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Presents a simplified mathematical model of electron transport in a one‐dimensional semiconductor device of N+ ‐ N ‐ N + type. The model is based on a singular perturbation approach of the kinetic equation which describes the transport processes. This so‐called Child‐Langmuir asymptotics is obtained by assuming that the injected electrons at the N + ‐ N junction on the source side have a very weak energy compared with what they are able to gain under the influence of the electric field. Formally establishes the limit model when a realistic collision model for electron‐phonon interaction is considered. Compares the results with both experiments and particle simulations.

This paper is devoted to the numerical study, using the deterministic particle method, of the parallel transport of a bidimensional electron gas confined in a potential well near a heterojunction interface. The geometry makes it possible to solve independently the transport under the electric field and the well shape. We simulate the electronic transport with a kinetic model and use the deterministic particle method. As for the description of the potential well, we use different models and compare their influence on the thermodynamic equilibrium and on the transport properties of the electron gas.

The progress of semiconductor fabrication technology, particularly the heteroepitaxial technology (MOCVD, MBE, etc.) has permitted the fabrication of structures and devices whose behaviour is dominated by ballistic and/or quantum‐interference effects through heterojunctions.

The purpose of this paper is to develop a Vortex-In-Cell (VIC) method with the semi-Lagrangian scheme and apply it to the high-Re lid-driven cavity flow.

The VIC method is developed for simulating high Reynolds number incompressible flow. A semi-Lagrangian scheme is incorporated in the convection term to produce unconditional stability, which gets rid of the constraint of the convection Courant-Friedrichs-Lewy (CFL) condition; the adaptive time step is used to maintain the numerical stability of the diffusion term; and the velocity boundary condition is readily converted to the vorticity formulation to suit discontinuous boundary treatment. The VIC simulation results are compared with those produced by other gird methods reported in open literature studies.

The lid-driven cavity flow is simulated from Re = 100 to 100,000. Similar vortex birth mechanisms are exhibited though, but distinct flow characteristics are revealed. At Re = 100 to 7,500, the cavity flow is confirmed steady. At Re = 10,000, 15,000 and 20,000, the cavity flow is periodical with a primary vortex held spatially at the center. In particular, at Re = 100,000 highly turbulent characteristics is first revealed and an analogous primary vortex is formed but in motion rather than stationary, which is caused by the considerable flow separation at all the boundaries.

In the lid-driven cavity, the flow becomes extremely complex and highly turbulent at Re = 100,000, and the analogous primary vortex structure is observed. Boundary layer separation is observed at all walls, producing small vortices and causing the displacement of the analogous primary vortex. Such a finding original and has not yet been reported by other investigators. It may provide a basis for conducting in-depth studies of the lid-driven cavity flow.

This paper intends to present a hydrodynamical model which describes the hole motion in silicon and couples holes and electrons.

The model is based on the moment method and the closure of the system of moment equations is obtained by using the maximum entropy principle (hereafter MEP). The heavy, light and split‐off valence bands are considered. The first two are described by taking into account their warped shape, while for the split‐off band a parabolic approximation is used.

The model for holes is coupled with an analogous one for electrons, so obtaining a complete description of charge transport in silicon. Numerical simulations are performed both for bulk silicon and a p‐n junction.

The model uses a linear approximation of the maximum entropy distribution in order to close the system of moment equations. Furthermore, the non‐parabolicity of the heavy and light bands is neglected. This implies an approximation on the high field results. This issue is under current investigation.

The paper improves the previous hydrodynamical models on holes and furnishes a complete model which couples electrons and holes. It can be useful in simulations of bipolar devices.

The results of the paper are new since a better approximation of the band structure is used and a description of both electron and hole behavior is present, therefore the results are of a certain relevance for the theory of charge transport in semiconductors.

The purpose of this paper is to reply to the following question: do there exist piecewise smooth solutions to the 2D MEP hydrodynamical model of charge transport in semiconductors with smooth parts separated by a surface of strong discontinuity?

A standard approach is used to obtain jump conditions for the balance equations under consideration.

For the balance equations of charge transport in semiconductors based on the maximum entropy principle Rankine‐Hugoniot jump conditions were derived and studied. Considering the important case of planar discontinuity, the authors discuss the legitimacy of the introduction of surface charge and surface current in the Rankine‐Hugoniot jump conditions.

