Showing papers by "Vittorio Romano published in 2000"

Central Schemes for Balance Laws of Relaxation Type

Abstract: Several models in mathematical physics are described by quasi-linear hyperbolic systems with source term and in several cases the production term can become stiff. Here suitable central numerical schemes for such problems are developed and applications to the Broadwell model and extended thermodynamics are presented. The numerical methods are a generalization of the Nessyahu--Tadmor scheme to the nonhomogeneous case by including the cell averages of the production terms in the discrete balance equations. A second order scheme uniformly accurate in the relaxation parameter is derived and its properties analyzed. Numerical tests confirm the accuracy and robustness of the scheme.

Non parabolic band transport in semiconductors: closure of the production terms in the moment equations

Abstract: Closure relations for the production terms of the balance equations describing the motion of electrons in semiconductors are obtained by using the distribution function given, according to 1], by the maximum entropy principle in the case of the Kane dispersion relation for the energy band. Scatterings of electrons with non polar optical phonons (both for intervalley and intravalley interactions), acoustic phonons and impurities are considered. Applications to bulk silicon are presented. In particular the overshoot and saturation eeects are described with good accuracy.

Extended hydrodynamical model of carrier transport in semiconductors

Abstract: 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.

Hydrodynamical Modeling of Charge Carrier Transport in Semiconductors

Abstract: 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.

Numerical solution for hydrodynamical models of semiconductors

Abstract: Numerical solutions of recent hydrodynamical models of semiconductors are computed in one-space dimension. Such models describe charge transport in semiconductor devices. Two models are taken into consideration. The first one has been developed by Blotekjaer, Baccarani et al., and the second one by Anile et al. In both cases the system of equations can be written as a convection-diffusion type system, with a right-hand side describing relaxation effects and interaction with a self-consistent electric field. The numerical scheme is a splitting scheme based on the Nessyahu–Tadmor scheme for the hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results are compared to detailed Monte-Carlo simulation.

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

Abstract: 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.

Cross-Validation of numerical schemes for extended hydrodynamical models of semiconductors

Abstract: The numerical integration of the hydrodynamical model of semiconductors based on extended thermodynamics has been tackled. On account of the mathematical complexity of the system, no theoretical conditions of convergence are available for the existing schemes. Therefore in order to obtain numerical solution it was almost mandatory to resort to a cross-validation comparing the results given by two different methods. The kinetic scheme and the finite difference method represented by a suitable modification of the Nessyahu–Tadmor scheme furnish numerical results for the ballistic diode problem in good agreement even for non-smooth solutions.

Simulation of submicron silicon diodes with a non-parabolic hydrodynamical model based on the maximum entropy principle

Abstract: Modeling modern submicron electron devices requires an accurate description of energy transport in order to cope with high-field phenomena such as hot electron propagation, impact ionization and heat generation in the bulk material. Most implemented hydrodynamic 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 leads to serious inconsistencies with the Onsager reciprocity relations. In this paper we use a recently introduced moment approach in which the closures for the fluxes and for the production terms are based on the maximum entropy principle in the case of the Kane dispersion relation. Explicit closure relations for higher order fluxes and production terms have been obtained without any free parameters. A preliminary validation of this model has been successfully performed in bulk silicon. We test the model by simulating a one dimensional n/sup +/n-n/sup +/ submicron silicon diode for different values of the channel, applied bias and doping profile. Comparisons with Monte Carlo simulations show that the results are sufficiently accurate for CAD purposes.