Strained silicon: A dielectric-response calculation

Strain-induced birefringence is calculated with crystalline silicon for pressure applied along the [001] and [111] directions of the crystal. Results for the dielectric function and its change under hydrostatic strain are also given. The results are calculated for photon energies in the range 0–3.25 eV, i.e., below the direct band gap. We have made a fully-self-consistent Kohn-Sham local-density-approximation calculation, in the pseudopotential, plane-wave scheme, with a self-energy correction in the form of a rigid shift of the conduction bands of magnitude Δ=0.9 eV. Agreement with experiment is very good in the static limit, considering disagreements among the experimental values. Values of the photoelastic tensor for [001] strain are ${\mathit{p}}_{11}$-${\mathit{p}}_{12}$=-0.118 (theory) and -0.111±0.005, -0.127±0.005 (expt.). For [111] strain, we obtain ${\mathit{p}}_{44}$=-0.050 (theory) and -0.051±0.002, -0.051±0.002 [sic] (expt.); for hydrostatic distortions, ${\mathit{p}}_{11}$+2${\mathit{p}}_{12}$=-0.067 (theory) and -0.055±0.006, -0.070±0.008 (expt.). For the static dielectric constant, we obtain 10.9, compared to 11.7 and 11.4 (0 K) (expt.). All experiments quoted are at room temperature, except as noted. Above 2 eV, the calculation predicts less dispersion than seen by the experiments. Thermal effects and electron-hole interactions are estimated to resolve some of the discrepancies with experiment. The experimental data for [001] strains is not consistent with a single-oscillator model, and is therefore suspect.