Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices: Proceedings of a Symposium Organized Along with the International Conference on Nonlinear Dynamics and Pattern Formation in the Natural Environment Noordwijkerhout, The Netherlands, J

278 Pages·1995·3.57 MB·English

by  L. L. Bonilla (auth.)

Springer
Proceedings in Physics 79
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Volumes 1-45 are listed at the end of the book
F.-J. Niedemostheide (Ed.)
Nonlinear Dynamics
and Pattern Formation
in Semiconductors
and Devices
Proceedings of a Symposium Organized Along with
the International Conference
on Nonlinear Dynamics and Pattern Formation
in the Natural Environment
Noordwijkerhout, The Netherlands, July 4-7, 1994
With 168 Figures
Springer
Dr. Franz-Josef Niedemostheide
Institut fUr Angewandte Physik
CorrensstraBe 2/4
0-48149 Miinster, Germany
ISBN-13 :978-3-642-79508-4 e-ISBN-13:978-3-642-79506-0
DOl: 10.1007/978-3-642-79506-0
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Preface
This volume contains the contributions given at the symposium about Nonlinear
Dynamics and Pattern Formation in Semiconductors and Devices in the frame of
the International Conference on Nonlinear Dynamics and Pattern Formation in
the Natural Environment (ICPF'94) held at Noordwijkerhout, the Netherlands
July 4-7, 1994. As the conference aimed at the communication of new results
and the exploration of new ideas concerning the theory of nonlinear dynamics
and the study of pattern generating phenomena in diverse biological, chemical
and physical systems, the central issues discussed during the semiconductor
symposium involved fundamental self-organization processes and the physics of
electrical instabilities in semiconductors and semiconductor devices.
One of today's most challenging questions concerns the understanding of
evolution of life. This in turn entails the question of how and on what condi
tions patterns may arise from spatially uniform distributions and which minimal
ingredients are necessary to achieve an aspired degree of complexity. In the
last decades great progress in investigating this matter has been made in many
fields of sciences, and fundamental concepts and basic mechanisms leading to
the spontaneous appearance of spatial, temporal and spatia-temporal patterns
have been developed. It turned out that many of the basic mechanisms appear
in entirely different systems and, consequently, a concept worked out for the de
scription of pattern formation in one system very often can be applied to a whole
class of systems including systems of other fields. However, many questions are
still unsolved and sometimes we are even far from a complete understanding of
systems appearing very simple on a first view.
In comparison with biological or chemical systems, physical systems have a
great advantage concerning preparation, handling, and parameter controlling.
Among the physical systems, semiconductors and semiconductor devices are
most suitable for investigations concerning self-organization and pattern for
mation because, on the one hand, a mature technology for their production is
available and many theoretical works concerning the understanding of the micra
scopic processes have been done. On the other hand, two basic presuppositions
for the evolution of dissipative structures, the existence of nonlinearities and the
possibility to force the system into a state far from equilibrium, can be achieved
in semiconductors in manifold ways, leading to a huge variety of spatiotemporal
patterns reaching from simple stationary kinks, solitary structures or periodic
patterns over structures showing regular dynamic behaviour as the propaga
tion of fronts, various oscillation modes of localized structures, target or spiral
patterns to complex spatiotemporal patterns as chaotic oscillations of localized
structures or irregular wavepatterns. The contributions included in this volume
VI Preface
take up many of these phenomena and discuss various mechanisms for pattern
formation being of importance not only for semiconductors and devices.
The articles are organized in the following way. In the first four chapters
the main attention is focussed on the development of models describing pat
tern formation in semiconductors and devices. Specific models concerning the
dynamics of electric field domains in superlattices (Chapt. 1 and Chapt. 2), cur
rent filaments in heterostructures (Chapt. 2) and nonlinear waves in extrinsic
semiconductors (Chapt. 3) are presented and a survey of the properties of cur
rent filaments and field domains is given (Chapt. 4). In the next five chapters,
the emphasis is on experiments. The contributions deal with complex spatiotem
poral luminescence patterns in a two-dimensional excitable medium consisting
of a II-VI compound (Chapt. 5), nonlinear behaviour in organic and anor
ganic crystals (Chapt. 6) and current filaments in gallium arsenide (Chapt. 7).
Furthermore, stationary and dynamic patterns of current filaments and various
bifurcation sequences in silicon ~n-~n (Chapt. 8) and ~i-n devices (Chapt. 9)
are studied and corresponding models are developed. The last two chapters fo
cus on possible applications of nonlinear phenomena. By means of low frequency
oscillations appearing spontaneously, e. g., in II I-V compounds, deep levels in
semiconductors are analyzed (Chapt. 10) and the application of maximum and
minimum detectors based on the winner-takes-all mechanism is proposed for
optical pattern recognition and optical fuzzy logic computing (Chapt. 11).
