Deformation Potentials in Silicon. I. Uniaxial Strain

The rate of splitting with uniaxial strain of the fourfold degenerate (J=32) 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.