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

Abstract

The resistivity of germanium containing between $N=3\ifmmode\times\else\texttimes\fi{}{10}^{17} \mathrm{and} {10}^{19}$ antimony atoms per cc was measured at 1.2\ifmmode^\circ\else\textdegree\fi{}K under uniaxial compressions of up to ${10}^{10}$ dyn ${\mathrm{cm}}^{\ensuremath{-}2}$. 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 $N<{10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ the mobility increases with $N$ and shows impurity-band effects; for $N>{10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ the mobility decreases and ionized-impurity scattering is the dominant scattering process. The latter range is $N>3\ifmmode\times\else\texttimes\fi{}{10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ 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 $\frac{{\ensuremath{\mu}}_{\ensuremath{\perp}}}{{\ensuremath{\mu}}_{\mathrm{II}}}=3.9\ifmmode\pm\else\textpm\fi{}0.1$ for $N>4\ifmmode\times\else\texttimes\fi{}{10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. 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.