Analytic expression for the FowlerNordheim V I characteristic including the series resistance effect
Abstract
It is shown in this communication that the FowlerNordheim (FN) tunneling expression for the currentvoltage ( I V) characteristic can be analytically inverted so that an exact expression for the voltagecurrent ( 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 closedform expression for W based on a Padétype approximation is also provided.
 Publication:

Solid State Electronics
 Pub Date:
 July 2011
 DOI:
 10.1016/j.sse.2011.03.015
 Bibcode:
 2011SSEle..61...93M