1.
Introduction

Methylammonium mixed lead halides (MAPbXs), which are known for their excellent optical and electrical properties, have drawn a great deal of attention for photovoltaic applications in recent years^[1–4]. MAPbX has unique characteristics, such as large absorption coefficients enabled by direct optical transitions, small exciton binding energies, existence of free carriers, and long carrier diffusion lengths. Therefore, the optoelectronic conversion efficiency of the MAPbX perovskite solar cell (PSC) has been significantly enhanced from 3.8% to 22.1% in a short time span of eight years^[5–7]. Although MAPbXs provide many superior performances, the use of the toxic element lead could be problematic for large-scale implementation. Therefore, replacing lead with environment-friendly elements could greatly increase its potential for practical application and production.



Tin halide MASnI₃ (MA = CH₃NH₃) perovskite solar cells have been intensively investigated for lead-free alternatives^[8–10]. CH₃NH₃SnI₃ has a narrower band gap of 1.3 eV compared to their Pb-based counterparts (~1.6 eV), which makes it possible to cover a wider range of the visible spectrum, and then a larger short-circuit current (J_SC) is expected for MASnI₃ PSC. Although MASnI₃ PSC has shown excellent performance, its efficiency is still less than 9%^[11–13], which can be attributed to several reasons. The easy oxidation of Sn²⁺ to Sn⁴⁺ causes severe device deterioration in an ambient environment^[14]. The low formation energy of Sn vacancies usually leads to high doped hole concentration, which results in severe carrier recombination in the solar cells. Moreover, the functional layers in Sn-based perovskite solar cells, such as hole or electron transport layer, may cause poor energy level alignment and severe interface recombination, which further limit the device performance.



In order to further improve the conversion efficiencies of MASnI₃ PSC, it is required to deeply understand the internal electron dynamics and corresponding interfacial engineering, and to clarify the limiting physical mechanism of the conversion efficiency. It is well known that an excellent interface quality is the key factor for a high efficiency PSC due to a strong interface recombination of defect states.



Numerical simulation is now becoming increasingly important for the understanding, design, and optimization of high-efficient solar cells. The simulation method allows an intuitive examination of each parameter in the solar cell and thus identifies the optimal conditions for operating. Up to now, there has been no report concerning the numerical simulation of MASnI₃ PSC.



In this paper, influences of defect states in the absorption layer and on the interfaces of absorber/electron transport layer (ETL) or absorber/hole transport layer (HTL) on MASnI₃ PSC efficiency are investigated by a one-dimensional device simulation with SCAPS-1D (version 3.3.02) ^{[15, 16]}. The SCAPS-1D program is a general solar cell simulation program that is based on Poisson and Continuity equations, and it has been employed to model planar structure perovskite based solar cells due to their structural similarity to thin film solar cells and Wannier type excitons in perovskites^[17–20]. In this paper, effects of the defects in the perovskite absorption layer and interface defects of absorber/ETL (or HTL) were deeply investigated. Considering the effects of defect states, a simulated cell efficiency of more than 29% is achieved by optimization of the various parameters. An in-depth understanding of the transport properties can help in improving the efficiency of solar cells and provide a useful guidance to the actual PSC manufacturing.

