Use of a spreadsheet for Fowler-Nordheim equation calculations

Cold field emission of electrons is governed by the Fowler-Nordheim (FN) equation, and when the tunneling barrier includes the image potential the calculation of emission current density involves evaluation of elliptic integrals. Results are expressed as correction factors, sometimes called Nordheim functions and often denoted by v(y), s(y) and t(y). Values:were tabulated long ago, but the calculation procedure is not well documented. Some new Nordheim functions have recently been introduced as part of a revised procedure for extracting emission area from the intercept of a Fowler-Nordheim plot. One of these, the emission-area extraction function needs to be known as a function of work function and emission-current density;:this requires inversion of the FN equation to give values of the parameter y as a function of work function and emission-current density. All necessary mathematical formulas and numerical algorithms, both for direct calculation of the Nordheim functions and FN characteristics, and for inversion of the FN equation are given in this article. A modem notation and the rmks equation system are employed. Modern portable personal computers are sufficiently powerful that these calculations are,easily carried out using the spreadsheet facility of a wordprocessing package. Organization of the calculation is described, the computational performance:is discussed, and;the convenience of using spreadsheets for such calculations is noted. (C) 1999 American Vacuum Society. [S0734-211X(99)07902-0].