Pattern formation in S-shaped negative differential conductivity material

To study the electrical current density and the potential distribution inS-shaped negative differential conductivity materials, a theoretical model is developed which is based upon the introduction of an interface dividing the material into two parts of different electrical behaviour. This interface model which leads to a set of coupled nonlinear evolution equations for two physical quantities at the boundary layer is that of an activator inhibitor type as used to describe self-controlled processes in chemistry and biology. Numerical calculations of inhomogeneous stationary states are presented for various parameters. From the numerical calculations these states are found to be stable with respect to small variations of the parameters (structure-stability) and fluctuations of the dependent variables. The model is confirmed by experiments performed on silicon pin diodes. The measured potential distribution is in a good qualitative agreement with the theoretical calculations.