Experimental progress in the nonlinear behavior of semiconductors

During the past five years spontaneous oscillations and chaotic behavior have been observed in the electronic transport of many semiconductors. Whereas the temperature range of some experiments extends up to room temperature, the majority of the measurements have been performed at liquid helium temperatures. We summarize these experimental developments and discuss their impact on the field of nonlinear dynamics which is rapidly progressing at present.  

Stochastic method for in-situ damage analysis

We are going to apply dissipative energy method, considered as perturbation method, in order to investigate the effects of electron-optical phonon coupling on the electronic transport of armchair single wall carbon nanotubes. This method almost deals with the modeling of the behavior of electrons near ballistic regime. The results of calculations indicate that this model can be applied in estimating the current and the differential conductance of the armchair single-wall carbon nanotubes at low bias; however the perturbation method fails to reproduce the current and differential conductance at high voltages. Furthermore, this approach suggests a method that the observation of phonon energy modes involved in electron-phonon coupling becomes possible experimentally at low temperature.  

A Generalization of Scaling Models of Turbulence

We report on some implications of the theory of turbulence developed by V. Yakhot (Phys. Rev. E 57(2):1737, 1998). In particular we focus on the expression for the scaling exponents ζ _n . We show that Yakhot’s result contains three well known scaling models as special cases, namely K41, K62 and the theory by V. L’vov and I. Procaccia (Phys. Rev. E 62(6):8037, 2000). The model furthermore yields a theoretical justification for the method of extended self-similarity (ESS).  

Drift and diffusion based models of driver behavior

Based on experimental data taken from a driving simulator, we present different ways of how a stochastic model of the driver’s behavior can be estimated directly from the data. The aim is to generate a drift and diffusion based stochastic model, which is equivalent to a potential based model. Depending on the data, different strategies are presented. Even in the case of non-equidistant or transient data, the method will be used to estimate appropriate models in one or higher dimensions.  

Small scale behavior of financial data

A new approach is presented to describe the change in the statistics of the log return distribution of financial data as a function of the timescale. To this purpose a measure is introduced, which quantifies the distance of a considered distribution to a reference distribution. The existence of a small timescale regime is demonstrated, which exhibits different properties compared to the normal timescale regime for timescales larger than one minute. This regime seems to be universal for individual stocks. It is shown that the existence of this small timescale regime is not dependent on the special choice of the distance measure or the reference distribution. These findings have important implications for risk analysis, in particular for the probability of extreme events.  

Regeneration of stochastic processes: an inverse method

We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, even at the early stages of the disease development.  

Stochastic analysis of different rough surfaces

This paper shows in detail the application of a new stochastic approach for the characterization of surface height profiles, which is based on the theory of Markov processes. With this analysis we achieve a characterization of the scale dependent complexity of surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method is applied to several surfaces with different properties, for the purpose of showing the utility of this method in more detail. In particular we show evidence of the Markov properties, and we estimate the parameters of the Fokker-Planck equation by pure, parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction of the conditional probability density functions. The results are compared with those from the analysis of multi-affine and extended multi-affine scaling properties which is often used for surface topographies. The different surface structures analysed here show in detail the advantages and disadvantages of these methods.Received: 5 April 2004, Published online: 12 October 2004PACS: 02.50.-r Probability theory, stochastic processes, and statistics - 02.50.Ga Markov processes - 68.35.Bs Surface structure and topography of clean surfaces  

Logarithmic frequency scaling of semiconductor oscillations caused by a modified saddle-node bifurcation on a limit cycle

The oscillatory behavior of low-temperature impact ionization breakdown inp-type germanium is investigated experimentally. We explain the anomalous scaling behavior of a saddle-node bifurcation on a limit cycle in terms of a simple model approach. It represents the low-dimensional analog to a new type of intermittency proposed recently.  

Electron-beam induced instability during filamentary current transport inn-GaAs

We report experimental investigations on the current transport ofn-GaAs under the conditions of impact ionization avalanche breakdown at low temperatures. The spontaneous formation of a single current filament was observed by means of low-temperature scanning electron microscopy. An electron-beam induced instability occurs at the onset of filamentation. We demonstrate this instability to be due to the local disturbance at the boundaries of the current filament. Our results are compared to the similar behavior ofn-GaAs under IR irradiation (firing wave instability).  

Classification of current instabilities during low-temperature breakdown in germanium

We present experimental investigations on the spatio-temporal nonlinear current flow in the post-breakdown regime of p-germanium at liquid-helium temperatures. The basic nonlinear effects are characterized in terms of the underlying semiconductor physics, taking into account the influence of different experimental parameters.