Contribution of the electron redistribution effect to the piezoelectric constant due to the bond bending in tetrahedral crystals

The electron-cloud distortion of GaAs and ZnSe under uniaxial stress is discussed using the Chadi-Cohen empirical linear-combination-of-atomic-orbitals band theory. The electron localizability $\lambda =\frac{(a^2-b^2)}{(a^2+b^2)}$, where $a$ is the weight of the anion atomic wave function and $b$ is that of the cation atomic wave function in the valence-state wave function ${\psi }_v=a{\psi }^{\alpha }+b{\psi }^{\beta }$, changes with the bond bending of the tetrahedral structure induced by [111]-directional external stress. This electron redistribution effect gives a large contribution to the piezoelectric constant. $\frac{e_b^{*}}{e_0}$ is 0.32 for GaAs and 0.27 for ZnSe, $e_b^{*}$ being the effective charge due to the bond-bending effect.