Electronic Structure of In3-x Se4 Electron Transport Layer for Chalcogenide/p-Si Heterojunction Solar Cells.

In this article, we perform density functional theory calculation to investigate the electronic and optical properties of newly reported In3-x Se4 compound using CAmbridge Serial Total Energy Package (CASTEP). Structural parameters obtained from the calculations agree well with the available experimental data, indicating their stability. In the band structure of In3-x Se4 (x = 0, 0.11, and, 0.22), the Fermi level (E F) crossed over several bands in the conduction bands, which is an indication of the n-type metal-like behavior of In3-x Se4 compounds. On the other hand, the band structure of In3-x Se4 (x = 1/3) exhibits semiconducting nature with a band gap of ∼0.2 eV. A strong hybridization among Se 4s, Se 4p and In 5s, In 5p orbitals for In3Se4 and that between Se 4p and In 5p orbitals were seen for β-In2Se3 compound. The dispersion of In 5s, In 5p and Se 4s, Se 4p orbitals is responsible for the electrical conductivity of In3Se4 that is confirmed from DOS calculations as well. Moreover, the bonding natures of In3-x Se4 materials have been discussed based on the electronic charge density map. Electron-like Fermi surface in In3Se4 ensures the single-band nature of the compound. The efficiency of the In3-x Se4/p-Si heterojunction solar cells has been calculated by Solar Cell Capacitance Simulator (SCAPS)-1D software using experimental data of In3-x Se4 thin films. The effect of various physical parameters on the photovoltaic performance of In3-x Se4/p-Si solar cells has been investigated to obtain the highest efficiency of the solar cells. The optimized power conversion efficiency of the solar cell is found to be 22.63% with V OC = 0.703 V, J SC = 38.53 mA/cm2, and FF = 83.48%. These entire theoretical predictions indicate the promising applications of In3-x Se4 two-dimensional compound to harness solar energy in near future.

Introduction

Nowadays, the renewable energy sources are taking place over world’s finite dominant energy sources (oil, coal, uranium) to meet up the increasing demand of power supply. The need for inexpensive and large-scale, carbon-neutral energy sources has stimulated a search for revolutionary concepts in solar-to-electricity energy conversion. The silicon solar cell covers over 90% of the global market, although it has an indirect band gap with weak light absorption and extreme processing temperature of ∼1400 °C.[1] Researchers are focusing on making alternative efficient and cheap solar cells.

Recently, silicon/organic hybrid solar cells have gained extensive research interest as they are promising to combine the benefits of organic materials being cheap and easy to process and inorganic materials possessing better charge carrier mobilities and low exciton binding energies.[2−5] A number of promising heterojunction solar cells have been demonstrated based on this type of architecture, such as devices that use Si in conjunction with conjugated polymers. Specifically, the comprehensive studies on conductive polymer poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) to modify its properties, texturing of silicon, and interface engineering between Si/cathode have led to remarkable progress in efficiency (power conversion efficiency, PCE) of 12–15.9%.[7−11]

In addition, it is advantageous to use p-type Si compared to n-type one due to its low cost. The photogenerated carriers can be effectively collected using p-type silicon as minority carrier diffusion length is larger in p-type silicon than that in n-type silicon. This phenomenon provides low recombination rates, enhanced photocurrent, and improved solar cell performance when p-type silicon is used.[12] However, proper n-type organic materials have not been founded yet that can be combined with p-type Si for efficient device performance. So far, C60 and its derivatives have been studied as candidates as n-type acceptors for use in Si/organic heterojunction solar cells with p-type Si without providing high power, although they displayed outstanding dark rectifying effect.[13−17] Most recently, Yun et al. have reported this type of solar cells with an efficiency of about 8.43% using thermal evaporation of C60.[12]

