) material, which contains pore and nitrogen atoms, has been successfully synthesised with a bottom-up wet-chemical reaction method [20] with a bandgap energy of ~ 1.96 eV [28,29,30]. Theoretical reports predict that the band edge positions and the bandgap of C2N sheet can be tuned by changing their layer number, external electric field and stacking order with promising high-performance photovoltaic properties [31]. C2N sheet contains benzene rings that are been bridged by the pyrazine rings, having a six-membered D2h ring with the two nitrogen atoms facing each other [29]. The phonon modes of C2N monolayer are close to graphene; this suggests that C2N can have high structural stability, which can be useful to generate high energy for photovoltaic cell [32].

As a field-effect transistor device, C2N shows a 107 on/off ratio that is higher than that of graphene [30]. Unlike other 2D semiconductor materials, C2N is low cost and easy to be synthesised [33]. These properties make it a more promising material for applications in a photovoltaic cell and nanoelectronic and nano-optoelectronics devices [34,35,36]. The distributions of charges from the valence band maximum (VBM) to conduction band minimum (CBM) states are not well separated, which can reduce the absorbing efficiency of light due to the fast recombination of photogenerated electrons and holes [37]. Nevertheless, to improve the performance of C2N as a photovoltaic cell, usually, the electronic structure of the 2D materials should be coupled with other 2D materials [38]. The 2D van der Waals (vdWs) heterostructure materials are used to improve the absorption of solar energy in PV cells in order to generate efficient energy that can be converted into direct electrical energy.

Recently, several studies have shown that suitable bandgap structures and well efficient charge separation are important in achieving an efficient photovoltaic device [39]. In a photovoltaic cell, electron–hole pairs are separated when visible light irradiates on the semiconductor surface, where electrons (e−) will be promoted to the n-type and holes (e+) will be on the p-type [40]. However, there is still high rapid recombination of charge carriers in C2N. Lately, vdWs heterostructure has been an efficient way of adjusting the properties of 2D materials, such as band structure tuning and charge carrier separation [41]. Type-I (symmetric), type II (staggered) and type III (broken) band alignments in vdW heterostructures have their own specific applications to allow various device varieties [42,43,44,45]. To enhance the effective charge separation of C2N nanosheet, the GaS monolayer is coupled with C2N nanosheet [46]. GaS is a semiconductor with an indirect bandgap of 2.59 eV [47]. A GaS semiconductor is considered as a promising material, close to blue light-emitting devices [46]. Furthermore, it has the ability to emit in both photoluminescence and electroluminescence regions [48, 49] because they both give an insight into carrier dynamics and lateral relation to reducing electron–hole pairs recombination [50].

In this paper, we investigate a GaS/C2N vdW heterostructure as a photovoltaic cell using density functional theory (DFT) calculations. The DFT calculations are based on geometry optimisation, the total projected density of states, charge population analysis, optical properties as well as power conversion efficiency. Moreover, the band structure properties are predicted, which are more critical in designing new photovoltaic cells. The theoretical results will offer insights into designing other 2D-based photovoltaic materials.

2 Computational details

In this study, first-principle calculations of GaS/C2N heterostructure and the individual components are performed by means of plane-wave DFT method as implemented in the Cambridge Serial Total Energy Package (CASTEP) code [51] of Material Studio 2016 [52]. The generalised gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE) is used to define the exchange-correlation effect [53]. The plane-wave kinetic energy cut-off is set to be 400 eV. The geometry structures are well relaxed until the energy converged to 10−6 eV, where the maximum force of atoms is set to be 0.3 eV/Å, maximum stress to be 0.5 GPa and the maximum displacement of the atoms to be 0.01 Å. The vdWs corrections in GaS/C2N heterostructure and the monolayers were treated by applying DFT-D2 method of Grimme [54]. This method has been demonstrated to give a reliable description of the vdW heterostructures [55, 56]. The electronic configurations of C (2s2 2p2), S (3s2 3p4) and Ga (3d10 4s2 4p1) are treated as the valence electrons. In addition, the hybrid Heyd–Scuseria–Ernzerhof (HSE06) [57] functional was used in order to get the accurate electronic properties since GGA-PBE functional underestimates the bandgap energy of most semiconductors [57]. The Brillouin zone is sampled using Monkhorst-Pack k-point grid of 5 × 5 × 1 for GaS monolayer and 2 × 2 × 1 for C2N monolayer, and GaS/C2N heterostructure was used for the calculation of structural relaxation and electronic properties. To avoid artificial interactions, the two layers are constructed with a large vacuum space of about 20 Å.

