A Theoretical Study of Hot Electrons in Metal Films
STANFORD UNIV CA STANFORD ELECTRONICS LABS
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An analysis of the motion of hot electrons when passing through a thin metal film is given, with particular reference to the cold-cathode emitter and photoelectric-type devices. Electron-electron collisions are considered to be responsible for the slowing down processes within the film and sufficient collisions are assumed to occur so that the motion is diffusive. The differential scattering cross section is assumed to be almost spherically symmetrical in the center-of-mass system of coordinates, and thus the equations deduced by Wolff which include electron multiplication may be used. Methods of solving the integrodifferential equation are given. The effects of the Exclusion Principle are incorporated and a partial-differential equation, involving the electron-electron mean free path and the energy loss per collision as energy dependent parameters, is deduced. This equation is solved in detail using boundary conditions which allow for a large percentage about 90 of the hot electrons to be reflected from the film surfaces. It is found that, for diffusive motion, the total current emitted is approximately proportional to the inverse of the film thickness. An analysis of electron tunneling through an insulator is also made in relation to the cold-cathode emitter.
- Solid State Physics