Resistivity of Ge1-xSix single crystals under hydrostatic pressure

Abstract

Ge1-xSix alloys consider as one of the best thermoelectric material at high temperature range as follow from experimental data [1,2]. As well known in the strongly strained germanium single crystal 1- valleys play essential part in transport phenomena. For this reason the follow energetic model for Ge1-xSix alloy single crystal have been considered: four L1-valleys oriented along <111> crystallographic axis, six 1- germanium valleys and six 1-silicon valleys with the same orientation along <100>. The both 1- valleys are 0.18 eV above the L1-valleys in non-deformed single crystal. The deformation potentials of L1- and 1- valleys and their occupation numbers have been calculated and their pressure behavior has been analyzed under low (78K) and room (300K) temperatures. At the condition of strong elastic deformation an electron transfer takes place from L1 to 1- valleys. The hydrostatic pressure don’t change the cubic symmetry of crystal but in the strained crystal the contribution of each valley can change significantly which originate no traditional dependences on resistivity in respect of composition x and stress P. The theory of anisotropic scattering, generalized for the case of strong elastic deformation of single crystal has been used to calculate the resistivity. The intraband mixed scattering of electrons by acoustic phonons and impurity ions and interband nonequivalent electron scattering between L1- and 1- valleys as well as interband equivalent f- and g-scattering between 1- valleys have been considered. The results of the numerical calculation of resistivity as function of straining stress P, composition x and for temperatures T=78K, 300K, 450K are shown on graphics.