The jump conditions are derived for the balance equations written for the case of the parabolic approximation of energy bands. However, it is possible also to perform the analysis of corresponding jump conditions for the case of Kane dispersion relation approximation.

The paper presents derivation and study of Rankine‐Hugoniot jump conditions for the 2D MEP hydrodynamical model of charge transport in semiconductors.

To present a new direct solution method for the Boltzmann‐Poisson system for simulating one‐dimensional semiconductor devices.

A combination of finite difference and finite element methods is applied to deal with the differential operators in the Boltzmann transport equation. By taking advantage of a piecewise polynomial approximation of the electron distribution function, the collision operator can be treated without further simplifications. The finite difference method is formulated as a third order WENO approach for non‐uniform grids.

Comparisons with other methods for a well‐investigated test case reveal that the new method allows faster simulations of devices without losing physical information. It is shown that the presented model provides a better convergence behaviour with respect to the applied grid size than the Minmod scheme of the same order.

The presented direct solution methods provide an easily extensible base for other simulations in 1D or 2D. By modifying the boundary conditions, the simulation of metal‐semiconductor junctions becomes possible. By applying a dimension by dimension approximation models for two‐dimensional devices can be obtained.

The new model is an efficient tool to acquire transport coefficients or current‐voltage characteristics of 1D semiconductor devices due to short computation times.

New grounds have been broken by directly solving the Boltzmann equation based on a combination of finite difference and finite elements methods. This approach allows us to equip the model with the advantages of both methods. The finite element method assures macroscopic balance equations, while the WENO approximation is well‐suited to deal with steep gradients due to the doping profiles. Consequently, the presented model is a good choice for the fast and accurate simulation of one‐dimensional semiconductor devices.

In this paper, we present the results of submicron pseudomorphic AlGaAs/InGaAs/ GaAs HEMT simulations. Our main interest is the study of electronic temperature behavior in the device and improvement of the current‐voltage characteristic curves. Three types of models are being used. The first is the well known drift‐diffusion model. The second is of the hydrodynamic type and the third is a combination of the two preceding models. The numerical treatment is based on the discretization by the Galerkin finite element method for both Poisson and continuity equations with the streamline‐diffusion method being used for the energy equation. A comparison of the different approaches have been realized and a synthesis on the validity of each of these models is being drawn.

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.

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.

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.

Presents the results of simulations of n⁺ ‐n‐n⁺ GaAs diode and Gunn oscillator.

The purpose of this paper is to investigate the computational features of the Flowfield Dependent Variation (FDV) method, a numerical scheme built to simulate flows characterized by multiple speeds, multiple physical phenomena, and by large variations in flow variables.

Fundamentally, the FDV method may be regarded as a variant of the Lax-Wendroff Scheme (LWS) that is obtained by replacing the explicit time derivatives in LWS by a weighted combination of explicit and implicit time derivatives. The weighting factors – referred to as FDV parameters – may be broadly classified as convective and diffusive parameters which, for example, are determined using flow quantities such as the Mach number and Reynolds number, respectively. Hence, the reference to these parameters and the method as “flow field dependent.” A von Neumann Fourier analysis demonstrates that the increased implicitness makes FDV both more stable and less dispersive compared to LWS, a feature crucial to capturing shocks and other phenomena characterized by high gradients in variables. In the current study, the FDV scheme is implemented in a Taylor-Galerkin-based finite element method framework that supports arbitrarily high order, unstructured isoparametric elements in one-, two- and three-dimensional geometries.

At first, the spatial accuracy of the implemented FDV scheme is established using the Method of Manufactured Solutions, wherein the results show that the order of accuracy of the scheme is nearly equal to the order of the shape function polynomial plus one. The dispersion and dissipation errors of FDV, when applied to the compressible Navier-Stokes and energy equations, are investigated using a 2-D, small-amplitude acoustic pulse propagating in a quiescent medium. It is shown that FDV with third-order shape functions accurately captures both the amplitude and phase of the acoustic pulse. The method is then applied to cases ranging from low-Mach number subsonic flows (Mach number M=0.05) to high-Mach number supersonic flows (M=4) with shock-boundary layer interactions. For all cases, fair to good agreement is observed between the current results and those in the literature.

The spatial order of accuracy of the FDV method, its stability and dispersive properties, as well as its applicability to low- and high-Mach number flows are established.