Phonon-limited carrier mobility in semiconductors: importance of the dynamical quadrupoles

First-principles computations of phonon-limited carrier mobilities in semiconductors have recently gained popularity. Such calculations are indeed crucial for the discovery and development of new functional materials.
In state-of-the-art approaches, Fourier-based interpolation schemes are used to obtain the electron-phonon matrix elements on the very dense wavevector grids needed to converge carrier lifetimes and mobilities. In polar semiconductors, the long-range electrostatic interactions lead to a divergence of the matrix elements, rendering their interpolation unstable. For this reason, ab initio methods have been recently developed to model the non-analytical behavior of the matrix elements for q→0 [1].
Most of the studies performed so far have focused on this Fröhlich divergence generated by dynamical dipoles. However, additional non-analytical terms are present in the q→0 limit [2]. In this work, we analyze the role played by the dynamical quadrupoles and show that an accurate interpolation is obtained only when both dipolar and quadrupolar fields are taken into account. We discuss their impact on the accuracy and on the convergence of carrier mobilities both in polar and non-polar semiconductors.

[1] Phys. Rev. Lett. 115, 176401 (2015)
[2] Phys. Rev. B 13, 694 (1976)