Subband diffusion models for quantum transport in a strong force regime

We derive semiclassical approximations to quantum transport models in thin slabs with applications to SOI (silicon oxide on insulator)-type semiconductor devices via a subband approach. In the regime considered, the forces acting on the particles across the slab are much larger than the forces in the lateral direction of the slab. In a semiclassical limit the transport picture can be described on large time scales by a system of subband convection-diffusion equations with an interband collision operator, modeling the transfer of mass (charge) between the different eigenspaces and driving the system towards a local Maxwellian equilibrium.