We present an asymptotic analysis of the Gunn effect in a driftdiffusion model-including electric-field-dependent generation-recombination processes-for long samples of strongly compensated p-type Ge at low temperature and under dc voltage bias. During each Gunn oscillation, there are different stages corresponding to the generation, motion and annihilation of solitary waves. Each stage may be described by one evolution equation for only one degree of freedom (the current density), except for the generation of each new wave. The wave generation is a faster process that may be described by solving a semiinfinite canonical problem. As a result of our study we have found that (depending on the boundary condition) one or several solitary waves may be shed during each period of the oscillation. Examples of numerical simulations validating our analysis are included.

We present and numerically solve a model of the photorefractive Gunn effect. We find that high field domains can be triggered by phase-locked interference fringes, as it has been recently predicted on the basis of linear stability considerations. Since the Gunn effect is intrinsically nonlinear, we find that such considerations give at best order-of-magnitude estimations of the parameters critical to the photorefractive Gunn effect. The response of the system is much more complex including multiple wave shedding from the injecting contact, wave suppression and chaos with spatial structure. 72.20.Ht, 42.70Nq

Abstract. An efficient numerical scheme is described for the solution of certain types of nonlinear hyperbolic equations with an integral constraint which are used to model the Gunn effect in semiconductors with impurity capture. We analyze the stability and convergence properties of the scheme and present the results of numerical simulations. Depending on the value of the parameters defining the problem, a great variety of solutions are obtained, including periodic recycling of solitary waves and chaotic regimes.Key words. Gunn effect, oscillations, chaos, numerical simulation, stability, convergence AMS subject classifications. 35L70, 39A11, 65M06, 65M12, 65C20 PII. S00361429993602871. Introduction. Pattern formation and oscillatory phenomena involving recycling and motion of charge dipole waves have often been observed in semiconductors displaying nonlinear electrical conduction. These phenomena were first observed by Gunn [9] in bulk n-type GaAs for which the electron velocity is an N-shaped function of the electric field. When planar contacts are attached to an n-GaAs sample and an appropriate dc voltage bias is kept between them, there appear self-sustained oscillations of the current with frequencies in the microwave range. These oscillations are accompanied by periodic recycling and motion of charge density dipole waves (solitary waves of the electric field).After Gunn's discovery, many materials were shown to have similar current selfoscillations, although the physical mechanisms causing the oscillations were often very different. However, all these materials had N-shaped current-voltage characteristics, which is an essential feature of the Gunn effect (see [2]). N-shaped current-voltage characteristics can appear due to impurity capture processes; such is the case in pGe [19] and many other semiconductors [16]. Precise measurements of the Gunn effect in p-Ge are reported in [14] and [18]. Experiments show that intermittency and spatiotemporal chaos are observed in addition to the usual time periodic oscillations [14].The Gunn effect and other instabilities of the current have been studied by analyzing models of charge transport in semiconductors (see [16], [17]). For bulk semiconductor devices, charge transport may be described by the semiclassical Boltzmann equation or hydrodynamic or drift-diffusion models. Each class of models describes phenomena occurring at a different length and time scales [17]. For sufficiently large devices, hydrodynamic or drift-diffusion descriptions are appropriate and involve less computational cost.

Carbohydrate-coated nanoparticles—glyconanoparticles—are finding increased interest as tools in biomedicine. This compilation, mainly covering the past five years, comprises the use of gold, silver and ferrite (magnetic) nanoparticles, silicon-based and cadmium-based quantum dots. Applications in the detection of lectins/protein toxins, viruses and bacteria are covered, as well as advances in detection of cancer cells. The role of the carbohydrate moieties in stabilising nanoparticles and providing selectivity in bioassays is discussed, the issue of cytotoxicity encountered in some systems, especially semiconductor quantum dots, is also considered. Efforts to overcome the latter problem by using other types of nanoparticles, based on gold or silicon, are also presented.