Modelling of Bipolar Device Phenomena

  • Henk C. de Graaff
  • François M. Klaassen
Part of the Computational Microelectronics book series (COMPUTATIONAL)


In this chapter we will first discuss some general problems in bipolar device modelling, namely the choice between injection and transport models and the validity of the charge control principle. After that we will show how the various device phenomena like main currents, Early effect, depletion capacitance etc., can be described by means of compact, explicit and analytical mathematical expressions. Unless stated otherwise, the device structure considered here is that of a vertical npn transistor. In most cases the vertical pnp transistor only needs a change of sign in its model formulas. The lateral pnp transistor, which is quite different, will be treated in a separate chapter.


Collector Current High Injection Bipolar Transistor Doping Profile Charge Control 
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  1. [3.1]
    H. K. Gummel: Measurement of the Number of Impurities in the Base Layer of a Transistor. Proc. I.R.E. 42, 1761 (1954).CrossRefGoogle Scholar
  2. [3.2]
    H. C. de Graaff, J. W. Slotboom, A. Schmitz: The Emitter Efficiency of Bipolar Transistors. Solid-State Electr. 20, 515 (1977).CrossRefGoogle Scholar
  3. [3.3]
    H, Schaber et al: Process and Device Related Scaling Considerations for Polysilicon Emitter Bipolar Transistors. IEDM Techn. Digest 170 (1987).Google Scholar
  4. [3.4]
    R. Beaufroy, J. J. Sparkes: The Junction Transistor as a Charge-Controlled Device. Automat. Tel. Eng. J. 13, 310 (1957).Google Scholar
  5. [3.5]
    J. te Winkel: Past and Present of the Charge-Control Concept in the Characterization of the Bipolar Transistor. Adv. Electr. and Electr. Phys. 39, 253 (1975).CrossRefGoogle Scholar
  6. [3.6]
    J. J. Ebers, J. L. Moll: Large Signal Behaviour of Junction Transistors. Proc. I.R.E. 42, 1761 (1954).CrossRefGoogle Scholar
  7. [3.7]
    J. L. Moll, J. M. Ross: The Dependence of Transistor Parameters on the Distribution of Base Layer Resistivity. Proc. I.R.E. 44, 72 (1956).CrossRefGoogle Scholar
  8. [3.8]
    H. K. Gummel: A Charge-Control Relation for Bipolar Transistors. Bell Syst. Techn. J. 49, 115 (1970).Google Scholar
  9. [3.9]
    H. K. Gummel, H. C. Poon: An Integral Charge-Control Model for Bipolar Transistors. Bell Syst. Techn. J. 49, 827 (1970).Google Scholar
  10. [3.10]
    L Getreu: Modeling the Bipolar Transistor. Tektronix Inc., Beaverton OR (1979).Google Scholar
  11. [3.11]
    H. C. de Graaff, W. J. Kloosterman: New Formulation of the Current and Charge Relations in Bipolar Transistor Modeling for CACD Purposes. IEEE Trans. Electr. Dev. ED-32, 2415 (1985).CrossRefGoogle Scholar
  12. [3.12]
    J. L. Moll: Physics of Semiconductors. McGraw-Hill, New York (1964).MATHGoogle Scholar
  13. [3.13]
    H. C. de Graaff: Review of Models for Bipolar Transistors. In: Process and Device Modeling for Integrated Circuit Design ( F. van de Wiele, W. L. Engl, P. G. Jespers, eds.). Noordhoff, Leiden (1977).Google Scholar
  14. [3.14]
    H. C. Poon, H. K. Gummel: Modeling of the Emitter Capacitance. Proc. IEEE 57, 2181 (1969).CrossRefGoogle Scholar
  15. [3.15]
    C. T. Kirk: A Theory of Transistor Cut-Off Frequency (f T) Fall-Off at High Current Densities. I.R.E. Trans. Electr. Dev. ED-9, 164 (1962).Google Scholar
  16. [3.16]
    J. M. Early: Effects of Space-Charge Layer Widening in Junction Transistors. Proc. I.R.E. 40, 1401 (1952).CrossRefGoogle Scholar
  17. [3.17]
    J. W. Slotboom: Iterative Scheme for 1- and 2-Dimensional D.C. Transistor Simulation. Electr. Ltrs. 5, 677 (1969).CrossRefGoogle Scholar
  18. [3.18]