In recent years, metal chalcogenide-based n-Si heterojunction solar cells have been reported.[18−20] More recently, CdS/p-Si heterojunction solar cells have also been reported with an efficiency of 12.29%.[21] Furthermore, n-InSe/p-Si heterojunction solar cells have been demonstrated as a promising structure to harness solar energy, although they show a very low efficiency due to high interfacial defects.[22] Moreover, it is also reported that chalcogenide thin films can be fabricated by low-cost solution process, which indicates their potential in future solution-processed chalcogenide/c-Si heterojunction solar cell applications.[23−25] Indium selenide (InSe) is a III–VI two-dimensional (2D) compound semiconductor composed of stacking of Se–In–In–Se atoms bonded with van der Waals force between quadruple layers.[26,27] The In–Se system can exist in many phases such as InSe, In2Se, In2Se3, In4Se3, and In6Se7.[22] There are some reports showing that the In–Se system can also exist in the In3Se4 phase.[28−31] The study of InSe thin films is motivated by the potential applications in photovoltaic (PV) cells,[32,33] solid-state batteries,[34] phase-change memories,[35] nanoelectronics,[36] optoelectronic devices,[37,38] field-effect transistors,[37] and thermoelectric power conversion.[39,40]

However, the use of n-type InSe with p-type Si to make solar cells has several drawbacks such as high series resistance and high defect density at the junction interface.[22] Thus, a common thread in this system is the trade-off between efficient light absorption and charge collection. Charge can be effectively collected when highly conducting InSe electron transport layer can be used. It has already been reported that InSe provides a very high electron mobility[37] and also high conductivity.[28−31] Now, it is required to make InSe thin films with high mobility as well as high conductivity. This will make a pn junction with p-Si as well as effectively transport electron to cathode. To overcome this practical limit, new material synthesis approaches are needed. Although In3Se4 has been synthesized and few physical properties have been reported by some researchers, the electronic and optical properties of this material are yet to be revealed.[28−30] There is also a report unveiling that highly insulating β-In2Se3 encounters a transition to metallic In3Se4 phase.[31]

In this article, we demonstrate the electronic structure of newly reported In3–Se4 2D compound by first-principles study and its potential as an electron transport window layer for the chalcogenide/p-Si heterojunction solar cells as there are much scope for additional investigations to realize high power conversion efficiency of In3–Se4/p-Si heterojunction solar cells.

Results and Discussion

Structural Properties of In3–Se4 Compound

The optimization of lattice constants and atomic positions of In3–Se4 compound as a function of normal stress with minimum total energy has been performed by density functional theory (DFT) calculation using CAmbridge Serial Total Energy Package (CASTEP) code. The optimized crystal structure of the In3–Se4 (x = 1/3, 0) compound is depicted in Figure as unit cell and 2D view in the ab plane. The rhombohedral crystal structure with space group R3̅m (#166) of In3–Se4 compound has already been confirmed by experimental studies. The calculated ground-state lattice constants are listed in Table . These calculated values agree well with the reported experimental results.[29,41]

Figure 1

Crystal structure of rhombohedral β-In2Se3 (In3–Se4 with x = 1/3) (a) and In3Se4 (In3–Se4 with x = 0) compounds (b).

Table 1

Calculated Lattice Constants of In3–Se4 (a and c) in Å and Volume in Å3

compound	lattice constants (expt(29,41))		lattice constants (this study)		volume (V)
In3–xSe4 (when x = 1/3) or In2Se3	a = 4.05	c = 29.41	a = 3.97 (x = 1/3)	c = 30.23 (x = 1/3)	414.208
In3–xSe4 (when x = 0.22 or 0.11)	a = 3.96	c = 39.59	a = 3.98 (x = 0.22)	c = 36.31 (x = 0.22)	499.52 (x = 0.22)
			a = 3.98 (x = 0.11)	c = 36.30 (x = 0.11)	499.82 (x = 0.11)
In3–xSe4 (when x = 0) or In3Se4	a = 3.96	c = 39.59	a = 3.98	c = 36.30	499.56

The rhombohedral structure (space group R3̅m) of β-In2Se3 has 15 lattice sites comprising the six In atoms forming trigonal pyramidal cages with three Se neighbors (Figure a), whereas the In3Se4 structure has 21 lattice sites comprising the nine In atom sites forming octahedral cages with six Se neighbors and 12 Se atom sites forming trigonal pyramidal cages with three In neighbors (Figure b). The bond lengths in the octahedral (In–Se) and trigonal pyramidal (Se–In) planes for In3Se4 structure are 2.61843 and 2.84135 Å, respectively. In contrast, the only trigonal pyramidal bond (In–Se) length of 2.66773 Å is observed for the β-In2Se3 phase.

