ENERGY-EXCHANGE PROCESSES IN ELECTRON-EMISSION AT HIGH FIELDS AND TEMPERATURES

A new more complete theory for energy exchange processes in electron e mission is formulated. It is found that the tunneling contribution to the availability of vacant states is necessary to explain the replacem ent process occurring in the emitter region. The introduction of the t unneling states now makes it possible to obtain both the average energ ies of the emitted and replacement electrons using the same formalism. At T=0 K, the average energy of replacement electrons, [epsilon(r)] i s the same as the average energy of the emitted electrons, [epsilon(e) ]. As T increases, [epsilon(r)], increases rapidly until it reaches a maximum and then decreases slowly, while [epsilon(e)] increases monoto nically. When T equals the inversion temperature T(i), [epsilon(e)]=[e spilon(r)] and the energy exchange DELTAepsilon=0. We have also calcul ated both DELTAepsilon and T(i) as a function of field F. For high tem perature and fields, the value of T(i) differs considerably from that obtained without the tunneling state contribution and T(i) exhibits no nlinear behavior as a function of field. Tunneling state contributions are essential for explaining the steady state condition in the conduc tion process, especially at very low temperatures. These results are c rucial for resolving the controversial problem of the replacement proc ess in electron emission. Contrary to the assertion of Nottingham [Phy s. Rev. 59, 907 (1941)] that the replacement energy is the Fermi energ y, the current results indicate that the average value can be 10-10(2) meV less than the Fermi energy in agreement with Fleming and Henderso n [Phys. Rev. 58, 887 (1940)]. Nonequilibrium effects evaluated within the relaxation time approximation are significant only for large fiel ds.