Optical absorption and collective modes of surface space-charge layers on (110) and (111) silicon

The electronic properties of surface space-charge layers on semiconductors whose constant-energy surfaces are ellipsoids arbitrarily oriented with respect to the surface are investigated. Optical absorption and its relation to collective modes of the system are examined within a framework of energy-functional perturbation theory. Linear-response theory of a quasi-two-dimensional system is applied to study the polarization dependence of the intersubband absorption spectra for Si(111) and Si(110) surface inverstion layers. Both the normal (six- or fourfold) valley occupancy and a reduced (twofold) valley occupancy are considered. The resonance frequencies and their strengths are calculated for both $p$- and $s$-polarized incident light. Resonances occur at frequencies which are shifted from the quasiparticle energy separations by an amount which depends upon the polarization of the light and valley occupancy of the system. In general, the resonance strength depends upon the angle of incidence and the thickness of the oxide layer and the gate electrode. Results are compared with existing theories and experiments.