Photoconversion Efficiency Modeling in Perovskite Solar Cells

Abstract

A theoretical approach to photoconversion efficiency modeling in perovskite p-i-n structures is developed. The results of this modeling compare favorably with the experiment and indicate that the surfaces of the perovskite solar cells (SCs) are naturally textured. It is shown that photoconversion efficiency in the limiting case of negligible Shockley-Read-Hall and surface recombination and in the absence of optical losses reaches the value of 29%. In the realistic case, the current-voltage curve ideality factor equals 2. This value is not due to recombination in the space-charge region; rather, it can be explained by taking into account the effect of the rear surface and high excitation level. PACS numbers:Although photoconversion efficiency in perovskite solar cells (SCs) presently achieved is about 20% [1, 2], there is a lack of publications on the theoretical modeling of these novel energy sources. This makes it difficult to systematically optimize the parameters of perovskite SCs.Here, a theory of photoconversion in p-i-n structures is developed, for which the following criteria are fulfilled: (i) Diffusion length is much higher than the i-region thickness, L d ≫ d; (ii) Excess electron-hole pair concentration generated by light notably exceeds the equilibrium carrier concentration in the i-region, ∆n ≫ n 0 . Note that this inequality holds quite well, because, according to [3], n 0 ≈ 10 11 cm −3 in FAPbI 3 , whereas the estimated value of ∆n exceeds 10 13 cm −3 .These criteria allow one to use the approach introduced earlier for heterojunction solar cells modeling, see [4][5][6]. The distinct feature of this approach is that it accounts for the contribution of the SCs rear surface, located near the isotype n-n + junction, both to the current-voltage (I-V) curves and to the open-circuit voltage.As shown in [4][5][6], under the conditions (i) and (ii), the light-generated current density at applied bias V is described by the expressionwhere J SC is the short-circuit current density, A SC is the SC surface area, kT is thermal energy, R S and R sh are series and shunt resistance, and J 0 is saturation current density. For a p-i-n structure, it is given byHere, q is the elementary charge, τ SRH is Shockley-Read-Hall lifetime, A is the radiative recombination parameter, and n i = √ N c N v e −Eg/(2kT ) is the intrinsic charge carrier concentration in the semiconductor with the effective densities of states N c and N v in the conduction and valence bands, respectively, and the bandgap E g . As seen from (1), the ideality factor equals 2. This value is not due to the recombination in the space-charge region, but due to the high excitation level and the rear surface contribution to the I-V curve.The open-circuit voltage, V OC , is obtained from (1) by setting the current density to zero. Furthermore, by multiplying the current by voltage and setting the derivative d(J L (V )V )/dV to zero, one can determine the photogenerated voltage V m at maximal power. Substitution of this result into (1) gives the corresponding c...