Bifurcation Scenarios of Spatio-temporal Spiking in Semiconductor Devices

Various semiconductor devices with an S-shaped current-voltage characteristic exhibit complex self-organized spatio-temporal spiking where a current lament nu-cleates and vanishes immediately afterwards. We analyze a simple generic model for this type of behaviour, and nd a variety of scenarios where stationary laments , homogeneous relaxation oscillations, periodic spiking and chaotic spiking (via period-doubling or intermittency) occur, including bistability between spiking and a stable lament. Fourier and Lyapunov spectra and Kaplan-Yorke dimensions are provided. Semiconductor devices with S-shaped negative diierential conductivity often exhibit lamentary current transport, when they are operated under current controlled conditions in the middle branch of the current-density eld characteristic. In a current lament the current density is not distributed homogeneously over the cross section of the device, but two well-separated areas with high and low current density, respectively, coexist. Frequently, this lamenta-tion process is associated with complex self-organized dynamical behaviour. Symanczyk, Gaelings and JJ ager 1] have reported spontaneous current and voltage oscillations close to the rst jump in the current-voltage characteristic of pin diodes. By measuring the spatial distribution of the surface potential, which is connected with the local current density, they proved that these oscillations are caused by current laments switching on and oo. Similar behaviour has been reported in various semiconductor systems like bulk n-GaAs and p-Ge in the regime of impurity impact ionization breakdown 2,3] and pnpn devices 4]. We call this behaviour spatio-temporal spiking. Theoretically, it has been described in Ref..5,6] for a speciic model system consisting of a GaAs/AlGaAs heterojunction, the Heterostructure Hot-Electron Diode (HHED).