However, it is suitable to denote the unit cell as 3(R3–VX4), where V is considered as vacancy in In atoms. For R2X3 compounds, 3/3 sites of the nine In sites per unit cell are empty, i.e., x = 1/3, and for the R3X4 phases, there are no empty sites, i.e., x = 0. The ionic behavior of the In3–Se4 lattice can be formulated as (In3+)3–V(Se2–)4(e–1)1–3.[42] In β-In2Se3, the two In3+ ions provide six electrons to the chemical bonding, which are captured by the 3 Se2– ions. Therefore, there are no excess electrons for the electrical conduction, resulting in highly insulating In2Se3 compound. On the other hand, in the In3Se4 phase, nine bonding electrons are provided by the three In3+ ions, eight of which are captured by four Se–2 ions, resulting in an excess of one electron to the conduction band per formula unit and three free electrons per unit cell.

The carrier concentration of In3–Se4 phase is given by[42]where NA denotes Avogadro’s number, d represents the density, and M denotes the molecular weight.

Mass density d can be calculated bywhere Z is the formula unit, NA is Avogadro’s number, M is the molecular weight, and V is the volume.

The reported[43] and calculated values of d for the In3Se4 phase are 6.11 and 6.6 g/cm3, respectively.

Thus, the stoichiometric In3–Se4 compound (with x = 0) gains a free-electron concentration of 6.01 × 1021 cm–3. The appearance of x vacancies provides (1 – 3x) electrons in the conduction band. Therefore, during the transition from β-In2Se3 to In3Se4 phase, there is a metallic transition as the empty sites are filled with In ions providing excess electrons. The carrier concentrations for different values of x are shown in Table S1 in the Supporting Information.

The carrier can also be calculated theoretically by the formulawhere V is the volume of the unit cell in cm3, as shown in Table , and coefficient 3 is introduced due the fact that every unit cell provides three free electrons to the In3Se4 system. Using this formula, the carrier concentration is found to be 6.01 × 1021 cm–3 similar to the value obtained from eq , which agrees well with the reported values.[31]

Band Structure of In3–Se4 Compound

The electronic properties of a compound are revealed by the band structure, partial density of states (PDOS), and total density of state (TDOS), which are also closely related to charge density distribution and Fermi surface.[44] The results of band structure calculations along the high-symmetry directions within the Brillouin zone for In3–Se4 are presented in Figure a–d. The horizontal dashed line is the signature of Fermi level, EF, while the valence and conduction bands are indicated by blue and red, respectively. Figure a depicts a clear gap between valence and conduction bands for the In3–Se4 compound for x = 1/3. The valence band maxima occurs at Γ point, whereas the conduction band minima occurs at M point, so there exhibits an indirect band gap of Eg ∼ 0.2 eV. On the other hand, it is seen from Figure b–d that with x = 0.22, 0.11, and 0, the Fermi level (EF) shifted to the conduction band is an implication of their metal-like n-type conductivity. However, this phenomenon might be rare but can happen due to the doping effect of In, which generates additional free electrons, and consequently, EF cuts the conduction band showing degeneracy of these materials.[45]

Figure 2

Electronic band structure of In3–Se4 compound for different (x) values: x = 1/3 (a), x = 0.22 (b), x = 0.11 (c), and x = 0 (d).

