Piezoresistance ofn-Type Germanium

Abstract

The change of electrical resistance in uniaxial tension has been measured over the range 6\ifmmode^\circ\else\textdegree\fi{}K to 300\ifmmode^\circ\else\textdegree\fi{}K for several single-crystal specimens of germanium doped with arsenic or antimony. The tensile stress was varied from 1\ifmmode\times\else\texttimes\fi{}${10}^{7}$ to 5\ifmmode\times\else\texttimes\fi{}${10}^{8}$ dynes/${\mathrm{cm}}^{2}$. Particularly at low temperatures where most of the carriers are bound to impurity centers, the piezoresistance of the conduction band departs strongly from linearity in stress. For the large piezoresistance effects measured with uniaxial stress in [110] direction, these departures depend in size and magnitude on the kind of donor impurity. It is shown that if the strain-induced shift of the Fermi energy is taken into consideration these effects are to be expected from the electron transfer model, which attributes the large piezoresistance to the strain-induced changes of the electron concentrations in the various conduction band valleys. Theoretical predictions concerning the lowest donor states---a one-fold $1s$-like ground state and a higher lying three-fold state---are verified for As in Ge. The energy separation between these two states is (4.10\ifmmode\pm\else\textpm\fi{}0.15)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ ev for As and at least by an order of magnitude smaller for Sb in Ge. The deformation potential constant (conduction band) for pure shear strain was found to be ${E}_{2}=19.2\ifmmode\pm\else\textpm\fi{}0.4$ ev at 6.6\ifmmode^\circ\else\textdegree\fi{}K. The mobility anisotropy of a valley was found to decrease with decreasing $T$ because of anisotropic scattering by ionized impurities.