Analytical expressions for the drain current of a nanotransistor in the off-state regime



Recently, we have suggested a scale-invariant numerical model for a planar nanotransistor based on a Fowler-Nordheim-type of formula. In this this model we introduce a set of approximations to obtain simple analytical expressions for the drain current in the off-state regime. For this purpose the saddle point approximation is applied to the Fowler-Nordheim integral. Furthermore, we are using the WKB-expression for transmission coefficient and a series approximation for Fermi-Dirac integrals by Mc Dougal and Stoner to evaluate the supply function. The resulting analytical formula is in qualitative agreement with the traces of an experimental transistor. It becomes quite simple for small gate voltages, i.e. in the deep off-state regime. Systematic steps to improve our approximations towards a quantitative agreement are discussed. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)