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A Monte Carlo technique for the solution of the Wigner transport equation has been developed, based on the generation and annihilation of signed particles (Nedjalkov et al. in Phys Rev B 70:115319, 2004). A stochastic algorithm without time discretization error has been recently introduced (Muscato and Wagner in Kinet Relat Models 12(1):59–77, 2019). Its derivation is based on the theory of piecewise deterministic Markov processes. Numerical experiments are performed in the case of a GaAs resonant tunneling diode. Convergence of the time-splitting scheme to the no-splitting algorithm is demonstrated. The no-splitting algorithm is shown to be more efficient in terms of computational effort.

Charge transport phenomena can been tackled in silicon quantum wires using a subband hydrodynamic model. This has been formulated by closing the moment system derived from the Schödinger-Poisson-Boltzmann equations on the basis of the Maximum Entropy Principle. The model can be used to deal with thermoelectric effects in Local equilibrium and off-equilibrium regimes.

Electron transport phenomena in silicon nanowires are investigated for square and equilateral triangle cross-sections of the wire by using an Extended Hydrodynamic model coupled to the Schrodinger–Poisson system. This model has been formulated by closing the moment system derived from the Boltzmann equation on the basis of the maximum entropy principle of Extended Thermodynamics, including scattering of electrons with acoustic and non-polar optical phonons and by considering the conduction band described by the Kane dispersion relation. Applications to the case of bulk silicon for different cross-sections of the wire are presented.

The Wigner transport equation can be solved stochastically by Monte Carlo techniques based on the theory of piecewise deterministic Markov processes. A new stochastic algorithm, without time discretization error, has been implemented and studied in the case of the quantum transport through a rectangular potential barrier.

Silicon nanowires (SiNWs) are quasi-one-dimensional structures in which electrons are spatially confined in two directions and they are free to move in the orthogonal direction. The subband decomposition and the electrostatic force field are obtained by solving the Schrödinger–Poisson coupled system. The electron transport along the free direction can be tackled using a hydrodynamic model, formulated by taking the moments of the multisubband Boltzmann equation. We shall introduce an extended hydrodynamic model where closure relations for the fluxes and production terms have been obtained by means of the Maximum Entropy Principle of Extended Thermodynamics, and in which the main scattering mechanisms such as those with phonons and surface roughness have been considered. By using this model, the low-field mobility of a Gate-All-Around SiNW transistor has been evaluated.

The Wigner equation represents a promising model for the simulation of electronic nanodevices, which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. During these years, a Monte Carlo technique for the solution of this kinetic equation has been developed, based on the generation and annihilation of signed particles. This technique can be deeply understood in terms of the theory of pure jump processes with a general state space, producing a class of stochastic algorithms. One of these algorithms has been validated successfully by numerical experiments on a benchmark test case.

Silicon nanowires (SiNWs) are quasi-one-dimensional structures in which electrons are spatially confined in two directions and they are free to move in the orthogonal direction. The subband decomposition and the electrostatic force field are obtained by solving the Schrodinger—Poisson coupled system. The electron transport along the free direction can be tackled using a hydrodynamic model, formulated by taking the moments of the multisubband Boltzmann equation. We shall introduce an extended hydrodynamic model where closure relations for the fluxes and production terms have been obtained by means of the Maximum Entropy Principle of Extended Thermodynamics, and in which the main scattering mechanisms such as those with phonons and surface roughness have been considered. By using this model, the low field mobility for a Gate-All-Around (GAA) SiNW transistor has been evaluated.

Non-equilibrium electron transport in silicon nanowires has been tackled with a hydrodynamic model. This model has been formulated by taking the moments of the multisubband Boltzmann equation, coupled to the Schrodinger–Poisson system. Closure relations are obtained by means of the maximum entropy principle (MEP) of extended thermodynamics, including scattering of electrons with acoustic and nonpolar optical phonons. Simulation results for a quantum n+ − n − n+ silicon diode are shown.

Silicon nanowires (SiNW) are quasi-one-dimensional structures in which the electrons are spatially confined in two directions, and they are free to move along the axis of the wire. The spatial confinement is governed by the Schrödinger–Poisson system, which must be coupled to the transport in the free motion direction. For devices with the characteristic length of a few tens of nanometers, the transport of the electrons along the axis of the wire can be considered semiclassical, and it can be dealt with by the multi-sub-band Boltzmann transport equations (MBTE). By taking the moments of the MBTE, a hydrodynamic model has been formulated, where explicit closure relations for the fluxes and production terms (i.e., the moments on the collisional operator) are obtained by means of the maximum entropy principle of extended thermodynamics, including the scattering of electrons with phonons, impurities and surface roughness scattering. Numerical results are shown for a SiNW transistor.

A hydrodynamic model for silicon quantum wires is formulated by taking the moments of the multisubband Boltzmann equation, coupled to the Schrodinger-Poisson system. Explicit closure relations for the fluxes and production terms (i.e. the moments on the collisional operator) are obtained by means of the Maximum Entropy Principle of Extended Thermodynamics, including scattering of electrons with acoustic and non-polar optical phonons. By using this model, thermoelectric effects are investigated.

