Band-Electron vs. Polaron Mobility in Metal–Halide Perovskites

Matthew Wolf (U Bath)

Dec 12. 2019, 16:10 — 16:30

Despite the meteoric rise in power conversion efficiencies of metal–halide perovskite based cells, there remain a number of fundamental questions regarding the materials’ properties which remain unanswered [1]. One such question relates to the origin of the observed ~T−1.5 dependence of the charge carrier mobility in MAPbI3 [2]. According to standard semi-classical theory under the relaxation time approximation [3], this dependence can be recovered if acoustic phonon scattering is assumed to be the pre-dominant scattering mechanism; however, such an assumption also leads to values for the room temperature mobility that are (at least) an order of magnitude larger than that observed. On the other hand, carrying out a similar analysis based on the assumption that polar optical phonon scattering is the pre-dominant scattering mechanism, leads to room temperature mobilities of the “correct” order of magnitude, but a ~T−0.5 dependence. A number of recent papers have argued that this apparent inconsistency can be resolved by taking into account the effects of large polaron formation, but with mixed success, and in some cases using novel, and therefore untested, theoretical frameworks [4,5,6]. The present study is an attempt to determine, quantitatively, the effects of large polaron formation on the mobility of charge carriers in MAPbI3. The analysis is carried out within the framework of the Boltzmann transport equation (BTE) for polarons introduced by L. Kadanoff [7], which allows us to make direct comparisons with the results of standard semi-classical transport theory for band electrons. We will present temperature and energy dependent acoustic and polar optical phonon, and ionised impurity, scattering rates for polarons; provide evidence that the range of validity of the polaron BTE is considerably greater than originally thought; and calculate the polaron mobility by solving the polaron BTE using a Monte Carlo approach, thereby circumventing the need to make the relaxation time approximation. References: [1] D. A. Egger et al., Adv. Mater. (2018) 30, 1800691 [2] L. M. Herz, J. Phys. Chem. Lett. (2018) 9, pp 6853–6863 [3] F. J. Blatt, Physics of Electronic Conduction in Solids, McGraw-Hill (1968) [4] J. M. Frost, Phys. Rev. B (2017) 96, 195202 [5] M. Zhang et al., Phys. Rev. B (2017) 96, 195203 [6] C. Motta and S. Sanvito, J. Phys. Chem. C (2018) 122, pp1361–1366 [7] L. P. Kadanoff, Phys. Rev. (1963) 130, 1364

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Polarons in the 21st Century (Workshop)
Jozef Devreese (U Antwerpen)
Cesare Franchini (U of Vienna)
Georg Kresse (U of Vienna)
Jacques Tempere (U Antwerpen)