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 the 1.0-2.0 \mu m 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 \mu m when E = 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 10 ¹⁸ carriers/cm ³ produces an index change of \pm1.5 \times 10^{-3} at \lambda = 1.3 \mu m.