Reflective Boundary conditions in Discontinuous Galerkin Methods for Boltzmann-Poisson Models of Electron Transport in Semiconductors and Zero Flux Condition for General Mixed Reflection

We shall discuss the use of Discontinuous Galerkin (DG) Finite Element Methods to solve Boltzmann Poisson (BP) models of electron transport in semiconductor devices at nano scales. We consider the mathematical and numerical modeling of Reflective Boundary Conditions in 2D devices and their implementation in DG-BP schemes. We study the specular, diffusive and mixed reflection BC on physical boundaries of the device for the modeling of surface roughness, comparing the influence of these different reflection cases in the computational prediction of moments close to the boundaries and their associated scale. We observe an effect due to diffusivity at the reflection boundaries over the kinetic moments of the probability density function, whose influence is not restricted to the boundaries but rather over the position space domain.