Inherent internal p-n junction assisted single layered n-type iron pyrite solar cell

The high absorption coefficient and low cost with plentiful availability make the material iron pyrite (FeS2) promising for solar cell applications. However, their efficiency in the literature is still around 2.8% due to their low VOC. The presence of an acceptor-type surface inversion layer (SIL) with a significant band gap (0.56 eV–0.72 eV) is the main cause of this low performance. A detailed study considering these two parameters is not available in the literature to relate device performance to underlying phenomena. Therefore, a comprehensive analysis of the band gap and doping variation of SIL was performed in this article to explore the efficiency potential of FeS2 solar cells. The results showed that SIL with a low bandgap is highly undesirable, and it is recommended to fabricate SIL with a higher band gap of 0.72 eV and a doping of 1019 cm−3 in the laboratory to achieve a conversion efficiency of 5.36%. It was also confirmed that FeS2-based solar cells without a SIL layer have the potential to deliver 10.3% conversion efficiency. The results reported in this study will pave the way for underestimating the workings of iron pyrite solar cells and developing highly efficient FeS2 solar cells.


Introduction
Green and sustainable energy are the infinite units capable of producing cheap and stable electricity. These types of energies are environmentally friendly and, therefore in high demand. Additionally, they are carbon-free and do not emit greenhouse gases, allowing the world to be primarily powered by this clean energy for years to come. Additionally, solar energy is the most widely used energy source among all renewable energy sources, including wind, tidal, and geothermal [1][2][3][4][5][6]. In solar energy, the Sun's energy is directly converted into electricity using a solar cell made from semiconducting materials. The optoelectronic properties of semiconducting materials play a crucial role in selecting the appropriate material for developing solar cells. Among the top materials used in PV research and development are silicon (Si), perovskite, CZTSSe, SnS, and CIGS. However, due to their widespread availability and improved manufacturing processes, silicon-based solar cells have been market leaders from the start. But the fundamental problem with Si is that it requires thick layers due to its low absorption coefficient, making it bulky and expensive [7,8].
Moreover, the record efficiency of 26.7% of silicon solar cells [9,10] is very close to the Auger limit of 29.4% [11], and hence further improvement in power conversion efficiency is difficult. Therefore, researchers started exploring new materials like perovskite, an emerging material in this field [12][13][14][15][16][17][18][19]. However, perovskite-based solar cells suffer from pinhole defects and have stability issues [20]. Therefore, there is a need for novel solar cell materials that are more lightweight and affordable. Additionally, there are two key factors to consider while selecting the solar cell absorber layer: (i) the material should absorb maximum photons, and (ii) it should be able to extract the carriers from the solar cell into the external circuit. In this regard, iron pyrite (FeS 2 ) has been identified, which is an inexpensive, widely available, and naturally pure material [21]. Further, it has the merits of a high absorption coefficient (5 × 10 5 cm −1 ), non-toxicity, high carrier mobility (200-300 cm 2 V −1 S −1 ), abundance on Earth, an acceptable bandgap (0.9-0.95 eV), and low processing cost that make it suitable for PV applications [22][23][24][25]. It has also been noted that FeS 2 has an absorption coefficient two orders of magnitude higher than Si, meaning that a layer merely 40 nm thick can absorb more than 90% of incident light [26][27][28]. In 2009, a survey of 23 semiconductor materials (including Si) for solar cells was performed based on their material extraction cost and supply constraints, and among them, FeS 2 is the front-runner [29]. Accordingly, it is claimed that a 4% efficient FeS 2 -based solar cell would generate the same amount of energy over its lifespan as a 19% efficient Si-based solar cell [27,30].
The FeS 2 -based solar cell was first proposed in 1984 with a 2.8% efficiency, and the root cause of this low efficiency is linked to low open circuit voltage (∼200 mV) [31,32]. Since then, researchers have been continuously investigating the reason behind this low V OC . Ultimately, the main hypotheses in the literature involve a metallic FeS-like surface layer, surface states that result in a hole-rich surface inversion layer, ionization of deep donor states, and a more significant concentration of bulk point defects [25,27,33]. Subsequently, this surface inversion layer (SIL) has a bandgap that is significantly smaller than that of bulk [33]. Due to this, a fewer potential barrier height is created, and thus low V OC is obtained.
Further, this layer dominates when the surface layer holes are more significant than the bulk electrons [33]. Additionally, it is reported that if V OC improves to 500 mV, an efficiency of 20% can be achieved [27]. Moreover, to improve the efficiency of this FeS 2 -based solar cell, researchers proposed new fundamental research on the stoichiometric effect of FeS 2 . Yang et al have reported their work on the effect of surface stoichiometry on the bandgap of the FeS 2 surface layer. It has been reported that the surface has a tunable bandgap and can vary from 0.56-0.72 eV [34]. The low PV performance of FeS 2 -based solar cells is attributed to the SIL layer; however, a detailed analysis of SIL in terms of bandgap and doping concentration is missing in the literature to understand the fundamental cause behind the low performance. Therefore, a detailed simulation analysis is reported in this work regarding bandgap and doping of the SIL layer to understand the fundamental working principle of FeS 2 -based solar cells and the cause behind the low performance. The outline for this paper is as follows: After the introduction section, the detailed description of FeS 2 -based solar cells used in simulation and materials' optical and electrical properties have been mentioned in section II. Subsequently, the results of the proposed device in terms of doping and bandgap variation of the surface inversion layer have been explained in section III. The thickness variation of bulk material is also discussed. Finally, the conclusion drawn by research efforts is explained in section IV.

