Analytical model for nanowire and nanotube transistors covering both dissipative and ballistic transport

We present an analytical model for silicon nanowire and carbon nanotube transistors that allows us to seamless cover the whole range of transport regimes from drift-diffusion to ballistic, taking into account the one-dimensional electron or hole gas in the channel. We propose an analytical description of the transition from drift-diffusion to ballistic transport based on the Buttiker approach to dissipative transport. We start from the derivation of an analytical expression for ballistic nanowire transistors and show that a generic transistor with finite scattering length can be described as a chain of elementary ballistic transistors. Then, we are able to compact the behavior of an arbitrary ballistic chain in a simple analytical model, suitable for circuit simulators. In the derivation of the model, we find a relation between the mobility and the mean free path that has deep consequences on the understanding of transport in nanoscale devices.