POLAR OPTICAL MODES AND ELECTRON-PHONON INTERACTION IN SEMICONDUCTOR NANOSTRUCTURES

The basic analytical properties of the linear differential operator de scribing the ng-wave phenomenological model of polar optical modes in semiconductor nanostructures are studied under very general conditions . While full account is taken of the coupling between longitudinal and transverse parts of the mechanical vibration amplitude u and of u wit h the electrostatic potential field phi, the analysis holds for interf aces of arbitrary geometry and for any type of nanostructure. The herm iticity of the linear differential operator, the orthogonality of the eigenvectors u, and the consequent completeness relation are establish ed (i) without need to resort to the explicit form of the eigenvectors (ii) in a way which bears out the role of the matching rules at the i nterfaces. From this the amplitude of phi and the consequent electron- phonon interaction Hamiltonian are obtained for arbitrary geometry and structure under general conditions.