A deterministic solution method for the coupled system of transport equations for the electrons and phonons in polar semiconductors

Mathematical properties of a kinetic transport model for carriers and phonons in semiconductors

“…It is based on an upwind scheme, so that the stability of the numerical technique can be achieved. For more details on the discretized force term used, we refer to [8].…”

“…Additionally, a phonon-phonon relaxation term is included in the phonon equations of our multigroup transport model, which is based on a relaxation time approximation. Details on this interaction term are found in [8]. The phonon relaxation time τ L is obtained from a spectroscopically fitted two-channel-decay formula [15]:…”

“…The collision coefficients A xy ij→ab , E xy ij→ab and C ij→ab can be evaluated analytically, as it is shown, for instance, in [8].…”

“…We study the spatially homogeneous case with vanishing electric field, but we construct the multigroup equations in a way that they allow the description of particle distributions of arbitrary anisotropy with respect to a main direction imposed, for example, by an electric field. Hence, the transport model can easily be extended to describe field dependent, spatially inhomogeneous problems by including multigroup formulations of the advection terms in the BBP equations following the procedures given in [7], [8]. A deterministic transport model is the more reliable, the more mathematical properties the model equations and the original BBP equations possess in common grounds.…”

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

“…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 refer to [8,6,9] for previous and alternative attempts for developing 1D deterministic solvers for BTE.…”