Giorgio Mugnaini | Searcharxiv

arXiv2015

Generalization of Lambert $W$ function, Bessel polynomials and transcendental equations

Employing the Lagrange inverting series, a solution of the transcendental equation $(x-a)(x-b)=le^{x}$, that can be considered a quadratic generalization of the equation defining Lambert $W$ function, has been found in terms of Bessel orthogonal polynomials. Once again a transcendental equation can be formally solved by means of classic orthogonal polynomials, suggesting a link between Rodrigues formulas and the terms of Lagrange series. A novel representation for Bessel polynomials has been found, by means of differential identity : $\left(x^{2}D\right)^{n}=x^{n+1}D^{n}x^{n-1}$

math.CA↗

arXiv2009

Analytical model of nanowire FETs in a partially ballistic or dissipative transport regime

The intermediate transport regime in nanoscale transistors between the fully ballistic case and the quasi equilibrium 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 MonteCarlo 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.

cond-mat.mes-hall↗