Electronic Raman scattering in thin bismuth films

Abstract

The theory of the electron Raman scattering (ERS) in a size-quantized film within the framework of the Abrikosov-Cohen model for the energy spectrum of Bi is developed. The wavefunctions and spectrum of electrons in the film are obtained. It is shown that the zero boundary conditions must be imposed on the total wavefunction instead of on the envelope. The boundary conditions for the envelope have a complicated form and are similar to those found by Volkov and Pinsker (1976). It is shown that unlike the standard model of the energy spectrum of carriers the scheme of an intraband ERS process with an intermediate state in the valence band is realized within the framework of the Abrikosov-Cohen spectrum. On the basis of the scheme described, the frequency dependence of the ERS differential cross section is calculated. The cross section has a non-zero value for any Delta n ( Delta n is the change in the electron quantum number due to the ERS process) at arbitrary orientation of the polarization vectors of incident and scattered radiation with respect to the film surface.