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 Henderson controversy concerning the average energy of the replacement electrons in field emission. In addition to thermal excitation, we introduce the tunnelling-state contribution as a mechanism to vacate levels available for replacement electrons. It is found that the condition for a steady-state current is not satisfied without the tunnelling-state contribution. The present result of the net energy exchange Δε{lunate} per electron obtained as a function of both temperature and field shows much improved agreement with experimental data. The inversion temperature T_i as a function of field is now in good quantitative agreement with existing experimental data. Contrary to the assertion of Nottingham [Phys. Rev. 59 (1941) 907] that the replacement energy is equal to the chemical potential of the emitter, our results favor the argument of Fleming and Henderson [Phys. Rev. 58 (1940) 887] that the replacement process takes place in the available energy states below the Fermi energy in the emitter. Non-equilibrium effects in the emitter due to fields and temperature gradients evaluated within the relaxation time approximation are noticeable only for large fields.