The band structure and band gap of In3–Se4 were calculated by the software CASTEP as shown in the figures using localized density approximation (LDA) function yielding a band gap of β-In2Se3 phase of about 0.2 eV, whereas the experimental band gap is reported to be 1.55 eV.[46] This happens as the LDA function consistently underestimates the band gap.[47] The optical band gap is normally calculated using hybrid functional HSE06 function based on DFT for accurate value, although it is reported that DFT-based hybrid functional cannot always give exact band gaps of the materials found in the experiments.[48,49] However, HSE06 function was not performed in this study due to system limitations. The crystal structure of In3Se4 is similar to that of the β-In2Se3 phase, as reported another work.[29] The relative shifts in EF to those of the β-In2Se3 phase are 1.06, 1.10, and 1.62 eV for the x values of 0.22, 0.11, and 0, respectively, in In3–Se4 compounds, as shown in Figure b–d. The optical band gap of the nonstoichiometric In3Se4 thin films is reported to be ∼1.8 eV with metallic conductivity.[31] Therefore, from these figures, it can be concluded that the optical band gap of stoichiometric In3Se4 phase should not be less than 1.62 eV, consistent with the report as Fermi level must cross the conduction band for indicating high degeneracy of the phase.[31,45,50] These results indicate that when β-In2Se3 encounters a transformation to the In3Se4 phase, optical band gap and conductivity increase similar to the case of rare-earth chalcogenide thin films from Ce2S3 to Ce3S4.[42,51,52]

TDOS and PDOS are calculated and depicted in Figure a–d to exhibit the contributions of various orbitals/atoms and nature of chemical bonding in the In3–Se4 compound. The structural instabilities are indicated by the sharp peak of the DOS at EF; on the other hand, a deep and broad valley of DOS might be liable for the structural stability. Consequently, the overall DOS profile of these compounds unveils the structural stability. It is seen that for x = 1/3, the TDOS around EF arises mostly from Se 4p with a little contribution from In 5p (Figure a), but for x = 0.22, 0.11, and 0, TDOS originates from In 5s, In 5p, and Se 4s, Se 4p, respectively (Figure b–d). Therefore, there is strong hybridization between Se 4p and In 5p for x = 1/3 and In 5s, In 5p and Se 4s, Se 4p for x = 0.22, 0.11, and 0, respectively. Thus, a strong binary In–Se covalent bond in In3–Se4 results owing to these strong hybridizations. Remarkably, the value of TDOS of In3–Se4 at EF is found to be 7.83, 5.77, 5.79, and 5.63 states/eV/unit cells for x = 1/3, 0.22, 0.11, and 0, respectively. Therefore, it is clearly seen from the band structure and DOS that the effect of varying composition of In for x = 0.22, 0.11, and 0 is relatively same apart from x = 1/3.

Figure 3

DOS of In3–Se4 compound for different (x) values: x = 1/3 (a), x = 0.22 (b), x = 0.11 (c), and x = 0 (d).

Fermi Surface of In3–Se4 Compound

The Fermi surface topologies of In3–Se4 for x = 1/3, 0.22, 0.11, and 0 are shown in Figure a–d for the bands crossing the EF. The Fermi surface topologies of In3–Se4 for x = 0.22, 0.11, and 0 are almost similar, but no Fermi surface was found in the case of x = 1/3 for its insulating nature (Figure a). For x = 0.22, 0.11, and 0, as shown in Figure b–d, three central sheets are the electron-like sheets with spherical cross section centered along the A–G direction of the Brillouin zone. A star-shaped sheet is also surrounding the central sheets. Far from the central sheets, three distinguished middle-sagged U-shaped close sheets are observed along the G–M direction and expanded along the M–L direction in the same sheet as well. The surfaces also include two V-shaped holelike sheets centered at the corners of the Brillouin zone along the G–K direction, which are further expanded along the K–H direction. However, these Fermi surfaces are predominantly constructed due to the dispersion of In 5s, In 5p and Se 4s, Se 4p orbitals resulting in the higher electrical conductivity of the compounds that can also be ensured from DOS (Figure b–d).

Figure 4

Fermi surface of In3–Se4 compound for different (x) values: x = 1/3 (a), x = 0.22 (b), x = 0.11 (c), and x = 0 (d).

