In electron field emission from silicon emitters some researchers apply Fowler-Nordheim equation taking into account the effective work function as the electron affinity when emission is considered from the conduction band. They also take (effective work function = electron affinity + energy gap) when emission is assumed to take place from valence band. I found different forms of mathematical expressions relating work function and electron affinity. Could anyone help me with the most popular / physically correct mathematical expression? Thanks.