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) SiO₂ 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.