Deformation Potentials in Silicon. I. Uniaxial Strain

Abstract

The rate of splitting with uniaxial strain of the fourfold degenerate ($J=\frac{3}{2}$) valence-band edge of silicon is computed by applying perturbation theory to the Si wave functions calculated previously by Kleinman and Phillips. Based on a "self-consistent" model the calculated values for strain along the [100] and [111] directions are 40% larger than Hensel's experimental values. A primary objective of this calculation was to test the rigid-ion and deformable-ion models often used in the theory of electron-phonon coupling. The rigid-ion model agrees with experiment to within the accuracy of the calculation while the deformable-ion model disagrees with experiment by 300%. For [111] strain the crystal symmetry is so reduced that the separation of the two atoms in each unit cell is not uniquely determined from the macroscopic strain. We have used a model in which the atoms locate themselves in such a way that nearest-neighbor covalent bonds are unchanged in length by shearing strains. This "bond-bending" model is contrasted with a model in which the atomic separation changes with strain like a macroscopic vector. The latter model yields a deformation potential of opposite sign to the experimental one.