Interband Scattering inn-Type Germanium

The pressure dependence of the electrical conductivity of $n$-type germanium has been measured to pressures of 30 000 kg/${\mathrm{cm}}^2$ at temperatures between 273° and 350°K. A satisfactory explanation of the results requires the existence of two different types of minima in the conduction band, separated by between 0.15 and 0.21 ev at 350°K with the lower range of values slightly preferred. The higher energy minima lie in the [100] direction in reciprocal space, and are similar in properties to the lowest set of minima in silicon. The changes in position of the two minima with pressure are determined. For the minima that are lowest at atmospheric pressure, $\frac{d(E_{111}-E_v)}{\mathrm{dP}}=(4.9\mathrm{}\pm 0.5)\times {10}^{-6\mathrm{}}$ ev/kg-${\mathrm{cm}}^{-2\mathrm{}}$, and for the [100] set, $\frac{d(E_{100}-E_v)}{\mathrm{dP}}=\left({0_{-2\mathrm{}}}^{+1\mathrm{}}\right)\times {10}^{-6\mathrm{}}$ ev/kg-${\mathrm{cm}}^{-2\mathrm{}}$. The change in average electron mobility with pressure is explained in terms of a sharing of electrons between states in the two sets of minima, and an additional relaxation process that scatters carriers from one type of minimum into the other. The effect of pressure on the effective masses, the elastic constants, and the deformation potential is briefly considered.