Field penetration, electron supply and effective work function in semiconductor field-emission cathodes

Summary form only given. It is widely assumed that n-type silicon field-emission cathodes should be heavily doped to maximize the availability of electrons at the emission surface. Field emission from semiconductors, however, is different than from metals in that, among other things, the concept of an independent supply function is likely not valid. Penetration of the external field into semiconductor cathodes, which is dependent on dopant concentration, enables hot electron accumulation and impact ionization near the surface. The application of the Fowler-Nordheim model, as is useful with ideal metal cathodes, is insufficient for this more complicated condition. As donor concentration decreases in the cathode, the electron supply is increasingly drawn from the larger volume of the semiconductor away from the tunneling surface. Furthermore, the drift of electrons within the semiconductor creates a condition where the tunneling electrons at the surface need to overcome an "effective" work function, which is less than the equilibrium value. The result is a higher current density from an applied external field than would be obtained from a metal or degenerately-doped semiconductor with the same equilibrium work function. We present here modeling results which suggest that an "optimum" doping level exists somewhere between light and degenerate concentrations.