Theory of electron emission into dielectrics with arbitrary band structure

The previously proposed theory of electron emission in dielectrics, based on the quasi-free electron model, is further extended in order to include insulators with arbitrary band structure. Using a generalized formula for the transition probability, formal expressions for the total energy distribution of the emitted electrons and for the current density are derived. A rather general band structure of the insulator is proposed which permits to express explicitly the temperature and field dependence of the energy distribution and of the current for all possible emission conditions using appropriate barrier shape approximations.