A tin-based perovskite solar cell with an inverted hole-free transport layer to achieve high energy conversion efficiency by SCAPS device simulation

: Recently, organic-inorganic halide perovskite solar cells (PSCs) have received extensive research in the field of optoelectronic materials due to their unique optical and electrical properties, especially lead-based PSCs. However, the toxicity and stability of these devices, as well as the expensive hole transport layer (HTL) and other factors inhibit their commercial production. In this work, the non-toxic tin was applied as the battery material, the perovskite solar cell adopts an inverted HTL-free structure, and the one-dimensional solar cell capacitor simulator SCAPS-1D (Solar Cell Capacitance Simulator) was adopted for numerical simulation and found that FTO/CH 3 NH 3 SnI 3 /C 60 /Au structure PSCs also showed excellent photovoltaic performance. We studied the influence of the thickness of the absorber layer, the defect density, the doping concentration of different layers, and the thickness of the electron transport layer (ETL) under different directions of illumination on the battery performance. The simulation results show that the optimized inverted HTL-free tin-based PSCs based on C 60 are with inspiring performance: a short-circuit current density (J SC ) of 30.1646 mA/cm 2 , open-circuit voltage (V OC ) of 1.0465V, fill factor (FF) of 59.49% and power conversion efficiency (PCE) of 18.78%. We also introduced light from different directions to irradiate PSCs, and the results show that the HTL-free perovskite adopting an inverted structure can retain the light intensity of the irradiated perovskite layer to the greatest extent and exhibit superior performance. Based on the inverted HTL-free tin-based PSCs, we also investigated the performance parameters of ETL batteries with different materials. This work provides new ideas for PSCs development in the future.

In recent years, PSCs have attracted great attention due to their simple structure [1,2], low preparation cost [3], suitable and adjustable band gap [4,5], high extinction coefficient [6,7], bipolar carrier transmission characteristics [8,9] and flexible devices [10]. The energy conversion efficiency has been improved from 3.8% [11] to 25.2% [12]. Such a speed of development is unprecedented in the photovoltaic field. Although the current research on PSCs has achieved remarkable results, these perovskite materials used to absorb sunlight contain the toxic heavy metal lead, which is not friendly to the environment. This will undoubtedly limit the large-scale application of PSCs in the future, so there is an urgent need for development of new green and environmentally friendly lead-free PSCs.
Tin-based perovskite has even better photoelectric properties than lead-based perovskite, such as high absorption coefficient, small exciton binding energy and high carrier mobility, etc., which is currently the strongest candidate [13][14][15][16]. According to the Shockley-Queisser limit theory [17], the highest efficiency of a single solar cell is 33% corresponding to an absorption band gap of 1.34 eV. The absorption band gap of lead halide perovskite is generally larger in the range of 1.5-1.8 eV, while that of tin-based perovskite is narrower in the range of 1.3eV, which is very close to the ideal value of 1.34 eV. Therefore, tin-based PSCs are expected to obtain higher short-circuit current density and reach the theoretical limiting conversion efficiency.
In contrast to the rapid development of lead-based PSCs, the PCE of tin-based PSCs has not seen a major breakthrough since 2014. Only in recent years has it been raised to nearly 10%.
There are several possible reasons for this: (1) Sn 2+ is unstable and very easy to be oxidized into Sn 4+ or become vacancies, which causes the concentration of holes in the perovskite to increase sharply and lose its original semiconductor characteristics; (2) The crystallization rate of tin-based perovskite is fast at room temperature, and it is difficult to synthesize uniform and be completely coated tin-based films without additives; (3) Most lead-free tin-based PSCs usually adopt a regular battery structure, in which HTL is deposited on the tin perovskite layer, and HTL with high performance usually contains lithium (Li) or cobalt (Co) salts, which destroy the thin film of tin-based perovskite and in turn leads poor device performance.
With a special design, PSCs inverted structure (p-i-n) has some the advantages: the reverse structure has good stability and the J-V hysteresis effect is weak. HTL takes up nearly half of the cost of PSCs, so it is important to develop HTL-free PSCs to address the issue of manufacturing cost [2]. The inverted HTL-free PSCs are expected to ensure the light intensity of the irradiatedperovskite layer to the greatest extent to get better performance. In this work, we design and develop a simple inverted HTL-free tin-based PSCs structure, FTO/CH3NH3SnI3/C60 /Au, which is non-toxic, no HTL to destroy the perovskite absorption layer film, and can reduce manufacturing costs and guarantee the light intensity irradiatedon the perovskite layer, so that higher battery power conversion efficiency has been achieved.

