Bifurcation analysis of stationary and oscillating domains in semiconductor superlattices with doping fluctuations

We investigate the effects of frozen-in spatial fluctuations of the doping density on the different forms of spatiotemporal pattern formation found in weakly coupled $n$-doped superlattices as described by a simple microscopic model. For heavy doping, multistable field domains are observed, while for lower doping space-charge oscillations are found. The corresponding bifurcation scenarios are discussed. We demonstrate that there occurs a qualitative change once the degree of disorder exceeds a certain threshold. For the case of moderate disorder and heavy doping, a direct correlation between the peak current of each branch of the current-voltage characteristic and the doping density in the corresponding quantum well is derived and applied to analyze a measured characteristic.