Charge transport in hybrid halide perovskites

Charge transport is crucial to the performance of hybrid halide perovskite solar cells. A theoretical model based on large polarons is proposed to elucidate charge transport properties in the perovskites. Critical new physical insights are incorporated into the model, including the recognitions that acoustic phonons as opposed to optical phonons are responsible for the scattering of the polarons; these acoustic phonons are fully excited due to the “softness” of the perovskites, and the temperature-dependent dielectric function underlies the temperature dependence of charge carrier mobility. This work resolves key controversies in literature and forms a starting point for more rigorous first-principles predictions of charge transport.

Figure 1

(a) Formation free energy as function of temperature; (b) the ratio of number of electrons ($N_e$) to the number of polarons ($N_P$) vs temperature.

Figure 2

Static dielectric constant as function of temperature in ${\mathrm{MAPbI}}_3$. The experimental data (squares) are taken from [19] and the solid line is a fit from Eq. (13).

Figure 3

(a) Polaron-polaron collision frequency as a function of $T$ determined by Eq. (19); (b) the polaron-${\mathrm{I}}^{-}$ vacancy collision frequency (circles) and the polaron-LA phonon collision frequency (solid line) as functions of $T$ determined by Eqs. (20) and (21). ${\varepsilon }_0=70$ and ${\varepsilon }_{\infty }=6.5$ [18] are used in the plot.

Figure 4

(a) Hole mobility $\mu$ vs $n_h^{-1}$ for $p$-doped ${\mathrm{MAPbI}}_3$. The experimental data (squares) are taken from [4]; the solid line is a fit of Eq. (22). (b) The logarithm of the effective carrier mobility, ${\log }_{10}\varphi \mathrm{\Sigma }\mu$, is plotted as a function of the logarithm of incident photon flux, ${\log }_{10}{I}_0$. The experimental data (circles) are taken from [5] and the solid line is a fit of Eq. (23).

Figure 5

Carrier mobility $\mu$ as a function of temperature. The solid curves are obtained from Eq. (21) with fitting a parameter of $n$. (a) The experimental data (crosses) is from [6] and $n=2.3\times {10}^{17}{\mathrm{cm}}^{-3}$. (b) The experimental data (squares) is from [7] and $n=8.3\times {10}^{17}{\mathrm{cm}}^{-3}$.

Figure 6

Product of generation yield $\varphi$ and mobility $\mathrm{\Sigma }\mu$ as function of temperature. Circles (diamonds) are measured during the heating (cooling) process [9]. The dash line is calculated from the experimental dielectric function [19] and the solid line is obtained by shifting the tetragonal-orthorhombic transition temperature from [19] to [9].