Ab initio calculation of many-body effects on the second-harmonic generation spectra of hexagonal SiC polytypes

We investigate the influence of crystal local fields and excitonic effects on the spectrum of the second harmonic generation of three polytypes of silicon carbide by using time-dependent density-functional theory including many-body effects, namely, quasiparticle corrections through the scissors operator, crystal local field effects, and excitonic interaction. The relation between the scalar density response and the components of the rank 3 tensor d(²) is established by calculating the response along different polarization directions. We find that local-field effects, although necessary for a rigorous description in the theory, yield only small contributions to the spectra, whereas excitonic effects have a strong influence on the second harmonic generation. We compare static values of the second harmonic coefficients to recent measurements and obtain very good agreement.