A. M. Anile

Extended Hydrodynamical Model of Carrier Transport in Semiconductors

A hydrodynamical model based on the theory of extended thermodynamics is pre- sented for carrier transport in semiconductors. Closure relations for fluxes are obtained by employing the maximum entropy principle. The production terms are modeled by fitting the Monte Carlo data for homogeneously doped semiconductors. The mathematical properties of the model are studied. A suitable numerical method, which is a generalization of the Nessyahu-Tadmor scheme to the nonhomogeneous case, is provided. The validity of the constitutive relations has been assessed by comparing the numerical results with detailed Monte Carlo simulations.

Modeling uncertain data with fuzzy B-splines

Abstract Fuzzy numbers are an alternative solution to the problem uncertain data modeling. The idea of fuzzy B-spline is here introduced: its power relies on the possibility of being used as approximating function both for fuzzy and crisp data. The fuzzy modeling of large collections of noisy data described in this paper, moreover, achieves a very high degree of compression with a relatively low computational complexity both for maintenance and interrogation of the model itself. An extensive description of the modeling technique is given, together with methods for interrogating the model. Experimental results are shown to prove the effectiveness of the proposed approach.

A thermodynamical approach to Eddington factors

Eddington factors are a common ingredient in many techniques for solving radiation hydrodynamics problems. Usually they are introduced in a phenomenological or ad hoc manner. In this paper a fundamental approach is devised for justifying Eddington factors on the basis of mathematical requirements arising from nonequilibrium thermodynamics.

Recent Developments in Hydrodynamical Modeling of Semiconductors

We present a review of recent developments in hydrodynamical modeling of charge transport in semiconductors. We focus our attention on the models for Si and GaAs based on the maximum entropy principle which, in the framework of extended thermodynamics, leads to the definition of closed systems of moment equations starting from the Boltzmann transport equation for semiconductors.

Hydrodynamical Modeling of Charge Carrier Transport in Semiconductors

Enhanced functional integration in modern electron devices requires an accurate modeling of energy transport in semiconductors in order to describe high-field phenomena such as hot electron propagation, impact ionization and heat generation in the bulk material. The standard drift-diffusion models cannot cope with high-field phenomena because they do not comprise energy as a dynamical variable. Furthermore for many applications in optoelectronics one needs to describe the transient interaction of electromagnetic radiation with carriers in complex semiconductor materials and since the characteristic times are of order of the electron momentum or energy flux relaxation times, some higher moments of the distribution function must be necessarily involved. Therefore these phenomena cannot be described within the framework of the drift-diffusion equations (which are valid only in the quasi-stationary limit). Therefore generalizations of the drift-diffusion equations have been sought which would incorporate energy as a dynamical variable and also would not be restricted to quasi-stationary situations. These models are loosely speaking called hydrodynamical models. One of the earliest hydrodynamical models currently used in applications was originally put forward by Blotekjaer [1] and subsequently investigated by Baccarani and Wordeman [2] and by other authors [3]. Eventually other models have also been investigated, some including also non-parabolic effects [4–6, 8–20]. Most of the implemented hydrodynamical models suffer from serious theoretical drawbacks due to the ad hoc treatment of the closure problem (lacking a physically convincing motivation) and the modeling of the production terms (usually assumed to be of the relaxation type and this, as we shall see, leads to serious inconsistencies with the Onsager reciprocity relations). In these lectures we present a general overview of the theory underlying hydrodynamical models. In particular we investigate in depth both the closure problem and the modeling of the production terms and present a recently introduced approach based on the maximum entropy principle (physically set in the framework of extended thermodynamics [21, 22]). The considerations and the results reported in the paper are exclusively concerned with silicon.

Propagation of weak shock waves

Abstract An asymptotic method is developed in order to treat the evolution of weak shock waves. One obtains a geometrical theory according to which weak shock waves propagate along rays and satisfy a transport law.

Moment Equations with Maximum Entropy Closure for Carrier Transport in Semiconductor Devices: Validation in Bulk Silicon

Balance equations based on the moment method for the transport of electrons in silicon semiconductors are presented. The energy band is assumed to be described by the Kane dispersion relation. The closure relations have been obtained by employing the maximum entropy principle.

Comparison among evolutionary algorithms and classical optimization methods for circuit design problems

This work concerns the comparison of evolutionary algorithms and standard optimization methods on two circuit design problems: the parameter extraction of device circuit model and the multi-objective optimization of an operational transconductance amplifier. We compare standard optimization techniques and evolutionary algorithms in terms of quality of the solutions and computational effort, that is, objective function evaluations needed to compute them. The experimental results obtained show as standard techniques are robust with respect evolutionary algorithms, while the latter are more effective in terms of the standard metrics and function calls. In particular for the multiobjective problem, the observed Pareto front determined by evolutionary algorithms has a better spread of solutions with a larger number of nondominated solutions with respect to the standard multi-objective techniques

NONLINEAR CLOSURES FOR HYDRODYNAMICAL SEMICONDUCTOR TRANSPORT MODELS

Abstract Linear and nonlinear closures are explicitly determined for a model of 13 moment equations for carrier transport in semiconductors in the case of a Fermi electron gas.

Hyperbolic Hydrodynamical Model of Carrier Transport in Semiconductors

A hydrodynamical model for semiconductors based on Extended Thermodynamics is presented and a suitable numerical scheme is proposed.