I would like to thank the organizers of the ICPF'94, Prof. A. van Harten and
Dr. A. Doelman, for their invitation to organize the semiconductor-symposium
as part of the ICPF'94 and Dr. H. Lotsch from Springer-Verlag for his excellent
cooperation.
Munster,
December 1994 F.-J. Niedernostheide
Table of Contents
1 Dynamics of Electric Field Domains in Superlattices
by L.L. Bonilla 1
1.1 Introduction.................... 1
1.2 Steady States . . . . . . . . . . . . . . . . . . . 5
1.2.1 Undoped Photoexcited SL, v = 0,1> 0 7
1.2.2 Doped SL, v > 0, 1 ~ 0 . . . . . . . . . 7
1.3 Phase Diagram and PC Time-Dependent Oscillations. 7
1.3.1 Undoped Photoexcited SL, v = 0,1> 0 7
1.3.2 Doped SL, v > 0, 1 ~ 0, 0 < c < 1 11
1.4 Asymptotics.. 13
1.5 Final Remarks ............... 18
2 Oscillatory Transport Instabilities and Complex
Spatio-Temporal Dynamics in Semiconductors
by E. Scholl, A. Wacker 21
2.1 Introduction........................... 21
2.2 Current Filaments in Crossed Electric and Magnetic Fields 23
2.3 Spiking in Layered Semiconductor Structures 30
2.3.1 Modelling the Dynamic Behaviour 31
2.3.2 Results ......... 33
2.4 Field Domains in Superlattices 36
2.4.1 The Model ....... 36
2.4.2 Static Characteristic . . 38
2.4.3 Spatia-Temporal Oscillations 40
2.5 Conclusions.............. 42
3 Space Charge Instabilities and Nonlinear Waves in Extrinsic
Semiconductors
by S. W. TeitstDorth, M.J. Bergmann, L.L. Bonilla 46
3.1 Introduction..................... 46
3.2 Full Rate Equation Model . . . . . . . . . . . . . 48
3.3 Non-Dimensionalization and the Reduced Model 51
VIII Table of Contents
3.4 The Case of Time-Independent (dc) Current Bias .. 54
3.4.1 Steady States and the J-E Curve ..... . 54
3.4.2 Periodic, Solitary and Monotone Wave Solutions 56
3.4.3 Dynamical Stability of Periodic, Solitary and Monotone
Waves ............... . 58
3.5 The Case of dc Voltage Bias . . . . . . . . . 60
3.5.1 Position-Dependent Steady States . 60
3.5.2 Numerical Studies of Solitary Waves 62
3.5.3 Stability Analysis and Hopf Bifurcations from the Steady
State ..... 66
3.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Autosolitons in Form of Current Fihunents and Electric Field
Domains in Semiconductors and Devices
by B.S. Kerner 70
4.1 Introduction.............................. 70
4.2 Formation of Current Filaments and Electric Field Domains in
Semiconductors with Positive Differential Conductivity. 72
4.2.1 Current Filaments in Transistor Structures ... 72
4.2.2 Multi-Filament Current States in Reverse-Biased
P-N Structures . . . . . . . . . . . . . . . . . . . 74
4.2.3 Current Filaments in Dense Electron Hole-Plasmas. 77
4.2.4 Electric Field Domains in Hot Electron Hole-Plasmas 80
4.3 Local Active and Damping Processes. Concept of "Activator"
and "Inhibitor" . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83
4.3.1 Possibility of the Appearance of Current Filaments or Elec-
tric Field Domains and Form of the Current-Voltage Char-
acteristic of Semiconductors . . 84
4.3.2 An Activator-Inhibitor Model. 86
4.4 Autosolitons in Semiconductors . . . 86
4.4.1 Form of Autosolitons . . . . . 86
4.4.2 Basic Types of Autosolitons . 89
4.5 Some Properties of Autosolitons .. 96
4.5.1 Main Types of Self-Organization Phenomena 96
4.5.2 "Nucleation Centre" for the Spontaneous Formation of
Autosolitons in Semiconductors . . . . . . . . . . . . . .. 97
4.5.3 Effects Determining the Evolution of Autosolitons .... 99
4.5.4 Processes of Random Appearance and Disappearance of
Autosolitons ......................... 103
4.5.5 Transitions Between Different Types of Autosolitons . . . 103
4.5.6 On Mechanisms of Spatiotemporal Chaos (Turbulence) in
Semiconductors . 105
4.6 Conclusions.............................. 106
Table of Contents IX
5 Pattern Formation of the Electroluminescence in AC ZnS:Mn
Devices
by Ch. Goflen, F.-J. Niedernostheide, H.-G. Purwins 112
5.1 Introduction......... 112
5.2 Experimental Set-Up. . . . 113
