Abstract A finite HgTe/CdTe superlattice with different dielectric media on either side of the surfaces is investigated by taking into account the wave function overlap not only between the interface states and plasmons but also between the interface states. The unit cell of the finite HgTe/CdTe superlattice consists of two electron-like states and a heavy-hole-like state in HgTe and two light-hole-like states in CdTe. Using the random phase approximation added with some assumptions, we have studied the density-density correlation function considering the wave functions of three different interface states overlapping with the electron-like states, the light-hole-like states, and the heavy-hole-like states. We have calculated the collective excitation spectra of the intrasubband for both the bulk plasmons and the surface plasmons of interface states. Raman intensities due to bulk and surface plasmons are expressed by the relative value of mode energy of the plasmons and as a function of the wave vector.