SHORT-WAVELENGTH PHONON EMISSION FROM A METAL-SEMICONDUCTOR INTERFACE

We believe that short-wavelength phonons (the phonons whose wave vecto rs correspond to the edge points of the Brillouin zone) may be emitted by electrons when crossing the interface if it is abrupt. To show thi s, we have obtained the exact solution of the Schrodinger equation for an electron whose effective mass is,a smooth steplike function of dis tance from the interface, where an electrostatic potential is supposed to be unchanged. We then analyzed the matrix element of the electron- phonon interaction and find it is exponentially small if the interface is smooth, so that the mean width of the step is much greater then th e phonon wavelength. This smallness should disappear if the interface becomes abrupt.