1 Introduction

Since their first demonstration in dye-sensitized solar cells by Miyasaka et al. in 2009 [1], metal halide perovskites have gathered enormous attention from the scientific community as excellent sunlight absorber materials for high efficiency and inexpensive photovoltaic applications. The steep rise in efficiencies from 3% to ~ 23% in a span of less than a decade has been remarkable and such meteoric upsurge in device efficiencies have not been noticed in other photovoltaic technologies to date [1,2,3]. Much of this success can be attributed to a number of favorable semiconducting properties of perovskite including tunable bandgap, long minority carrier lifetime and hence long diffusion length, high absorption coefficient, ultralow Urbach energy and high tolerance to defects [4, 5]. Moreover, the use of naturally abundant materials and the ability to be processed by solution-based methods make them attractive for low-cost manufacturing.

In general, the metal halide perovskite material has the general formula of ABX3, where A is a big size monovalent cation (either organic or inorganic) e.g. methyl-ammonium (MA), CH3NH3+ or formamidinum (FA), CH2(NH2)+2 or Cs+, or Rb+;B is a divalent small metallic cation (e.g. Cu2+, Mg2+, Ge2+, Sn2+, Pb2+, Eu2+, Yb2+ etc.) and X is a monovalent halide anion (e.g. Cl−, Br−, I− etc.) which binds to both cations [6]. The most commonly studied class of perovskite absorber is methyl-ammonium lead tri-halides (CH3NH3PbX3) with an optical bandgap ranging between 1.5 and 2.3 eV depending on the specific halide composition [7]. Recently, the experimental study of Sn doping on methyl-ammonium lead chloride perovskite is carried out for its photovoltaic performance enhancement [8].

Despite the ongoing pursuit of various research groups in the direction of improving the efficiencies of lead-based perovskite solar cells, a lot of efforts have also been devoted to find an alternative to lead for countering the challenges of toxicity which might otherwise hinder the widespread commercialization of this new technology [4]. Although a variety of divalent metals have been tested for the B-site in the perovskite composition, Tin (Sn) has been found to be the most successful in terms of delivering reasonably good efficiencies [9, 10]. In addition to that, replacement of lead (Pb) with Sn results in achieving a bandgap of ~ 1.3 eV [2], which is close to the ideal bandgap as postulated by the Shockley-Queisser limit [11]. When combined with a suitable wide bandgap perovskite sub-cell, such low bandgap Sn perovskites provide a pathway to fabricate high-efficiency all-perovskite tandem solar cells. However, besides the widely known problem of stability, such Sn based perovskites have also yet to achieve efficiencies comparable to their lead-based counterparts. Therefore, numerical study of the Sn based perovskites can be a more effective technique to trigger further developments in this field rather than going for extensive experimental investigations initially.

In this work, a Tin (Sn) based perovskite material (MASnI3) is sandwiched between p-doped NiO hole transporting material and n-doped PCBM (phenyl C61 butyric acid methyl ester) electron transporting material in a planar inverted configuration and the effects of thickness and doping concentration of various constituent layers on the device performance are studied using Solar Cell Capacitance Simulator (SCAPS) one-dimensional (1-D) simulation program. The simulation methodology and architecture of the device is discussed in Sect. 2 followed by results and discussion in Sect. 3. Brief description of PSC with Cu2O as HTM & PCBM as ETM and inorganic PSC, Cesium Lead Iodide (CsPbI3) is presented in Sect. 4 and 5 respectively. Finally, the conclusion is drawn in Sect. 6.

2 Simulation methodology and device structure and its physics

The proposed PSC as shown in Fig. 1 is simulated with SCAPS 1-D simulation program. The simulation program is based on solving Poisson’s equation, carrier-continuity equation and drift diffusion equation for the charge carriers as mentioned in Eqs. (1)–(3) [12, 13]. For various thin film solar cell technologies, the device performance is analyzed by using numerical methods

$${\text{Poisson's\;equation}}:\frac{{\partial^{2} \varphi }}{{\partial x^{2} }} = \frac{q}{\varepsilon }\left( {n - p} \right)$$
(1)
$${\text{Carrier}}\;{\text{continuity}}\;{\text{equation}}:\frac{\partial n}{\partial t} = \frac{1}{q}\frac{{\partial J_{n} }}{\partial x} + {\text{G}} - {\text{R}},\;\frac{\partial p}{\partial t} = - \frac{1}{q}\frac{{\partial J_{p} }}{\partial x} + {\text{G}} - {\text{R}}$$
(2)
$${\text{Drift}}\;{\text{diffusion}}\;{\text{equation}}:J_{n } = {\text{q}}D_{n} \frac{{\partial_{n} }}{{\partial_{x} }} - {\text{q}}\mu_{n} {\text{n}}\frac{{\partial_{\varphi } }}{{\partial_{x} }},\;J_{p} = - qD_{p} \frac{{\partial_{p} }}{{\partial_{x} }} - q\mu_{p} {\text{p}}\frac{{\partial_{\varphi } }}{{\partial_{x} }}$$
(3)

