Energy distribution and stability of electrons in electric fields

Abstract

Abstract The behaviour of free electrons in ionic crystals in the presence of an external field is studied. It is shown that the usual method of calculating the electric current is incorrect. The correct solution shows that—on the usual assumption that electrons are scattered by the lattice vibrations only—a stationary state is impossible. Stationary conditions can probably be obtained by considering collisions between electrons as well. For very small electron density, however, these latter collisions are negligible. It is shown that in this case the possibility of reaching stationary conditions depends on the behaviour of electrons whose energy is large enough to ionize or excite ions of the lattice.