Device analysis and simulation
The feS 2 -based solar cell under consideration is simulated using a SCAPS-1D device simulator developed by the University of Gent, Belgium [35,36]. This simulator is widely utilized for a realistic device simulation to understand the working of the device through numerical simulation [37][38][39][40][41]. The device structure used in this work is shown in figure 1(a). The thickness of the bulk FeS 2 layer is 160 nm (until otherwise mentioned), and the thickness of SIL is only 4.4 nm. Material properties for the simulation have been obtained from the literature and reported in table 1 [33,34]. Bulk and interface defects are also considered to account for recombination losses, and details are provided in tables 1 and 2. The absorption coefficient of FeS 2 material is high (10 5 cm −1 ), as reported in previous work [33,42]. The same has been utilized during the simulation. SCAPS-1D has detailed dedicated equations to solve the defect-related recombination phenomena, optical absorption, generate rate

Neutral defect
Neutral defect in SCAPS-1D contributed to the Shockley-Read-Hall (SRH) recombination mechanism and affected the electron and hole carrier lifetimes τ n and τ p, which are computed using the following equation p pt h t The electron and hole capture cross-section area is represented by s n and s , p v th is the thermal velocity and N t is the total defect density. Information about the values of these parameters is provided in table 1.

Optical model
Position-dependent generation of electron-hole pairs ( ) G x after being illuminated by incident photon flux ( ) l N phot 0 is calculated using some inbuilt equations. Initially, wavelength and position-dependent photon flux are calculated to get the wavelength and position-dependent generation of electron-hole pairs ( ) l G x , ,which is further integrated with all the wavelengths to get the final ( ) G x . The detailed equation relating variables mentioned above is provided below. The default value of 0 is used for . e x p .
0.6 0.6 Density at peak energy (1 cm −2 .eV) 1 × 10 14 1 × 10 18 . , phot min max min max 2.3. One-dimensional semiconductor equations SCAPS solves one-dimensional semiconductor equations, namely the Poisson and continuity equations, to obtain the illuminated current density-voltage (J-V) curves after being illuminated by the standard AM 1.5G spectrum shown in figure 1. Equations used during simulation are summarized below. Here, q, Y, p n p n , , , t t is the electronic charge, electrostatic field, free holes, free electrons, and trapped holes and trapped electrons, respectively. Ionized donor and acceptor-like doping concentration is represented by + -N N , D A and e e 0 is permittivity in medium and in free space. Electron and hole current density and recombination rate are represented by J n J , p and U n U . p The generation rate is denoted by G and m n m p is the electron, hole mobility. Electron and hole quasi-Fermi-level is represented by E Fn and E Fp

Results and discussion
The bandgap of SIL and acceptor doping significantly affects the band alignment and, thereby, the V OC as well as the J SC of the cell. Hence, analyzing the impact of SIL bandgap and doping is essential for an accurate performance assessment of the cell under consideration. Further, the thickness of FeS 2 determines the effective absorption and, subsequently, the generation and collection processes. Thus, to obtain an optimum thickness of the active layer, i.e., FeS 2, the influence of FeS 2 thickness on PV performance has been studied. The results obtained for variation have been described with valid justification in the following subsections.

