• Eckehard Schöll
Part of the Springer Series in Synergetics book series (SSSYN, volume 35)


This book deals with physical aspects of current instabilities in semiconductors, induced by generation and recombination (g-r) processes of the charge carriers. Although instabilities of semiconductors and insulators have been known for a very long time, for example in connection with dielectric breakdown in solids [1.1], the view of such an instability as a phase transition in a physical system far from equilibrium is a fairly recent development. The analogy of an overheating instability of the electron gas with an equilibrium phase transition was pointed out by Volkov and Kogan [1.2] in the late sixties, and Pytte and Thomas [1.3] drew this analogy in the case of the Gunn instability of the electron-drift velocity at about the same time. But generation-recombination (g-r) induced phase transitions in semiconductors were first noted by Landsberg and Pimpale [1.4] only a decade ago, stimulated by the similarity with Schlögl’sfamous chemical reaction models for nonequilibrium phase transitions [1.5]. During these past ten years both the experimental observation and theoretical understanding of g-r induced phase transitions have made great progress, and have established a wealth of novel phenomena and models, thus giving birth to a new member of the growing family of physical and nonphysical systems that exhibit nonequilibrium phase transitions. The study of these systems has generated a new interdisciplinary field of science for which Haken, who pioneered these phenomena in the field of laser physics [1.6], has coined the name “synergetics” [1.7–9].


Singular Point Hopf Bifurcation Phase Portrait Stable Limit Cycle Very Large Scale Integrate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References:Chapter 1

  1. 1.1
    K.W. Wagner: Trans. American Inst. Electr. Engin. 41, 288 (1922)CrossRefGoogle Scholar
  2. 1.1a
    H. Lueder, W. Sehottky, E. Spenke: Naturwiss. 24, 61 (1936)ADSCrossRefGoogle Scholar

Early Papers on Nonequilibrium Phase Transitions in Semiconductors:Overheating Instability

  1. 1.2
    A.F. Volkov, Sh.M. Kogan: Sov. Phys. Usp. 11, 881 (1969)ADSCrossRefGoogle Scholar
  2. 1.3
    E. Pytte, H. Thomas: Phys. Rev. 179, 431 (1969)ADSCrossRefGoogle Scholar

g-r Instability

  1. 1.4
    P.T. Landsberg, A. Pimpale: J. Phys. C9,1243 (1976)ADSGoogle Scholar
  2. 1.5
    F. Schlögl: Z. Phys. 253,147 (1972)ADSCrossRefGoogle Scholar


  1. 1.6
    R. Graham, H. Haken: Z. Phys. 213,420 (1968)ADSCrossRefGoogle Scholar
  2. 1.6a
    V. DeGiorgio, M.O. Scully: Phys. Rev. A2,1170 (1970)ADSGoogle Scholar


  1. 1.7
    H. Haken, R. Graham: Umschau 6,191 (1971)Google Scholar
  2. 1.8
    H. Haken: Synergetics, An Introduction, 3rd ed. (Springer, Berlin, Heidelberg 1983)zbMATHGoogle Scholar
  3. 1.9
    H. Haken: Advanced Synergetics (Springer, Berlin, Heidelberg 1983)zbMATHGoogle Scholar
  4. 1.9a
    see also Springer Series in Synergetics, ed. by H. Haken (Springer, Berlin, Heidelberg)Google Scholar

Textbooks on Applied Semiconductor Physics

  1. 1.10
    B.G. Streetman: Solid State Electronic Devices, 2nd ed. (Prentice-Hall, Englewood Cliffs, NJ 1980)Google Scholar
  2. 1.11
    S.M. Sze: Physics of Semiconductor Devices, 2nd ed. (Wiley, New York 1981)Google Scholar

Dissipative Structures

  1. 1.12
    G. Nicolis, I. Prigogine: Self-Organization in Non-Equilibrium Systems (Wiley, New York 1977)Google Scholar

