J. Peinke

Spatially resolved observation of current filament dynamics in semiconductors

Abstract Two-dimensional imaging of the nucleation and the dynamics of current filaments generated in homogeneous p -doped germanium at 4.2 K during impurity impact ionization induced avalanche breakdown has been performed. The images were obtained by scanning the specimen surface with an electron beam and by recording the beam-induced current change in the voltage-biased samples. This new method is expected to identify in particular the filament configurations showing chaotic temporal resistance behavior.

Spontaneous oscillations and chaos in p-germanium

Abstract We have observed spontaneous oscillations and the transition to chaos in the post-breakdown regime of p-Ge at temperatures between 1.7 and 4.2 K. At least three different routes to chaos were found.

A p-Ge semiconductor experiment showing chaos and hyperchaos

Abstract A p-Ge semiconductor experiment is investigated by the help of both probabilistic and dynamical characterization methods. Dimensions, Lyapunov exponents, and the corresponding scaling functions are calculated. Two exemplary files of data from the p-Ge semiconductor experiment exhibiting spontaneous (i.e., undriven) resistance oscillations in the low-temperature avalanche breakdown are shown to be chaotic and hyperchaotic, respectively. For the first file, we obtained a fractal dimension between two and three and one positive Lyapunov exponent, whereas for the second file we found a fractal dimension between three and four and two positive Lyapunov exponents. Adopting the terminology introduced by Rossler, the behavior corresponding to the latter file is called hyperchaotic. Furthermore, using the language of the thermodynamical formalism, the probabilistic scaling function evaluated for the hyperchaotic state indicates a phase-transition-like-behavior.

Resonance imaging of dynamical filamentary current structures in a semiconductor

Abstract The spatially resolved observation of the nonlinear dynamical behavior of spontaneous current oscillations obtained during low-temperature avalanche breakdown of homogeneously p-doped germanium is reported. Stationary current filaments developing in the breakdown regime through impurity impact ionization were observed two-dimensionally by means of a scanning electron microscope equipped with a liquid-helium cryostage. Further, spontaneous current oscillations showing typical transitions to chaos were localized two-dimensionally by means of a novel resonance imaging technique, which provides spatially resolved analysis of the nonlinear dynamical behavior. From these measurements different oscillation frequencies were clearly identified as spatially separated oscillation centers localized along the stationary current filaments. The electron beam was demonstrated to act as an exemplary control parameter, which can be manipulated both spatially and temporally.

Determination of electric transport properties in the pre- and post-breakdown regime ofp-germanium

Conductivity and Hall-effect measurements were performed on single-crystallinep-doped germanium, electrically driven into low-temperature avalanche breakdown via impurity impact ionization. The electric transport properties were determined as a function of the applied electric field in the pre- and post-breakdown regime. The characteristic field dependence of the carrier density, mobility, and drift velocity was found to be reflected in smooth variations of the integral current flow. The breakdown mechanism was demonstrated to involve a mobility which sensitively depends upon the density of the mobile charge carriers. Our experimental findings are qualitatively explained by simple model approaches developed from established breakdown theories.

Spatial and Temporal Current Instabilities in Germanium

Current filamentation and chaotic temporal resistance behavior generated in homogeneously p-doped germanium during low-temperature avalanche breakdown have been investigated. Spontaneous current oscillations showing typical chaotic scenarios were found under tiny variation of distinct control parameters (d.c. bias voltage, transverse magnetic field, temperature). By means of a scanning electron microscope equipped with a liquidhelium stage, two-dimensional imaging of current filaments has been performed. In particular, the filament nucleation and the subsequent growth processes could be resolved. Furthermore, the origin of the spontaneous oscillations was found to be closely linked to the formation of the current filament pattern.

Spatial correlations of chaotic oscillations in the post-breakdown regime of p-Ge

Abstract Spatial correlations and long-range crosstalk of chaotic behaviour between two electrically separated parts of a single p-Ge crystal at 4.2 K are investigated and theoretically explained in terms of energy relaxation oscillations of two hot carrier subsystems, driven by impact ionization, and coupled by phonons.

A simple morphogenetic reaction-diffusion model describing nonlinear transport phenomena in semiconductors

Originally designed to account for the main phenomena of symmetry-breaking morphogenesis, the well-known Rashevsky-Turing theory is a prototype model of many different synergetic systems in nature. The simplest version of Turings model can be realized by a two-cellular symmetrical reaction-diffusion system, consisting of two cross-inhibitorily coupled, potentially oscillating two-variable subsystems (4-D flow). We present numerical evidence of symmetry-breaking nonequilibrium phase transitions from “phase-locked” coherent to “phase-lagged” differentiated behavior of the two subsystems. We further investigate the structural change of the system flow from stable morphogenesis to boiling-type turbulence. Finally, we present experimental evidence that the spatiotemporal nonlinear behavior of impurity-impact-ionization-induced avalanche breakdown in semiconducting germanium can be described qualitatively by the present 4-D reaction-diffusion model.

Positive and Negative Differential Resistance in Electrical Conductors

A phase transition from one conducting state to another and the appearance of positive and negative differential resistance in the current-voltage characteristic is investigated experimentally for the gap instability in nonequilibrium superconductors and the avalanche breakdown in extrinsic semiconductors. Additional observation of spatial current structures in the transition regime of both solid-state systems stimulates a simple model approach connecting these spatial patterns to the measured current-voltage characteristics. Based on the underlying experimental situations considered, our model is extended to the framework of four substantial cases.

Imaging of spatio-temporal structures in semiconductors

Abstract Starting from a characterization of the spatio-temporal behavior of different semiconductor systems based upon the impact ionization of shallow impurities by hot charge carriers, we present experimental results concerning imaging of both stationary and dynamical structures by means of low-temperature scanning electron microscopy.