This paper studies a Boltzmann transport equation with several electron-phonon scattering mechanisms, which describes the charge transport in semiconductors. The electric field is coupled to the electron distribution function via Poisson's equation. Both the parabolic and the quasi-parabolic band approximations are considered. The steady state behaviour of the electron distribution function is investigated by a Monte Carlo algorithm. More precisely, several nonlinear functionals of the solution are calculated that quantify the deviation of the steady state from a Maxwellian distribution with respect to the wave-vector. On the one hand, the numerical results illustrate known theoretical statements about the steady state and indicate directions for further studies. On the other hand, the nonlinear functionals provide tools that can be used in the framework of Monte Carlo algorithms for detecting regions in which the steady state distribution has a relatively simple structure, thus providing a basis for domain decomposition methods.

The shape of the electron energy distribution (EED) is of paramount importance in order to predict disruptive phenomena in semiconductor devices. Monte Carlo simulations with parabolic bands prove that the EED tail is maxwellian [1], [2], and several analytic euristic models have been introduced for modeling the EED in the bulk case [3], [4]. Starting form the Bolzmann transport equation in the bulk case, with quasi parabolic band, scattering with impurities, acoustic and optical phonons, we prove analytically that its EED, for large values of the energy e, is of the following type

Hydrodynamic models for carrier transport in semiconductors can be derived by taking moments of the Boltzmann transport equation. The maximum entropy principle allows us to obtain a closed hydrodynamic model, containing no free parameters, in order to describe transport phenomena under conditions very far from thermodynamic equilibrium. Under suitable scaling assumptions, the above model reduces to the energy transport model, to the Navier-Stokes-Fourier model, or to the drift diffusion one, in which all the transport coefficients are now explicitly determined. In this paper we study the applicability of these models to an ultrathin base npn silicon bipolar transistor where the transport is quasiballistic. The validity of the constitutive equations for the fluxes and the production terms (which are the moments over the collisional operator) is investigated by using Monte Carlo simulations.

In questa tesi un modello idrodinamico per il trasporto di elettroni nei fili quantici al silicio (SiNW) e presentato. Tale modello e stato formulato considerando i momenti derivanti dall'equazione cinetica di Boltzmann e chiudendo il sistema dei momenti ottenuto per mezzo del Principio di Massima Entropia della Termodinamica Estesa. Questo modello di trasporto include necessariamente l'equazione di Schroedinger bidimensionale accoppiata all'equazione di Poisson 3D. Al fine di testare il modello, simulazioni numeriche per SiNW transistors sono eseguite. Importanti proprieta in tali dispositivi, come la mobilita elettronica, sono studiate e i risultati ottenuti sono confrontati con quelli conseguiti usando approcci diversi nella simulazione di dispositivi elettronici basati sui nanowires.

Hydrodynamic‐like models are commonly used for describing carrier transport in semiconductor devices. One major problem of this formulation is how to model the production terms. In this paper the relaxation‐time approximation and the moments expansion of the production terms are checked with Monte Carlo simulations for a one dimensional n+ – n – n+ silicon diode in the spherical parabolic band approximation.

In this paper we present an improved version of the Electrothermal Monte Carlo method. This modification has better approximation properties due to reduced statistical fluctuations. Simulation results in 2D structures are presented.

We present an extended hydrodynamic model describing the transport of electrons in the axial direction of a silicon nanowire. This model has been formulated by closing the moment system derived from the Boltzmann equations on the basis of the maximum entropy principle of Extended Thermodynamics, coupled to the Effective Mass and Poisson equations. Explicit closure relations for the high-order fluxes and the production terms are obtained without any fitting procedure, including scattering of electrons with acoustic and non polar optical phonons. By using this model, thermoelectric effects have been investigated.

We prove the behavior of high-energy tails for the Boltzmann transport equation for silicon semiconductors, in the stationary and homogeneous regime, for parabolic band approximation, and acoustic and optical phonons scattering.

In this work, some parametric nonlinear dynamic models for the pneumatic adhesion subsystem of the climbing robot Alicia II have been computed. The state-space structures of the models rely on the real system physics and on some heuristic considerations. The former allowed to classify the system as direction dependent; the latter allowed to compensate the models for some other kind of nonlinearities. Moreover the state-space form can help in giving some stability property for the designed model. The proposed system representations could be useful to implement and tune control algorithms for the pressure inside the pneumatic adhesion cup of the robot, in order to prevent it from falling down.

Transport phenomena in a submicron npn silicon bipolar junction transistor are described by using an 8-moment model for the electrons, combined with a solution of the drift–diffusion model for the holes. The validity of the constitutive equations for the fluxes and the production terms, obtained by means of the maximum entropy principle, and the hyperbolicity conditions are checked with direct simulation Monte Carlo. We verify numerically that the quadratic closure is more accurate with respect to the zero-order one, but some irregularities can appear in the solution due to the loss of hyperbolicity in some regions of the device.

