Linear electro-optic effect in semiconductors:Ab initiodescription of the electronic contribution

We propose an ab initio framework to derive the electronic part of the second-order susceptibility tensor for the electro-optic effect in bulk semiconductors. We find a general expression for ${\ensuremath{\chi}}⁽²⁾$ evaluated within time-dependent density-functional theory, including explicitly the band-gap corrections at the level of the scissors approximation. Excitonic effects are accounted for, on the basis of a simple scalar approximation. We apply our formalism to the computation of the electro-optic susceptibilities for several semiconductors, such as GaAs, GaN, and SiC. Taking into account the ionic contribution according to the Faust-Henry coefficient, we obtain a good agreement with experimental results. Finally, using different types of strain to break centrosymmetry, we show that high electro-optic coefficients can be obtained in bulk silicon for a large range of frequencies.