Device simulation of highly efficient eco-friendly CH3NH3SnI3 perovskite solar cell

Photoexcited lead-free perovskite CH3NH3SnI3 based solar cell device was simulated using a solar cell capacitance simulator. It was modeled to investigate its output characteristics under AM 1.5G illumination. Simulation efforts are focused on the thickness, acceptor concentration and defect density of absorber layer on photovoltaic properties of solar cell device. In addition, the impact of various metal contact work function was also investigated. The simulation results indicate that an absorber thickness of 500 nm is appropriate for a good photovoltaic cell. Oxidation of Sn2+ into Sn4+ was considered and it is found that the reduction of acceptor concentration of absorber layer significantly improves the device performance. Further, optimizing the defect density (1014 cm−3) of the perovskite absorber layer, encouraging results of the Jsc of 40.14 mA/cm2, Voc of 0.93 V, FF of 75.78% and PCE of 28.39% were achieved. Finally, an anode material with a high work function is necessary to get the device's better performance. The high-power conversion efficiency opens a new avenue for attaining clean energy.

www.nature.com/scientificreports/ hole mobility, good energy level alignment with CH 3 NH 3 PbI 3 and a longer lifetime of photo-generated charge carriers 33 . Cu 2 O is used as an HTL because of abundant availability on Earth, environmental-friendly, perfectly band alignment with CH 3 NH 3 SnI 3 and easily synthesized materials. It decreases the barrier height of metal contact and reduces the recombination loss of minority at anode 11,36,37 . Device simulation provides a strong way to improve PSC's efficiency after the optimization of various physical parameters. Solar cell capacitance simulator (SCAPS) was utilized by many theoreticians to predict the open circuit voltage (V oc ), short circuit current density (J sc ), fill factor (FF) and PCE of the perovskite based solar cell 27,38,39 . Hence, the simulation of lead-free CH 3 NH 3 SnI 3 as a photoactive material was studied using SCAPS. The impact of rectifying and ohmic contact behaviour on lead-free CH 3 NH 3 SnI 3 based PSC was also investigated.

Device structure and simulation
In this work, a numerical simulation of a planar heterojunction tin-based perovskite solar cell was performed using SCAPS. To obtain the performance parameters of the device like current density-voltage (J-V) curve, quantum efficiency and energy bands, Poisson Eq. (1) is solved with continuity equation of electron (2) and hole (3). These curves are used to calculate J sc , V oc , FF and PCE of the solar cell device.
where, G, τ n , τ p , D, q, Ψ, µ n , µ p , n (x), p (x), n t (x), p t (x), N − A (x) , N + D (x) and ξ denote the generation rate, electron life time, hole life time, diffusion coefficient, electron charge, electrostatic potential, electron mobility, hole mobility, concentration of free electrons, concentration of free holes, concentration of trapped electrons, concentration of trapped holes, ionized acceptor concentrations, ionized donor concentrations and electric field, respectively.
x denotes the direction along the thickness 29 .
The device's structure in the simulation is transparent conduction oxide (TCO)/buffer (ETL)/interface defect layer 1/absorber/interface defect layer 2/HTL. The simulation was done under the illumination of 1000 W/m 2 , at 300 K and an air mass of AM 1.5G. The active area of the studied device is 1 cm 2 . The device's configuration is illustrated in Fig. 1a where, p-type Cu 2 O is used as an HTL, CH 3 NH 3 SnI 3 is used as an absorber layer and n-type TiO 2 is used as an ETL. In addition, fluorine doped tin oxide (FTO) is selected as the contact material and various materials like Ag, Cu, Au and Pt is selected as an anode. The energy level diagram of the corresponding materials utilized in the device architecture is depicted in Fig. 1b.
The values of the device and material parameters that are adopted from theories, experiments and literature are summarized in Tables 1 and 2 [27][28][29]39 . Initially, the thickness of FTO (500 nm), TiO 2 (120 nm) and Cu 2 O (420 nm) were optimized for high PCE, as mentioned in Table 1.
