Strain Effects on Optical Critical-Point Structure in Diamond-Type Crystals

Abstract

The effects of strain on optical critical-point structure in the imaginary part ${\epsilon }_2$ of the dielectric function are considered. The motivation is to study how the symmetry-breaking effects of strain can be used to deduce the symmetry location of the critical points ${\mathrm{k}}_0$. This knowledge is valuable for the empirical determination of pseudopotential parameters. The applications are to the diamond structure, but quite similar results are to be expected for any cubic material. Effective strain and kinetic energy Hamiltonians are derived in the effective-mass approximation for $\Gamma$, $\Delta$, $L$, and $\Sigma$ critical points with and without spin-orbit splitting. The effects of exciton binding are considered. The low-strain-induced changes of the dielectric function can be described in terms of three functions of frequency ${\mathcal{W}}_1$, ${\mathcal{W}}_3$, and ${\mathcal{W}}_5$, which yield symmetry information for nondegenerate bands. For high strain, the individual critical points in the star of ${\mathrm{k}}_0$ [apart from the (${\mathrm{k}}_0$, —${\mathrm{k}}_0$) degeneracy] can be resolved, and much more symmetry information is available. Lifetime broadening limits the amount of information which can be obtained.