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

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

“…In particular, we demonstrate the capability of our WENO-BTE scheme [3] in giving reliable results for 2D realistic devices. We consider MESFET and MOSFET devices which have served as benchmarks for several other approximating models to device transport simulation, such as hydrodynamic, driftdiffusion, and energy transport solvers that have typically been compared to Monte Carlo results for solving the BTE [1,7].…”

“…We adopt the same fifth order finite difference WENO scheme coupled with a third order TVD Runge-Kutta time discretization to solve (1.10) as that used in our previous work [3]. The fifth order finite difference WENO scheme was first designed in [17], and the third order TVD Runge-Kutta time discretization was first proposed in [24].…”

“…In addition, deterministic solvers provide a tool to compute accurate transient calculations of strong non-statistical equilibrium states as was already shown in [3] for one space dimensional solvers simulating diodes. Our simulations for the two dimensional case indicate that one observes stabilization of moments in time and thus, we use small time variations of the density, current and energy as the code stopping criteria.…”

“…Following the main ideas of [19,2,3], we have introduced in our previous work [4] a suitable dimensionless formulation by a change of variables in the wave vector k that translates the original Boltzmann equation (1.1) in 2D into the following system: we use the coordinate transformation for the momentum vector k 1] is the cosine of the angle with respect to the x-axis and φ ∈ [0, 2π] is the azimuthal angle, respectively. We consider a two dimensional problem in the physical space and we define…”

“…The constant α is the dimensionless phonon energy and the energy mesh has to be chosen properly for computational simplification of the collision kernel computation. For all details and physical constants we refer to works [2,3,4].…”