where φ is electric potential, ɛ is dielectric constant, q is electronic charge, n is electron concentration, p is hole concentration, Jn is electron current density, Jp is hole current density, G is carrier generation rate, R is carrier recombination rate, Dn is electron diffusion coefficient, Dp is hole diffusion coefficient, µn is electron mobility, and μp is hole mobility [14]. In this study, the simulated device stack for lead-free perovskite solar cell (PSC) is shown in Fig. 1.

Fig. 1
figure 1

Stacked layers of perovskite solar cell for device simulation

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The symbols mentioned in the Table 1 represent their usual meanings. The proposed perovskite solar cell is an planar (P-i-N) type structure having ITO transparent conductive oxide as front contact followed by p-doped NiO, interface layer (IL1), intrinsic type CH3NH3SnI3 perovskite material, interface layer (IL2), n-doped PCBM layer and silver (Ag) back contact. The material parameters are taken from literatures are shown in Table 1. The capture cross-section of electrons and holes are considered to be 2 × 10−14 cm−2 with defect type “neutral” charge in both bulk and interface layers. The energetic distribution is Gaussian type and the reference for defect energy level Et is considered above Ei. The energy level with respect to reference is considered as 0.6 eV with characteristic energy at 0.1 eV. The total density of traps (Nt) uniformly considered in the perovskite materials and interface layers are 2.5 × 1013 cm−3 and 1 × 1017 cm−3 resulting diffusion length of carriers are 1 µm and 1.6 × 10−2 µm respectively. The electron and hole thermal velocities are kept constant i.e. 1 × 107 cm s−1 in all materials.

Table 1 Simulation parameters of the lead free PSC with various layers [5, 10, 14,15,16]
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3 Results and discussion

The J-V characteristics with the variation of perovskite layer thickness are plotted in Fig. 2. It is observed that there is an increase of Voc, Jsc, FF and efficiency with increase in the thickness of perovskite layer and optimum values of Voc = 0.98 V, Jsc = 34.86 mA/cm2, FF = 85.64% and efficiency (eta) = 29.19% are obtained at a thickness of 1000 nm.

Fig. 2
figure 2

The J–V characteristics with respect to the change of Perovskite Thickness

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This improvement in efficiencies is primarily ascribed to the greater absorption of sunlight in the near infrared region with increasing absorber thickness, thereby resulting in an increase in the photo generated current density [12].

It is observed from Fig. 3 that within the wavelength range of 350–900 nm, the absorption and the external quantum efficiency is very high (ideally 100%, but in practice it is much lower due to several optical and electrical losses). However, after 900 nm, the QE falls sharply till it reaches zero at 950 nm (corresponding to the bandgap energy of 1.3 eV).

Fig. 3
figure 3

The quantum efficiency of NiO/MASnI3/PCBM solar cell

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It is realized that with the change of NiO (hole transport layer) thickness and PCBM (electron transport layer) thickness from 10 nm to 50 nm there is a very small reduction of Voc, Jsc, FF and efficiency. Hence the optimum thickness of NiO and PCBM is kept at 10 nm.

The doping concentration of a photoactive material in the solar cell architecture decides the electrical behavior of the layers which will affect the performance of the device [16]. In order to understand the doping effect on the device performance, the doping levels are varied and observed for both NiO and PCBM. With the variation of doping concentration from 1 × 1013 to 1 × 1019 in NiO hole transport material, it is observed from Table 2, that the PCE increases from 22.17 to 29.19%. This increase in PCE primarily results from the rise in the conductivity of NiO, which thereby reduces the series resistance of the entire device. Hence, the optimum doping concentration is fixed to 1x1019. It is also visible in the table that Voc increases which is due to the decrease in the reverse saturation current with increase in doping concentration. Jsc increases slightly and because of the increase in the conductivity of the device, FF also increases as the doping concentration increases.

