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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.

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 simulate charge transport in monolayer graphene on a substrate made of hexagonal boron nitride (h-BN). This choice is motivated by the fact that h-BN is one of the most promising substrates on account of the reduced degradation of the velocity due to the remote impurities.

The semiclassical Boltzmann equations for electrons in the monolayer graphene are numerically solved by an approach based on a discontinuous Galerkin (DG) method. Both the conduction and valence bands are included, and the inter-band scatterings are taken into account as well.

The importance of the inter-band scatterings is accurately evaluated for several values of the Fermi energy, addressing the issue related to the validity of neglecting the generation-recombination terms. It is found out that the inclusion of the inter-band scatterings produces sizable variations in the average values, like the current density, at zero Fermi energy, whereas, as expected, the effect of the inter-band scattering becomes negligible by increasing the absolute value of the Fermi energy.

The correct evaluation of the influence of the inter-band scatterings on the electronic performances is deeply important not only from a theoretical point of view but also for the applications. In particular, it will be shown that the time necessary to reach the steady state is greatly affected by the inter-band scatterings, with not negligible consequences on the switching on/off processes of realistic devices. As a limitation of the present work, the proposed approach refers to the spatially homogeneous case. For the simulation of electron devices, non-homogenous numerical solutions are required. This last case will be tackled in a forthcoming paper.

As observed in Majorana et al. (2019), the use of a Direct Simulation Monte Carlo (DSMC) approach, which properly describes the inter-band scatterings, is computationally very expensive because the valence band is highly populated and a huge number of particles is needed. Even by simulating holes instead of electrons does not overcome the problem because there is a certain degree of ambiguity in the generation and recombination terms of electron-hole pairs. The DG approach, used in this paper, does not suffer from the previous drawbacks and requires a reasonable computing effort.

The optimization of the cross section of an axisymmetric induction heating device is performed by means of genetic algorithms (GAs).

The hybrid finite element method–Dirichlet boundary condition iteration method is used to deal with the unbounded nature of the field. The formulation of the electromagnetic problems takes into account skin and proximity effects in the source currents.

The convergence of GAs towards the optimum is very fast, since less than a thousand analyses have been necessary.

A special derivation of the finite element global system is presented which allows us to save computing time.

This paper proposes an algorithm for the extraction of reduced order models of MEMS switches, based on using a physics aware simplification technique.

The reduced model is built progressively by increasing the complexity of the physical model. The approach starts with static analyses and continues with dynamic ones. Physical phenomena are introduced sequentially in the reduced model whose order is increased until accuracy, computed by assessing forces that are kept in the reduced model, is acceptable.

The technique is exemplified for RF-MEMS switches, but it can be extended for any device where physical phenomena can be included one by one, in a hierarchy of models. The extraction technique is based on analogies that are carried out for both the multiphysics and the full-wave electromagnetic phenomena and their couplings. In the final model, the multiphysics electromechanical phenomena is reduced to a system with lumped components with nonlinear elastic and damping forces, coupled with a system with distributed and lumped components which represents the reduced model of the RF electromagnetic phenomena.

Contrary to the order reduction by projection methods, this approach has the advantage that the simplified model can be easily understood, the equations and variables have significance for the user and the algorithm starts with a model of minimal order, which is increased until the approximation error is acceptable. The novelty of the proposed method is that, being tailored to a specific application, it is able to keep physical interpretation inside the reduced model. This is the reason why, the obtained model has an extremely low order, much lower than the one achievable with general state-of-the-art procedures.

The paper introduces and illustrates the use of numerical models for the simulation of electromagnetic and thermal processes in an absorbing ceramic layer (susceptor) of a new millimeter-wave (MMW) heat exchanger. The purpose of this study is to better understand interaction between the MMW field and the susceptor, choose the composition of the ceramic material and help design the physical prototype of the device.

A simplified version of the heat exchanger comprises a rectangular block of an aluminum nitride (AlN) doped with molybdenum (Mo) that is backed by a thin metal plate and irradiated by a plane MMW. The coupled electromagnetic-thermal problem is solved by the finite-difference time-domain (FDTD) technique implemented in QuickWave. The FDTD model is verified by solving the related electromagnetic problem by the finite element simulator COMSOL Multiphysics. The computation of dissipated power and temperature is based on experimental data on temperature-dependent dielectric constant, loss factor, specific heat and thermal conductivity of the AlN:Mo composite. The non-uniformity of patterns of dissipated power and temperature is quantified via standard-deviation-based metrics.