A deterministic solution method for the coupled Boltzmann-Poisson system regarding spatially two-dimensional problems is presented. The method is based on a discontinuous piecewise polynomial approximation of the carrier distribution function. The conduction band of silicon is modelled by a non-parabolic six-valley model. In particular, we applied the multicell method to simulate the transients of a silicon MESFET. The results are compared to Monte Carlo simulations.

Electron transport models in Si transistors with channel length of 0.4 microns and 50 nanometers are examined and compared between classical Direct Monte Carlo Simulations and deterministic WENO solvers for a self-consistent kinetic field-relaxation Poisson model. This model is a well accepted low density reduction of the full non-equilibrium transport phenomena. In this comparison we control the calibration of the field dependent, saturated mobility. Our computations show that, at channel length of order 0.4 microns, the relaxation model captures the the first two moments of the particle distribution function inside the channel. In particular a domain decomposition technique that implements classical drift diffusion in the high density regions and augmented drift diffusion inside the channel region gives a correction to the classical drift diffusion simulations, and produces similar qualitative results to the Monte Carlo simulations with a 0.002 CPU time reduction factor. However, we show that in the case of a 50 nanometer channel, the kinetic field-relaxation model fails to approximate well even the first moment, and in particular it does not approximate weil the current voltage curve output from Monte Carlo simulations, making it necessary to incorporate high energy effects into the collision operator.

Sobolev norm in H -2 is used to measure the distance between Maxwellian-like distribution functions and particle sets generated by Direct Simulation Monte Carlo method in bulk silicon. This norm can be used as a criteria to determine the domain of validity of the kinetic/macroscopic approaches.

Relaxation-time approximations of the collisional operator of the Boltzmann transport equation are used for simulating carrier transport in silicon semiconductors. Solutions of these kinetic models are obtained through the use of exact-integral representations in the stationary and homogeneous regime. Some properties of these solutions have been discussed and their validity have been assessed by Monte Carlo simulations in bulk silicon.

Monte Carlo simulations are used to check the consistency of an Extended Hydrodynamic model describing charge transport in bulk silicon.

We propose Radibot, a simple and cheap robotic arm for remote inspection, which interacts with the radwaste environment by means of a scintillation gamma detector and a video camera representing its light (< 1 kg) payload. It moves vertically thanks to a crane, while the other three degrees of freedom are obtained by means of revolute joints. A dedicated algorithm allows to automatically choose the best kinematics in order to reach a graphically selected position, while still allowing to fully drive the arm by means of a standard videogame joypad.

During these years several hydrodynamic-like models for simulating carrier transport in semiconductors have been developed. In this paper we check the consistency of these models with the Onsager Reciprocity Principle, which is one of the fundamental principles of Linear Irreversible Thermodynamics. Monte Carlo simulations for silicon in the inhomogeneous case are shown.

A set of closed hydrodynamic-like equations is derived from Boltzmann’s Transport Equation describing charge transport in semiconductors. The moment hierarchy is closed by using the entropy principle and the model is compared with homogeneous Monte Carlo simulations for silicon.

We use an extended hydrodynamical model, recently proposed by Anile and Pennisi, to simulate a silicon submicron diode. The relaxation times are obtained by Monte Carlo data. The comparison of our simulations with the Monte Carlo ones shows that the viscosity plays a role in the modelling.

A set of closed hydrodynamiclike equations is derived from Boltzmann's transport equation (BTE) describing charge transport in semiconductors. The production terms are modeled as relaxation terms consistently with the Onsager reciprocity principle. Stationary and homogeneous solutions are explicitly treated. The form of the production terms is checked by applying the Grad method of moments to the BTE. Finally the model is compared with Monte Carlo simulations for silicon.

Relativistic magnetofluiddynamics is a subject of importance for astrophysics and laboratory plasma physics. In this paper some exact solutions of the full nonlinear equations of relativistic magnetofluiddynamics are studied, which correspond to simple waves. The Riemann invariants are explicitly determined for various cases of noticeable physical interest.

The breaking of relativistic simple waves, for one-dimensional flow in the space-time of special relativity, is investigated. The cases of relativistic acoustic and magnetoacoustic waves are treated in detail and the critical time for breaking is evaluated.

Simple wave solutions for test-relativistic magneto-fluid dynamics in a flat space-time are considered for one-dimensional flow. A numerical integration of the equations has been performed and a discussion of the qualitative behaviour of the solution is also given.

A set of closed hydrodynamic-like equations is derived from Boltzmann's transport equation (BTE) describing charge transport in semiconductors. The moment hierarchy is closed by using the entropy principle and the production terms are modeled as relaxation terms consistently with the Onsager Reciprocity Principle. Finally the model is compared with Monte Carlo simulations for silicon.

A set of closed hydrodynamic-like equations is derived from Boltzmann's transport equation (BTE) describing charge transport in semiconductors. The moment hierarchy is closed by using the entropy principle: such closure is checked with Monte Carlo simulations for silicon.

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.

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.The validity of the constitutive equations for fluxes and production terms of the balance equations has been checked with a comparison to detailed Monte Carlo simulations in the case of bulk silicon.