CURRENT DENSITY EVALUATION AT THE BARRIER MAXIMUM

摘要

Modern electron sources are subject to conditions such that the estimation of the emitted electron distribution departs from that assumed in the derivation of the Fowler Nordheim Equation (FN) and Richardson-Laue-Dushman (RLD) Equation. Those equations rely on different asymptotic limits of the Transmission Coefficient for the barrier. We develop a general approximation to T(E) Transmission Coefficient for conditions where FN and RLD approximations are inadequate: low work function surfaces subjected to moderate temperatures and intermediate fields (such as may be characteristic for photocathodes under development), conditions where tunneling and thermionic emission are comparable, and where the image charge lowering of the barrier is reduced or eliminated altogether. The methodology can treat "warm" field and "cool" thermionic emission, as well as electron transport between material interfaces. Leading order corrections to the FN and RLD equations are given. Comparisons to exact approaches are shown.