First-principles study of electron and hole mobilities of Si and GaAs

With first-principles calculated electron-phonon coupling matrix elements, the phonon-limited electron and hole mobilities of Si and GaAs are studied using the Boltzmann transport equation. The calculated mobilities agree well with the experimental measurements. For electrons in GaAs, the calculated mobility is very sensitive to the band structure characterized by the effective mass and the energy gap between $\mathrm{\Gamma }$ and L valleys, which clarifies the discrepancies between recent literature findings [J.-J. Zhou and M. Bernardi, Phys. Rev. B 94, 201201(R) (2016); T.-H. Liu et al., Phys. Rev. B 95, 075206 (2017)]. Unlike electrons in GaAs, where the longitudinal optical phonon dominates the scattering, the other phonon branches have a comparable influence on the mobility of holes in GaAs. In Si and GaAs, the spin-orbit coupling interaction has a significant effect on the valence bands and, further, on the hole mobilities, without which the calculated mobility is underestimated, especially at relatively low temperatures, while it has almost no effect on the electrons.

Figure 1

(a) Electronic band structure of Si calculated with and without spin-orbit coupling interaction. (b) Phonon dispersion of Si along high-symmetry directions compared to the experimental data from Ref. [29].

Figure 2

Calculated mobilities of Si with respect to different ($\mathbf{k},\mathbf{q}$) grids at room temperature.

Figure 3

Calculated mobilities of Si with respect to the iterative step at room temperature.

Figure 4

Electron mobilities of Si calculated with the ERTA (dashed line), MRTA (dash-dotted line), and iterative solution (solid line) of the BTE. Symbols represent experimental measurements, with squares from Ref. [30], circles from Ref. [31], triangles from Ref. [32], and diamonds from Ref. [33].

Figure 5

Hole mobilities of Si calculated with the ERTA (dashed line), MRTA (dash-dotted line), and iterative solution (solid line) of the BTE. Symbols are experimental measurements, with squares from Ref. [35], circles from Ref. [30], triangles from Ref. [31], and diamonds from Ref. [36].

Figure 6

Scattering rates and corresponding mean free paths of (a) electrons vs energy above the CBM and (b) holes vs energy below the VBM in Si at room temperature.

Figure 7

(a) Electronic band structure of GaAs calculated with and without spin-orbit coupling interactions. (b) Phonon dispersion of GaAs along high-symmetry directions compared to experimental data from Ref. [50].

Figure 8

Calculated mobilities of GaAs with respect to different ($\mathbf{k},\mathbf{q}$) grids at room temperature.

Figure 9

Calculated mobilities of GaAs with respect to the iterative step at room temperature.

Figure 10

Electron mobilities of GaAs calculated with the ERTA (dashed line), MRTA (dash-dotted line), and iterative solution (solid line) of the BTE. Symbols are experimental measurements, with squares from Ref. [52], circles from Ref. [53], triangles from Ref. [54], and diamonds from Ref. [55].

Figure 11

Electron mobilities of GaAs calculated with (a) the lattice constant correction and (b) the $GW$ correction, compared with Zhou et al. [14] and Liu et al. [15] as well as experiments (symbols).

Figure 12

Electron mobilities of GaAs calculated using the same $GW$-corrected conduction bands, while other related quantities are obtained from the raw calculation of this work, the lattice correction based on Zhou et al. [14], and the $GW$ correction based on Liu et al. [15].

Figure 13

Hole mobilities of GaAs calculated with the ERTA (dashed line), MRTA (dash-dotted line), and iterative solution (solid line) of the BTE. Symbols are experimental measurements, with squares from Ref. [56], circles from Ref. [57], triangles from Ref. [58], and diamonds from Ref. [59].

Figure 14

Scattering rates and corresponding mean free paths of (a) electrons vs the energy above the CBM and (b) holes vs the energy below the VBM in GaAs at room temperature.

Figure 15

Scattering rates of (a) electrons vs the energy above the CBM and (b) holes vs the energy below the VBM contributed by different phonon branches in GaAs at room temperature. Inset: Relative contribution from the LO branch.