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 findDelta n = 1.3 times 10^5atlambda = 1.07 mum whenE = 10^5V/cm, while the Kerr effect givesDelta n = 10^-6at that field strength. The charge-carrier effects are larger, and a depletion or injection of 1018carriers/cm3produces an index change ofpm1.5 times 10^-3atlambda = 1.3 mum.