Further studies in the emission of electrons from cold metals

Abstract

Fowler and Nordheimj- and Oppenheimerj have already independently studied the theory of the emission of electrons from cold metals under the effect of an intense electric field, and have obtained results in good qualitative agreement with experiment. The formula for this “ auto-electronic ” current density, —I, obtained by the former authors is I = ε/2 πh μ 1/2 / ( X + μ ) X 1/2 F 2 e -4/3 kX 3/2 / F (1) at ordinary temperatures. In this formula k 2 = 8 π 2 m/h 2 ; μ is the parameter of the metallic electron distribution in the Fermi-Dirac statistics; X is the thermionic work function for the metal; — ε is the charge on the electron; h is Planck’s constant and — F is the derivative of the potential energy of the electron along the outward normal at the cathode surface; I, F and ε are then all positive. When the unit of energy is the electron-volt and the unit of current density is amperes per square centimetre this reduces to I = 6.2 x 10 -6 μ 1/2 / ( X + μ ) X 1/2 F 2 e -6.8 x 10 7 X 3/2 / F (2)