Calculating polaron mobility in halide perovskites

Abstract

Lead halide perovskite semiconductors are soft, polar, materials. The strong driving force for polaron formation (the dielectric electron-phonon coupling) is balanced by the light band effectivemasses, leading to a strongly-interacting large-polaron. A first-principles prediction of mobility would help understand the fundamental mobility limits. Theories of mobility need to consider the polaron (rather than free-carrier) state due to the strong interactions. In this material we expect that at room temperature polar-optical phonon mode scattering will dominate, and so limit mobility. We calculate the temperature-dependent polaron mobility of hybrid halide perovskites by variationally solving the Feynman polaron model with the finite-temperature free-energies of Osaka. This model considers a simplified effective-mass band-structure interacting with a continuum dielectric of characteristic response frequency. We parametrise the model fully from electronicstructure calculations. In methylammonium lead iodide at 300 K we predict electron and hole mobilities of 133 and 94 cm 2 V −1 s −1 respectively. These are in acceptable agreement with singlecrystal measurements, suggesting that the intrinsic limit of the polaron charge carrier state has been reached. Repercussions for hot-electron photo-excited states are discussed. As well as mobility, the model also exposes the dynamic structure of the polaron. This can be used to interpret impedance measurements of the charge-carrier state. We provide the phonon-drag mass-renormalisation, and scattering time constants. These could be used as parameters for larger-scale device models and band-structure dependent mobility simulations.

Quantifying Charge‐Carrier Mobilities and Recombination Rates in Metal Halide Perovskites from Time‐Resolved Microwave Photoconductivity Measurements

“…[50] That is, acoustic phonons predict that μ ∝ T −1.5 , whereas for polarons this is T -0.5 . [48,51,52] Since we and others have found that for many [47] Interestingly, not only the mobility but also the lifetime of mobile charges follow the same temperature dependence in MAPbI3 and CsPbI3, as shown in Figure 7b. That is, for a range of excitation densities between 10 15 and 10 17 cm −3 , the lifetime is enhanced on lowering the temperature.…”

First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials

“…Shortly after, these findinges were confirmed by Frost [101], who obtained electron and hole mobilities of 133 and 94 cm 2 /Vs, respectively, using the more refined Hellwarth model [225].…”

Charge Transport in Halide Perovskite Single Crystals: Experimental and Theoretical Perspectives

“…[ 28] The observed T À 3/2 dependence (Figure 4) is generally a signature of acoustic phonon scattering limited carrier transport. However, the estimate of mobility from acoustic phonon scattering are generally at the order of thousands cm 2 V À 1 s À 1 , [27,29] which are too large to justify the measured value. Also, it has been pointed out that the polaron can also exhibit power-law temperature dependence and the 3/2 power can be mimicked.…”

“…The theory and simulation above assume the interacting phonons to be optical phonons, as well established in traditional semiconductors. For HaPs, the possibility of acoustic phonon involvement has also been explored . In particular, acoustic phonon scattering would explain the temperature dependence of Hall mobility in single crystals of MAPbBr 3.…”

“…For HaPs, the possibility of acoustic phonon involvement has also been explored. [27] In particular, acoustic phonon scattering would explain the temperature dependence of Hall mobility in single crystals of MAPbBr 3.…”