Herein, χ is the electron affinity, E g is the band gap, ε r is the relative permittivity, N c is the density of state of the conduction band, N v is the density of state of the valence band, µ n is the mobility of electron, µ p is the mobility of hole, N A is the acceptor density, N D is the donor density and N t is the defect density. The thermal velocity of electron and hole are set be 10 7 cm/s. The absorption coefficient of FTO, Cu 2 O, CH 3 NH 3 SnI 3 and TiO 2 were extracted from experimental results 15,[40][41][42] . The diffusion lengths of electron and hole were set to 260 nm and 560 nm, respectively, similar to the experimentally observed value of Ma et al. 28 .

Results and discussion
With these initial parameters in Tables 1 and 2, energy band diagram, J-V characteristic and quantum efficiency of the cell was plotted, as shown in Fig. 2a-c, respectively. After illumination, electron-hole pairs are generated inside the absorber layer. Due to the junction field electrons and holes move towards ETL and HTL, respectively. These electrons and holes are collected at the cathode and anode, respectively and generates a voltage. The J sc of 39.72 mA/cm 2 , V oc of 0.66 V, FF of 69.82%, and PCE of 18.31% are obtained. The J sc of the device depends upon the absorption coefficient, thickness and mobility of the active material. The higher the absorption coefficient, the higher the photo current will be 9,12,29,39,43 . The second important parameter is the thickness of the absorber. It must be thick enough to absorb the highest cut off wavelength of the incident solar radiation 27,29 . Apart from that, mobility plays a very crucial role for getting the high J sc . Ideally, the J sc is equivalent to solar cell current after illumination. Ma 27 . In this simulation, the mobility of electron and hole was adopted from recently studied researcher 27,28,43,44 . Since, current density is linearly proportional to the mobility of charge carriers, and hence the high value of J sc was achieved. However, Devi et al. 45 and Khattak et al. 46 have considered the significantly smaller and identical values of electron and hole mobilities, which are 1.6 cm 2 /Vs and 0.16 cm 2 /Vs, respectively and reported good J sc (~ 30 mA/cm 2 ). Another aspect is that diffusion length is proportional to the square root of mobilit 45 . Hence, diffusion length becomes more for high mobility of charge carrier, and hence recombination of charge carriers decreases. This may be other reasons for getting the comparatively higher value of J sc as compare to recently reported results 45,46 . The (2) dp n dt   27,29,39 . The quantum efficiency curve covers the entire visible spectrum, which is in good accordance with the recently published results 47,48 . Further enhancement in photovoltaic performance is possible. Figure  Absorber thickness. The absorber layer plays a significant role in the performance of device. The previously published report shows that the photovoltaic parameters such as J sc , V oc , FF and PCE are influenced by the absorber layer thickness 27,39 . To get the absorber layer's role in the device simulation, the absorber layer's thickness was varied from 100 to 1000 nm, and other parameters tabulated in a Tables 1 and 2 remain the same. The simulation results, i.e., the variation of photovoltaic parameters concerning the absorber layer's thickness, is shown in Fig. 3. It is observed that J sc increases steeply up to 700 nm and then varies slowly with thickness. The large value of J sc was obtained (~ 42.70 mA/cm 2 ) with a thickness 900 nm is mainly due to the large absorption coefficient of the perovskite 29 . V oc falls off smoothly, which may be attributed to the enhanced recombination of free charge carriers in the thicker absorber 27 . The decreasing value of FF with respect to absorber thickness may be due to the increased series resistance 29,53 . In addition, PCE initially increases and reaches a maximum (~ 18.36%) at 500 nm and decreases with a further increase in absorber thickness. Firstly, the absorber thickness is smaller than the diffusion length of charge carriers; therefore, most of the charge carriers reach at the electrodes, and therefore PCE increases. However, recombination occurs for thick absorber layer, and hence PCE decreases with a further increase in thickness 27,29,39 .

Acceptor carrier concentration (N A ) of the absorber.
