FULL-BAND-STRUCTURE CALCULATION OF 2ND-HARMONIC GENERATION IN ODD-PERIOD STRAINED (SI)N/(GE)N SUPERLATTICES

We report a full-band-structure calculation of frequency-dependent second-harmonic generation in odd-period strained [(Si)n/(Ge)n]/Si (001) superlattices for n = 1, 3, and 5. We derive sum rules to show that for materials with filled valence bands and empty conduction bands, independent of crystal symmetry, the expression for X<-->(2) (-2-omega; omega, omega) does not diverge in the zero-frequency limit. We use a minimal-basis orthogonalized linear combination of Gaussian orbitals technique, in conjunction with a linearized sampling method, to obtain X<-->(2)(-2-omega; omega, omega). We then use these results and a simple model to estimate second-harmonic generation at Si/Ge interfaces.