Analytical Model of Nanowire FETs in a Partially Ballistic or Dissipative Transport Regime

Abstract

The intermediate transport regime in nanoscale transistors between the fully ballistic case and the quasiequilibrium case described by the drift-diffusion model is still an open modeling issue. Analytical approaches to the problem have been proposed, based on the introduction of a backscattering coefficient, or numerical approaches consisting in the Monte Carlo solution of the Boltzmann transport equation or in the introduction of dissipation in quantum transport descriptions.In this paper we propose a very simple analytical model to seamlessly cover the whole range of transport regimes in generic quasi-one dimensional field-effect transistors, and apply it to silicon nanowire transistors. The model is based on describing a generic transistor as a chain of ballistic nanowire transistors in series, or as the series of a ballistic transistor and a drift-diffusion transistor operating in the triode region. As an additional result, we find a relation between the mobility and the mean free path, that has deep consequences on the understanding of transport in nanoscale devices.

Analytical Model of One-Dimensional Carbon-Based Schottky-Barrier Transistors

“…The numerical solution of the complete chain of N elements: 2 of the boundary kind and N − 2 of internal kind, will be addressed as the B(N) model. Now we note that for the internal part of the chain the analysis developed in [24] applies. In particular it has been shown that the current in an ohmic-contact ballistic chain of N elements, after a linearization procedure, can be arranged in a to a drift-diffusion-like form (that we refer as the DD(N) model) in which the current is calculated through the formula…”

“…The linearized DD model (35) has also the advantage of dealing with non integer N = L/ℓ, and is therefore more flexible than the ballistic chain itself. As noted in [24], (35) can be rearranged in a local form, analogous to a DD equation…”

An analytical model for square GAA MOSFETs including quantum effects

“…Some attempts towards this definition have been made previously [24,25]. Here, we have followed [25] and dealt with this issue by defining an ideal square (depicted in dashed lines in Fig. 6) with its sides parallel to the semiconductor-insulator interfaces.…”

“…First, the semiconductor-insulator interface is not isopotential, making Eq. (9) an approximate expression [8,19,25]. Moreover, there are no closed analytical expressions either for C ins or for C ch .…”

Silicon-Based Nanowire MOSFETs: From Process and Device Physics to Simulation and Modeling

“…Another capacitance based analytic model of ballistic silicon nanowire is also given in (Wang, 2005). Working out an analytic model covering ballistic and diffusive transport and also realizing transition between both (Michetti et al,2009) is another challenging task. With the above mentioned preliminary compact model for silicon nanowire MOSFET implemented into circuit simulations by Verilog-A, several representative logic circuits are simulated (Yang et al, 2008).…”