First-principles predictions of Hall and drift mobilities in semiconductors

Abstract

Carrier mobility is one of the defining properties of semiconductors. Significant progress on parameter-free calculations of carrier mobilities in real materials has been made during the past decade; however, the role of various approximations remains unclear and a unified methodology is lacking. Here, we present and analyse a comprehensive and efficient approach to compute the intrinsic, phonon-limited drift and Hall carrier mobilities of semiconductors, within the framework of the first-principles Boltzmann transport equation. The methodology exploits a novel approach for estimating quadrupole tensors and including them in the electron-phonon interactions, and capitalises on a rigorous and efficient procedure for numerical convergence. The accuracy reached in this work allows to assess common approximations, including the role of exchange and correlation functionals, spin-orbit coupling, pseudopotentials, Wannier interpolation, Brillouin-zone sampling, dipole and quadrupole corrections, and the relaxation-time approximation. A detailed analysis is showcased on ten prototypical semiconductors, namely diamond, silicon, GaAs, 3C-SiC, AlP, GaP, c-BN, AlAs, AlSb, and SrO. By comparing this extensive dataset with available experimental data, we explore the intrinsic nature of phonon-limited carrier transport and magnetotransport phenomena in these compounds. We find that the most accurate calculations predict Hall mobilities up to a factor of two larger than experimental data; this could point to promising experimental improvements in the samples quality, or to the limitations of density-function theory in predicting the carrier effective masses and overscreening the electron-phonon matrix elements. By setting tight standards for reliability and reproducibility, the present work aims to facilitate validation and verification of data and software towards predictive calculations of transport phenomena in semiconductors.

First-principles study of electron transport in ScN

“…We also note that our calculations are for the drift mobility, while some of the experimental data [2,24,25] are for the Hall mobility. Recent benchmarks on standard semiconductors indicate that the calculated electron Hall mobility is typically lower than the drift mobility [55].…”

“…Recent work highlighted the importance of dynamical quadrupoles in calculations of carrier mobilities [53,54]. In this work we do not include quadrupole corrections because ScN crystallizes in the F m 3m space group, hence quadrupole tensors vanish by symmetry (see for example the similar case of SrO in [55]).…”

“…This agreement indicates that the band velocities and effective masses are reasonably accurate in LDA. The underestimation of the band gap in LDA likely leads to a small amount of overscreening of the electron-phonon matrix elements, therefore the calculated mobility should be understood as a theoretical upper bound to the measured mobility [55]. As a quantitative measure of the agreement between LDA and HSE results in the vicinity of the CBM, we compare electron effective masses calculated with LDA with those calculated with HSE, as listed in Table I.…”