Giovanni Mascali

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.

Exact Maximum Entropy Closure of the Hydrodynamical Model for Si Semiconductors: the 8-Moment Case

An exact closure is obtained of the 8-moment model for semiconductors based on the maximum entropy principle in the case of silicon semiconductors. The validity of the model is assessed, and comparisons with an approximate closure are presented and discussed.

A non parabolic hydrodynamical subband model for semiconductors based on the maximum entropy principle

Abstract A hydrodynamic subband model for semiconductors is formulated by closing the moment system derived from the Schrodinger–Poisson–Boltzmann equations on the basis of the maximum entropy principle, by taking into account non parabolic energy bands of Kane’s type. Explicit closure relations for fluxes and production terms are obtained, including scattering of electrons with acoustic and non polar optical phonons and surface scattering. Numerical simulations of a quantum diode show the feasibility of the model. The importance of the non parabolicity is assessed.

Simulation of Gunn oscillations with a non‐parabolic hydrodynamical model based on the maximum entropy principle

Purpose – On the basis of the maximum entropy principle, seeks to formulate a hydrodynamical model for electron transport in GaAs semiconductors, which is free of any fitting parameter.Design/methodology/approach – The model considers the conduction band to be described by the Kane dispersion relation and includes both Γ and L valleys. Takes into account electron‐non‐polar optical phonon, electron‐polar optical phonon and electro‐acoustic phonon scattering.Findings – The set of balance equation of the model forms a quasilinear hyperbolic system and for its numerical integration a recent high‐order shock‐capturing central differencing scheme has been employed.Originality/value – Presents the results of simulations of n+ ‐n‐n+ GaAs diode and Gunn oscillator.

A hydrodynamic model for silicon semiconductors including crystal heating

We present a macroscopic model for describing the electrical and thermal behaviour of silicon devices. The model makes use of a set of macroscopic state variables for phonons and electrons that are moments of their respective distribution functions. The evolution equations for these variables are obtained starting from the Bloch–Boltzmann–Peierls kinetic equations for the phonon and the electron distributions, and are closed by means of the maximum entropy principle. All the main interactions between electrons and phonons, the scattering of electrons with impurities, as well as the scattering of phonons among themselves are considered. In particular, we propose a treatment of the optical phonon decay directly based on the expression of its transition rate (Klemens 1966 Phys. Rev. 148 845; Aksamija & Ravaioli 2010 Appl. Phys. Lett. 96 , 091911). As an application of the model, we evaluate the silicon thermopower.

A hydrodynamical model for holes in silicon semiconductors: The case of non-parabolic warped bands

This paper can be considered as the natural prosecution of Mascali and Romano (2009) [5]. Here, we describe the motion of holes in silicon by also taking into account the non-parabolicity of the heavy and light bands. The model is still based on the moment method and the closure of the system of equations is obtained by using the maximum entropy principle. Comparisons are made with the results in [5], in the case of bulk silicon, in order to establish the importance of non-parabolicity.

Theoretical foundations for tail electron hydrodynamical models in semiconductors

In this article, we present a theoretical foundation for tail electron hydrodynamical models (TEHM) in semiconductors.

Simulation of a double-gate MOSFET by a non-parabolic energy-transport subband model for semiconductors based on the maximum entropy principle

Abstract A nanoscale double-gate MOSFET is simulated with an energy-transport subband model for semiconductors including the effects of non-parabolicity by means of the Kane dispersion relation. The closure relations are derived on the basis of the maximum entropy principle and all the relevant scattering mechanisms of electrons with acoustic and non polar optical phonons are taken into account. The model is shown to form a system of nonlinear parabolic partial differential equations. The results of the simulations validate the robustness of the numerical scheme and the accuracy of the model. In particular, the importance of taking into account the non-parabolicity is assessed, since a relevant difference in the currents is obtained in comparison with the parabolic band case.

A non-linear determination of the distribution function of degenerate gases with an application to semiconductors

In this paper we consider an extended thermodynamic model for degenerate gases in which the first twenty moments of the gas distribution function are used as state variables. Exploiting the maximum entropy principle, we determine an analytic expression for the non-equilibrium distribution function of Bose and Fermi gases by means of a non-linear expansion with respect to the local thermodynamical equilibrium. Once the distribution function is given, we find the constitutive functions which appear in the fluxes of the balance equations. Explicit results can be obtained for classical ideal gases and strongly degenerate Bose and Fermi gases. We also consider an application to silicon semiconductors for which we test the accuracy of the closure relations by a comparison with Monte Carlo results.

A hydrodynamical model for covalent semiconductors with a generalized energy dispersion relation

We present the first macroscopical model for charge transport in compound semiconductors to make use of analytic ellipsoidal approximations for the energy dispersion relationships in the neighbours of the lowest minima of the conduction bands. The model considers the main scattering mechanisms charges undergo in polar semiconductors, that is the acoustic, polar optical, intervalley non-polar optical phonon interactions and the ionized impurity scattering. Simulations are shown for the cases of bulk 4H and 6H-SiC.