General thermal-field emission equation

A general electron emission equation is developed to account for both tunneling and thermal emission for general potentials, particularly when both processes are non-negligible. It is then applied to the image charge potential that is the basis for the Fowler-Nordheim (FN) [Proc. R. Soc. London A119, 173 (1928)] and the Richardson-Laue-Dushman (RLD) equations of electron emission [Proc. R. Soc. London A107, 377 (1925)]. The leading order terms in a series expansion are used to derive a “refined” FN-RLD equation that extends the range of validity of the FN and RLD equations for parameters where the traditional forms either fail or perform poorly.