Energy exchange in field emission from semiconductors

In order to evaluate the energy exchange in field emission, we have investigated the replacement of electrons. The occupied energy levels near the surface are emptied by tunneling of electron through the surface barrier. They are reoccupied with electrons supplied from the back contact. This replacement process in the emitting region is not usually considered in the description of field emission. However, it has to be taken into account to evaluate the energy gain or loss of the cathode during the complete process of field emission. This energy exchange, the so-called Nottingham effect, changes from one of heating to one of cooling at the inversion temperature where the net energy exchange per electron is zero.Recently we have formulated the replacement process for semiconductor. The energy exchange is the difference between the average energies of the field and replacement electrons.