P1–28: Use, in Fowler-Nordheim-type equations, of accurate solution of the Schrödinger equation for the Schottky-Nordheim barrier

The Schottky-Nordheim (SN) barrier is used in the "standard" theory of cold field electron emission (CFE) developed by Murphy and Good in 1956. For the SN barrier, it is mathematically impossible to derive analytical solutions of the Schrödinger equation in terms of the common functions of mathematical physics. Existing simple analytical CFE theories are based on so-called "quasi-classical" quantum-mechanical methods, typically a JWKB-type approximation. Recently, numerical methods have been applied to the SN barrier that should generate accurate solutions for the transmission coefficient D_T. This poster is a "tidy-up" exercise that explores quantitatively how these accurate solutions put correction factors into Fowler-Nordheim-type equations.