Apart from the absorber layer thickness, the photovoltaic cell's device performance is significantly affected by the acceptor density of holes in the absorber layer. CH 3 NH 3 SnI 3 oxides in which Sn 2+ is converted into Sn 4+ (self-doping process) when the device is exposed to air. Unfortunately, this process deteriorates the performance of the device and making it a p-type semiconductor 28 55 . Takashi et el. found out that the hole concentration in the CH 3 NH 3 SnI 3 absorber layer can be varied up to 10 19 cm −356 . Therefore, to get to know how acceptor doping concentration affects the photovoltaic parameters, the acceptor density of the CH 3 NH 3 SnI 3 layer was varied from 10 14 to 10 18 cm −3 . Figure 4 provides the variation of J-V characteristics and PCE with respect to acceptor densi-   Fig. 4a. Another aspect is that built-in potential increases with increasing the acceptor doping concentration. Due to this, charge separation promotes and hence V oc increased. However, initially, J sc decreases slightly up to 10 15 cm −3 and then decreases drastically. It may be due to the increase in the recombination rate of charge carriers inside the perovskite absorber layer 39 . However, PCE drops rapidly when N A exceeds 10 15 cm −3 . The absorber layer's defect state leads to a considerable drop in power conversion efficiency, as exposed in Fig. 4b. Defect density (N t ). The effect of defect density of absorber was also investigated. Defects are inevitable in absorber layer. They exist in the bulk and at surfaces. In perovskite absorber layer, defects present in the form of point defects such as lattice vacancy, interstitial, Schottky and Frenkel defects. Apart from that, the higher order defects like dislocations and grain boundaries may also be present 57 . The self-doping process, which makes the semiconductor p-type, produces impurity defect in absorber layer 15,28,43,55 . These defects introduce deep or shallow levels in the energy band gap 57 . As a result of these defects, charge carriers can trap and facilitate nonradiative electron-hole recombination 27,39 . It is noted that the diffusion length of charge carriers is increased up to ~ 3 µm in Sn-based perovskite absorber layer using tin-reduced precursor solution 58 . Since, diffusion length of charge carriers is related to the defect density 45 . Therefore, in order to see the effect of diffusion length on photovoltaic responses, diffusion length of electron was varied from 0.046 to 4.6 µm by changing defect density from 10 18 to 10 14 cm −359 . Similar change in defect density has also been adopted by Lazemi et al., Du et al. and Hao et al. 27,30,39 . Based on these studies, the defect density was varied from 10 14 to 10 18 cm −3 and depicted its variation on photovoltaic properties in PSC, as shown in Fig. 5. It is observed that the performance of the device improved with the reduction of defect density. The absorber layer's initial defect density was set to be 3.029 × 10 16 cm −3 (as per Table 2). Because for this value of defect density, the diffusion length of electron and hole is nearly similar to experimentally observed values 28 . When the defect density is 10 15 per cm −3 , the cell performance is significantly improved, attaining the J sc of 40.13 mA/cm 2 , V oc of 0.81 V, FF of 75.17% and PCE of 24.54%. Now, further decrease of N t , from 10 15 to 10 14 cm −3 , slight variation is observed in J sc (40.14 mA/cm 2 ) and FF (75.78%) but considerable changes occurred in V oc (0.93 V) and PCE (28.39%). However, experimentally, it is not easy to synthesize a material with such a low value of defect density 39 . The Shockley-Read-hall (SRH) recombination model can be utilized to get information about the influence of the absorber layer's defect density on device performance 27,29,52 . To get the influence of N t on the performance of the device acutely, the effect of defect density on the recombination rate based on the SRH recombination model was studied. Figure 6 shows the variation of recombination rate with depth from the surface for different value of N t . It is detected that with increasing the defect density recombination rate increases, which is the reason for the www.nature.com/scientificreports/ reduction of cell performance with the increased value of defect density. Since, recombination rate increases with increasing the defect density; therefore, V oc decreases with increasing the defect concentration, as shown in Fig. 5. According to SRH model, the recombination rate (R) can be expressed like where, τ n,p , n, p, n i , E i and E t are the lifetime of charge carriers, the density of electron, the density of hole, intrinsic density, intrinsic energy level and energy level of the trap defects, respectively. Lifetime of charge carriers is given by where, σ n,p , v th and N t are the capture cross section of charge carriers, velocity of charge carriers, and the absorber layer's defect density, respectively. Therefore, with increasing the defect density, the relaxation time of charge carriers decreases (as per Eq. 5) and hence recombination rate increases (according to Eq. 4) as confirmed by Fig. 6. The interface recombination depends upon the conduction band offset between the buffer and absorber layer. The interface recombination at the absorber/buffer interface reduces due to the creation of positive CBO 49-51 . Minemoto et al. theoretically studied the effect of CBO at the absorber/buffer interface 49 . He reported that about 0.3 eV CBO offset minimizes the recombination at the interface due to this photovoltaic parameter increases. Hence, the recombination rate is significantly low at the absorber/ETL interface as compared to previously reported results 39,52 .