Bifurcation Theory

  1. 1.13
    D.H. Sattinger: Topics in Stability and Bifurcation Theory (Springer, Berlin 1973)zbMATHGoogle Scholar
  2. 1.14
    O. Gurel, O.E. Rössler (eds.): Bifurcation Theory and Applications in Scientific Disciplines. Annals of the New York Academy of Sciences, Vol. 316 (New York Academy of Sciences, New York 1979)Google Scholar
  3. 1.15
    G. Iooss, D.D. Joseph: Elementary Stability and Bifurcation Theory (Springer, Berlin, Heidelberg 1981)Google Scholar
  4. 1.16
    S.N. Chow, J.K. Hale: Methods of Bifurcation Theory (Springer, Berlin, Heidelberg 1982)zbMATHCrossRefGoogle Scholar

Mathematical Theory of Dynamic Systems-Variable Systems

  1. 1.17
    A.A. Andronov, E.A. Leontovich, LI. Gordon, A.G. Maier: Vol. 1: Qualitative Theory of Second-Order Dynamic Systems (Wiley, New York 1973)zbMATHGoogle Scholar
  2. 1.17a
    Theory of Bifurcations of Dynamic Systems on a Plane (Israel Program for Scientific Translations, Jerusalem 1971)Google Scholar

Variable Systems

  1. 1.18
    J. Guckenheimer, P. Holmes: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, Heidelberg 1983)zbMATHGoogle Scholar

Catastrophe Theory

  1. 1.19
    R. Thorn: Structural Stability and Morphogenesis (Benjamin, New York 1975) (Original ed. Paris 1972)Google Scholar
  2. 1.20
    E.C. Zeeman: Catastrophe Theory. Selected Papers (Addison-Wesley, Reading, Mass. 1977)zbMATHGoogle Scholar
  3. 1.21
    T. Poston, I. Stewart: Catastrophe Theory and its Applications (Pitman, London 1978)zbMATHGoogle Scholar
  4. 1.22
    V.I. Arnold: Catastrophe Theory (Springer, Berlin, Heidelberg 1984)zbMATHGoogle Scholar


  1. 1.23
    R.K. Bullough, P.J. Caudrey (eds.): Solitons, Topics Curr. Phys., Vol. 18 (Springer, Berlin, Heidelberg 1980)Google Scholar
  2. 1.23a
    G.L. Lamb: Elements of Soliton Theory (Wiley, New York 1980)zbMATHGoogle Scholar
  3. 1.23b
    G. Eilenberger: Solitons, Springer Ser. Solid-State Sci., Vol. 19 (Springer, Berlin, Heidelberg 1981)Google Scholar


  1. 1.24
    H.G. Schuster: Deterministic Chaos (Physik-Verlag, Weinheim 1984)zbMATHGoogle Scholar

Stochastic Measures in Nonequilibrium Thermodynamics

  1. 1.25
    F. Schlögl: Physics Reports 62, 267–380 (1980)ADSCrossRefGoogle Scholar
  2. 1.25.a
    Rostocker Physikalische Manuskripte 8, 30 (1985)Google Scholar

Overviews of Instabilities in Semiconductors

  1. 1.26
    A.F. Volkov, Sh.M. Kogan: Sov. Phys. Usp. 11, 881 (1969)ADSCrossRefGoogle Scholar
  2. 1.27
    H. Hartnagel: Semiconductor Plasma Instabilities (Elsevier, New York 1969)Google Scholar
  3. 1.28
    F. Stöckmann: “Elektrische Instabilitäten in Halb- und Photoleitern”, in Festkörperprobleme 9, 138 (Vieweg, Braunschweig 1969)Google Scholar
  4. 1.29
    J.E. Carroll: Hot Electron Microwave Generators (Arnold, London 1970)Google Scholar
  5. 1.30
    V.L. Bonch-Bruevich, LP. Zvyagin, A.G. Mironov: Domain Electrical Instabilities in Semiconductors (Consultant Bureau, New York 1975)Google Scholar
  6. 1.31
    M.P. Shaw, H.L. Grubin, P. Solomon: The Gunn-Hilsum Effect (Academic Press, New York 1979)Google Scholar
  7. 1.32
    J. Pozhela: Plasma and Current Instabilities in Semiconductors (Pergamon, Oxford 1981)Google Scholar
  8. 1.33
    M. Asche, Z.S. Gribnikov, V.V. Mitin, O.G. Sarbei: Hot Electrons in Many- Valley Semiconductors (in Russian) (Naukova Dumka, Kiev 1982)Google Scholar
  9. 1.34
    M.P. Shaw, N. Yildirim: Adv. Electr. Electron Phys. 60, 307 (1983)Google Scholar
  10. 1.35
    M.P. Shaw, H.L. Grubin, E. Schöll: The Physics of Instabilities in Solid State Electron Devices (Plenum, New York), in preparationGoogle Scholar

