Determination of Hot-Carrier Distribution Functions in Uniaxially Stressedp-Type Germanium

This paper gives a description of an experimental determination of distribution functions in $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space of hot holes in uniaxially compressed germanium. The hot-carrier studies were made at 85\ifmmode^\circ\else\textdegree\fi{}K at fields up to 1000 V/cm and uniaxial stresses up to 11 800 kg/${\mathrm{cm}}^{2}$. The field and stress were always in the $〈111〉$ direction. For the highest stresses, the maximum fields were close to the threshold for current oscillations. The distribution functions were obtained from experimental modulation of intervalence-band absorption of infrared radiation. In order to interpret the results, a parametrized distribution function has been assumed. The parameters of the distribution function are then fitted to the experimental modulation. The calculation of absorption was performed numerically, using a four-band $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ model. This model was checked for consistency by comparing with piezoabsorption measurements performed in thermal equilibrium. The average carrier energy calculated from the distribution function shows a fast increase with stress and almost saturates when the strain splitting of the two ${p}_{\frac{3}{2}}$ levels reaches the optical-phonon energy. This saturation is interpreted in terms of the change in scattering probabilities with stress. A model based on the nonparabolicity of the upper ${p}_{\frac{3}{2}}$ level is proposed for the negative differential conductivity in stressed $p$-type Ge.