The diffusion length of charge carriers can be written like where, D is the diffusion coefficient. Since, the diffusion coefficient is proportional to the mobility of charge carriers and the mobility of electron (~ 2000 cm 2 /Vs) and hole (300 cm 2 /Vs) is large as experimentally observed by various researchers 30,44 . Due to the large value of mobility, diffusion length is large, which is why obtaining the very high value of PCE (28.39%). Because of the low recombination rate and large diffusion length, a very high value of PCE was achieved. Hence, the obtained outcomes are found to be better than previously published results 27,29,39,60 . Metal electrode work function. To study the ohmic or rectifying behaviour at metal contact/HTL interface, a work function study was carried out by varying various anode materials. Simulation was done using Ag, Cu, Au and Pt as an anode for PSC. The work function of Ag, Cu, Au and Pt are 4.74 eV, 5.0 eV, 5.1 eV and 5.7 eV, respectively 61,62 . The energy band diagram with various anode materials is shown in Fig. 7a,b. As clearly shown that the barrier layer for hole increases with decreasing the wave function of contact materials (Fig. 7a). Figure 8a,b presents the anode material's effect on J-V characteristics and photovoltaic properties of PSC. We can see that PCE decreases with decreasing the work function of the anode. In the case of Ag, Cu and Au, the anode's work function is less than the work function of Cu 2 O 61,62 . Hence, a rectifying Schottky barrier contact was formed for Ag, Cu and Au anode materials at an anode/Cu 2 O interface, as indicated by the dashed oval frame in Fig. 7a. This Schottky barrier hinders the hole transport to the anode, decreasing the FF and PCE as confirmed    Fig. 8b 29 . However, in the case of Pt anode, the work function of Pt is higher than the work function of Cu 2 O 63 . The ohmic contact was formed at an anode/Cu 2 O interface, as indicated by the dashed oval frame in Fig. 7b. The ohmic contact allows the hole transport at the interface 62 . Therefore, further improvement in J sc (42.63 mA/cm 2 ) and PCE (19.67%) are observed as shown in Fig. 8. The surface potential energy barrier ( φ B ) at the anode/Cu 2 O interfaces is given by Here, E g is the band gap of Cu 2 O, χ is the electron affinity of Cu 2 O and φ M is the anode's work function. Due to the decrease in the value of work function the surface potential energy barrier increases (as per Eq. 7), hence the FF and PCE decreases.

Conclusion
Lead-free CH 3 NH 3 SnI 3 perovskite as light harvester is investigated. A planner heterojunction perovskite solar cell with the structure FTO/TiO 2 /CH 3 NH 3 SnI 3 /Cu 2 O/anode was numerically analysed. Photovoltaic parameters were optimized with respect to several factors such as absorber layer thickness, acceptor density, defect density and work function of anode materials. The optimized perovskite thickness of 500 nm significantly enhances the PCE (18.36%). Reducing the defect density and improving the Sn 2+ stability of absorber layers are the critical issues for future research, which might be resolved by refining the device's fabrication techniques. The results indicated that the appropriate defect density improves the cell performance; however excessive concentration leads to a higher recombination rate of charge carriers and poor cell performance. The Schottky junction was formed at an anode/Cu 2 O interface for lower work function contact materials; therefore, high work function material is necessary for ohmic contact like Pt. The reported CH 3 NH 3 SnI 3 -based PSC provide a viable path to realizing environmentally benign, low-cost, and high-efficiency PSC.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.