NUMERICAL-SIMULATION OF FIELD-EMISSION FROM SILICON

A common method for estimating current from semiconductor field emission is to assume that the potential inside the semiconductor is the same as that which would occur if no current were emitted [zero emitted current approximation (ZECA)], and then to use the calculated density at the surface in a standard Fowler-Nordheim analysis familiar from metallic field emission calculations. At high fields, it is obvious that this method fails, as the effect of current is no longer negligible in the calculation of the band bending effects. In this work, we shall present methods for calculating the band bending effects at arbitrary fields in the ZECA model; a comparison of the Wentzel-Kramers-Brillouin and Fowler-Nordheim approaches to field emission for silicon will be compared to the airy function approach of evaluating the transmission coefficient (TC) in the ZECA model; and finally, the limits of ZECA for field emission from silicon will be analyzed by comparing the TC calculations to Wigner distribution function (WDF) simulations performed with full band bending effects and scattering. As anticipated, the ZECA model, whether calculated by the TC or WDF approach, diverges from the full band bending WDF model for high fields. A discussion of this behavior is given in light of the density and current profiles.