Understanding Dark Current-Voltage Characteristics in Metal-Halide Perovskite Single Crystals

Hybrid halide perovskites have great potential for application in optoelectronic devices. However, an understanding of some basic properties, such as charge-carrier transport, remains inconclusive, mainly due to the mixed ionic and electronic nature of these materials. Here, we perform temperature-dependent pulsed-voltage space-charge-limited current measurements to provide a detailed look into the electronic properties of methylammonium lead tribromide (${\mathrm{MA}\mathrm{Pb}\mathrm{Br}}_{3}$) and methylammonium lead triiodide (${\mathrm{MA}\mathrm{Pb}\mathrm{I}}_{3}$) single crystals. We show that the background carrier density in these crystals is orders of magnitude higher than that expected from thermally excited carriers from the valence band. We highlight the complexity of the system via a combination of experiments and drift-diffusion simulations and show that different factors, such as thermal injection from the electrodes, temperature-dependent mobility, and trap and ion density, influence the free-carrier concentration. We experimentally determine effective activation energies for conductivity of (349 \ifmmode\pm\else\textpm\fi{} 10) meV for ${\mathrm{MA}\mathrm{Pb}\mathrm{Br}}_{3}$ and (193 \ifmmode\pm\else\textpm\fi{} 12) meV for ${\mathrm{MA}\mathrm{Pb}\mathrm{I}}_{3}$, which includes the sum of all of these factors. We point out that fitting the dark current density-voltage curve with a drift-diffusion model allows for the extraction of intrinsic parameters, such as mobility and trap and ion density. From simulations, we determine a charge-carrier mobility of 12.9 cm${}^{2}$/Vs, a trap density of 1.52 \ifmmode\times\else\texttimes\fi{} 10${}^{13}$ cm${}^{\ensuremath{-}3}$, and an ion density of 3.19 \ifmmode\times\else\texttimes\fi{} 10${}^{12}$ cm${}^{\ensuremath{-}3}$ for ${\mathrm{MA}\mathrm{Pb}\mathrm{Br}}_{3}$ single crystals. Insights into charge-carrier transport in metal-halide perovskite single crystals will be beneficial for device optimization in various optoelectronic applications.