Stochastic Methods

  1. 1.36
    N.G. van Kampen: Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam 1981)zbMATHGoogle Scholar
  2. 1.37
    C.W. Gardiner: Handbook on Stochastic Methods, 2nd. ed., Springer Ser. Syn., Vol. 13 (Springer, Berlin, Heidelberg 1986)Google Scholar
  3. 1.38
    W. Horsthemke, R. Lefever: Noise-Induced Transitions, Springer Ser. Syn., Vol. 15 (Springer, Berlin, Heidelberg 1983)Google Scholar
  4. 1.39
    H. Risken: The Fokker-Planck Equation, Springer Ser. Syn., Vol. 18 (Springer, Berlin, Heidelberg 1984)Google Scholar
  5. 1.39.a
    Combinations of SNDC and NNDC Instabilities (see also [Ref. 1.33, p. 147 (Fig. 33)])Google Scholar
  6. 1.40
    J. Peinke, A. Mühlbach, R.P. Huebener, J. Parisi: Phys. Lett. 108A, 407 (1985)ADSGoogle Scholar
  7. 1.41
    C.L. Dick, B. Aneker-Johnson: Phys. Rev. B5, 526 (1972)ADSGoogle Scholar
  8. 1.42
    V.A. Pogrebnyak: Sov. Phys. Semicond. 14, 1210 (1980)Google Scholar
  9. 1.43
    V.V. Mitin: Sov. Phys. Semicond. 11, 727 (1977)Google Scholar

Domains and Filaments in NDC Elements

  1. 1.44
    B.K. Ridley: Proc. Phys. Soc. 82, 954 (1963)ADSCrossRefGoogle Scholar
  2. 1.44.a
    H. Thomas: Lecture Notes: Conf. on Fluctuation Phenomena. Chania, Crete (1969)Google Scholar
  3. 1.45
    E. Schöll: Festkörperprobleme 26, 309 (Vieweg, Braunschweig 1986)Google Scholar

Violation of Minimum Entropy Production Principle in Current Filaments

  1. 1.46
    A.F. Volkov, Sh.M. Kogan: Sov. Phys. JETP 25,1095 (1967)ADSGoogle Scholar
  2. 1.47
    K. Takeyama, K. Kitahara: J. Phys. Soc. Jpn. 39,125 (1975)ADSCrossRefGoogle Scholar

Validity of Minimum Entropy Production Principle

  1. 1.48
    R. Landauer: Phys. Rev. A12, 636 (1975)ADSGoogle Scholar
  2. 1.49
    F. Schlögl: “On the statistical background of the Glansdorff-Prigogine criterion”, in Thermodynamicsand regulation of biological processes, ed. by A.I. Zotin (Nauka, Moscow 1984)Google Scholar

Influence of the Load Line on the Stability of NDC States

  1. 1.50
    J.L. Jackson, M.P. Shaw: Appl. Phys. Lett. 25, 666 (1974)ADSCrossRefGoogle Scholar
  2. 1.51
    M. Büttiker, H. Thomas: Z. Phys. B34, 301 (1979)ADSGoogle Scholar

