Coupling and thermal effects in semiconductor devices

In this thesis we deal with two different aspects of the theory that describes the semiconductor devices. A first aspect concerns a system of partial diàƒ à,¯àƒ à,¬ erential-algebraic equations which model an electric network containing semiconductor devices. The zero-dimensional diàƒ à,¯àƒ à,¬ erential-algebraic network equations are coupled with multi-dimensional elliptic partial differential equations which model the devices. For the network equations we treat two different cases: index-1 and index-2, and for these two kinds of coupled model we prove an existence result. The other aspect that we have considered is the modelling of thermal effects in a semiconductor device. For this aspect we consider a MEP hydrodynamical model obtained from a set of transport equations for the distribution functions of electrons in conduction band and phonons. We assume that the MEP model contains equations for the electron density fluxes and energy fluxes, and for the phonons energy fluxes. For this system we introduce a small parameter, related to the transition probabilities in the collision terms, and a diffusive scaling at the level of the Lagrangian multipliers appearing in the closure relations. In the diffusive limit, as the small parameter tends to zero, we obtain a model that can be physically interpreted in the framework of linear irreversible thermodynamics.