A NEW MODEL FOR THE REPLACEMENT PROCESS IN ELECTRON-EMISSION AT HIGH FIELDS AND TEMPERATURES

A new model is presented to resolve the Nottingham-Fleming and Henders on controversy concerning the average energy of the replacement electr ons in field emission. In addition to thermal excitation, we introduce the tunnelling-state contribution as a mechanism to vacate levels ava ilable for replacement electrons. It is found that the condition for a steady-state current is not satisfied without the tunnelling-state co ntribution. The present result of the net energy exchange DELTAepsilon per electron obtained as a function of both temperature and field sho ws much improved agreement with experimental data. The inversion tempe rature T(i) as a function of field is now in good quantitative agreeme nt with existing experimental data. Contrary to the assertion of Notti ngham [Phys. Rev. 59 (1941) 907] that the replacement energy is equal to the chemical potential of the emitter, our results favor the argume nt of Fleming and Henderson [Phys. Rev. 58 (1940) 8871 that the replac ement process takes place in the available energy states below the Fer mi energy in the emitter. Non-equilibrium effects in the emitter due t o fields and temperature gradients evaluated within the relaxation tim e approximation are noticeable only for large fields.