Ab initio electron mobility and polar phonon scattering in GaAs

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

Figure 1

(a) The converged scattering rate in Eq. (1) (curve labeled as “Total”), expressed in terms of $\mathrm{Im}{\mathrm{\Sigma }}^{e\text{-ph}}$ in meV units. Shown are also the long-range and remainder contributions, which add up to the total. (b) Convergence of the scattering rate near the CBM. Shown are the results for Lorentzian (L) and Gaussian (G) broadenings. The broadening parameter, in meV units, is given in parentheses.

Figure 2

(a) $e\text{−}\mathrm{ph}$ scattering rate and (b) RT for electrons in GaAs with energies within $\sim 0.4$ eV of the CBM, which is the origin of the energy axis. Data points in blue (red) are for electronic states in the $\mathrm{\Gamma } \left(L\right)$ valley. The scattering rate associated with LO phonon scattering alone is also shown in (a). The inset in (b) shows a schematic of the $\mathrm{\Gamma }$ valley, and of the $L$ and $X$ valleys in GaAs, with energies of $E_L\approx 0.25$ eV and $E_X\approx 0.45$ eV above the CBM, respectively.

Figure 3

Mode-resolved $e\text{−}\mathrm{ph}$ scattering rates. (a) Total scattering rate, shown along with the contributions from the LO and LA modes alone. (b) Contributions from the transverse modes. (c) Comparison of ab initio RTs including PP scattering (red curve), as computed in this work, with previous calculations in Ref. [11] that neglect PP scattering (gray curve).

Figure 4

(a) Electron mobilities close to room temperature. The experimental values are taken from Refs. [37, 38], and compared with our computed ab initio mobilities (red line). (b) Convergence of the integrand in Eq. (2) and the mobility (values given as a table) at 300 K with respect to the fine $\mathbf{k}$ grids used for the tetrahedron integration in Eq. (3). The blue, green, purple, and red curves are computed using fine grids of ${80}^3,{150}^3,{320}^3,{600}^3 \mathbf{k}$ points in the BZ, respectively.

Figure 5

Electron mobilities computed using both the DFT-relaxed and thermal expansion corrected lattice parameters, for temperatures above 300 K. The sources of the experimental data are the same as in Fig. 4.