Table 2 J-V characteristic parameters with the variation of dopant concentration in NiO (hole transport material) keeping PCBM concentration 1 × 1020 cm−3
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Again, it is observed from Table 3, that PCE is also influenced by the variation of the doping concentration of PCBM electron transport material. The Jsc is constant which shows that Jsc is not related to the doping concentration of PCBM. With increase in doping concentration, the recombination rate also increases. So, both the Voc and FF are increasing initially and then Voc remains constant and FF started reducing from 1 × 1019. Similarly, PCE also increases with the increase in doping concentration and remains constant when the PCBM doping concentration reached to 1 × 1020 cm−2.

Table 3 J-V characteristic parameters with the variation of dopant concentration in PCBM (electron transport material) keeping NiO concentration at 1 × 1019 cm−3
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From Table 4, it is observed that the variation in the doping concentration of perovskite material also affects the overall device performance. The efficiency reaches the maximum of 29.19% when doping concentration is 1 × 1013 cm−3 and it sharply declines after 1 × 1019 cm−3 until it reaches the lowest value of 5.73% at 1 × 1020 cm−3. It is because a heavily p-type doped material short-circuited a solar cell, and does not work as an effective absorber [9].

$$V_{oc} = \frac{k T}{q}\ln \left[ {\frac{{J_{sc} }}{{J_{o} }} + 1} \right]$$
(4)
Table 4 J-V characteristic parameters with the variation of dopant concentration in Perovskite material, keeping PCBM concentrations as 1 × 1020 cm−3 and NiO concentrations as 1 × 1019 cm−3
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From the above equation, it is observed that Voc is a function of both Jsc and the reverse saturation current of the device (Jo). Jsc also depends on the thickness of the layer and thus, there is a variation in the open circuit voltage, Voc with change in layer thickness. In Fig. 4, Jsc is increasing slowly from 33.09 to 34.771 mA/cm2 which is due to the increase in carrier generation, then remains almost constant when perovskite thickness is from 1000 to 1200 nm. FF is almost constant with the increase in perovskite layer thickness as shown in Fig. 5.

Fig. 4
figure 4

Voc and Jsc with the variation of perovskite absorber layer thickness

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Fig. 5
figure 5

FF and PCE with the variation of perovskite absorber layer thickness

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Because of the production of new charge carriers, the power conversion efficiency increases with increase in thickness. However, efficiency becomes almost constant from thickness 850 nm and started decreasing from 1050 nm since the recombination process increases and extraction rate of electron and hole pairs become lesser [17]. Finally, the optimized PCE of 29.19% is found when perovskite layer thickness is kept to be 1000 nm as shown in Fig. 5.

4 PSC with Cu2O as HTM and PCBM as ETM

A highly efficient lead free perovskite solar cell based on CH3NH3SnI3 absorber material with Cu2O as HTM and PCBM as ETM is investigated [13]. The device is optimized using absorber thickness and doping concentrations of HTM, ETM and perovskite absorber which influence the device performance. The maximum value of PCE is obtained as 30.59% with Voc of 0.99 V, Jsc of 35.13 mA/cm2 and FF of 87.12%. From these results it is expected that lead free perovskite solar cell can be a potential choice of achieving high efficiency and toxic free solar cell.

5 Cesium lead iodide (CsPbI3) PSC

CsPbI3 is one of the promising inorganic halide perovskites for high stability, where Cesium (Cs+) is used instead of organic perovskites such as methyl- ammonium or formamidinum. The volatile organic components induce thermal and chemical instability in hybrid organic–inorganic perovskites. In order to enhance the stability and photovoltaic performance, inorganic halide perovskite is obtained by substituting the volatile organic components with Cs+. In this work, a detailed theoretical investigation on the CsPbI3 based inorganic, i-PSCs is performed and the following photovoltaic performance parameters are obtained such as Voc of 1.4 V, Jsc of 11.75 mA/cm2, FF of 86.47% and PCE of 14.19%.

6 Conclusion

A lead free, Sn based perovskite solar cell is proposed with NiO as HTM and PCBM as ETM resulting PCE above 29%. Lead free PSC with Cu2O as HTM and PCBM as ETM delivered PCE above 30%. Due to its high efficiency and low toxicity, the proposed PSC can be a replacement for the commonly used MAPbI3 based perovskite solar cell and used as a bottom sub-cell in an all perovskite tandem cell. However, it is noted that in practice, the morphology of perovskite film and its interface with charge transporting layers greatly influence the shunt resistance of the device (not considered in this work) may lower the device performance drastically. Nevertheless, this study provides an insight into the dependence of the device performance of Sn-based perovskite solar cell on the thickness, doping concentration of the absorber and the charge transporting layers. The in-organic, i-CsPbI3 PSCs can be explored for high stability and high PCE.