Electron Charge Density Map of In3–Se4 Compound

Figure a–d shows the valence electronic charge density maps (in the units of e/Å3), which delineate the distribution of the total electronic charge density of In3–Se4 materials. The right-hand-side scale represents the intensity of the electron concentration. Low concentration of electrons is presented by blue, whereas high concentration of electrons is presented by red. It is seen from Figure b–d that the distribution of charge is mainly spherical around all of the atoms for In3–Se4 (x = 0, 0.11, and 0.22) compounds under this study, thereby showing the ionic nature. The ionic nature is an effect of metallic characteristics,[53] which indicates that In–Se bonds in the aforementioned compositions manifest metallic nature. Thus, a strong isotropic combination of ionic and metallic interactions stands for In3–Se4 compounds. On the other hand, for x = 1/3 (β-In2Se3) compound, the electronic charge density of In/Se atoms shows potential overlapping of charge and they are not perfectly spherical rather somewhat zigzag in shape. This nonideal shape of atoms and their potential overlapping are an indication of covalent bonding nature of the materials.

Figure 5

Electronic charge density of In3–Se4 compound for different (x) values: x = 1/3 (a), x = 0.22 (b), x = 0.11 (c), and x = 0 (d).

This covalent nature might also be correlated to the insulating property of the β-In2Se3 material, as seen from the electronic properties calculations (Figure ).

Optical Properties of In3–Se4 Compound

The optical properties of a material are determined by a number of parameters such as dielectric function, refractive index, loss function, conductivity, reflectivity, and absorption coefficient, which completely depend on the energy of the incident electromagnetic radiation.[45]

The frequency-dependent optical properties of In3–Se4 are investigated, where various the optical parameters fairly agree with the characteristic features of the electronic properties. Both the electronic band structure and optical conductivity reveal strong metal-like conductivity for the In3–Se4 (x = 0, 0.11, and 0.22) compound.

Figure a shows the calculated spectra of the dielectric function of In3–Se4. The dielectric constant at zero frequency is known as the static dielectric constant. The static dielectric constant of In3–Se4 is found to be 16.93, 30.81, 30.35, and 30.72, respectively, for x = 1/3, 0.22, 0.11, and 0.

Figure 6

Energy-dependent dielectric function (a), refractive index (n, k) (b), optical conductivity (σ) (c), absorption (α) (d), reflectivity (R) (e), and loss function (L) (f) of the In3–Se4 compound.

The calculated refractive index values n(0) of In3–Se4 for x = 1/3, 0.22, 0.11, and 0 are 4.11, 5.57, 5.52, and 5.56, respectively, as shown in Figure b. The refractive index varies with the applied energy, revealing that the In3–Se4 compound has the photorefractive effect.

The optical conductivity (σ) spectrum of In3–Se4 is shown in Figure c. The maximum photoconductivity for this compound is 6.43 found at 4.16 eV for x = 1/3 and ∼6 found at 3.75 eV for x = 0.22, 0.11, and 0.

Figure d illustrates the absorption spectra of In3–Se4. Normally, the low-energy infrared part of the spectra originated by the intraband transition. On the other hand, the interband transition may contribute to the appearance of the peaks in the high-energy region of the absorption and conductivity spectra. Notably, it is observed in Figure c that the change in the conductivity spectra is identical to that in the absorption spectra. Therefore, we may conclude that the photoconductivity of the In3–Se4 compound rises as a result of photon absorption.

The reflectivity (R) spectra of In3–Se4 are displayed in Figure e. A higher reflectivity is seen in the infrared region approximately 37% for x = 1/3 and 48% for x = 0.22, 0.11, and 0 of the total radiation, and in the high-energy region, some peaks arise due to interband transition. However, the high reflectivity spectra of this material indicate that it could be used as a promising coating material to diminish solar heating. The high value of reflectivity in the low-energy region reveals the characteristics of high conductance in the low-energy region.[54]

The energy loss spectra (L) of In3–Se4 are exhibited in Figure f. The energy loss function is a significant index to express the loss of energy of a fast moving electron when it goes through a material.[55] In the graph of loss function, the highest peak is related to the plasma resonance and its associated frequency is called plasma frequency, ωp.[56] The highest peak is observed at about 15.97 eV for x = 1/3 and 16.34 eV for x = 0.22, 0.11, and 0, which reveal the plasma frequency of compounds. The In3–Se4 compounds become transparent when the incident light frequency is higher than the plasma frequency.

