SMALL CALCULATED 2ND-HARMONIC GENERATION IN SI1GE1

We report a small coefficient of second-harmonic generation, d123, in Si1Ge1 [for instance, d123=-1.9 pm/V for a Si(001) substrate] that is one order of magnitude smaller than previous calculations [Ghahramani et al., Phys. Rev. Lett. 64, 2815 (1990), d123=-18.4 pm/V] and the coefficient of second-harmonic generation in GaAs (d123=81 pm/V). This offers an alternative explanation to recent experiments [Bottomley et al., Appl. Phys. Lett. 63, 2324 (1993); Phys. Rev. B 50, 8564 (1994)] that do not detect strong bulk second-harmonic generation in SinGem superlattices (n,m odd) in contrast to the theoretical predictions of Ghahramani and co-workers. Our results therefore put an additional limitation on the realization of Si/Ge-based electro-optic modulators. Tensile in-plane strain enhances d123. We predict a factor of 4 increase of d123 using a Ge instead of a Si substrate. The theoretical description of second-harmonic generation in Si1Ge1 is difficult due to the similarity of Si and Ge. We find that nonlinear core charge corrections are essential for a reliable description of second-harmonic generation in Si1Ge1 since they ensure a consistent charge transfer in the Si-Ge bond (Si=anion, Ge=cation) and reduce otherwise large local-field effects. Hardness conservation and differences between exchange-correlation functionals are of minor importance since they affect the results on a 10% level or less. © 1995 The American Physical Society.