No. 6, 1997


Vit Novak: Symposion on nonlinear dynamics and pattern formation in semiconductors and plasmas. Preface to the proceedings. 643–722

The papers which follow in this issue summarize oral presentations given during the Symposion on Nonlinear Dynamics and Pattern Formation in Semiconductors and Plasmas in Prague from October 6th to October 8th 1997. All contributions deal with various aspects of a theme they all have in common-self-organization. Indeed, terms like self-organized or self-organizing may be found frequently in contributions of most of the authors. However natural this seems to be regarding the Symposion's title, it is surprising to realize that there is probably no unique definition of the phenomenon of self-organization.

Though already penetrating the common speech, the notion is mentioned only once in all the 32 volumes of the actual edition of Encyclopaedia Britannica: in History of self-organization of Galician Ukrainians [1]. Searching the scientific literature, especially that on nonlinear physics, one can find numerous explanations of what is meant by self-organization in the particular context. Comparing these-rather liberal-definitions the two examples may be picked up to shed light on an important difference. The first one is from Haken [2]: "... system is self-organizing if it acquires a spatial, temporal or functional structure without specific interference from the outside". The second example is taken from Tagg [3]: self-organization is a process, in which some "nonequilibrium systems spontaneously order themselves into cooperative motion with well defined patterns and length scales".

The second definition is more restrictive in one particular point: besides the presence of the characteristic patterns it calls also for the existence of a characteristic length in the pattern. This additional condition reduces the field of self-organization remarkably. Among others, even the almost paradigmatic Benard convective cells are eliminated, since their diameter is controlled in a wide range by the distance of the horizontal plates [4] and no other characteristic lengths can be found in an infinitely extended system. Nevertheless, if the fluid is also constrained by lateral boundaries, a new distinguished class of patterns arises being observable through transparent plates [4], which definitely complies also to the latter definition.

We do not aim to decide on the feasibility of the above mentioned definitions. Instead, we would like to point out one related definitoric problem which has turned out in the course of the vivid discussions during the Symposion: there are two ways in which the notion of "self-organized current filament" is understood and used by different authors. Some define the current filament generally as a high conducting channel embedded in a low conducting environment of the same material, arguing that no specific external force controls the place of filament occurrence. Other authors require the additional condition of characteristic length, considering the above filaments to be merely a pair of fronts. This schism may be encountered throughout these Proceedings, too.

The Proceedings are laid out as follows. First a survey of the experimental techniques available for visualization of the filamentary current flow is presented by Prettl and Novak. Next, Hirschinger et al. report on experimental results obtained in n-GaAs in low temperature breakdown regime. Schwarz and Scholl then review extensively the theoretical works on current filamentation in that regime, including the latest results in simulation of samples with Corbino contact geometry. The contributions of Novak et al. deal with two-dimensional stationary modelling of the current filament, and with experimental determination of the electron mobility inside the current filaments. Oswald et al. present the photoluminescence measurement in the filamentary regime of n-GaAs, and Klimenta and Prettl report on investigations of current filaments in an arc-formed sample in a magnetic field, thus closing the group of contributions concentrated on the low temperature breakdown regime of semiconductors. Finally, self-organized patterns in films of ZnS:Mn are investigated in the paper by Kukuk et al. The seminary talks by Belkov, Muller, and Hlina are not presented in these Proceedings.

Wilhelm Prettl, Vit Novak: Visualization of impact ionization generated current filaments in semiconductors, 647–659

Semiconductors are dissipative systems whose transport properties are governed by nonlinear dynamic processes. In particular high-purity materials are intensively investigated as they are available with low, but well defined and uniform impurity concentrations prepared by modern epitaxial growing techniques. The most important nonlinearity in sufficiently pure semiconductors at low temperatures is the autocatalytic generation of free carriers by impact ionization of shallow impurities. At a critical bias voltage an avalanche breakdown occurs which, under the global constraint of controlled current, causes a phase separation between low- and high-conducting regions due to the spontaneous formation of a current filament. In the present article experimental methods to visualize inhomogeneous filamentary current flow are reviewed. Optical methods are discussed in particular detail because of their technical simplicity. Experimental results demonstrating the potential of these methods are shown for n-GaAs epitaxial layers.

Jurgen Hirschinger, Franz-Josef Niedernostheide, Wilhelm Prettl, Vit Novak, Miroslav Cukr, Jiri Oswald, Helmar Kostial: Current filamentation in n-GaAs samples with different contact geometries, 661–667

The formation of current filaments has been visualized in different contact geometries in the regime of low-temperature impurity breakdown. Independend on the contact geometry filaments appear as high conducting channels with parallel borders. The filament width increases linearly as a function of the sample current. In a normal magnetic field stable filament configurations have been found deflected in direction of the Lorentz-force. For high currents a new regime of S-shaped filaments has been found in samples with point contacts.

