R. M. Pidatella

Assessment of a High Resolution Centered Scheme for the Solution of Hydrodynamical Semiconductor Equations

Hydrodynamical models are suitable to describe carrier transport in submicron semiconductor devices. These models have the form of nonlinear systems of hyperbolic conservation laws with source terms, coupled with Poissons equation. In this article we examine the suitability of a high resolution centered numerical scheme for the solution of the hyperbolic part of these extended models, in one space dimension. Because of the lack of physically significant exact analytical solutions, the method is assessed against a benchmark for the system of compressible, unsteady Euler equations with source terms, which has an exact solution; the latter is shown to be nearly identical to the numerical one. The method is then used to solve the extended hydrodynamical model (EM) based on the maximum entropy closure recently introduced by Anile, Romano, and Russo, simulating a ballistic diode n+-n-n+, which models a metal oxide semiconductor field effect transistor (MOSFET) channel. Results are presented for the reduced- and full-equation EM formulation at steady state, for an initially discontinuous electron density at the junctions. Transient results show the evolution of highly nonlinear waves emanating from the neighborhood of the junctions.

Comments on the properties of Mittag-Leffler function

Abstract The properties of Mittag-Leffler function are reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to define the relevant semigroup properties. We analyse the relevant role in the solution of Schrödinger type and heat-type fractional partial differential equations and explore the problem of operatorial ordering finding appropriate rules when non-commuting operators are involved. We discuss the coherent states associated with the fractional Schödinger equation, analyze the relevant Poisson type probability amplitude and compare with analogous results already obtained in the literature.

ENO/WENO INTERPOLATION METHODS FOR ZOOMING OF DIGITAL IMAGES

In this paper we use interpolation methods like ENO and WENO techniques, generally used to solve hyperbolic PDEs, for the zooming process of digital images. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. Our experiments show that the proposed method beats in quality pixel replication, bilinear and bicubic interpolation. Moreover our algorithm is competitive both for quality and efficiency with the other traditional techniques of zooming. [ DOI : 10.1685 / CSC06136] About DOI

Hydrodynamical models for semiconductors

We use an extended hydrodynamical model, recently proposed by Anile and Pennisi, to simulate a silicon submicron diode. The relaxation times are obtained by Monte Carlo data. The comparison of our simulations with the Monte Carlo ones shows that the viscosity plays a role in the modelling.

A New Finite Difference Scheme for the Boltzmann — Poisson System on Semiconductor Devices

We consider the Boltzmann — Poisson (BP) system to describe the electron flow in a semiconductor device. We discretized this system by a new finite difference scheme to simulate a n + − n − n + silicon diode.

3-D mixed finite element schemes for charge transport equations

Abstract We use the Raviart-Thomas-Nedelec space to discretize the current continuity equations of the drift-diffusion semiconductor models with Mixed Finite Element methods in R 3. An asymptotic analysis of the behaviour od the scheme when the potential is very large is given.