NDC Devices (Original Papers):Tunnel Diode

  1. 1.52
    L. Esaki: Phys. Rev. 109, 603 (1958)ADSCrossRefGoogle Scholar
  2. 1.53
    P.T. Landsberg, M.S. Abrahams: Electron. Lett. 21, 59 (1985)ADSCrossRefGoogle Scholar

Gunn Diode (see also [6.7-15])

  1. 1.54
    J.B. Gunn: IBM J. Res. Develop. 8,141 (1964)CrossRefGoogle Scholar


  1. 1.55
    W. Shockley: Bell Syst. Tech. J. 33, 799 (1954)Google Scholar
  2. 1.56
    W.T. Read: Bell Syst. Tech. J. 37,401 (1958)Google Scholar


  1. 1.57a)
    W. Fulop: IEEE Trans. ED-10,120 (1963)Google Scholar
  2. 1.57b)
    M. Stoisiek, R. Sittig: Festkörperprobleme 26, 361 (Vieweg, Braunschweig 1986)Google Scholar

Pin Diode

  1. 1.58
    R.C. Prim: Bell Syst. Tech. J. 32, 665 (1953)Google Scholar

Ovonic Switch

  1. 1.59
    S.R. Ovshinsky: Phys. Rev. Lett. 21,1450 (1968)ADSCrossRefGoogle Scholar

Reviews on Mechanisms for Drift Instabilities

  1. 1.60
    J.C. McGroddy, M.I. Nathan, J.E. Smith, jr.: IBM J. Res. Develop. 13, 543, 554 (1969)Google Scholar
  2. 1.61
    H. Thomas: In Synergetics, ed. by H. Haken (Stuttgart, Teubner 1973), p. 87Google Scholar

Original Papers

  1. 1.62
    M. Büttiker, H. Thomas: Solid-State Electron. 21, 95 (1978); Z. Phys. B33, 275 (1979); 34, 301 (1979)CrossRefGoogle Scholar

Mechanisms for g-r instabilities (see also [6.16-21]):Field-Assisted Trapping (NNDC)

  1. 1.63
    B.K. Ridley, T.B. Watkins: J. Phys. Chem. Solids 22,155 (1961)ADSCrossRefGoogle Scholar
  2. 1.64
    B.K. Ridley, R.G. Pratt: J. Phys. Chem. Solids 26,21 (1965)ADSCrossRefGoogle Scholar
  3. 1.65
    V.L. Bonch-Bruevich: Sov. Phys. Solid State 6,1615 (1965)Google Scholar
  4. 1.66
    V.L. Bonch-Bruevich, S.G. Kalashnikov: Sov. Phys. Solid State 7, 599 (1965)Google Scholar
  5. 1.67
    K.W. Boer: IBM J. Res. Develop. 13, 573 (1969)CrossRefGoogle Scholar

Low Temperature Impurity Breakdown (SNDC) (see also [2.3-13, 24-36])

  1. 1.68
    R.P. Khosla, J.R. Fischer, B.C. Burkey: Phys. Rev. B7, 2551 (1973)ADSGoogle Scholar
  2. 1.69
    E. Schöll: Z. Phys. B46, 23 (1982)ADSCrossRefGoogle Scholar

Switching in Amorphous Thin Films (SNDC) (see also [1.59])

  1. 1.70
    D. Adler, M.S. Shur, M. Silver, S.R. Ovshinsky: J. Appl. Phys. 51, 3289 (1980)ADSCrossRefGoogle Scholar
  2. 1.71
    P.T. Landsberg, D.J. Robbins, E. Schöll: Phys. Status Solidi (a) 50,423 (1978)ADSCrossRefGoogle Scholar

Double Injection in pin Diodes (SNDC)

  1. 1.72
    M.A. Lampert, P. Mark: Current Injection in Solids (Academic, New York 1970)Google Scholar
  2. 1.72a
    M.A. Lampert, R.B. Schilling: Semicond. Semimetals 6,1 (1970)CrossRefGoogle Scholar
  3. 1.72b
    R. Baron, J.W. Mayer: Semicon. Semimetals 6, 202 (1970)Google Scholar