Bandgap variation of the surface inversion layer in FeS 2 solar cell
One of the significant problems with FeS 2 solar cells is their SIL, whose bandgap (E g ) is smaller than the bulk bandgap [33]. Due to this bandgap variation at the bulk and surface, the V OC of this solar cell is very low [43]. Therefore, in this section, the impact of various SIL bandgaps (in eV) (0.56, 0.58, 0.60, 0.62, 0.64, 0.66, 0.68, 0.70, and 0.72) on the PV performance of a FeS 2 solar cell has been analyzed to understand the root cause behind V OC loss in actual experimental devices. Firstly, to understand the carrier dynamics, the energy band diagram (EBD) with SIL bandgap values of 0.56 eV and 0.72 eV is obtained, as shown in figure 2(a). The lowest and highest bandgaps are deliberately chosen to understand the carrier dynamics in extreme cases. SIL with a low bandgap (0.56 eV) resulted in a minor potential difference across the absorber layer, which further resulted in a smaller slope of the energy band, whereas, for a higher bandgap, a much higher potential difference is validated through EBD, which resulted in a higher slope. The V OC of the cell directly depends on potential differences across the absorber layer at thermal equilibrium. Therefore, a higher V OC is expected with the SIL layer with a bandgap of 0.72 eV.
Further, to examine the PV performance of the cell, the J-V curve and EQE curve for various SIL bandgaps (0.56 eV-0.72 eV) is examined, as shown in figures 2(b) and (c), respectively. The results depict that, as the bandgap of SIL increases, the V OC delivered by the cell also increases along with an increase in J SC owing to the higher potential difference across the absorber layer with a high bandgap of SIL as shown in figure 2 [44][45][46]. Improvement in J SC credited to higher strength of electric field across absorber layer with an assist in drifting the light generated charge carriers towards collecting electrodes. Optical response in terms of external quantum efficiency (EQE) is also reported in figure 2(c), which depicts that the EQE increases with an increase in the bandgap of SIL. Further, the PV parameters shown in figure 2(d) reveal that the V OC increases linearly from 0.08 V to 0.24 V while increasing the bandgap of SIL from 0.56 eV to 0.72 eV. A similar trend in J SC is also observed, which increases rapidly from 33 mA cm −2 to 35.47 mA cm −2 till the SIL band gap of 0.62 eV and then increases linearly from 35.47 mA cm −2 to 37.14 mA cm −2 while sweeping the SIL Eg to 0.72 eV. A better slope in energy bands offers smooth transfer of charge carriers, increasing the FF from 36.7% to 58.4% while increasing the bandgap from 0.56 eV to 0.72 eV. Further, the PCE is determined by the collective impact of J SC , V OC, and FF, which are almost increasing linearly; therefore, PCE increases linearly from 1.06% to 5.36% while increasing the SIL bandgap from 0.56 eV to 0.72 eV.
Reported Eg range 0.56 eV to 0.72 eV for SIL [34] is considered and thoroughly investigated in this section which concludes that the deviation in the bandgap of the SIL layer compared to the bandgap in the bulk layer is a highly undesirable phenomenon that affects the deliverable V OC of the FeS 2 and overall conversion efficiency. Also, the surface quality of FeS 2 needs to be improved to avoid bandgap quenching for better performance.

