Armando Majorana

A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: performance and comparisons with Monte Carlo methods

In this paper we develop a deterministic high order accurate finite-difference WENO solver to the solution of the 1-D Boltzmann-Poisson system for semiconductor devices. We follow the work in Fatemi and Odeh [9] and in Majorana and Pidatella [16] to formulate the Boltzmann-Poisson system in a spherical coordinate system using the energy as one of the coordinate variables, thus reducing the computational complexity to two dimensions in phase space and dramatically simplifying the evaluations of the collision terms. The solver is accurate in time hence potentially useful for time-dependent simulations, although in this paper we only test it for steady-state devices. The high order accuracy and nonoscillatory properties of the solver allow us to use very coarse meshes to get a satisfactory resolution, thus making it feasible to develop a 2-D solver (which will be five dimensional plus time when the phase space is discretized) on todays computers. The computational results have been compared with those by a Monte Carlo simulation and excellent agreements have been found. The advantage of the current solver over a Monte Carlo solver includes its faster speed, noise-free resolution, and easiness for arbitrary moment evaluations. This solver is thus a useful benchmark to check on the physical validity of various hydrodynamic and energy transport models. Some comparisons have been included in this paper.

2D semiconductor device simulations by WENO-Boltzmann schemes: Efficiency, boundary conditions and comparison to Monte Carlo methods

We develop and demonstrate the capability of a high-order accurate finite difference weighted essentially non-oscillatory (WENO) solver for the direct numerical simulation of transients for a two space dimensional Boltzmann transport equation (BTE) coupled with the Poisson equation modelling semiconductor devices such as the MESFET and MOSFET. We compare the simulation results with those obtained by a direct simulation Monte Carlo solver for the same geometry. The main goal of this work is to benchmark and clarify the implementation of boundary conditions for both, deterministic and Monte Carlo numerical schemes modelling these devices, to explain the boundary singularities for both the electric field and mean velocities associated to the solution of the transport equation, and to demonstrate the overall excellent behavior of the deterministic code through the good agreement between the Monte Carlo results and the coarse grid results of the deterministic WENO-BTE scheme.

A Direct Solver for 2D Non-Stationary Boltzmann-Poisson Systems for Semiconductor Devices: A MESFET Simulation by WENO-Boltzmann Schemes

We present preliminary results of a high order WENO scheme applied to deterministic computations for two dimensional formulation of the transients for the Boltzmann-Poisson system describing electron transport in semiconductor devices. The collisional term models optical-phonon interactions which become dominant under strong energetic conditions corresponding to nanoscale active regions under applied bias. We treat the Boltzmann Transport equation in a spherical coordinate system for the wave-vector space. The problem is three dimensional in the wave-vector space and two dimensional in the physical space, plus the time variable driving to steady states. The new formulation avoids the singularity due to the spherical coordinate system.

A WENO-Solver for the 1D Non-Stationary Boltzmann–Poisson System for Semiconductor Devices

In this work we present preliminary results of a high order WENO scheme applied to a new formulation of the Boltzmann equation (BTE) describing electron transport in semiconductor devices with a spherical coordinate system for the phase velocity space. The problem is two dimensional in the phase velocity space and one dimensional in the physical space, plus the time variable driving to steady states. The new formulation avoids the singularity due to the spherical coordinate system.

Analysis of thermal, sound, and shear waves according to a relativistic kinetic model

In this paper a kinetic model describing a relativistic gas is considered. The collision frequency is assumed to depend upon the particle speed in a way suggested in a previous paper by the authors. The new model has more satisfactory properties than one previously studied. Several results of both analytic and numerical character concerning the sound and heat waves with frequencies comparable to the intermolecular collision frequency are given.

Magnetoacoustic shock waves in a relativistic gas

Fast and slow magnetoacoustic shocks are studied in the framework of relativistic magneto‐fluid dynamics with the Synge equation of state. An approximate analytical solution is presented in a particular case. The general case is treated by numerical methods.

Deterministic kinetic solvers for charged particle transport in semiconductor devices

Statistical models [F91], [L00], [MRS90], [To93] are used to describe electron transport in semiconductors at a mesoscopic level. The basic model is given by the Boltzmann transport equation (BTE) for semiconductors in the semiclassical approximation:

A Discontinuous Galerkin Solver for Full-Band Boltzmann-Poisson Models

\frac{{\partial f}} {{\partial t}} + \frac{1} {\hbar }\nabla _k \varepsilon \cdot \nabla _x f - \frac{\mathfrak{e}} {\hbar }E \cdot \nabla _k f = Q(f),