Abstract
We apply a microscopic model to calculate the different contributions to the nonlinear (second-order) susceptibility required in the calculation of second-harmonic generation (SHG). These terms are classified according to 1\ensuremath{\omega} and 2\ensuremath{\omega} transitions and to the surface or bulk character of the states among which the transitions take place. As an example, we analyze the effects of these microscopic susceptibilities on the SHG spectrum of a clean Si(100) $c(4\ifmmode\times\else\texttimes\fi{}2)$ surface. Three resonances seen experimentally in SHG are analyzed through this approach. They are the ${E}_{1}$ resonance of bulk Si at $2\ensuremath{\omega}\ensuremath{\sim}3.3$ eV and two others at $2\ensuremath{\omega}\ensuremath{\sim}2.2$ and 3 eV. The physical nature of the microscopic susceptibilities calculated with our formalism allows us to understand the origin of these surface SHG resonances.
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