  1. 1.73
    W.E. Schroeder, G.I. Haddad: Proc. IEEE 61,153 (1973)CrossRefGoogle Scholar
  2. 1.74
    P. Bauhahn, G.I. Haddad: IEEE Trans. ED-24, 634 (1977)ADSGoogle Scholar

Scattering-Induced NDC in 2-Dimensional Systems

  1. 1.75
    B.K. Ridley: Proc. 17th Int’l. Conf. Physics of Semiconductors (San Francisco 1984), ed. by J.D. Chadi, W.A. Harrison (Springer, New York 1985) p. 401;Google Scholar
  2. 1.75a
    M.A.R. Al-Mudares, B.K. Ridley: Physica 134B, 526 (1985)Google Scholar

Reviews on Thermal Breakdown

  1. 1.76
    L. Altcheh, N. Klein: IEEE Trans. ED-20, 801 (1973)Google Scholar
  2. 1.77
    N. Klein: Thin Solid Films 100, 335 (1983)ADSCrossRefGoogle Scholar

Reviews on Transport in Semiconductors

  1. 1.78
    CM. Snowden: Rep. Prog. Phys. 48, 223 (1985)ADSCrossRefGoogle Scholar
  2. 1.79
    C. Jacoboni, L. Reggiani: Rev. Mod. Phys. 55, 645 (1983)ADSCrossRefGoogle Scholar
  3. 1.80
    H.L. Grubin, D.K. Ferry, G.J. Iafrate, J.R. Barker: VLSI Electronics Microstructure Sci. 3, 197–299 (Academic, New York 1982)Google Scholar
  4. 1.81
    J.R. Barker; In Physics of Non-linear Transport in Semiconductors, ed. by D.K. Ferry, J.R. Barker, C. Jacoboni. (Plenum, New York 1980) p. 127 and 589Google Scholar
  5. 1.82
    L. Reggiani (ed.): Hot Electron Transport in Semiconductors, Topics Appl. Phys., Vol. 58 (Springer, Berlin, Heidelberg 1985)Google Scholar
  6. 1.83
    G. Baccarani, M.R. Wordeman: Solid-State Electron. 28,407 (1985)ADSCrossRefGoogle Scholar
  7. 1.83.a
    G. Baccarani, M. Rudan, R. Guerrieri, P. Ciampolini: “Physical Models for Numerical Device Simulation”, in Advances in CAD for VLSI, Vol. 1, ed. by W. Engl (North Holland, Amsterdam 1986), pp. 107–158Google Scholar
  8. 1.84
    E.M. Conwell: High-Field Transport in Semiconductors (Academic, New York 1967)Google Scholar
  9. 1.85
    B. Nag: Theory of Electrical Transport in Semiconductors (Pergamon, Oxford 1972)Google Scholar
  10. 1.86
    K.C. Kao, W. Hwang: Electrical Transport in Solids (Pergamon, Oxford 1981)Google Scholar

First-Principle Derivation of Macroscopic Transport Equations

  1. 1.87
    H. Stumpf: Quantum Processes in Polar Semiconductors and Insulators, Pts. 1 and 2 (Vieweg, Braunschweig 1983)Google Scholar

Textbooks on Semiconductor Physics

  1. 1.88
    O. Madelung: Grundlagen der Halbleiterphysik (Springer, Berlin, Heidelberg 1970)Google Scholar
  2. 1.89
    K.H. Seeger: Semiconductor Physics, 3rd ed. (Springer, Berlin, Heidelberg 1985)Google Scholar

Semiconductor Junctions and Contacts (see also [4.40-44])

