A finite type-I semiconductor superlattice with different dielectric media on either side of the surface is considerd on the basis of a simple model of a parabolic confining potential well and a half-parabolic confining potential well. Using the random-phase approximation, the density-density correlation function, including intrasubband and intersubband level transitions, is obtained in a multiple quantum well for the parabolic confining potential well and for the half-parabolic confining potential well, respectively. The dispersion relations for the surface and the bulk states are obtained as functions of the momentum wave vector for the two cases. The Raman intensities due to the bulk and the surface for the parabolic confining potential well and for the half-parabolic confining potential well are also obtained for incoming light energy as functions of the momentum wave vector.

Keywords: Multiple quantum well, Type-I superlattice, Random phase approximation, Density-density correlation function