2.
Device simulation parameters

The simulated PSC structure is the transparent conductive oxide (TCO) glass/TiO₂/MASnI₃/Spiro-OMeTAD/metal back contact, and the sunlight is illuminated from TCO glass. TiO₂ acts as ETL, Spiro-OMeTAD as HTL, and MASnI₃ as the absorption layer. The absorber is assumed to be fully depleted and the electric field is formed by high densities of electron and hole of TCO and HTL, respectively. In order to simulate a more realistic PSC, we intentionally insert a very thin interface layer in the absorber region with a large number of defect states. The interface defect layer (IDL) is assumed to take into account the interface recombination, and IDL-ETL and IDL-HTL are inserted between ETL/absorber and absorber/HTL layers, respectively. Material parameters were selected from experimental data and theoretical results. The main simulated parameters are listed in Table 1^{[11, 12, 14, 16, 19–27]}. Here, N_A and N_D denote acceptor and donor densities, ε_r is relative permittivity, χ is electron affinity, E_g is band-gap energy, μ_n and μ_p are mobility of electron and hole, N_t is defect density in the film, and D_it is interface defect density of ETL/absorber and absorber/HTL. The N_t of IDL was changed from 10¹⁵ to 10²¹ cm^?3, which corresponds to a change in D_it from 10⁹ to 10¹⁵ cm^?2 in case of the thickness of 10 nm for IDL-ETL and IDL-HTL. Considering the high density of the defects and short carrier diffusion length at the interfaces of ETL/absorber and absorber/HTL, it is appropriate to set the thickness of IDL-ETL and IDL-HTL to 10 nm. The following parameters were set to be identical in all layers. Effective densities of states of the conduction band (N_C) and valence band (N_V) are 2.0 × 10¹⁸ and 2.0 × 10¹⁹ cm^?3, respectively. Thermal velocities (v_th) of electron and hole were both set to be equal to 10⁷ cm/s. The defect energy level is at the center of the band gap, and the energetic distribution is Gaussian with characteristic energy of 0.1 eV. The defect type in TiO₂, MASnI₃, and Spiro-OMeTAD thin films is neutral. However, defect types in the interfaces of ETL/absorber and absorber/HTL were set to neutral, donor, and acceptor, respectively. The capture cross section of electron or hole (σ_n or σ_p) is 1.0 × 10^?15 cm². A flat band was applied to the front and back contacts to prevent a contact potential. The absorption coefficient spectra of ETL and HTL materials were calculated by α(E) = A_α(hν – E_g)^1/2, and the pre-factor A_α was extracted from Ref. [11]. In the simulation, AM 1.5 radiation was used as the illumination source with a power density of 100 mW/cm³, and the device temperature was set as 300 K.

Parameter	TCO	TiO2 (ETL)	IDL-ETL	MASnI3 (absorber)	IDL-HTL	Spiro-OMeTAD (HTL)
Thickness (nm)	500	200	10	600	10	200
Eg (eV)	3.50	3.20	1.30	1.30	1.30	3.17
χ (eV)	4.00	4.26	4.17	4.17	4.17	2.05
εr	9.0	9.0	8.2	8.2	8.2	3.0
μn/μp (cm2/(V·s))	20/10	20/10	2.0/2.0	2.0/2.0	2.0/2.0	2/2 × 10?4
ND (cm?3)	2 × 1019	1 × 1016	–	–	–	–
NA (cm?3)	–	–	1 × 1015	1 × 1015	1 × 1015	2 × 1018
Nt (cm?3)	1 × 1015	1 × 1015	1 × 1015–21	1 × 1011–19	1 × 1015–21	1 × 1015
Nit (cm?2)	–	–	1 × 109–15	–	1 × 109–15	–

Table1.
Simulation parameters of Sn-based PSC.



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Parameter	TCO	TiO2 (ETL)	IDL-ETL	MASnI3 (absorber)	IDL-HTL	Spiro-OMeTAD (HTL)
Thickness (nm)	500	200	10	600	10	200
Eg (eV)	3.50	3.20	1.30	1.30	1.30	3.17
χ (eV)	4.00	4.26	4.17	4.17	4.17	2.05
εr	9.0	9.0	8.2	8.2	8.2	3.0
μn/μp (cm2/(V·s))	20/10	20/10	2.0/2.0	2.0/2.0	2.0/2.0	2/2 × 10?4
ND (cm?3)	2 × 1019	1 × 1016	–	–	–	–
NA (cm?3)	–	–	1 × 1015	1 × 1015	1 × 1015	2 × 1018
Nt (cm?3)	1 × 1015	1 × 1015	1 × 1015–21	1 × 1011–19	1 × 1015–21	1 × 1015
Nit (cm?2)	–	–	1 × 109–15	–	1 × 109–15	–

3.
Results and discussion

The influence of the thickness and doping concentration of each layer of PSC on the device performance were extensively investigated^{[23, 28–30]}. The spectral response is a key factor in determining device performance and it is closely related to the device thickness. The short-circuit current density (J_SC) increases with the thickness of the perovskite absorption layer and then saturates due to the limit of the carrier diffusion length. The open-circuit voltage (V_OC) decreases slightly due to an increased charge recombination in thicker films. With the increase of the HTL (or ETL) layer thickness, the conversion efficiency gradually decreases, which results from a reduction in light absorption. Hence, the optimized thickness of absorber, HTL, and ETL were selected as 600, 200, and 200 nm, respectively.