Methodology
PSCs model is established in this work through theoretical methods to analyze the influencing factors of PSCs so as to optimize its performance, which is conducive to avoiding experiment duplication and reducing resource waste. In the process of simulating and optimizing solar cells, SCAPS-1D software developed by M. Burgelman of the University of Gent in Belgium is applied, which is suitable for simulating cells with various homojunction and heterojunction structures. Its basic principle is to solve the Poisson equation and current continuity equation under these constraints based on the established battery structure model and the input material parameters [18,19].
By setting the material parameters and corresponding boundary conditions, the above equations are solved with SCAPS-1D software through numerical calculations to obtain the relevant characteristics of the solar cells. Where, φ is the electric potential, p and n are the concentration of free carrier holes and electrons, Jn and Jp are electron current density and hole current density, R and G are the recombination rate and generation rate of electron hole pairs, NA and ND represent the acceptor and donor doping concentration.

Device structure and simulation parameters
The device structure diagram and energy band structure diagram of inverted HTL-free tin-based PSCs are shown in Fig. 1 Table 1 includes the basic physical and device parameter settings of each layer [20][21][22][23][24][25]. εr is the relative permittivity, χ is the electron affinity, Eg is the band gap energy, μn and μp are the electron mobility and hole mobility, and Nt is the defect density. The thermal velocities of the electrons and holes are set to 10 7 cm/s. The defect state in the absorption layer is set to a neutral Gaussian distribution, and the characteristic energy is 0.1 eV, and the defect energy level is in the middle of the band gap. The trapping cross-section of electrons and holes in the absorption layer is 2×10 -14 cm 2 , and the trapping cross-section of electrons and holes in other layers is 1×10 -15 cm 2 .
Taking into account the carrier recombination at the interface, an interface defect layer is added between the FTO/absorption layer and the absorption layer/electron transport layer. The energy distribution of the interface defect layer is set as a single neutral defect, and the trapping cross section of the defect is 1×10 -15 cm 2 , and the total defect density is 1×10 18 cm -3 , which is located 0.6eV above the top of the valence band. Table 2 lists the defect density inside and at the interface of the light-absorbing layer. In this simulation, the surface of each layer and the optical reflection of the interface between the layers are not considered.

Simulation analysis of the proposed device
According to the initial parameters given in Table 1 and Table 2 LUMO level of C60 matches with the conduction band minimum of absorber layer, so efficient electron transport can happen from FASnI3 to Au electrode. HOMO level of C60 is also lesser than that of valance band maximum of perovskite, so there is no hole transportation from FASnI3, i.e., holes are blocked effectively. In this way, charge recombination at interface is prevented and photovoltaic performance is in turn improved. Fig 2(b) is based on the initial parameters of the above table1,2, and it demonstares that the simulated VOC=0.8291 V, JSC =19.5411 mA/cm 2 , FF=64.33%, and PCE=10.42%, which are close to the experimental data in the literatures as shown in Table 3, proving the effectiveness of the simulation. The quantum efficiency (QE) curve shown in Fig 2(c) is also the simulated result under the same parameters. Based on the analysis of the data shown in Fig.2, the band gap of CH3NH3SnI3 is 1.3eV, which is narrower than the 1.55eV of CH3NH3PbI3, so that the absorption wavelength of tin-based perovskite is shifted to 950nm.
The range of the external quantum efficiency curve covers the entire visible spectrum, and the absorption from 360nm to 750nm is the strongest, exceeding 50%, which is consistent with the PCE spectrum measured in the literature [31]. The red-shifted external quantum efficiency curve is more conducive to light absorption in the infrared wavelength range.

Results and discussion
The following results and discusses are based on the simulation results.

