Reducing lead toxicity in the methylammonium lead halide ${\mathrm{MAPbI}}_3$: Why Sn substitution should be preferred to Pb vacancy for optimum solar cell efficiency

Methylammonium lead halide $\left({\mathrm{MAPbI}}_3\right)$ perovskite has emerged as one of the frontier optoelectronic semiconductors. To avoid lead toxicity, the role of Sn substitution and Pb vacancy (Pb-$⊠)$ are addressed in regulating stability and solar cell efficiency of ${\mathrm{MAPb}}_{1-X-Y}{\mathrm{Sn}}_X{⊠}_Y{\mathrm{I}}_3$ perovskite using hybrid density functional theory (DFT). The role of spin-orbit coupling (SOC) and the electron's self-interaction error are examined carefully. We find to reduce the Pb content from pristine ${\mathrm{MAPbI}}_3$, Sn substitution has a more favorable thermodynamic stability than creating Pb-$⊠$. Moreover, on substituting Sn, due to strong $s\text{−}p$ and $p\text{−}p$ couplings, the lower parts of the conduction band gets shifted downwards, which results in the reduction of the band gap (direct). This further helps us to get a high optical absorption coefficient (redshifted) and maximum solar cell efficiency in ${\mathrm{MAPb}}_{1-X}{\mathrm{Sn}}_X{\mathrm{I}}_3$ for $0<X\le 0.5$.

Figure 1

(a) Band edge alignment using PBE without SOC, $\mathrm{PBE}$ + SOC, and $\mathrm{HSE}06(\alpha =0.50)+\mathrm{SOC}$. (b) Calculated absorption spectra using the $\text{HSE}06+\text{SOC}$ functional for three different values of exact exchange fraction $\left(\alpha \right)$: $\alpha =0.25$ corresponds to peak at 0.94 eV, $\alpha =0.43$ gives rise to peak at 1.36 eV, and for $\alpha =0.50$, the peak lies at 1.53 eV.

Figure 2

(a) Relaxed crystal structure of ${\mathrm{MAPbI}}_3$. (b) Crystal structure of Sn substitutions and Pb-$⊠\mathrm{s}$ in ${\mathrm{MAPbI}}_3$. Formation energy $\mathrm{[}{E}_f(x,y)]$ of different ${\mathrm{MA}}_8{\mathrm{Pb}}_{8-x-y}{\mathrm{Sn}}_x{⊠}_y{\mathrm{I}}_{24}$ structures is represented as a function of Sn substitution and Pb-$⊠$. The color bar represents $E_f(x,y)$ in eV using ${\epsilon }_{xc}$ (c) PBE and (d) $\text{HSE}06+\text{SOC}$. A guide to the eye for the configurations with minimum $E_f(x,y)$ corresponding to each Sn substitution is marked with red arrows.

Figure 3

(a) The total density of states (DOS) of the stable conformers, partial DOS of (b) I-$5p$ orbital, (c) Pb-$6s$ orbital, (d) Pb-$6p$ orbital, (e) Sn-$5s$ orbital, and (f) Sn-$5p$ orbital.

Figure 4

(a) Imaginary part of a dielectric function, i.e., $\mathrm{Im}\left(\epsilon \right)$, and (b) real part of a dielectric function $\mathrm{Re}\left(\epsilon \right)$ of pristine ${\mathrm{MAPbI}}_3$ and Sn-substituted ${\mathrm{MAPbI}}_3$.

Figure 5

(a) Absorption coefficient and (b) SLME as a function of film thickness.