Lattice Mobility of Holes in III-V Compounds

We review the circumstances under which polar mode scattering is important in the III-V compounds and conclude that it is the dominant intrinsic scattering mechanism only in the $n$-type direct-gap materials. For $n$-type indirect-gap materials, the most important scattering mechanisms are acoustic and nonpolar optical (NPO) mode intra- and intervalley scattering. For $p$-type III-V materials, we find that the dominant hole-scattering mechanism is a combination of acoustic and NPO mode scattering. This is in disagreement with previous treatments of hole mobility which emphasized polar mode scattering. It should be noted, however, that the usual expression for polar mobility was derived for nondegenerate $s$-like bands and is therefore not applicable to the complex $p$-like valence bands of the III-V compounds. Using acoustic ($E_{\mathrm{AC}}$) and NPO mode ($E_{\mathrm{NPO}}$) deformation potentials which are essentially the same as those obtained for $p-\mathrm{G}\mathrm{e}$ and $p-\mathrm{S}\mathrm{i}$ [$3<\mathrm{}{E}_{\mathrm{AC}}<8\mathrm{}$ eV and ${\left(\frac{E_{\mathrm{NPO}}}{E_{\mathrm{AC}}}\right)}^2\approx 4$], we obtain excellent fits for the magnitude and temperature dependence of published Hall-mobility data for $p$-type GaP, GaAs, InP, and AlSb. A simple expression is given which shows that the variation in Hall mobility for $p$-type group-IV and group-III-V materials is attributable to small variations in material parameters rather than different scattering mechanisms.