P2–31: Simple derivation of formula for Sommerfeld supply density

This poster presents a simple derivation of the result that (for a large free-electron conductor) the electron supply density is constant in energy-space and is given by the Sommerfeld supply density z_S, and also proves the formula for z_S. This result is the best starting point for deriving Richardson-Schottky-type and Fowler-Nordheim-type equations. For small emitters the supply density is not constant in energy-space; consequently, emission from small emitters is not well described by these equations.