Figure a–f shows that all of the curves of In3–Se4 for x = 0.22, 0.11, and 0 overlap with each other, which means there is no change of optical properties at those compositions but showing a different picture for x = 1/3.

In3–Se4/p-Si Heterojunction Solar Cells

Figure a,b delineates the schematic structure and energy band diagram of In3–Se4/p-Si heterojunction solar cell, respectively. In In3–Se4, the Fermi energy (EF) and electron affinity of indium selenide are about ∼4.4 and 4.55 eV, respectively.[31,57] Therefore, Fermi level will reside within the conduction band in In3–Se4. On the other hand, the electron affinity of Si is ∼4.05 eV. As a result, In3–Se4 builds a favorable junction with Si, as schematically depicted in Figure b. Moreover, it has also been reported that the band gap as well as the conductivity of the chalcogenides can be modulated using electron beam irradiation, which may also play an important role in the formation of favorable chalcogenide/p-Si heterojunction for the photovoltaic (PV) applications.[58]

Figure 7

Schematic structure (a) and energy band diagram (b) of In3–Se4/p-Si heterojunction solar cells.

Thickness- and Doping Concentration-Dependent PV Performance

The simulated J–V curves of the In3–Se4/p-Si heterojunction solar cells with the variation of thicknesses of In3–Se4 and silicon substrate are shown in Figure a,b, respectively. Figure a delineates that the highest PCE, η, of the solar cell is 20.69% with JSC = 38.96 mA/cm2, VOC = 0.683 V, and FF = 82.55%, for solar cell having In3–Se4 and Si layer thicknesses of 0.10 and 300 μm, respectively. However, the thickness of In3–Se4 with η = 20.32% is set to 0.20 μm for the simulation as thinner transport layer introduces huge defects resulting in poor PV performance of the solar cells. Figure b reveals that the efficiency of the In3–Se4/p-Si heterojunction solar cells increases with the increase of thickness of Si substrate that happens due to the fact that thicker Si absorber layer absorbs higher number of photons. The summarized PV parameters of the corresponding In3–Se4/p-Si heterojunction solar cells are shown in Table . The higher JSC and FF of the solar cells can be attributed to the high transparency and metallic behavior of the In3–Se4 layer.[6,59] The high open-circuit voltage instigates the better junction properties of the solar cells. The change in PV parameters with respect to the thicknesses of In3–Se4 and Si is also shown in Figure S1 in the Supporting Information.

Figure 8

Simulated J–V curves of In3–Se4/c-Si heterojunction solar cells with varying In3–Se4 (a) and Si substrate (b) thickness.

Table 2

Thickness-Dependent PV Performance of In3–Se4/p-Si Heterojunction Solar Cells

thickness (μm)		JSC (mA/cm2)	VOC (V)	FF (%)	η (%)
In3–xSe4 (Si, NA = 1016 cm–3)	0.05	39.01	0.643	81.54	20.46
	0.10	38.96	0.643	82.55	20.69
	0.15	38.27	0.634	83.34	20.24
	0.20	38.22	0.643	82.69	20.32
	0.25	37.83	0.634	83.91	20.12
Si (In3–xSe4, ND = 1021 cm–3)	100	36.11	0.608	81.40	17.88
	150	36.67	0.625	81.43	18.66
	200	37.32	0.627	82.19	19.22
	250	37.69	0.629	83.49	19.81
	300	37.99	0.632	83.57	20.07
	350	38.94	0.634	83.66	20.66

