Scattering tensors and optical transitions in Si and Ge

Abstract

The selection rules (SR’s) for the Kronecker product (KP) of Si and Ge irreducible representations (irreps) are required to determine the intervalley scattering processes. The SR’s for transitions between the lowest conduction band minima at Γ, X and L high symmetry points and the highest maximum of the valence band (VB) in the Brillouin zone of Oh7 space group symmetry are determined. The elements of El-Ph scattering tensors are linear combinations of the Clebsch-Gordon coefficients (CGC’s). Here we have computed the coupling coefficients relevant to scattering tensors. Our theoretical results confirm the available experimental data. In this work, we focused on utilisation of group theory with regard to matrix elements of scattering tensors which are a linear combination of Clebsch-Gordon coefficients. The required phonon symmetries are determined by irreps contained in KP. We have calculated the U matrix for the LA phonon which diagonalizes the intervalley scattering between the Г2- valley and the four Lvalleys of the same star symmetry. We also have estimated an electron energy loss to X-valley acoustic phonon emission due to L-valleys electron scattering in a quasi-elastic process in agreement with available experimental data.