Georg Schwarz, Eckehard Scholl: Simulation of Current Filaments in Semiconductors with Point Contacts and Corbino Disks, 669–684

We report recent theoretical advances in the modelling of spatio-temporal dynamics induced by impact ionization of hot electrons in semiconductors. A model for low-temperature impurity breakdown is presented which combines Monte-Carlo simulations of the microscopic scattering and generation-recombination processes with macroscopic nonlinear spatio-temporal dynamics. Different two-dimensional sample geometries including point contacts are considered. In particular we present recent simulations of the nascency of current filaments in Corbino disks.

Vit Novak, Jurgen Hirschinger, Wilhelm Prettl, Franz-Josef Niedernostheide: 2-D stationary model of current filament in point contact geometry, 685–692

Two-dimensional stationary model of breakdown induced current filament is constructed, based on a reduced transport equation and a black-box description of the filament border forming mechanism. Its validity is examined by comparison with experimental results obtained on n-GaAs samples with point and Corbino contact geometry, without and with applied normal magnetic field.

Jiri Oswald, Josef Pastrnak, Otto Petricek, Frantisek Karel, Miroslav Cukr: Luminescence of n-type GaAs breakdown regime, 693–698

Conductivity and luminescence measurements were performed on epitaxial layer of n-doped GaAs, electrically driven into low temperature avalanche breakdown. The dependence of I–V characteristics on the intensity of additional illumination was found. The luminescence intensity of different types of radiative transitions was determined as a function of applied electric field.

Jurgen Hirschinger, Franz-Josef Niedernostheide, Wilhelm Prettl, Vit Novak, Helmar Kostial: Spatial oscillations of current filaments, 699–704

In the regime of low-temperature impurity breakdown in high-purity semiconductors the influence of a magnetic field on current filaments often leads to nonlinear voltage oscillations. Using the quenching of photoluminescence inside filaments the spatial character of magnetic field induced voltage oscillations has been visualized in n-GaAs epitaxial layers, revealing a lateral oscillation of a filament between two point contacts and a rotation of a filament around the center contact in a sample with concentric contacts.

Vit Novak, Jurgen Hirschinger, Wilhelm Prettl, Franz Josef Niedernostheide, Miroslav Cukr, Jiri Oswald: Mobility measurement in current filaments, 705–710

The mobility of electrons inside of current filaments in n-GaAs is investigated with the aid of visualization of galvanomagnetic transport. The obtained values are compared with those of nonfilamentary regime. The Hall factor and its dependence on magnetic field are discussed.

Harald Klimenta, Wilhelm Prettl, Helmar Kostial: Geometry-induced negative magnetoresistance in n-GaAs at filamentary current flow, 711–716

Current-voltage characteristics and self-generated oscillations at filamentary current flow have been investigated as a function of magnetic field in n-GaAs with two different sample geometries. It is shown that filament oscillations are suppressed by pinning of filaments at the sample borders. In arc-shaped samples a geometry induced negative magneto-resistance is observed which is attributed to a competition between one-sided lateral growth of a pinned filament and the usual positive magneto-resistance.

Bernd Kukuk, Sandra Zuccaro, Franz-Josef Niedernostheide, Hans-Georg Purwins: Pattern formation and bifurcations in electroluminescent ZnS:Mn films, 717–722

The spatiotemporal behaviour of electroluminescence distributions and bifurcation sequences in thin ac driven ZnS:Mn films has been investigated. Among stationary filaments, moving strings, and their coexistence, the formation of filament clusters is considered.

Jurgen Hirschinger, Ulrich Margull, Harald Klimenta, Wilhelm Prettl, Helmar Kostial, Vit Novak: Laterally oscillating current-filaments in n-GaAs layers with point contacts, 723–731

The selfgenerated voltage oscillations in high purity n-GaAs layers in the regime of low-temperature impurity breakdown have been investigated under the influence of a perpendicular magnetic field. The detailed analysis of the oscillation character as well as the filament reconstructions obtained by a non-invasive filament imaging technique shows convincingly that one particular type of electrical oscillations can be attributed to lateral spatial oscillations of the current filament.

Viktor Pekarek: Electromagnetic radiation through electron spin, spectrum of the hydrogen atom, 733–740

The spinning motions of the electron are shown to be the possible mechanism producing the electromagnetic radiation in atoms. The energy is emitted through the electron's transitions between the energy states quantized via the spin quantum numbers. Applying the theory to the hydrogen atom, all the classical series of the hydrogen spectrum are calculated with a great precision. The concept removes the well-known drawbacks of the Bohr model, concerning the evalulation of the space integral and radius of the electron trajectory.

Maciej Hajduga, Jaroslav Kucera: Temperature dependence of Fe-wires oxidation in ambient air, 741–757

The oxidation of Fe-wires is investigated as a function of temperature in this paper. Iron samples were oxidized at 940 up to 1100 C in ambient air. The time periods of oxidation varied from 10 to 160 hrs. Weight and size measurements, metallography and chemical microanalysis were used as experimental methods. The time dependence of Fe-wires oxidation obeys exponential law y = A[1 - e-Bt]. The parameters A, B vary with the temperature of oxidation. This temperature dependence may be partly attributed to iron and oxygen interdiffusion in scale and partly to the chemical reactions occurring during the process of iron wires oxidation. Iron remainder in incompletely oxidized sample is calculated on the basis of relative weight gain and mean oxygen concentration in the