Onset of the Gunn effect in semiconductors: bifurcation analysis and numerical simulations

In this note, the onset of the Gunn effect in the classical 1D unipolar drift-diffusion model is investigated through a Hopf bifurcation analysis of the spontaneous current oscillation. It is found that in the case that the dimensionless semiconductor length is of order unity the bifurcation is supercritical, and becomes subcritical for dimensionless lengths above a certain critical value.