Because the self-doping process of Sn²⁺ is easily oxidized to Sn⁴⁺, the tin-based perovskite exhibits a p-type conductive behavior^[25]. Experimental results indicate that the doping level in MASnI₃ film can be varied in a range of 10¹⁴ – 10¹⁷ cm^{?3[7, 12]}. An appropriate doping concentration of the perovskite absorption layer is beneficial to the improvement of PSC efficiency. When the doping concentration of the absorption layer increases, the built-in electric field in PSC enhances, which improves the separation efficiency of carriers, hence improving the cell performance. Further increasing the doping concentration above 1 × 10¹⁸ cm^?3, the cell performance deteriorates due to a higher Auger recombination rate. An increase in the recombination rate affects the cell performance greatly and should be avoided effectively. Therefore, combining experiments and simulation results, the suitable doping concentration of the MASnI₃ absorption layer was set to 1.0 × 10¹⁵ cm^?3.



The properties and the amount of defects in the perovskite absorber play a key role in determining device performance, because photogenerated carriers are mainly generated in this layer and the carrier recombination is dominant in determining the V_OC of PSC. Therefore, for simplicity, we did not consider the effects of the defects in HTL or ETL. The device performances are improved significantly with the reduction of the defect density N_t in MASnI₃ thin film, as shown in Fig. 1. When the N_t in MASnI₃ is lower than 1 × 10¹² cm^?3, the PSC efficiency (Eff) is 36% without considering the influence of interface defects between the interfaces of the ETL/absorber and absorber/HTL. Further analysis shows that N_t in MASnI₃ is lower than 1 × 10¹⁰ cm^?3，Eff is no longer increased and reaches its maximum value (40.5%, no display in Fig. 1). For the solar cell of a single homogenous junction with E_g = 1.34 eV, the theoretical Eff limit by the Shockley–Queisser theory is 33.7%^{[31, 32]}. For the simulated perovskite solar cell, the band-gap energy of ETL (TiO₂), the absorber layer (MASnI₃), and HTL (Spiro-OMeTAD) are 3.20, 1.30, and 3.17 eV, respectively. Therefore, the simulated solar cell can be approximately regarded as a double junction solar cell with a theoretical Eff limit of 44.3%^[33].






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Figure1.
(Color online) Solar cell parameters of PSC with (or without) IDL as a function of defect density N_t in MASnI₃ thin film.




Without considering the influence of the interface defect, the V_OC is almost linearly reduced with the exponential increase of N_t. V_OC is given by

${V_{{ m{OC}}}} = frac{{kT}}{q}{ m{ln}}left( {frac{{{I_{ m{L}}}}}{{{I_{ m{0}}}}} + 1} ight),$

(1)

where q is the electronic charge, k is the Boltzmann constant, T is the temperature, I_L is the light-generated current, and I₀ is the saturation current. While I_L typically has a small variation, the key factor affecting V_OC is I₀, since this may vary by orders of magnitude. The saturation current (I₀) depends on recombination in the solar cell, and can be written by

${I_0} = AkTn_{ m{i}}^2left( {frac{{{mu _{ m{n}}}}}{{{L_{ m{n}}}{N_{ m{A}}}}} + frac{{{mu _{ m{p}}}}}{{{L_{ m{p}}}{N_{ m{D}}}}}} ight),$

(2)

where A is the quality factor, n_i is the intrinsic carrier concentration, and L_n (L_p) is the electron (hole) diffusion length. The most important factor affecting I₀ is diffusion length, which is given by

${L_{ m{n,p}}} = sqrt {frac{{{mu _{ m{n,p}}}kT}}{q}frac{1}{{{sigma _{ m{n,p}}}{v_{ m{th}}}{N_{ m{t}}}}}} .$

(3)

According to Eqs. (1)–(3), the V_OC is almost linearly decreased with the exponential increase of N_t, which is consistent with the simulation results. The J_SC has almost no change in the case of N_t lower than 1 × 10¹⁶ cm^?3, however, J_SC decreases significantly with the further increase of N_t, as shown in Fig. 1. For a low N_t, L_n (or L_p) is larger than the absorber thickness, thus the impact of N_t to J_SC is rather small. However, for a large N_t (for example, 1 × 10¹⁶ cm^?3), L_n (or L_p) is smaller than the absorber thickness, so J_SC decreases rapidly with the increase of N_t. In fact, a low trap-assisted recombination rate in perovskite thin film has been reported by Herz et al.^[34], therefore, the suitable defect density in MASnI₃ thin film can be set to 1 × 10¹⁴ cm^?3.



