Injected Electron Currents Through Insulators

The previously presented unified theory of field and thermionic emission is extended to electron emission into dielectrics, including thin films between two metal electrodes. The current equations are derived under the assumption of a parabolic energy—momentum dependence and convenient barrier shape approximations for various thicknesses of the insulating layer, but the general method is used in the case of any arbitrary barrier shape. Both cases of equal and unequal effective electron masses in the insulator and the metals are considered. The current expressions obtained are applicable to the whole range of fields and temperatures between the limits of thermionic and field emission.