Doping variation of the SIL in FeS 2 solar cell
The previous section provided a detailed analysis of the PV performance of FeS 2 -based solar cells having SIL layers with varying bandgap from 0.56 eV to 0.72 eV; however, literature also revealed that the SIL layer is inherently acceptor type with different acceptor concentrations [43]. Therefore, the examination of the effect of SIL doping levels (from 1 × 10 15 cm −3 to 1 × 10 19 cm −3 ) on solar cell performance is focused on in this subsection. It is worth mentioning that as the maximum PCE of 5.36% was attained at the SIL bandgap of 0.72 eV, thus, for subsequent simulation, the bandgap of the SIL layer has been kept intact.
To analyze the impact of doping of SIL on carrier dynamics, the EBD at SIL doping 1 × 10 15 cm −3 and 1 × 10 19 cm −3 has been reported in figure 3(a). It depicts that the bands are shifted upwards for the higher acceptor doping value. Additionally, the J-V curve shown in figure 3(b) depicts that for lower doping, both J SC and V OC are less, and it increases with SIL doping. This increase in J SC with doping is owing to the enhanced electric field. Likewise, EQE increases insignificantly with SIL doping, as shown in figure 3(c).
Subsequently, the PV parameters shown in figure 3(d) reveal that the V OC increases linearly from 0.01 V to 0.24 V while increasing the doping of SIL from 1 × 10 15 cm −3 to 1 × 10 19 cm −3 . A similar trend in J SC is also observed, which increases rapidly from 18.7 mA cm −2 to 36.6 mA cm −2 till SIL doping from 1 × 10 15 cm −3 to 1 × 10 17 cm −3 and then gradually increases from 36.6 mA cm −2 to 37.1 mA cm −2 while sweeping the SIL doping to 1 × 10 19 cm −3 . A significant increase in FF is also observed from 25.8% to 58.4%, with the increase in SIL's doping from 1 × 10 15 cm −3 to 1 × 10 19 cm −3 . Subsequently, the results depict that this rise in V OC , J SC, and FF leads to a hike of PCE from 1.06% to 5.36% with an increase in SIL doping. So, to achieve high PCE, a heavily doped p-type SIL shall be used.  (d)). This validates the device's absence of PV effect with the abovementioned parameters. The bandgap beyond 0.62 eV started showing PV response at the lowest doping of 1 × 10 16 cm −3 . Therefore bandgaps higher than 0.62 eV are considered to discuss the trend in PV parameters at different doping levels. V OC increases linearly with the increase in doping for all the bandgaps. However, higher V OC is obtained with a larger bandgap of the SIL layer, i.e., 0.72 eV. Precisely at (0.64 eV) 0.72 eV while increasing the doping from 10 16 cm −3 to 10 19 cm −3, an increase in V OC from (11 mV) 65 mV to (167 mV) 247 mV has been obtained as shown in figure (a). J SC also raised significantly at elevated levels of doping and showed noticeable improvement with low bandgap compared to the higher bandgap of SIL as shown in figure 4(b). J SC increases from 12.2 mA.cm −2 to 35.9 mA.cm −2 and 32.4 mA.cm −2 to 37.1 mA.cm −2 while increasing the SIL doping from 10 16 cm −3 to 10 16 cm −3 at bandgap of 0.64 eV and 0.72 eV, respectively. Moreover, with the increase in doping concentration, the resistivity decrease, which increases FF. An increase in FF from 23% to 50% and 32% to 58% for similar doping variation at 0.64 eV and 0.72 eV, respectively, have been obtained, as shown in figure 4(c).
Further, the impact of this increase in V OC , J SC , and FF with the increase in both doping and bandgap is also shown in PCE, which is the product of these three parameters. At a higher value of doping, the increment in PCE concerning bandgap is significant ( for 0.56 eV and 0.72 eV bandgap, the value of PCE elevates from 0.03% to 3% and 0.68% to 5.36% when increasing the doping of SIL is from 10 16 cm −3 to 10 19 cm −3 ). The results show that the higher acceptor concentration and bandgap of SIL give rise to all the PV parameters and overall conversion efficiency. The results so far concluded that the presence of SIL with a low bandgap compared to bulk FeS 2 is highly undesirable since it results in a significant reduction in PV performance. Therefore SIL with a higher bandgap of 0.72 eV and doping of 10 19 cm −3 is recommended to be fabricated in the laboratory to get 5.36% conversion efficiency.

