At high electric fields negative differential resistance and oscillatory behavior of the current is observed in 2-dimensional electron gases in modulation doped heterostructures. We develop a model in which the understanding of these phenomena is provided by the ohmic contacts to the 2-dimensional electron gas. The key phenomenon is that at a high electric field, well below the threshold field for real space transfer across the interface between the GaAs and the Al xGa1-xAs, injection of electrons from the contacts into the AlxGa 1-xAs layer opens a conductive channel in the AlxGa1-xAs parallel to the 2-dimensional electron gas in the GaAs layer. We show that avalanche ionization in the AlxGa1-xAs layer leads to current filamentation. We studied this behavior for various experimental conditions by means of a novel technique which we developed for this purpose: the technique of time resolved optical beam induced current.