We have solved Maxwell's equations for the fields localized near the surface of a doped semiconductor possessing either a depletion layer, an accumulation layer, or an inversion layer. We present the dispersion relation for the frequency of the surface plasmon polariton as a function of the wave vector parallel to the surface for each of the three cases. The effect of the space charge at the surface is taken into account by dividing the surface region into layers and assuming a linear position dependence for the free-carrier concentration and the local dielectric constant within each layer. We have found the solution for the fields within each layer and have satisfied the boundary conditions for the normal and tangential components of the fields at each interface between layers. We show that the features of the dispersion curve can be used to obtain information about the space-charge region. For illustration, we compare our calculations with measured dispersion curves of $n$-type InSb.

• Received 13 March 1974

DOI:https://doi.org/10.1103/PhysRevB.10.3342