3 Results and discussion

3.1 Geometry structures

To gain more knowledge of the proposed 2D semiconductors, we first study the geometry structure and electronic properties of the individual materials. The composite structures of C2N and GaS are shown in Fig. 1.

Fig. 1
figure 1

a Side and b top views of GaS/C2N heterostructure

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The primitive unit cell of C2N sheets consists of 12 carbon atoms and 6 nitrogen atoms with existing uniform holes. The calculated optimised lattice constants of C2N sheet and GaS monolayer are a = 8.33 and 3.57 Å (see Table 1), respectively, as compared to the previous studies of 8.32 and 3.58 Å [58, 59].

Table 1 The lattice parameter, binding energy (Eb) and interface distance (d) for C2N, GaS and GaS/C2N
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Also, the bond lengths of C–N (1.34 Å), C–C1 (1.43 Å), C–C2 (1.47 Å) consistently agreed with earlier reported bond lengths 1.34, 1.43 and 1.47 Å [33, 60, 61], respectively. The bond angle of 117.7° for C–N–C slightly deviates from that obtained by Liang et al. [62]. The obtained bond length is 2.43 Å for Ga–S, whereas for Ga–Ga is 2.54 Å, which also agree very well with previous studies [63] of 2.327 and 2.451 Å for G–-S and Ga–Ga, respectively.

In order to avoid high lattice mismatch of the heterostructure, the well-stacking sheets of 3 × 3 of C2N and 7 × 7 for GaS supercells were used to get 0.30% lattice mismatch, which is desirable to produce the vdW heterostructure. The lattice mismatch (LM) is calculated using Eq. (1):

$${\text{LM}} = \left( {\frac{b - a}{a}} \right) \times 100$$
(1)

where a and b are the lattice constants for C2N sheet and GaS monolayers, respectively. The supercell contains 354 atoms (108 C, 54  N, 30 Ga and 30 S).

The top and side views of the optimised GaS/C2N heterostructure are shown in Fig. 1a and b, respectively. The optimised geometry of C2N sheet still sustains its unique planar structure without much distortion, while GaS monolayer remains its linear structure. The lattice parameters of GaS/C2N heterostructure are a = b = 25.75 (Table 1). The equilibrium distance between the optimised structures of C2N sheet and GaS monolayer is measured as 3.345 Å (Table 1), which agrees with C2N bilayer with stacking order (3.280 Å) [30]. In order to check the stability between the C2N sheet and GaS monolayer, the binding energy is calculated, where the two semiconductors are aligned vertically to each other. The binding energy of the heterostructure is calculated according to the following equation [64]:

$$E_{\text{b}} = E_{{{\text{GaS/C}}_{ 2} {\text{N }}}} - E_{\text{GaS}} - E_{{{\text{C}}_{ 2} {\text{N}}}}$$
(2)

where \(E_{{{\text{GaS/C}}_{ 2} {\text{N }}}} ,\,\, E_{\text{GaS}}\) and \(E_{{{\text{C}}_{2} {\text{N}}}}\) are the total energies of the relaxed GaS/C2N heterostructure, GaS monolayer and C2N sheet, respectively. An Eb value of − 0.069 meV was calculated; this suggests that C2N/GaS heterostructure is energetically favourable.

3.2 Electronic properties

The band structures of C2N sheet, GaS monolayer and GaS/C2N heterostructure are calculated in order to explore their photovoltaic performance. Moreover, the projected density of state (PDOS) is evaluated to further gain insight into the electronic structural interface and classification of the nature of orbital. The results of the band structures and PDOS are shown in Figs. 2 and 3, respectively.

Fig. 2
figure 2

The calculated HSE06 band structures of a C2N layer, b GaS monolayer and c GaS/C2N heterostructure

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Fig. 3
figure 3

The calculated HSE06 projected density of state of a C2N layer, b GaS monolayer and c GaS/C2N heterostructure

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Generally, C2N sheet band edges in Fig. 3a are dominated by the C 2p and N 2p states [39]. The CBM and VBM are both positioned at the G point, which makes C2N monolayer a direct bandgap semiconductor with a bandgap (Eg) energy of 1.96 eV, and this is in good agreement with previous theoretical studies [65]. For GaS monolayer, we observed an indirect bandgap of about 2.38 eV (Fig. 2b), which is close to the experimental value 2.59 eV [47] with a difference of about 0.21 eV. The potential density of state (PDOS) confirms that Ga 4p and S 3p states dominate the CBM of GaS monolayer, see Fig. 3b. The CBM for GaS is situated between the Y–G points, while the VBM is at G point. The VBM and CBM of GaS are mostly contributed by S 3p state.

