[Paper Review] Ab initio Electron Mobility and Polar Phonon Scattering in GaAs

Jin-Jian Zhou, Marco Bernardi|arXiv (Cornell University)|Aug 11, 2016

Electronic and Structural Properties of Oxides6 citations

TL;DR

This paper presents an efficient ab initio method to compute electron mobility and electron-phonon scattering rates in polar semiconductors like GaAs by separating long-range (Fröhlich) and short-range electron-phonon interactions. Using density functional perturbation theory and Wannier interpolation, the authors achieve excellent agreement with experimental mobility (within 5% at 300 K) by converging relaxation times on fine Brillouin zone grids, demonstrating that the relaxation time approximation is sufficient when properly converged.

ABSTRACT

In polar semiconductors and oxides, the long-range nature of the electron-phonon ( extit{e}-ph) interaction is a bottleneck to compute charge transport from first principles. Here, we develop an efficient ab initio scheme to compute and converge the extit{e}-ph relaxation times (RTs) and electron mobility in polar materials. We apply our approach to GaAs, where using the Boltzmann equation with state-dependent RTs, we compute mobilities in excellent agreement with experiment at 250$-$500~K. The $e$-ph RTs and the phonon contributions to intravalley and intervalley $e$-ph scattering are also analyzed. Our work enables efficient ab initio computations of transport and carrier dynamics in polar materials.

Motivation & Objective

• To overcome the computational bottleneck of long-range electron-phonon interactions in polar semiconductors like GaAs.
• To develop an efficient ab initio scheme for computing electron-phonon relaxation times (RTs) and mobility in polar materials.
• To achieve accurate, experimentally consistent mobility predictions using the Boltzmann transport equation with state- and temperature-dependent RTs.
• To demonstrate that the relaxation time approximation can yield accurate results when proper convergence and treatment of long-range interactions are applied.

Proposed method

• The electron-phonon matrix elements are split into short-range (g^S) and long-range (g^L) components to handle the 1/q divergence at q→0.
• The long-range part g^L is computed analytically using the Vogl model, generalizing the Fröhlich interaction.
• The short-range part g^S is computed via Wannier interpolation on coarse k- and q-grids, enabling efficient sampling on fine grids.
• Relaxation times are computed using the Boltzmann transport equation with temperature- and state-dependent RTs.
• Mobility is calculated by numerically integrating over fine k-point grids (up to 600^3) to ensure convergence.
• Finite-temperature effects are tested by applying thermal expansion corrections to the lattice parameter (a ≈ 5.57 Å), improving high-temperature agreement.

Experimental results

Research questions

• RQ1 Can ab initio electron mobility in polar semiconductors be computed accurately without empirical fitting?
• RQ2 Does the relaxation time approximation yield accurate mobility when properly converged and with correct treatment of long-range electron-phonon interactions?
• RQ3 What is the relative contribution of polar phonons versus acoustic phonons to intravalley and intervalley scattering in GaAs?
• RQ4 How does finite-temperature bandstructure renormalization affect high-temperature mobility predictions?

Key findings

• The computed electron mobility in GaAs agrees with experiment within 5% at 300 K when using converged k-point grids (600^3) and temperature-dependent relaxation times.
• Convergence of mobility requires more than 600^3 k-points; even 150^3 grids yield large errors, highlighting the need for fine sampling.
• Polar phonons dominate intravalley scattering and overall transport, while acoustic phonons are the primary source of intervalley scattering and hot carrier dynamics.
• The deviation from experiment at T > 500 K is reduced when using a thermally expanded lattice parameter (a ≈ 5.57 Å), suggesting bandstructure renormalization is critical at high temperatures.
• The method enables ab initio transport calculations in polar materials at computational cost comparable to nonpolar materials, overcoming previous limitations due to long-range electron-phonon coupling.