High-Stress Piezoresistance and Mobility in Degenerate Sb-Doped Germanium

Abstract

The resistivity of germanium containing between $N=3\mathrm{}\times {10}^{17} \mathrm{and} {10}^{19}$ antimony atoms per cc was measured at 1.2°K under uniaxial compressions of up to ${10}^{10}$ dyn ${\mathrm{cm}}^{-2\mathrm{}}$. These stresses are high enough to effect an observable saturation in the piezoresistance, that is, to transfer all electrons to a single conduction-band valley ([111] compression) or to two valleys ([110] compression). Two distinct ranges are observed in degenerate germanium: for $N<\mathrm{}{10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$ the mobility increases with $N$ and shows impurity-band effects; for $N>\mathrm{}{10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$ the mobility decreases and ionized-impurity scattering is the dominant scattering process. The latter range is $N>\mathrm{}3\mathrm{}\times {10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$ for large [111] compression. The resistivity was measured for current flowing parallel and perpendicular to the stress direction. The mobility anisotropy was found to be $\frac{{\mu }_{\perp }}{{\mu }_{\mathrm{II}}}=3.9\mathrm{}\pm 0.1$ for $N>\mathrm{}4\mathrm{}\times {10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$. This indicates that the mean free path is nearly isotropic. The mobility for electrons in 1, 2, and 4 valleys is compared with Csavinszky's partial-wave treatment of impurity scattering. The change of screening with the number of valleys was taken into account. Csavinszky's theory overestimates the $N$ dependence and the magnitude of the scattering. This is attributed to the failure of the individual-scattering assumption.