We have obtained the nonlocal dielectric tensor of an n-type inversion layer at a semiconductor surface on the basis of the random phase and effective mass approximations to the electronic Hamiltonian; Explicit expressions for the elements of this tensor are obtained for an inversion layer at a (001) surface of InSb, in the case that only the lowest electric sub-band is occupied. It is found that in the zero wave vector limit the xx and yy elements possess an interband contribution as well as a Drude-type contribution, while the zz element possesses only an interband contribution (z is the coordinate normal to the surface). The dielectric tensor so obtained is used to study the electromagnetic modes of p-polarization that are localized in the vicinity of the surface. The need to take into account the sub-band structure in a complete characterization of electromagnetic phenomena in inversion layers is borne out by our results. © 1978.
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