Nonlinear Oscillations and Chaos in Electrical Breakdown in Ge

Teitsworth, Stephen W.; Westervelt, R. M.; Häller, E. E.

doi:10.1103/physrevlett.51.825

Cited by 158 publications

(39 citation statements)

References 11 publications

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“…Taking into account that we have investigated a variety of different crystal samples and that the basic nonlinear features were observed in all cases, we conclude that the observed nonlinear effects are not linked to a particular acceptor concentration or crystal orientation. These findings are in agreement with similar chaos experiments performed on ultrapure p-Ge by Teitsworth et al [15] and Gwinn and Westervelt [16].…”

Section: System Characterizationsupporting

confidence: 83%

Classification of current instabilities during low-temperature breakdown in germanium

et al. 1989

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Abstract. 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. 05.45. + b, 72.20.Ht, 72.70. + m It is well known that a large number of physical and nonphysical systems show spontaneous formation of spatial or temporal structures as a result of instability. Close to such instability points the dynamics of the system and its emerging structures are determined by a set of, in general, a few collective variables, often called order parameters. The underlying synergetic approach introduced by Haken [1] can explain the unexpected order and coherence arising on the macroscopic scale, regardless of the large number of competing physical forces interacting on the microscopic scale. Motivation for the intensive study of cooperative dynamics and pattern formation phenomena during the past few years derives from an increasing appreciation of the remarkable diversity of behavior encountered in nonlinear systems and of universal features shared by entire classes of similar nonlinear dynamic processes. PACS:So far, it appears that the subject of such complex nonlinear behavior is dominated by theoretical investigations and computer studies, whereas experimental measurements on real physical systems represent the minority. Among the various objects which can be studied experimentally, solid-state turbulence in semiconductors appears particularly interesting [2]. Nonlinear current transport behavior during lowtemperature avalanche breakdown of extrinsic germanium comprises the self-sustained development of spatio-temporal dissipative structures in the formerly homogeneous semiconductor [3]. This kind of nonequilibrium phase transition between different conducting states results from the autocatalytic nature of impurity impact ionization generating mobile charge carriers [4]. The simple and direct experimental accessibility via advanced measurement techniques favors semiconductors as a nearly ideal study object for complex nonlinear dynamics compared to other physical systems. Further representing a convenient model reaction-diffusion system that exhibits distinct universal features, the present semiconductor system may acquire general significance for many synergetic systems in nature. Finally, in view of the rapidly growing application of semiconductor technologies, the understanding, control, and possible exploitation of sources of instability in these systems have considerable practical importance. This paper gives a classification of our experimental investigations on the spatio-temporal nonlinear current flow in the post-breakdown regime of p-germanium at liquid-helium temperatures. Section 1 briefly outlines an example of a set of nonlinear current instabilities obtained from our semiconductor system. Section 2 reports the characterization of the basic...

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Section: System Characterizationsupporting

confidence: 83%

Classification of current instabilities during low-temperature breakdown in germanium

et al. 1989

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“…Many of these phenomena have been successfully explained by means of a drift-diffusion model which includes impurity trapping of mobile holes and impact ionization of neutral acceptors [6,13]. Although much work has been done on this model problem (see [14] and references therein), important basic questions concerning its asymptotic description and chaos under time independent voltage bias are still open.…”

Section: Introductionmentioning

confidence: 99%

“…We focus here on a model of electrical conduction in extrinsic semiconductors (involving time and only one spatial dimension) which exhibits negative differential resistance (NDR) and moving domains of high electric field. The model is specifically relevant to experiments on cooled bulk p-type Ge under voltage bias conditions, [6,7], but much of the observed qualitative behavior applies to a broad class of semiconductor systems with space charge instabilities. Phenomena observed for the p-Ge system include time-periodic oscillation of the current in a purely resistive external circuit under dc voltage bias due to the periodic creation of a solitary wave at the injecting contact, its motion inside the semiconductor and its annihilation at the receiving contact [7].…”

Section: Introductionmentioning

confidence: 99%

Chaotic motion of space charge wave fronts in semiconductors under time-independent voltage bias

et al. 2001

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A standard drift-diffusion model of space charge wave propagation in semiconductors has been studied numerically and analytically under dc voltage bias. For sufficiently long samples, appropriate contact resistivity and applied voltage -such that the sample is biased in a regime of negative differential resistance -we find chaos in the propagation of nonlinear fronts (charge monopoles of alternating sign) of electric field. The chaos is always low-dimensional, but has a complex spatial structure; this behavior can be interpreted using a finite dimensional asymptotic model in which the front (charge monopole) positions and the electrical current are the only dynamical variables.

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“…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].…”

mentioning

confidence: 99%

“…For the materials used in the experiments in [14] and [18], relevant time scales are those corresponding to impurity trapping. Such scales are so slow (milliseconds) that the displacement current is negligible, which means that the charge density distribution is quasi-stationary.…”

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confidence: 99%

Numerical Study of Hyperbolic Equations with Integral Constraints Arising in Semiconductor Theory

Carpio¹,

Hernando²,

Kindelán³

2001

SIAM J. Numer. Anal.

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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.

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Nonlinear Oscillations and Chaos in Electrical Breakdown in Ge

Cited by 158 publications

References 11 publications

Classification of current instabilities during low-temperature breakdown in germanium

Classification of current instabilities during low-temperature breakdown in germanium

Chaotic motion of space charge wave fronts in semiconductors under time-independent voltage bias

Numerical Study of Hyperbolic Equations with Integral Constraints Arising in Semiconductor Theory

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