Average energy of the field emitted electrons from GaN

We have derived an analytic expression for the average energy of field emitted electrons from n-type GaN. By making an analytic evaluation of the band-structure integral, the average energy is obtained in terms of hypergeometric and Lerch transcendental functions. The obtained expression exhibits the apparent dependence of the average energy on the applied field, carrier concentration, and temperature. It also yields numerical values of the average energy in excellent agreement with those obtained using full band-structure calculation.