  1. 1.90
    M.P. Shaw: “Properties of Junctions and Barriers”, in Handbook on Semiconductors, Vol. 4, ed. by T.S. Moss (North Holland, Amsterdam 1981) Chap. 1Google Scholar
  2. 1.91
    A. Herlet, E. Spenke: Z. Angew. Phys. 7,99,149,195 (1955)Google Scholar
  3. 1.92
    H. Benda, A. Hoffmann, E. Spenke: Solid-St. Electron. 8, 887 (1965)ADSCrossRefGoogle Scholar
  4. 1.93
    J.A.G. Slatter, J.P. Whelan: Solid-St. Electron. 23,1235 (1980)ADSCrossRefGoogle Scholar

Coherent Macroscopic Electronic Excitations

  1. 1.94
    A. Stahl, I. Balslev: Electrodynamics of the Semiconductor Band Edge (Springer, Berlin, Heidelberg 1987)CrossRefGoogle Scholar

Solution of Quantum-Mechanical Boltzmann Equation by Cumulant Expansion

  1. 1.95
    B.C. Eu: J. Chem. Phys. 80, 2123 (1984)ADSCrossRefGoogle Scholar

Transport Processes in Gases

  1. 1.96
    S. Chapman, T.G. Cowling: The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, Cambridge 1970)Google Scholar

Critical Behavior:Equilibrium Phase Transitions

  1. 1.97
    H.E. Stanley: Phase Transitions and Critical Phenomena (Clarendon, Oxford 1971)Google Scholar
  2. 1.98
    S.K. Ma: Modern Theory of Critical Phenomena (Benjamin, New York 1976)Google Scholar
  3. 1.99
    V. Dohm, R. Folk: Festkörperprobleme 22,1 (Vieweg, Braunschweig 1982)Google Scholar
  4. 1.100
    V. Dohm: Z. Phys. B60, 61 (1985); 61,193 (1985)ADSCrossRefGoogle Scholar
  5. 1.101
    M.N. Barber: In Phase Transitions and Critical Phenomena, Vol. 8, ed. by C. Domb, J.L. Lebowitz (Academic, London 1983)Google Scholar
  6. 1.102
    H.W. Diehl, S. Dietrich: Festkörperprobleme 25, 39 (Vieweg, Braunschweig 1985)Google Scholar
  7. 1.103
    E. Eisenriegler: Z. Phys. B61,299 (1985); Th.W. Burkhardt, E. Eisenriegler: J. Phys. A18, L83 (1985)MathSciNetADSCrossRefGoogle Scholar
  8. 1.104
    F. Schlögl, E. Schöll: Z. Phys. B51, 61 (1983)ADSCrossRefGoogle Scholar

Nonequilibrium Phase Transitions

  1. 1.105
    A. Nitzan, P. Ortoleva, J. Deutch, J. Ross: J. Chem. Phys. 61,1056 (1974)ADSCrossRefGoogle Scholar

Bit Number Cumulants as Characteristic Critical Quantities (see also [1.25])

  1. 1.106
    F. Schlögl: Z. Phys. 267, 77 (1974); B20,177 (1975); B22, 301 (1975)ADSCrossRefGoogle Scholar
  2. 1.107
    F. Schlögl: Z. Phys. B52, 51 (1983)ADSCrossRefGoogle Scholar

Tricritical Exponents

  1. 1.108
    R.B. Griffiths: Phys. Rev. B7, 545 (1973)ADSGoogle Scholar

Tricritical Behavior in Laser Phase Transitions

  1. 1.109
    D. Walgraef, P. Borckmans, G. Dewel: Z. Physik B30,437 (1978)ADSGoogle Scholar

Examples of Various Synergetic Systems (see also [1.2-9,12]):Tunnel Diode

  1. 1.110
    R. Landauer: J. Appl. Phys. 33, 2209 (1962)ADSCrossRefGoogle Scholar

Chemical Reaction Systems (see also [1.5,12,105])

  1. 1.111
    W. Ebeling: Physik der Selbstorganisation und Evolution (Akademie-Verlag, Berlin 1982)Google Scholar

