Next, the semiconductor equations for variable lattice temperature are described which are derived from the BOLTZMANN transport equation. Some used approximations are discussed together with their effects in device simulation. The influence of the equations is discussed in respect to the selfheating effects.

The following section deals with the discretization of the lattice heat flow equation. The required thermal boundary conditions are discussed. The transient behaviour of the self heating effects is explained, especially the critical cases of high- and low frequency thermal simulations.

The next chapters deal with typical lattice temperature dependent models. The classical recombination model in case
of stationary and transient simulation and the implementation in the device simulator *MINIMOS-NT* is discussed. The
influence of the model is shown using a device leakage current simulation.

The next section describes the models of *``Trap Assisted Tunneling''* and *``Band to Band Tunneling''* as
well as their lattice temperature dependence. An essential part of this thesis deals with impact ionization in
semiconductors. Typical models which are used in the drift-diffusion- and hydrodynamic formalisms are discussed
together with their approximations.

All discussed models are finally applied using devices of n-channel MOSFETs and breakdown diodes. In this context a detailed discussion of carrier heating within the hydrodynamic model is given. This includes possible cooling effects which are caused by the generation models.

The last chapter deals with numerical aspects. Some convergence criteria are discussed together with strategies for
error detection. This is in context with the implementation of new models or new equation systems in the device
simulator *MINIMOS-NT*.

1998-10-09