Doping concentrations of In3–Se4(ND)- and Si(NA)-dependent simulated J–V characteristics of In3–Se4/p-Si heterojunction solar cells are depicted in Figure a,b, respectively. Figure a reveals that both short-circuit current and open-circuit voltage are almost independent of donor concentration of the In3–Se4 layer. The highest PCE, η, of the solar cell is found to be 22.69% with JSC = 38.53 mA/cm2, VOC = 0.703 V, and FF = 83.48%, for solar cell having In3–Se4 and Si layer thicknesses of 0.10 and 300 μm, respectively. On the other hand, Figure b shows that open-circuit voltage significantly increases with the increase of doping concentration of Si substrate. Table delineates the summarized photovoltaic performances of the corresponding In3–Se4/p-Si heterojunction solar cells. It is observed from the table that JSC reduces with the increase of doping density for both the cases. These results are the consequences of recombination losses in the absorber and transport layers due to higher doping.[60,61] The change in solar cell parameters due to the variation of doping concentration of In3–Se4 and Si, respectively, is also depicted in Figure S2 in the Supporting Information.

Figure 9

Doping concentration-dependent J–V curves of In3–Se4/p-Si heterojunction solar cells: In3–Se4 (a) and Si substrate (b).

Table 3

Doping Concentration-Dependent PV Performance of In3–Se4/p-Si Heterojunction Solar Cells

doping concentration (cm–3)		JSC (mA/cm2)	VOC (V)	FF (%)	η (%)
In3–xSe4 (Si = 350 μm)	1018	37.79	0.634	84.46	20.24
	1019	37.45	0.642	82.99	19.95
	1020	37.37	0.644	83.78	20.16
	1021	37.37	0.634	85.43	20.23
Si (In3–xSe4 = 0.20 μm)	1014	40.26	0.494	70.99	14.12
	1015	39.30	0.573	80.67	18.15
	1016	38.22	0.643	82.69	20.32
	1017	38.53	0.703	83.48	22.63

Figure S3a,b in the Supporting Information represents the simulated quantum efficiency (QE) of the In3–Se4/p-Si heterojunction solar cells with the variation of thickness of In3–Se4 and Si substrate, respectively. It is observed from the figures that QE of the solar cells is highly dependent on the In3–Se4 layer thickness, which arises due to the parasitic absorption of light in the In3–Se4 layer. It is also found that QE increases with Si substrate thickness. These results are due to the fact that longer-wavelength light is absorbed at longer distance from the junction.[60,62] The simulated quantum efficiencies (QE) with doping concentrations of In3–Se4 and Si substrate of the CuI/n-Si heterojunction solar cells are also shown in Figure S4a,b, respectively. The figures show that QE of the solar cells is lower for NA = 1014 cm–3 of Si substrate; on the contrary, it is almost independent of other doping, indicating that JSC is almost independent of In3–Se4 and Si substrate doping concentrations, which can also be observed from Figure a,b.

The simulated PV performances of In3–Se4/p-Si solar cells with the change in defect density of In3–Se4 layer are shown in Figure S5 in the Supporting Information. It is seen from the figure that PV performance of the In3–Se4/p-Si solar cells does not significantly change up to a defect density, Nt, of 1017 cm–3. The efficiency greatly decreases for Nt of 1018 cm–3. The defect-density-dependent PV parameters of In3–Se4/p-Si solar cells are also depicted in Figure S6.

Junction Formation at In3–Se4/p-Si Interface

The built-in potential (ψbi) at the In3–Se4/p-Si junctions has been investigated by the capacitive (C–V) response employing the Mott–Schottky analysis of the solar cells in Solar Cell Capacitance Simulator (SCAPS) simulation software.[63] The built-in potential, ψbi, at the junction can be determined from the intercept of the 1/C2–V plot of the following equation[6]where A denotes the diode area, ε0εSi denotes the permittivity of silicon, and V denotes the applied voltage. Figure shows the characteristic 1/C2–V plots for In3–Se4/p-Si devices with different doping concentrations of In3–Se4 and silicon substrate. The ψbi value is determined from the intercepts of V-axis by fitting and extrapolating the linear portions of the curves of eq . The calculated built-in potentials of the In3–Se4/p-Si heterojunction solar cells are summarized in Table .

Figure 10

C–V characteristic curves of In3–Se4/p-Si heterojunction solar cells with varying In3–Se4 (a) and Si substrate (b) doping concentration.