In case of considering the influence of an interface defect, the interface defect density (D_it-ETL or D_it-HTL) was set to a very low value ~1 × 10⁹ cm^?2. When N_t is larger than 1 × 10¹⁴ cm^?3, the insertion of the interface defect layer with a low D_it has almost no influence on the PSC performance, as shown in Fig. 1. As N_t is lower than 1 × 10¹⁴ cm^?3, the presence of interface defects deteriorates the PSC performance, which is caused by the interface recombination loss. Of course, if D_it was set to a larger value (for example, 1 × 10¹⁴ cm^?2), the interface defect has an important influence on PSC performance in case of any value of N_t.



The interface quality has a decisive influence on the efficiency of thin film solar cell because the presence of interface defects can lead to high levels of recombination. In real devices, it is difficult to characterize the interface defect density and recombination rate. In the simulation, the influence of an interface state on the device performance can be revealed by drastically changing the interface defect density. Here, two interface defects are considered, and they are the interface defect D_it-ETL located between the ETL and the absorber (TiO₂/MASnI₃) and the interface defect D_it-HTL between the absorber and HTL (MASnI₃/HTL). Two D_it values change from 10¹⁰ to 10¹⁴ cm^?3. In the perovskite absorption layer, the defect type (neutral, donor, or acceptor) has almost no influence on PSC performances, and the simulated results were not shown here. However, different defect types of D_it-ETL and D_it-HTL were considered, and their influences on PSC were investigated in depth.



For the simplicity, the neutral defect type was analyzed at first. The efficiencies of PSC with different defect densities at ETL/absorber and absorber/HTM interfaces were demonstrated, as shown in Fig. 2. As D_it-ETL or D_it-HTL was changed from 10¹⁰ to 10¹⁴ cm^?2, the other parameter D_it-HTL or D_it-ETL was fixed at 10¹⁰ cm^?2. The Eff decreases from 29.02% to 27.44% when D_it-HTL increases from 10¹⁰ to 10¹⁴ cm^?2. However, the Eff decreases from 29.02% to 22.57% with the increase of D_it-ETL from 10¹⁰ to 10¹⁴ cm^?2. Therefore, the interface quality at the absorber/HTL interface has a greater impact on PSC efficiencies than that at the ETL/absorber interface. When the sunlight changes its incident direction, namely, from the HTL to the ETL, the simulated results are just the opposite, as illustrated in Fig. 2. These results indicate that the interface quality of the sunlight incident side of PSC is far more important than that of the back side.






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Figure2.
(Color online) Efficiency of PSC with neutral interface defects as a function of interface defect density.




The difference is caused by the collection probability of photogenerated carriers, which is that a light generated carrier absorbed in a certain region of the device will be collected by the p-n junction and therefore contribute to the light-generated current. Similarly, if the carrier is generated more than a diffusion length away from the junction, then the collection probability of this carrier is quite low. If the carrier is generated closer to a region such as a surface with high recombination, then the carrier will be recombined. For high absorption coefficient of the pervoskite absorber, the number of photogenerated electron-hole pairs at the light irradiation side is high at the surface and significantly becomes small toward the back side. The presence of the localized recombination site, such as a surface or interface, has a stronger influence on the collection probability than a less severe localized recombination site. Therefore, as the sunlight irradiates from the side of ETL/absorber, the higher excess carrier density will be generated, which leads to a larger recombination rate at ETL/absorber than that at absorber/HTL. Thus, the interface defect at ETL/absorber has stronger influence on device performance than absorber/HTL. On the contrary, if the device is irradiated from the HTM side, the defect density of the absorber/HTM interface has a strong impact on the device performance, as shown in Fig. 2. In order to enhance the efficiency of the perovskite solar cell, improving the interface quality of the front side is much more important than that of the back side.



We have discussed the behavior of the interface with neutral defects, next we will analyze the impacts of the interface with donor or acceptor defects on PSC performance. If D_it-HTL was fixed at 10¹⁰ cm^?2 with neutral defects, the dependence of device efficiency on D_it-ETL with different defect type was given in Fig. 3. When the defect type of D_it-ETL is neutral or donor, the influence of interface defects on device efficiency is the same, and the Eff decreases from 29.02% to 22.50% with the increase of D_it-ETL from 10¹⁰ to 10¹⁴ cm^?2. However, in the case of acceptor defects, the Eff drops sharply from 29.02% to 0.96% when D_it-ETL increases from 10¹⁰ to 10¹⁴ cm^?2, which indicates that D_it-ETL with acceptor defects has a far more important influence on device efficiency than D_it-ETL with neutral or donor defects. Similarly, the impact of D_it-HTL with donor defects on device efficiency is much stronger than that of D_it-HTL with neutral or acceptor defects (not shown in this paper).






