Ab initio calculation of the deformation potential and photoelastic coefficients of silicon with a non-uniform finite-difference solver based on the local density approximation

The band diagram, deformation potential and photoelastic tensor of silicon are calculated self-consistently under uniaxial and shear strain by solving for the electronic wavefunctions with a finite-difference method. Many-body effects are accounted for by the local density approximation. In order to accommodate the large number of grid points required due to the diverging electrostatic potential near the atomic nuclei in an all-electron calculation, a non-uniform meshing is adopted. Internal displacements are taken into account by adding an additional coordinate transform to the method of Bir and Pikus. Good consistency of the calculated deformation potential and photoelastic coefficients is obtained with prior experimental and theoretical results, validating the numerical methods. Furthermore, it is shown that a slight correction of the multiplicative coefficient of the Xα approximation for conduction bands results in good agreement with experiment for both the direct and indirect bandgaps.