Table 4

Built-in Potential (ψbi) of In3–Se4/p-Si Heterojunction Solar Cells from C–V Analysis of SCAPS-1D Simulator

doping concentration (cm–3)		built-in potential, ψbi (V)
In3–xSe4 (Si, NA = 5 × 1016)	1018	0.684
	1019	0.688
	1020	0.675
	1021	0.685
Si (In3–xSe4, ND = 1019)	1015	0.557
	1016	0.692
	1017	0.813

The built-in potentials of In3–Se4/p-Si heterojunction devices are almost independent of In3–Se4 doping concentration, as seen in Figure a, whereas, they gradually increase with the silicon substrate doping, as delineated in Figure b. These findings reveal an abrupt pn+ junction at the In3–Se4/p-Si interface, where the transport mechanism is mainly dominated by the diffusion of minority carriers.[6]

Conclusions

The electronic and optical properties of the In3–Se4 compound have been studied employing CASTEP based on the DFT method. The band structure of the In3–Se4 compound (for x < 1/3) exhibits that the Fermi level (EF) crossed over several bands, which is an indication of highly degenerate n-type semiconducting or metallic behavior. On the contrary, a band gap of ∼0.2 eV was found for In3–Se4 (x = 1/3) from the band structure calculation. The DOS calculations ensured the metallic conductivity of In3Se4 through dispersion of In 5s, In 5p and Se 4s, Se 4p orbitals. The chemical bonding in In3–Se4 materials shows mainly the ionic or metallic and covalent nature from the electronic charge density map. Electron-like Fermi surface appeared in the compound, which implies its single-band character. The calculated value of carrier concentration is ∼6.01 × 1021 cm–3, which agrees well with the reported values. The optical study of In3–Se4 indicates that band gap of stoichiometric In3Se4 should be >1.62 eV, which is consistent with the reported values. We also demonstrate the highly efficient In3Se4–/p-Si heterojunction solar cells by SCAPS software using experimental data. These results indicate the potential of the In3–Se4 compound in solar energy harvesting in future.

Experimental Details

First-Principles Study

The density functional theory (DFT) calculation using CASTEP software was performed for demonstrating the band structure and optical properties of the In3–Se4 compound.[64] The crystal structures of the In3–Se4 material system were visualized by the software VESTA.[65] The localized density approximation (LDA) of a Perdew–Burke–Ernzerhof solid was carried out for assessing the electronic exchange correlation in this work.[66] The Broyden–Fletcher–Goldfarb–Shanno minimization algorithm was performed for optimization of the geometry of In3–Se4 system. To achieve the optimized geometry for the structure, convergence thresholds of 5 × 10–6 eV/atom for the total energy, 0.01 eV/Å for the maximum force, 0.02 GPa for the maximum stress, and 5 × 10–4 Å for the maximum displacement in the lattice were applied. For the sampling of the Brillouin zone of the In3–Se4 system, the plane-wave cutoff energy (Ecut) and Monkhorst–Pack k-point mesh of 300 and 500 eV and 4 × 4 × 2 and 4 × 4 × 1, respectively, were set in this calculation. For the compositional study, the value of x in the In3–Se4 compounds was varied in the range of 1/3 > x ≥ 0 changing the occupancy of In1 atom in 3a site of the In3Se4 phase as the metallic behavior comes from the excess In of the phases.[42,51,52] The structure of the β-In2Se3 compound was used for the value of x = 1/3 in the calculation. The occupancy of different sites in the unit cell of the In3–Se4 compounds is shown in Table S2 in the Supporting Information.

Device Simulation

For the device simulation of In3–Se4/p-Si heterojunction solar cells, we essentially utilized SCAPS (Solar Cell Capacitance Simulator) simulation software developed by Burgelman and his team at University of Gent.[67−70] The data of optical transmittance spectra, as shown in Figure S7, band gap, and carrier concentration were used in this simulation obtained from the experimental data, as reported elsewhere.[31] The device simulation parameters used in this study are shown in Table S3 in the Supporting Information.