Layer-by-layer analysis of second harmonic generation at a simple surface

Abstract

We present a general scheme, based on a a microscopic formulation, to obtain the second harmonic signal produced by each atomic layer of a semi-infinite crystal. Using the simple Si(111):H $(1\times 1)$ surface as an example, we obtain that the nonlinear polarization in the bulk does not decay to zero due to the lack of centrosymmetry of the individual layers. However, the sum of this polarization follows the physically correct picture that the second harmonic signal is zero at the centrosymmetric bulk and finite in the selvedge as the surface is approached and the centrosymmetry is broken. The results show that the selvedge region includes the surface and just a few layers below it.