5.3 Electroluminescence Basics 114
5.4 Experimental Results. . . . 116
5.4.1 Stationary Microfilaments and Hysteresis 116
5.4.2 Frontpropagation....... 117
5.4.3 Autowaves .............. 119
5.4.4 Mobile Filaments and Strings . . . . 120
5.4.5 Global Spatiotemporal Oscillations. 123
5.4.6 Summary of Experimental Results 126
5.5 Discussion................... 127
5.5.1 Formation of Microfilaments. . . . . 127
5.5.2 Comparison with Reaction-Diffusion Systems 128
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . 131
6 Structure Formation in Charge Density Wave Systems
by M.J. Bunner, G. Heinz, A. Kittel, J. Parisi 133
6.1 The Peierls Transition . . . . . . . . . . . . 133
6.2 Materials .. . . . . . . . . . . . . . . . . . 134
6.3 The Electronic Transport in CDW Systems 135
6.4 Structure Formation of CDW Systems . . . 137
6.4.1 Metastability, Memory, and Hysteresis 137
6.4.2 Intermittent Oscillations and S-Shaped Negative Differen-
tial Resistance ................ 139
6.4.3 Narrow-Band Noise and Broad-Band Noise 140
6.4.4 Mode-Locking.. 141
6.5 Conclusion and Outlook . . . . . . . . . . . . . . . 142
7 Current Filamentation in Dipolar Electric Fields
by V. Novak, W. Pretti 144
7.1 Introduction...................... 144
7.2 Stationary Current Filaments in a Dipolar Electric Field 145
7.2.1 Experimental Setup ................. 145
7.2.2 Large-Area Filament Reconstruction . . . . . . . . 147
7.2.3 One-Dimensional Model of a Large-Area Filament 148
7.2.4 Magnetic Field in the One-Dimensional Model 153
7.2.5 Equal-Areas Rule for Coexistence Field ... 155
7.2.6 Bendable Filament .............. 157
7.3 Filamentary Structure under Interband Illumination 158
7.3.1 Dynamic Behaviour of Illuminated Samples 158
7.3.2 Hypothesis on the Underlying Mechanism 162
7.3.3 Large Time Scale Dynamic Behaviour 165
7.4 Conclusions..................... 166
x Table of Contents
8 Spatiotemporal Patterns and Generic Bifurcations in a Semicon
ductor Device
by F.-I. Niedernostheide 168
8.1 Introduction.............................. 168
8.2 Measuring Techniques . . . . . . . . . . . . . . . . . . . . . . . . 170
8.3 Experimentally Observed Bifurcation Sequences by Increasing the
DC Voltage Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
8.3.1 The Current-Voltage Characteristic . . . . . . . . . . . . 172
8.3.2 Transition of a Spatially Uniform State to a Static Local-
ized Filament . . . . . . . . . . . . . . . . . . . . . . . . . 172
8.3.3 Transition of a Static to a Rocking Filament ....... 174
8.3.4 Period-Doubling Cascade and Chaotic Filament Motions. 175
8.3.5 Transition of a Rocking to a Travelling Filament . . 177
8.4 Influence of Other Parameters on the Dynamical Behaviour 179
8.4.1 Frequency-Locking and Quasiperiodicity . 179
8.4.2 Influence of the Temperature 181
8.4.3 Influence of a Magnetic Field 182
8.5 Model and Physical Mechanism . . . 183
8.5.1 Two-Layer Model. . . . . . . 183
8.5.2 Activation, Inhibition, Competition 186
8.6 Numerical Results .............. 187
8.6.1 Bifurcations to Static, Breathing, Travelling and Chaot-
ically Oscillating Filaments by Using Homogeneous Neu
mann Boundary Conditions . . . . . . . . . . . . . . . . . 188
8.6.2 Influence of the Time Constants .............. 194
8.6.3 Bifurcations to Static, Rocking and Travelling Filaments
by Using Mixed Boundary Conditions 194
8.7 Summary and Conclusions. . . . . . . . . . . . . . . . . . . . . . 197
9 Current Filamentation in P-I-N Diodes: Experimental
Observations and an Equivalent Circuit Model·
by R. Symanczylc 200
9.1 Introduction................. 200
9.2 Theoretical Description .......... 202
9.2.1 Double Injection with Deep Traps 202
9.2.2 Equivalent Circuit Model 204
9.3 Stationary Pattern Formation .... . 206
9.3.1 Experimental Technique ... . 207
9.3.2 Observations and Comparison. 208
9.4 Spatio-Temporal Dynamics .. . 211
9.4.1 Periodic Oscillations .. . 212
9.4.2 Nonperiodic Oscillations. 214
9.5 Conclusion ........... . 216