It is shown that with the power density of the plane wave on the block’s front face of 1.0 W/mm², at 95 GHz, 10 × 10 × 10-mm blocks with Mo = 0.25 – 4% can be heated up to 1,000 °C for 60-100 s depending on Mo content. The uniformity of the temperature field is exceptionally high – in the course of the heating, temperature is evenly distributed through the entire volume and, in particular, on the back surface of the block. The composite producing the highest level of total dissipated power is found to have Mo concentration of approximately 3%.

In the electromagnetic model, the heating of the AlN:Mo samples is characterized by the volumetric patterns of density of dissipated power for the dielectric constant and the loss factor corresponding to different temperatures of the process. The coupled model is run as an iterative procedure in which electromagnetic and thermal material parameters are upgraded in every cell after each heating time step; the process is then represented by a series of thermal patterns showing time evolution of the temperature field.

Determination of practical dimensions of the MMW heat exchanger and identification of material composition of the susceptor that make operations of the device energy efficient in the required temperature regime require and expensive experimentation. Measurement of heat distribution on the ceramic-metal interface is a practically challenging task. The reported model is meant to be a tool assisting in development of the concept and supporting system design of the new MMW heat exchanger.

While exploitation of a finite element model (e.g. in COMSOL Multiphysics environment) of the scenario in question would require excessive computational resources, the reported FDTD model shows operational capabilities of solving the coupled problem in the temperature range from 20°C to 1,000°C within a few hours on a Windows 10 workstation. The model is open for further development to serve in the ongoing support of the system design aiming to ease the related experimental studies.

Based on the framework of Krylov subspace-based model order reduction (MOR), compact models of the piezoelectric energy harvester devices can be generated. However, the stability of reduced piezoelectric model often cannot be preserved. In previous research studies, “MOR after Schur,” “Schur after MOR” and “multiphysics structure preserving MOR” methods have proven successful in obtaining stable reduced piezoelectric energy harvester models. Though the stability preservation of “MOR after Schur” and “Schur after MOR” methods has already been mathematically proven, the “multiphysics structure preserving MOR” method was not. This paper aims to provide the missing mathematical proof of “multiphysics structure preserving MOR.”

Piezoelectric energy harvesters can be represented by system of differential-algebraic equations obtained by the finite element method. According to the block structure of its system matrices, “MOR after Schur” and “Schur after MOR” both perform Schur complement transformations either before or after the MOR process. For the “multiphysics structure preserving MOR” method, the original block structure of the system matrices is preserved during MOR. 

This contribution shows that, in comparison to “MOR after Schur” and “Schur after MOR” methods, “multiphysics structure preserving MOR” method performs the Schur complement transformation implicitly, and therefore, stabilizes the reduced piezoelectric model.

The stability preservation of the reduced piezoelectric energy harvester model obtained through “multiphysics structure preserving MOR” method is proven mathematically and further validated by numerical experiments on two different piezoelectric energy harvester devices.

The purpose of this paper is to propose a physics-aware algorithm to obtain radio frequency (RF)-reduced models of micro-electromechanical systems (MEMS) switches and show how, together with multiphysics macromodels, they can be realized as circuits that include both lumped and distributed parameters.

The macromodels are extracted with a robust procedure from the solution of Maxwell’s equations with electromagnetic circuit element (ECE) boundary conditions. The reduced model is extracted from the simulations of three electromagnetic field problems, in full-wave regime, that correspond to three configurations: signal lines alone, switch in the up and down positions.

The technique is exemplified for shunt switches, but it can be extended for lateral switches. Moreover, the algorithm is able take frequency dependence into account both for the signal lines and for the switch model. For the later, the order of the model is increased until a specified accuracy is achieved.

The use of ECE as boundary conditions for the RF simulation of MEMS switches has the advantage that the definition of ports is unambiguous and robust as the ports are clearly defined. The extraction approach has the advantage that the simplified model keeps the basic phenomena, i.e. the propagation of the signal along the lines. As the macromodel is realized with a netlist that uses transmission lines models, the lines’ extension is natural. The frequency dependence can be included in the model, if needed.

Looks at the first 100 years of Italian cinema examining its role in Italy’s recent history. Provides a bibliography of major film directors, Italian cinema sources, reference works, histories, themes, theory and criticism and articles in journals.