The bandgap of C2N and GaS was greatly reduced by forming a heterostructure. The light-harvesting heterostructure with 1.2–1.4 eV narrow bandgap has the supreme efficiency according to the Shockley–Queisser limits [66]; therefore, the reduced bandgap energies of C2N nanosheet and GaS monolayer can be useful in enhancing the light absorption for solar cells. The indirect bandgap of heterostructure has fundamental importance to its optoelectronic application [67]. This indirect bandgap favours optical transition with significant changes in the wave vector, which can improve the visible light response. The photoexcited charge carriers of an indirect gap semiconductor undergo a change in their momentum state before recombination due to the occurrence of phonon emission [68]. The direct electronic bandgap of GaS/C2N vdW heterostructure (1.25 eV) in Fig. 2c falls within the range of 1.1–1.5 eV, which is the best bandgap range for PV cells [47, 69, 70]; therefore, the bandgap can lead to efficient absorption of visible light. While the optical transitions through the direct bandgap nature of a heterostructure are recommended, thus, the materials are efficient light emitters for photovoltaic cells [71]. The band alignment properties of C2N sheet and GaS monolayer form a type-I heterostructure. As the GaS/C2N heterostructure is exposed to the visible light region, the electrons are photoexcited from the VBM of C2N sheet. The photogenerated electrons of the GaS monolayer can move well to the CB of the C2N sheet.

3.3 Work function

Another factor that affects the properties of improving the solar cells is the energy level, and it is well investigated by calculating the work function (Φ) of the individual monolayers and the GaS/C2N heterostructure. The surface conditions of every material can easily affect the work function, which results from altering the surface electric field induced by the distribution of electrons at the interface [72]. The work function is the amount of energy required to remove an electron from the Fermi level surface of a solid vacuum at an absolute zero. The work function along the Z axis is calculated by aligning the Fermi energy level with reference to the vacuum energy level [73].

$$\varPhi = E_{\text{vacuum}} - E_{\text{Fermi}}$$
(3)

where Evacuum and EFermi are the energy of an electron at the stationary point in the vacuum in line with the surface and Fermi level, respectively.

The work function for GaS monolayer, C2N sheet and GaS/C2N heterostructure is estimated to be 5.79, 6.04 and 5.65 eV, respectively, see Fig. 4.

Fig. 4
figure 4

The calculated work function for a GaS monolayer, b C2N sheet and c GaS/C2N heterostructure

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The calculated work function of GaS monolayer and C2N sheets shows reduced energy as compared to the reported theoretical results of 6.10 eV for GaS monolayer and 6.18 eV for C2N sheets [74, 75], which is about 0.314 and 0.140 eV difference between GaS monolayer and C2N sheet, respectively. The GaS monolayer seems to have a lower work function than the C2N sheet due to the lower ionisation energy of the S atom as compared to N atom [76]. Therefore, the GaS monolayer that has a lower work function will determine the charge transfer at the interface. The electrons will move from GaS monolayer to C2N sheet with a low work function potential. In this case, the C2N sheet will be negatively charged, while GaS will be positively charged due to the high electrostatic induction.

The work function of the heterostructure is shown to be decreased from the two monolayers to 5.83 eV due to the efficient interfacial formation of interface and charge transfer [77]. The low work function clearly means that less of energy will be needed to dislodge electrons from the VBM to CBM edges; thus, more electrons will be transferred and the associated phenomenon is that the work function is directly proportional to the kinetic energy gained of an electron. In addition, the electrostatic potential difference at the interface of the GaS/C2N heterostructure can successfully reduce the charge carrier recombination rate and increase the transfer and separation of the induced charge carriers, which can enhance the power conversion efficiency.

3.4 Charge density difference

The interactions between the two monolayers (C2N sheet and GaS monolayer) signify the charge distribution between the semiconductors. To further understand the charge transfer of GaS/C2N heterostructure, a three-dimensional (3D) charger density difference is evaluated with an isosurface valued of 0.003 e/Å3, where GaS monolayer indicates a substantial charge transfer and separations of electrons after coupled with C2N sheet, as shown in Fig. 5.

