Two-component electron-hole liquid in Ge and Si crystals under tensile stress

Abstract

The properties of the two-component electron-hole liquid (TCEHL) in Ge and Si under tensile stress at $T=0$ are calculated. It is predicted that the TCEHL should not phase separate in Ge under $〈110〉$ tensile stress. In Ge under $〈111〉$ tensile stress the TCEHL should not phase separate for low concentrations of hot electrons but should phase separate for high concentrations of hot electrons. In Si under $〈001〉$ tensile stress the TCEHL should not phase separate for low concentrations of hot electrons, but for high concentrations of hot electrons the theory does not make a unique prediction. In Si under $〈110〉$ tensile stress the qualitative predictions for high and low hot-electron concentrations are similar to those for $〈001〉$ tensile stress for low and high hot-electron concentrations, respectively. The main differences between the cases of tensile and compressive stress are due to the differences in the structure of the conduction band. This makes experiments on the TCEHL under tensile stress a practical means of obtaining data which approximate those which would be obtained at high hot-electron concentrations under compressive stress, i.e., in a part of the phase diagram inaccessible to direct experimental study. This complementarity between compressive and tensile stress should be quite precise in Si but only qualitatively valid in Ge because of pronounced valence-band effects.