Current filamentation in point contact geometry and its 2D stationary model

Two-dimensional reconstructions of the filamentary current flow are shown, obtained by the spatially resolved photoluminescence of a sample of n-GaAs epitaxial layer with two point contacts. A mathematical model is constructed, based on a bistability of the local conductivity controlled by the local electric field strength. The interface between the high and low conductive states is assumed to occur always at a constant critical value of the field strength. Corresponding mathematical description of the model leads to the nonlinear Laplace free boundary problem. Its two-dimensional numerical solution is shown to satisfactorily reproduce the main characteristics of the filament observed in the experiment.