Fig. 5
figure 5

The 3D charge density difference for GaS/C2N side view heterostructure. The red and green region represents charge accumulation and depletion, respectively

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Moreover, high charge accumulation is found on the C2N sheet surface, consequentially becoming electron-rich surface, whereas the depletion occurred at the GaS monolayer surface, becoming a hole-rich region. The red region predicts that the electron-rich GaS can, therefore, expected to transfer electrons from the GaS monolayer surface to the C2N sheet surface. Subsequently, GaS monolayer acts as a photosensitiser in GaS/C2N heterostructure. Therefore, this improves the interaction of strong charge distribution within individual constituent and signifies the separation of electron–hole pairs within the GaS/C2N heterostructure. This demonstrates the enhancement mechanism of photovoltaic performance of the individual monolayers to form GaS/C2N heterostructure. The Mulliken charge population analysis shows that the total amount of charge transferred at the GaS/C2N heterostructure interface is 0.13 |e|. The S atoms have an average contribution of − 0.43 |e|. Notwithstanding, GaS monolayer makes a contribution of − 0.02 |e|; therefore, C2N monolayer receives an average of 0.13 |e|, whereas N is the one that receives more electrons with an average of − 0.31 |e|. This charge distribution at the interface may tune the electrostatic potential to enhance solar light detection and harvesting. This charge transfer at GaS/C2N heterostructure interface indicates that the formation can achieve strong orbital overlapping, leading to highly efficient electron transfer for photovoltaic performance.

3.5 Optical properties

A promising photovoltaic material should absorb as much visible light in order to achieve an efficient electric current conversion. Thus, the optical property of the GaS monolayer, C2N sheet and GaS/C2N heterostructure is studied through UV–visible light absorption spectrum. The redshift of the absorption of GaS/C2N heterostructure was further enhanced in the visible region because of the reduced indirect bandgap when compared to C2N and GaS counterparts, as shown in Fig. 6.

Fig. 6
figure 6

The calculated light absorption spectrum of a GaS monolayer, C2N sheet and GaS/C2N heterostructure

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Thus, comparing GaS monolayer and C2N sheet, the absorption edges move to the broader wavelength region for GaS/C2N heterostructure due to the coupled GaS monolayer and C2N sheet. The outcomes can be comparable to many bandgap semiconductors with very poor visible light absorption capacity [78, 79], where GaS/C2N heterostructure showed a more absorption intensity in the wide range of 410–800 nm. In this study, the results clearly predicted that the optical properties and the stability of GaS/C2N heterostructure can enhance the visible light absorption and can be used in photovoltaic devices for conversion of solar light to electrical current. It can be concluded that the GaS/C2N heterostructure indeed could be used as a photovoltaic material.

For any newly formed semiconductor to be considered as valuable for photovoltaic activity, ideally, the bandgap must be within 1.1–1.5 eV range to enhance the solar absorption energy. Effective charge separation and optical absorption are also influential in photovoltaic performance [80]. Based on the obtained optical absorption results, there is a promising enhancement for visible light for the photovoltaic activity of GaS/C2N heterostructure as compared to the individual materials. The improved photovoltaic activity affected by the efficient separation and transfer of photogenerated electrons depends heavily on the band structures of the individual parts [81]. The GaS/C2N heterostructure is assessed by analysing the band position of the valence band and conduction band in relation to the photoexcited electrons of the formed heterostructure. The VBM and CBM of GaS/C2N heterostructure are evaluated from the respective bandgaps of the individual components and their absolute electronegativity of atoms using the empirical equations:

$$E_{\text{VB}} = X - E_{\text{e}} + 0.5E_{\text{g}}$$
(4)
$$E_{\text{CB}} = E_{\text{VB }} - E_{\text{g}}$$
(5)

where X is the standard electrode potential (≃ 4.5 eV), Ee represents the energy of free electrons of the hydrogen scale, and Eg is the estimated bandgap of the studied semiconductor. EVB and ECB represent the conduction band and valence band edge potentials. The X values of C, N, Ga and S are 6.27, 7.30, 3.20 and 6.22 eV, respectively [82]. The X values of C2N sheet and GaS monolayer are calculated as 4.51 and 4.46 eV, respectively. Therefore, the EVB and ECB are calculated as 0.99 and − 0.97 eV for C2N, respectively. In addition, the corresponding band edges of GaS are calculated as 1.15 and − 1.23 eV, respectively. This clearly shows that the CB and VB of GaS are higher than those of C2N.

