In this paper a system of evolution equations for energy models of a semiconductor device is derived in a deductive way from a generally accepted expression for the free energy. Only first principles like the entropy maximum principle and the principle of partial local equilibrium are applied. Particular attention is paid to the inclusion of the electrostatic potential self-consistently. Dynamically ionized trap levels and models with carrier temperatures are regarded. The system of evolution equations has a Lyapunov function due to its compatibility with the corresponding entropy balance equation that contains a positively definite entropy production rate.

No abstract

In this paper we deal with equations modelling the transport of electrically charged species in heterostructures by diffusion, drift and reaction processes. We show that for such models the free energy decays monotonously and exponentially to its equilibrium value. For this purpose we prove an estimate of the free energy from above by the corresponding dissipation rate. Exactly the same results are obtained for the fully implicit discrete‐time scheme.

In this paper we prove a global existence result for pair diffusion models in two dimensions. Such models describe the transport of charged particles in semiconductor heterostructures. The underlying model equations are continuity equations for mobile and immobile species coupled with a nonlinear Poisson equation. The continuity equations for the mobile species are nonlinear parabolic PDEs involving drift, diffusion, and reaction terms; the corresponding equations for the immobile species are ODEs containing reaction terms only. Forced by applications to semiconductor technology, these equations have to be considered with nonsmooth data and kinetic coefficients additionally depending on the state variables.Our proof is based on regularizations, on a priori estimates which are obtained by estimates of the free energy and by Moser iteration, as well as on existence results for the regularized problems. These are obtained by applying the Banach fixed point theorem for the equations of the immobile species, and the Schauder fixed point theorem for the equations of the mobile species.

This paper demonstrates simulation tools for edge-emitting multi quantum well (MQW) lasers. Properties of the strained MQW active region are simulated by eight-band kp calculations. Then, a 2D simulation along the transverse cross section of the device is performed based on a drift-diffusion model, which is self-consistently coupled to heat transport and equations for the optical field. Furthermore, a method is described, which allows for an efficient quasi 3D simulation of dynamic properties of multisection edge-emitting lasers.