THE USE OF A NEW POTENTIAL BARRIER MODEL IN THE FOWLER-NORDHEIM THEORY OF FIELD EMISSION,

It is well known that for fields or 10 to the 7th power Vcm the observed field emitted current density is in agreement with the Fowler-Nordheim theory using the classical image-force barrier for the model of the surface potential. However, for fields or 5 x 10 to the 7th power Vcm, the measured current densities deviate from the linear log j versus 1F curve, becoming progressively less than predicted values as the field increases. It was suggested that the departures from theory were due to space-charge distortions of the cathode field by high current densities. There are, however, other effects that occur at high fields which may also produce significant departures from the Fowler-Nordheim Law. One such possibility is the inaccuracy of the classical image-force barrier at small distances several angstroms from the surface. We have examined the effect of a modified surface potential barrier on the emitted current and energy distributions in the field emission region. The new potential represents quantum modifications to the classical imageforce and is based on quantum-mechanical calculations of the electronic potential in the surface region of a metal. The result for the current density is obtained in analytic form. Deviations from the linear FowlerNordheim plot begin about 5 x 10 to the 7th power Vcm and decrease progressively to a value about 4 lower at the highest fields. Energy distributions of the field emitted electrons have been calculated for the normal and total energy cases. These are given for the zero temperature limit and the T-F region. Author