3.6 Charge carrier mechanism

Based on the band edges results, the possible reaction and transfer of energised electrons are proposed for GaS/C2N heterostructure, as shown in Fig. 7.

Fig. 7
figure 7

Band alignment showing the conduction band and valence band of C2N sheet and GaS monolayer

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The photoexcited electrons and holes in the CB and VB, respectively, of the GaS monolayer, can be easily transferred to C2N sheet. The mechanism in Fig. 7 further confirms the type-I heterostructure formation with CB and VB of C2N sheet which is lower than that of GaS monolayer. The type-I band alignment of GaS/C2N heterostructure signifies that the formation can yield better improvement of sunlight and transfer of charge carriers [83].

4 Power conversion efficiency

In the numerical calculations of power conversion efficiency for GaS/C2N heterostructure based on the obtained bandgap, the maximum open-circuit voltage (Vo), short-circuit current density (Jsc) and power conversion efficiency (η) of the formed heterostructure are calculated using Eqs. 7 and 8:

$$qV_{\text{OC }} = E_{\text{g}} - E_{\text{loss}}$$
(7)

The relationship between the variable parameter \(E_{\text{loss}}\) (adopted with the values of 0.7 eV) [66] and the \(E_{\text{g}}\) of the GaS/C2N heterostructure was used to calculate the maximum open-circuit voltage (qVoc) using the above equation.

The maximum short-circuit current density (Jsc) can be used to evaluate the incident photons, where the formed GaS/C2N heterostructure will generate electron-hole pairs after absorbing the incoming photons. The absorption can only occur if the energy of the incident photons is equal to or larger than the of the formed GaS/C2N heterostructure. The following equation can be used to calculate Jsc

$$J_{\text{SC}} = q\mathop \int \limits_{{E_{\text{g}} }}^{\infty } b_{\text{s}} \left( E \right)\,{\text{d}}E,$$
(8)

where \(b_{\text{s}} \left( E \right)\) signifies the incident spectral photon flux density and q is the electron charge.

The maximum power conversion efficiency (η) of GaS/C2N heterostructure is calculated by introducing the total incident power density (Ps) of 100 mW cm−2 [84]. The high fill factor (FF) of 0.85 [85] was essentially used to calculate the PCE of GaS/C2N heterostructure for PV cells, with a maximum short-circuit current density (Jsc of 37.9 mA/cm−2) [86]. The fill factor (FF) is a parameter which, in conjunction with Voc and Isc, determines the maximum power from a solar cell. The FF is defined as the ratio of the maximum power (Pmax) from the solar cell to the product of Voc and Isc. Graphically, the FF is a measure of the squareness of the solar cell and is also the area of the largest rectangle which will fit in the IV curve. The total incident power density (Ps) is achieved by applying integration normalisation spectral irradiance stated by National Renewable Energy Laboratory (NREL) and is calculated with the following equation:

$$P_{\text{s}} = \mathop \int \limits_{0}^{\infty } Eb_{\text{s}} \left( E \right){\text{d}}E$$
(9)

Finally, PCE (η) formula is calculated as:

$$\eta = \frac{{{\text{FF}} \cdot J_{\text{SC}} \cdot V_{\text{oc}} }}{{P_{\text{s}} }}$$
(10)

For the 2D GaS/C2N heterostructure, the excellent electron–hole pairs transport properties, the reduced bandgap, and enhanced optical absorption are more effective in increasing the power conversion efficiency. It is clear that GaS/C2N heterostructure can improve the photovoltaic performance since both Voc and Isc result in a high PCE of about 17.8%. This suggests that GaS/C2N heterostructure can be an ideal material to be used in photovoltaic cells.

5 Conclusion

In this study, the first-principle DFT calculations were used to explore the performance of GaS/C2N heterostructure as a photovoltaic cell. The obtained electronic properties of the heterostructure clearly show a reduced indirect bandgap of 1.251 eV as compared to their individual counterparts. Furthermore, the formed 2D GaS/C2N heterostructure shows a very strong visible light absorption edge with a lower work function of 5.649 eV. The GaS/C2N vdWs heterostructure exhibits PCE of 17.8%, which is enhanced by the reduced indirect bandgap and enhanced visible light absorption edge. As a search for lead-free materials, still a major consent in the photovoltaic cells, the results predicted that GaS/C2N vdWs heterostructure can be a very suitable replacement for leaded materials to reduce the toxicity that it possesses on human health and environment.