Ab initio electron-two-phonon scattering in GaAs from next-to-leading order perturbation theory

Abstract

Electron-phonon (e-ph) interactions are usually treated in the lowest order of perturbation theory. Here we derive next-to-leading order e-ph interactions, and compute from first principles the associated electron-two-phonon (2ph) scattering rates. The derivations involve Matsubara sums of two-loop Feynman diagrams, and the numerical calculations are challenging as they involve Brillouin zone integrals over two crystal momenta and depend critically on the intermediate state lifetimes. Using Monte Carlo integration together with a self-consistent update of the intermediate state lifetimes, we compute and converge the 2ph scattering rates, and analyze their energy and temperature dependence. We apply our method to GaAs, a weakly polar semiconductor with dominant optical-mode long-range e-ph interactions. We find that the 2ph scattering rates are as large as nearly half the value of the one-phonon rates, and that including the 2ph processes is necessary to accurately predict the electron mobility in GaAs from first principles.

Piezoelectric Electron-Phonon Interaction from Ab Initio Dynamical Quadrupoles: Impact on Charge Transport in Wurtzite GaN

“…This trend is physically correct-our computed mobilities for an ideal crystal are an upper bound to the experimental mobilities. Other possible mechanisms not included in our calculations, such as the two-phonon scattering processes [59], are expected to lower the mobility and bring it in greater agreement with experiment.…”

“…The temperature dependence of the electron mobility is only in reasonable agreement with experiment. Including twophonon processes may be needed to further improve the temperature trend [59].…”

Electronic noise of warm electrons in semiconductors from first principles

“…This behavior is qualitatively consistent with the sublinear current voltage characteristic (CVC) of n-type GaAs [21], or a decrease in mobility with increasing electron temperature. More quantitatively, the absolute value of the cold electron mobility is known to be overestimated in the present treatment owing to a lack of higher-order phonon scattering processes [16], preventing an absolute direct comparison with the mobility at higher fields. Focusing on the trend with electric field, the predicted dependence of the mobility appears to be slightly overestimated as well, with the experimental mobility varying weakly with electric field [6,66].…”

“…Currently, Perturbo accounts for first-order e-ph (1ph) processes, and thus only these processes are included in the present work. Higher-order interactions are known to be significant in GaAs [16]. Our method will be extended to incorporate these contributions in a future work.…”

“…Such a description is now possible owing to advances in electronic structure codes that enable the ab-initio computation of the transition matrix elements given by Fermi's golden rule performed in conjunction with the numerical solution of the Boltzmann equation describing carrier dynamics [7][8][9][10]. While method development is ongoing, these calculations are now routine for various semiconductors including Si [11][12][13], GaAs [14][15][16], phosphorene [7], and others [17][18][19][20].…”