Ballast Resistor and Superconducting Hot Spots

  1. 1.112
    D. Bedeaux, P. Mazur: Physica 105A, 1 (1981)MathSciNetADSGoogle Scholar
  2. 1.112.a
    L. Freytag, R.P. Huebener: J. Low Temp. Phys. 60, 377 (1985)ADSCrossRefGoogle Scholar

Semiconductors with g-r Instabilities (see also [1.4,45])

  1. 1.113
    E. Schöll, P.T. Landsberg: Proc. R. Soc. (London) Ser. A365,495 (1979)ADSCrossRefGoogle Scholar
  2. 1.113.a
    E. Schöll: Z. Phys. B46, 23 (1982); 48,153 (1982); 52, 321 (1983)ADSCrossRefGoogle Scholar
  3. 1.114
    P.T. Landsberg: Eur. J. Phys. 1, 31 (1980) (review of the early work)CrossRefGoogle Scholar

Semiconductor Lasers

  1. 1.115
    E. Schöll, P.T. Landsberg: J. Opt Soc. Am. 73,1197–1206 (1983)ADSCrossRefGoogle Scholar
  2. 1.115.a
    E. Schöll, D. Bimberg, H. Schumacher, P.T. Landsberg: IEEE J. QE-20, 394–399 (1984)CrossRefGoogle Scholar
  3. 1.115.b
    D. Bimberg, K. Ketterer, E. Schöll, H.P. Vollmer: Electron. Lett. 20, 640–641 (1984); Physica 129B, 469 (1985)ADSCrossRefGoogle Scholar
  4. 1.115.c
    D. Bimberg, K. Ketterer, E.H. Böttcher, E. Schöll: Int. J. Electronics 60, 23 (1986) (review)CrossRefGoogle Scholar

Traffic Flow on Motorways

  1. 1.116
    R. Kühne: Physik in unserer Zeit 15, 84 (1984)ADSCrossRefGoogle Scholar

Recent Conference Proceedings

  1. 1.116.a
    see Springer Series in Synergetics, ed. by H. Haken, Vols. 2-6, 8, 9, 11, 12, 17, 21-24, 26-32 G. Benedek, H. Bilz, R. Zeyher (eds.): Statics and Dynamics of Nonlinear Systems Springer Ser. Solid-State Sci., Vol. 46 (Springer, Berlin, Heidelberg 1983)Google Scholar

Large Bibliography up to 1981

  1. 1.117
    P.C. Hohenberg, J.S. Langer: J. Stat. Phys. 28,193 (1982)ADSCrossRefGoogle Scholar

Hot Electron Phenomena (see also [1.79-84])

  1. 1.118
    E. Gornik (ed.): Proc. 4th Int’l. Conf. on Hot Electrons in Semiconductors (Innsbruck 1985), Physica 134B (1985)Google Scholar
  2. 1.119
    D. Bimberg, H. Münzel, A. Steckenborn: Physica 117 and 118B, 214 (1983)Google Scholar
  3. 1.120
    T. Grave, E. Schöll, H. Wurz: J. Phys. C16,1693 (1983)ADSGoogle Scholar

Nonequilibrium Recombination Statistics (Reviews and Monographs)

  1. 1.121
    P.T. Landsberg: Festkörperprobleme 6,174 (Vieweg, Braunschweig 1966)Google Scholar
  2. 1.122
    D.A. Evans: In Solid State Theory, ed. by P.T. Landsberg (Wiley, New York 1969)Google Scholar
  3. 1.123
    P.T. Landsberg: “Semiconductor Statistics”, in Handbook on Semiconductors, ed. by T.S. Moss, Vol. I, Chap. 8 (North Holland, Amsterdam 1982)Google Scholar
  4. 1.124
    J.S. Blakemore: Semiconductor Statistics (Pergamon, Oxford 1962)zbMATHGoogle Scholar
  5. 1.125
    P.T. Landsberg, M J. Adams: J. Lum. 7, 3 (1973)ADSCrossRefGoogle Scholar
  6. 1.126
    W. Schulz: Festkörperprobleme 5,165 (Vieweg, Braunschweig 1966)Google Scholar
  7. 1.127
    H.J. Hoffmann, F. Stöckmann: Festkörperprobleme 19, 271 (Vieweg, Braunschweig 1979)Google Scholar