Thickness variation of FeS 2 layer on the performance of the solar cell
In the previous subsection, a detailed investigation of SIL's bandgap and doping parameters is considered, and this ongoing subsection is devoted to the thickness variation of the bulk FeS 2 layer. Pyrite, under consideration, has a higher absorption coefficient and, therefore, can deliver higher current density even with a few nanometers of thickness. Therefore, a comprehensive study of FeS 2 thickness variation is also carried out and reported in this section. The thickness of the FeS 2 layer is altered from 10 nm to 150 nm, and their impact on all PV performance is studied as depicted in figures 5(a)-(c). The FeS 2 thickness increases the effective absorption; hence, the JSC and EQE increase, as shown in figures 5(a) and (b), respectively. The EQE curve illustrated in figure 5(b) demonstrated that for low thicknesses of FeS 2 , the FeS 2 layer is insufficient to absorb the full absorption spectrum at lower wavelengths.
Further, as the thickness of the FeS 2 layer increases, more absorption is there, and hence the EQE increases. For 0.8 μm wavelength, a 10 nm thick solar cell delivers 39% quantum efficiency, whereas a 100 nm thick solar cell delivers 74% quantum efficiency. The influence of FeS 2 thickness on PV parameters has been summarised in figure 5(d). The results show a marginal increment in V OC and FF from 0.20 V to 0.24 V and from 56.8% to 58.2%, respectively, with the increase in thickness of the SIL layer from 10 nm to 150 nm. Further, there is a substantial increase in J SC from 20.36 mA cm −2 to 37.16 mA cm −2 with an increase in thickness from 10 nm to 150 nm, i.e., 82.51%. It has also been obtained that the increase in J SC saturates after 90 nm thick FeS 2 . Therefore, the increase in efficiency is also marginally after 90 nm thickness ( for 90 nm thickness, the PCE is 5.2%, and for 150 nm thickness, the PCE is 5.35%) of the FeS 2 layer. Due to this, it is worth mentioning that a 90 nm thick FeS 2 solar cell can deliver 5% conversion efficiency. It should be noted that the significant contribution to this high efficiency is the enhanced J SC (at thick FeS 2 ), as shown in figure 5(a).

Optimized FeS 2 solar cell
According to the previous three subsections, the maximum efficiency of 5.3% can be achieved while incorporating the SIL effect, including doping and bandgap. However, in literature, its efficiency is still struggling at around 2.3%. As already mentioned, the presence of SIL with a bandgap less than bulk material is highly undesirable; therefore, another study is reported in this section where the presence of SIL with a low bandgap is ignored. However, accepter doping is considered to create an internal p-n junction. Therefore, to propose a cell that can have better performance, the device is re-analysis while ignoring the bandgap narrowing of an inversion layer. This has been accomplished by considering the SIL bandgap equivalent to the bulk FeS 2 layer, i.e., 0.9 eV and for 160 nm thick FeS 2 layer. This could be obtained by using various engineering strategies in the future with an experimental approach to eliminate the bandgap narrowing effect.
The performance of the cell with 0.9eV SIL bandgap, i.e., illuminated J-V curve and EQE values, are shown in figures 6(a)-(b). Results depict that by overcoming the bottleneck of bandgap narrowing at the surface, a FeS 2 cell can deliver V OC of 0.36 V, J SC of 41.9 mA cm −2 , FF of 67.11%, and PCE of 10.28%. This is inferred that significant improvement in PV parameters can be made by overcoming the bandgap narrowing of SIL while taking into account their acceptor doping.

Conclusion
This study uses the SCAPS-1D simulator to perform a numerical simulation of FeS 2 solar cells. The literature claims that the efficiency of the FeS 2 -based solar cell is only 2.8%, which is extremely low. The main reason for this low efficiency is the low V OC of around 200 mV. A surface inversion layer (SIL) at the surface of the FeS 2 layer, which has a significant band gap, is the leading cause of this low V OC . Therefore, this work analyses the impact of this SIL band gap variation on the solar cell's performance. Apart from this, the SIL layer also has a higher doping concentration, so an analysis of the effect of the acceptor-type doping concentration variation on the FeS 2 -based solar cell is also performed. The results show that the optimal band gap and doping value of 0.72 eV and 1 × 10 19 cm −3 are required to achieve the conversion efficiency of 5.36%. In addition, by analyzing the thickness variation of the FeS 2 layer, it was determined that a 90 nm thick FeS 2 layer could effectively absorb solar radiation. In addition, it has been calculated that a V OC of 0.36 V, a J SC of 41.9 mA cm −2 , FF of 67.11%, and a PCE of 10.28% can be achieved if this SIL's bandgap change can be reduced in any way. Findings in this paper could open the way to fabricating FeS 2 solar cells with high efficiency and low cost.