Abstract
We review the modeling and simulation of electrical transport instabilities in semiconductors with a special emphasis on recent progress in the application to semiconductor microstructures. The following models are treated in detail: (i) The dynamics of current filaments in the regime of low-temperature impurity breakdown is studied. In particular we perform 2D simulations of the nascence of a filament upon application of a bias voltage. (ii) Vertical electrical transport in layered semiconductor structures like the heterostructure hot electron diode is considered. Periodic as well as chaotic spatio-temporal spiking of the current is obtained. In particular we find long transients of spatio-temporal chaos preceding regular spiking.