Analytic expression for the Fowler-Nordheim V- I characteristic including the series resistance effect

It is shown in this communication that the Fowler-Nordheim (FN) tunneling expression for the current-voltage ( I- V) characteristic can be analytically inverted so that an exact expression for the voltage-current ( V- I) characteristic can be obtained. The solution of the resulting implicit equation is found using the Lambert W function, i.e. the solution of the transcendental equation we ^w = x. The reported expressions are supported by experimental I- V curves measured in thin (≈5 nm) SiO ₂ films in MOS capacitors. The analysis includes the case of a tunneling oxide with a large series resistance. For practical purposes, a closed-form expression for W based on a Padé-type approximation is also provided.