Effect of changing absorption layer parameters
For PSC, the spectral response of the device is highly dependent on the thickness of the absorption layer, which has a great influence on the overall performance of the device. The absorption layer thickness varies from 50nm to 700nm, and other input parameters are shown in Table 1 and Table 2.  Tin-based PSCs are in an unfavorable self-doping process, and their unstable oxidation state Sn 2+ is easily oxidized to a stable Sn 4+ oxidation state at room temperature. In this work, the doping concentration of CH3NH3SnI3 absorption layer varies from 10 14 cm -3 to 10 18 cm -3 , and the optimized VOC, JSC, FF and PCE are 0.7690V, 24.8115 mA/cm 2 , 62.61% and 11.95% respectively when NA is 10 16 cm -3 , as shown in Fig. 4 (a) and (b). With the increase of doping concentration in the absorption layer, the electric field inside the perovskite layer also increases. The enhancement of electric field promotes the separation of charge carriers, which leads to the improvement of photovoltaic performance and PCE curve shows an upward trend. However, the main interference factor is that with the increase of doping concentration, unnecessary recombination process may be increased. When the doping concentration of the absorption layer is increased, that is, more than 10 16 cm -3 , it is easy to increase the photon recombination, and the PCE curve shows a downward trend. Only proper doping concentration can improve JSC and VOC well, and then improve the energy conversion efficiency. Therefore, it is necessary to adjust the NA at a reasonable doping concentration.

Research on PSCs under different light conditions
In order to verify that the inverted structure is more conducive to improving the photovoltaic performance of HTL-free tin-based PSCs, it was studied under different lighting conditions and the results are shown as Fig. 6 (the input parameters are shown in Table 1 and Table 2). The light irradiatedfrom both sides of FTO and Au was simulated, being with other parameters unchanged.
It is worthy being noted that it is difficult to achieve in a practical device due to the visible reflectivity of the gold electrode, whereas it is very easy to achieve in the simulation of the SCAPS program. With the SCAPS program, the basic parameter of the gold electrode is its work function, which is not absolute and essentially contains other parameters such as band gap, light absorption coefficient, and etc. As an electrode, gold can be regarded as a transparent material in the ultraviolet-visible wavelength range, and its work function is 5.1 eV. Therefore, we can theoretically discuss and simulate the light irradiated from the Au side.
The J-V curves and VOC, JSC, FF and PCE curves of light irradiated from the Au side corresponding to different C60 thickness are shown in Fig. 6 (a) and (c). The thickness of electron transport layer C60 is between 10nm and 100nm. The graphs of light irradiated from the FTO side corresponding to different C60 thicknesses are shown as Fig 6 (b) and (d). From Fig (b) and ( Table 4: the thickness of the absorption layer is 550nm, the doping concentration is 1.00×10 16 cm -3 , and the defect density is 1.00×10 15 cm -3 . The FTO doping concentration is 1.00×10 19 cm -3 . The thickness of the ETL is 30 nm.  (refer to Tables 1 and Tables 2 for other parameters), where VOC=1.0465V, JSC=30.1646mA/cm 2 , FF=59.49%, and PCE=18.78%.

Conclusion
In this work, SCAPS-1D software was used to simulate the proposed inverted HTL-free tin-based PSC structure design, and the VOC was 1.0465 V, JSC was 30.1646 mA/cm 2 , FF was 59.49%, and PCE was 18.78%. In order to optimize the structure, we individually changed the parameters of the device to observe and analyze its impact on the PSC performance.
The simulation results show that the photovoltaic performance can be improved by changing the thickness of the absorber layer, the doping concentration and reducing the density of defect states. When the thickness of the absorption layer is 550nm, the PCE growth tends to be stable, and the thickness of 550nm is the optimal value. As the doping concentration of the absorption layer increases, the PCE curve increases first and then decreases. This is because the continuous increase of the doping concentration easily leads to the recombination of photons. The maximum PCE is obtained when the NA is 10 16 cm -3 . The larger the defect density of the absorption layer is, the greater the impact on PSC and the worse the performance is. Therefore, the defect density should be reduced as much as possible. The defect density of this work was selected as 10 15 cm -3 .
By inverting the HTL-free tin-based PSC, the FTO will be in direct contact with the perovskite layer. It is valuable to study the influence of FTO parameters on the device. Changing the FTO doping concentration NA, it is found that the smaller NA devices have poor performance and abnormal J-V curve, which may be unsuitable for electrodes due to the low conductivity of FTO.
PCE is the optimal value when NA is 10 19 cm -3 .
Through the study of PSCs under different illumination conditions, the thickness of C60 is changed, and when light is irradiated from the Au (or FTO) side, it is found that the impact on the battery performance from the Au side is greater than that from the FTO side, and the PCE is lower.
The results show that the inverted PSCs can ensure the light intensity of the incident perovskite layer to the maximum extent on the basis of HTL-free, and show better photovoltaic performance.