Electrooptical effects in silicon

A numerical Kramers-Kronig analysis is used to predict the refractive-index perturbations produced in crystalline silicon by applied electric fields or by charge carriers. Results are obtained over the1.0-2.0 \mum optical wavelength range. The analysis makes use of experimental electroabsorption spectra and impurity-doping spectra taken from the literature. For electrorefraction at the indirect gap, we find\Delta n = 1.3 \times 10^{5}at\lambda = 1.07 \mum whenE = 10^{5}V/cm, while the Kerr effect gives\Delta n = 10^{-6}at that field strength. The charge-carrier effects are larger, and a depletion or injection of 1018carriers/cm3produces an index change of\pm1.5 \times 10^{-3}at\lambda = 1.3 \mum.