Mathematical structure of the transport equations for coupled 2D-3D electron gasses in a mosfet

In a previous paper [1] we have studied the coexistence of coupled 2DEG and 3DEG in the proximity of a silicon-oxide interface in a MOSFET devising a hydrodynamical model obtained by taking the moment of the kinetic transport equation and by resorting to the maximum entropy principle for the closure relations. Here we classify the model from the point of view of PDEs by showing that it is hyperbolic in the relevant physical region of density, energy, velocity and energy fluxes in each subband and bulk electrons

Coupled quantum-classical transport in silicon nanowires

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 equation on the basis of the maximum entropy principle of Extended Thermodynamics, coupled to the Schr¨odinger-Poisson system. 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. We derive, using this model, the electron mobility

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

Hydrodynamic modeling of electron transport in gated silicon nanowires transistors

We present a theoretical study of the low-field electron mobility in rectangular gated silicon nanowire transistors at 300 K based on a hydrodynamic model and the selfconsistent solution of the Schrödinger and Poisson equations. The hydrodynamic model has been formulated by taking the moments of the multisubband Boltzmann equation, and closed on the basis of the Maximum Entropy Principle. It includes scattering of electrons with acoustic and non-polar optical phonons and surface roughness scattering

Hydrodynamic modeling of electron transport in silicon quantum wires

In questa tesi un modello idrodinamico per il trasporto di elettroni nei fili quantici al silicio (SiNW) è presentato. Tale modello è 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 proprietà in tali dispositivi, come la mobilità elettronica, sono studiate e i risultati ottenuti sono confrontati con quelli conseguiti usando approcci diversi nella simulazione di dispositivi elettronici basati sui nanowires

Efficient GPU implementation of a Boltzmann‑Schrödinger‑Poisson solver for the simulation of nanoscale DG MOSFETs

81–102, 2019) describes an efficient and accurate solver for nanoscale DG MOSFETs through a deterministic Boltzmann-Schrödinger-Poisson model with seven electron–phonon scattering mechanisms on a hybrid parallel CPU/GPU platform. The transport computational phase, i.e. the time integration of the Boltzmann equations, was ported to the GPU using CUDA extensions, but the computation of the system’s eigenstates, i.e. the solution of the Schrödinger-Poisson block, was parallelized only using OpenMP due to its complexity. This work fills the gap by describing a port to GPU for the solver of the Schrödinger-Poisson block. This new proposal implements on GPU a Scheduled Relaxation Jacobi method to solve the sparse linear systems which arise in the 2D Poisson equation. The 1D Schrödinger equation is solved on GPU by adapting a multi-section iteration and the Newton-Raphson algorithm to approximate the energy levels, and the Inverse Power Iterative Method is used to approximate the wave vectors. We want to stress that this solver for the Schrödinger-Poisson block can be thought as a module independent of the transport phase (Boltzmann) and can be used for solvers using different levels of description for the electrons; therefore, it is of particular interest because it can be adapted to other macroscopic, hence faster, solvers for confined devices exploited at industrial level.Project PID2020-117846GB-I00 funded by the Spanish Ministerio de Ciencia e InnovaciónProject A-TIC-344-UGR20 funded by European Regional Development Fund

Entropy Principle and Recent Results in Non-Equilibrium Theories

We present the state of the art on the modern mathematical methods of exploiting the entropy principle in thermomechanics of continuous media. A survey of recent results and conceptual discussions of this topic in some well-known non-equilibrium theories (Classical irreversible thermodynamics CIT, Rational thermodynamics RT, Thermodynamics of irreversible processes TIP, Extended irreversible hermodynamics EIT, Rational Extended thermodynamics RET) is also summarized