Temperature-and-Field Emission of Electrons from Metals

Both the current density and the distribution in energy of electrons emitted from metals are calculated for various combinations of temperature, applied surface electric field, and work function. A wider range of those variables than previously achieved is made possible by use of numerical integration. The integrand is the usual function based on the free-electron theory of metals and the wave-mechanical barrier transmission coefficient of Sommerfeld and Bethe which assumes a classical image force and a plane surface. Results, which are presented in graphical form, are consistent with the Fowler-Nordheim field emission equation for low temperatures, and with the Richardson thermionic emission formula at low fields. Predicted emission at temperatures up to 3000°K is compared with cold emission at fields between ${10}^7$ and ${10}^8$ v/cm. A qualitative comparison is made between the present results and previous experiments on the transition between field emission and the vacuum arc.