Three-Particle Auger Processes

  1. 1.128
    P.T. Landsberg: J. Phys. C9, L 111 (1976)ADSGoogle Scholar
  2. 1.128.a
    P.T. Landsberg: J. Phys. C9, L 111 (1976); A. Pimpale: J. Phys. C11, 1085 (1978)ADSGoogle Scholar

Reviews on Impact Ionization

  1. 1.129
    DJ. Robbins: Phys. Status Solidi (b) 97,9, 387; 98,11 (1980)ADSCrossRefGoogle Scholar
  2. 1.130
    F. Capasso: “Physics of avalanche photodiodes”, in Semicond. Semimetals 22D, 1 -172 (Academic, New York 1985)Google Scholar

Band-Band Impact Ionization

  1. 1.131
    W. Shockley: Solid-State Electron. 2, 35 (1961)ADSCrossRefGoogle Scholar
  2. 1.132
    B.K. Ridley: J. Phys. C16, 3373; 4733 (1983)ADSGoogle Scholar
  3. 1.132.a
    M.G. Burt: J. Phys. C18, L477 (1985)ADSGoogle Scholar
  4. 1.132.b
    S. McKenzie, M.G. Burt: J. Phys. C19,1959 (1986)ADSGoogle Scholar

Impact Ionization from Impurities (see also [1.95])

  1. 1.133
    A. Zylbersztejn: Phys. Rev. 127, 744 (1962)ADSCrossRefGoogle Scholar
  2. 1.134
    M.E. Cohen, P.T. Landsberg: Phys. Rev. 154, 683 (1967); Phys. Status Solidi (b) 64, 39 (1974)ADSCrossRefGoogle Scholar
  3. 1.134.a
    Phys. Status Solidi (b) 64, 39 (1974)ADSCrossRefGoogle Scholar
  4. 1.135
    D.J. Robbins, P.T. Landsberg: J. Phys. C13, 2425 (1980)ADSGoogle Scholar
  5. 1.136
    V.F. Bannaya, L.I. Velesova, E.M. Gershenzon, V.A. Chuenkov: Sov. Phys. Semicond. 7, 1315 (1974)Google Scholar
  6. 1.137
    R.M. Westervelt, S.W. Teitsworth: J. Appl. Phys. 57, 5457 (1985)ADSCrossRefGoogle Scholar
  7. 1.138
    V.V. Mitin: Appl. Phys. A39,123 (1986)ADSGoogle Scholar

Nonlinear Oscillations

  1. 1.139
    J.J. Stoker: Nonlinear Vibrations (Wiley, New York 1950)zbMATHGoogle Scholar
  2. 1.140
    N. Minorsky: Nonlinear Oscillations (Van Nostrand, Toronto 1962)zbMATHGoogle Scholar
  3. 1.141
    A.A. Andronov, A. Witt, S.E. Khaikin: Theory of Oscillators (Pergamon, London 1966)zbMATHGoogle Scholar
  4. 1.142
    P. Hagedorn: Nonlinear Oscillations (Oxford Univ. Press, Oxford 1981)Google Scholar

Global Bifurcation of Limit Cycles in Chemical Reaction Systems

  1. 1.143
    C. Escher: Z. Phys. B35, 351 (1979)MathSciNetADSGoogle Scholar
  2. 1.143.a
    Ber. Bunsenges. Phys. Chem. 84, 387 (1980)Google Scholar

Early Investigation of Solitons

  1. 1.144
    H. Seeger, H. Donth, A. Kochendörfer: Z. Phys. 134,173 (1953)ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Eckehard Schöll
    • 1
  1. 1.Institut für Theoretische PhysikRheinisch-Westfälische Technische HochschuleAachenFed. Rep. of Germany

Personalised recommendations