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Figure3.
(Color online) Efficiency of PSC with donor (or acceptor) interface defects as a function of interface defect density.




The further investigations on the band bending and carrier recombination were shown in Fig. 4. In order to analyze only the band bending and recombination at the interfaces of ETL/absorber and absorber/HTL, the horizontal axis of Fig. 4 starts from 0.2 μm (the thickness of ETL) and ends at 0.82 μm (IDL-ETL (0.01 μm) + absorber (0.6 μm) + IDL-HTL (0.01 μm)). As D_it-ETL with acceptor defects increases, the reduction of the band bending is obviously enhanced, as shown in Fig. 4(a). However, in case of D_it-ETL with donor (or neutral) defects, the interface defect density has almost no influence on band bending, as shown in Fig. 4(b). The band bending affects the photo-generated carrier flow, which leads to the decrease in V_OC and deterioration of device performance. The dependences of the interface defect type and defect density on carrier recombination rate are also shown in Figs. 4(c) and 4(d). Similar to the influence on band bending, D_it-ETL with acceptor defects has a much greater impact on recombination rate than D_it-ETL with donor (or neutral) defects.






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Figure4.
Distributions of total recombination and energy band in the cell thickness direction for varying interface defect density.




When interface defect states of the n-type-ETL/p-type-absorber or p-type-absorber/n-type-HTL heterojunction are occupied, charges are trapped at the interface in the space charge region of the heterojunction. As the defect type of D_it-ETL is donor or neutral, the space charge region is not significantly affected, and the electric field extends up to the neutral region of the perovskite absorber with the increase of D_it-ETL . However, for D_it-ETL with acceptor defects, the trapped charges prevent the extension of the space charge region into the absorber since the polarity of the interface charge is the same as the polarity of the majority carrier of the perovskite absorber. Therefore, the band bending in the absorber is reduced, which results in a lowering of the effective barrier and consequently a decrease in V_OC. In addition, a reduction of the band bending causes an enhancement of the majority carrier concentration at the interface, which leads to an increased recombination probability. Similarly, D_it-HTL with donor defects has a much greater impact on the band bending and recombination rate than D_it-HTL with acceptor (or neutral) defects.



In the actual preparation process of Sn-based perovskite solar cells, some divalent Sn compounds, for example, SnF₂, as an additive, can be used as Sn vacancy suppressors to reduce the defect density in the perovskite absorber and improve device performance^{[35, 36]}. In order to reduce the interface defect density at the absorber/ETL (or HTL), energy band matching between the absorber layer and ETL (or HTL) and composition engineering (such as mixing of the monovalent cations) have proven to be an effective way to tailor the properties of perovskites and enhance the performance of PSCs^{[37, 38]}.

4.
Conclusion

The planar heterojunction CH₃NH₃SnI₃ solar cell was simulated with one-dimensional device simulator SCAPS, which is widely used in inorganic thin film solar cells. The defects in the perovskite absorber and at the ETL/absorber or absorber/HTL interface were deeply investigated. In the case of defect density in a perovskite absorber lower than 1 × 10¹⁶ cm^?3, J_SC has almost no change and high efficiency (> 19.0%) can be obtained. The absorber interface density at the sunlight incident side is a decisive factor for efficiency due to the high absorption coefficient of the pervoskite absorber. The defect density at the ETL/absorber interface with acceptor defects has a far more important influence on device efficiency than that with neutral or donor defects. Similarly, the impact of the defect density at the absorber/HTL interface with donor defects on device efficiency is much stronger than that with neutral or acceptor defects. The polarity of the interface charge has a different impact on the band bending and recombination rate. Considering the effects of defect states, a simulated cell efficiency of more than 29% is achieved by optimization of the various parameters, which highlights the great potential of perovskite in achieving high efficiency. The simulation based on this study will be useful for further understanding of device operation and efficiency improvement.

Acknowledgements

The author would like to thank Professor Marc Burgelman, Department of Electronics and Information Systems, University of Gent for the development of the SCAPS software package and allowing its use.



This work was supported by the Zhejiang Provincial Natural Science Foundation of China (No. LY17F040001), the Technology Development Project Program of Hengdian Group DMEGC Magnetics Co., Ltd (No. 2016330001002138), the Open Project Program of Surface Physics Laboratory (National Key Laboratory) of Fudan University (No. KF2015_02), and the Open Project Program of National Laboratory for Infrared Physics, Chinese Academy of Sciences (No. M201503).