Intervalley and intersubband scattering in a quantized silicon inversion layer

Intersubband and intervalley-intrasubband transitions of electrons in a quantized silicon inversion layer are studied. Components of the phonon wave vector, both parallel and normal to the surface, are considered, and selection rules for the transitions are established. It is shown that when the thickness of the inversion layer is not too small, the transitions may be described by $g$ and $f$ phonons. An expression for the relaxation time corresponding to $f$ phonons is given by using the variational wave functions. For the $g$ phonons, an analytic expression for the collision integral is derived by using the same function.