On the Theory of Electron Multiplication in Crystals

The theory of the multiplication of electrons in strong electrostatic fields is investigated. It is found that the non-polar coupling between electrons and lattice has an important effect on the retardation of electrons in polar materials as well as in non-polar ones if the electron is to be accelerated to an energy at which it may ionize the bulk material. The retardation arising from this coupling is a maximum when the energy of the electron corresponds to a value near the boundary of the Brillouin zone, in contrast with the retardation arising from purely polar interaction in polar crystals which has its maximum when the energy is near the energy of the polar modes. The existence of the non-polar interaction seems to make the difference between the breakdown criteria of von Hippel and Fr\"ohlich of less practical importance than was supposed hitherto. It is found that statistical fluctuations in the velocity of the electrons plays a very important role in determining electron multiplication and that the field required to produce breakdown in a standard specimen actually is no more than twenty percent of the value obtained from the criteria of von Hippel and Fr\"ohlich.