    J. R. A. Beale, J. A. G. Slatter: The Equivalent Circuit of a Transistor with a Lightly Doped Collector Operating in Saturation. Solid-State Electr. 11, 241 (1968).CrossRefGoogle Scholar
  19. [3.19]
    J. A. Pals, H. C. de Graaff: On the Behaviour of the Base-Collector Junction of a Transistor at High Collector Current Densities. Philips Res. Rep. 24, 53 (1969).Google Scholar
  20. [3.20]
    L. A. Hahn: The Effect of Collector Resistance Upon the High Current Capability of n-p-v-n Transistors. IEEE Trans. Electr. Dev. ED-16, 654 (1969).CrossRefGoogle Scholar
  21. [3.21]
    D. L. Bowler, F. A. Lindholm: High Current Regimes in Transistor Collector Regions. IEEE Trans. Electr. Dev. ED-20, 257 (1973).CrossRefGoogle Scholar
  22. [3.22]
    H. C. de Graaff: High Current Density Effects in the Collector of Bipolar Transistors. In: Process and Device Modeling for Integrated Circuit Design ( F. van de Wiele, W. L. Engl, P. G. Jespers, eds). Noordhoff, Leiden (1977).Google Scholar
  23. [3.23]
    L. J. Turgeon, J. R. Mathews: A Bipolar Transistor Model of Quasi-Saturation for Use in CAD. IEDM Techn. Digest 394 (1980).Google Scholar
  24. [3.24]
    H. C. de Graaff: Compact Bipolar Transistor Modeling. In: Process and Device Modeling ( W. L. Engl, ed.). North-Holland, Amsterdam (1986).Google Scholar
  25. [3.25]
    G. M. Kull et al.: A Unified Circuit Model for Bipolar Transistors Including Quasi-Saturation Effects. I.E.E.E. Trans. Electr. Dev. ED-32, 1103 (1985).CrossRefGoogle Scholar
  26. [3.26]
    S. L. Miller: Ionization Rates for Holes and Electrons in Silicon. Phys. Rev. 105, 1246 (1957).CrossRefGoogle Scholar
  27. [3.27]
    R. W. Dutton: Bipolar Transistor Modeling of Avalanche Generation for Computer Simulation. I.E.E.E. Trans. Electr. Dev. ED-22, 334 (1975).Google Scholar
  28. [3.28]
    D. A. Divekar, R. E. Lovelace: Modeling of Avalanche Current of Bipolar Junction Transistors for Computer Circuit Simulation. I.E.E.E. Trans. CAD Int. Circ. and Syst. CAD-1, 114(1982).Google Scholar
  29. [3.29]
    H. C. Poon, J. C. Meckwood: Modeling of Avalanche Effect in Integral Charge Control Model. I. E.E.E. Trans. Electr. Dev. ED-19, 90 (1972).Google Scholar
  30. [3.30]
    S. M. Sze: Physics of Semiconductor Devices, 2nd ed. John Wiley & Sons, New York (1981).Google Scholar
  31. [3.31]
    J. R. Hauser: The Effects of Distributed Base Potential on Emitter Current Density and Effective Base Resistance for Stripe Transistor Geometries. I.E.E.E. Trans. Electr Dev. £D-11, 238(1964).Google Scholar
  32. [3.32]
    J. E. Lary, R. L. Anderson: Effective Base Resistance of Bipolar Transistors. I.E.E.E Trans. Electr. Dev. ED-32, 2503 (1985).CrossRefGoogle Scholar
  33. [3.33]
    G. Rey: Effets de la Défocalisation sur le Comportement des Transistors à Jonctions Solid-State Electr. 12, 645 (1969).Google Scholar
  34. [3.34]
    H. Groendijk: Modeling Base Crowding in a Bipolar Transistor. I.E.E.E. Trans Electr. Dev. ED-20, 329 (1973).CrossRefGoogle Scholar
  35. [3.35]
    H. C. de Graaff: Electrical Behaviour of Lightly Doped Collectors in Bipolar Transis tors. Thesis, University of Technology, Eindhoven (1975).Google Scholar
  36. [3.36]
    H. C. de Graaff: Approximate Calculations on the Spreading Resistance in Multi Emitter Structures. Philips Res. Rep. 24, 34 (1969).Google Scholar
  37. [3.37]
    J. Lindmayer, C. Y. Wrigley: Fundamentals of Semiconductor Devices. Van Nostrand, Princeton (1965).Google Scholar
  38. [3.38]
    J. te Winkel: Extended Charge-Control Model for Bipolar Transistors. I.E.E.E. Trans. Electr. Dev. ED-20, 389 (1973).CrossRefGoogle Scholar
  39. [3.39]
    J. G. Possum, S. Veeraraghavan: Partitioned-Charge-Based Modeling of Bipolar Transistors for Non-Quasi-Static Circuit Simulation. I.E.E.E. Electr. Dev. Ltrs. EDL-7, 652 (1986).Google Scholar
  40. [3.40]
    H. Klose, A. W. Wieder: The Transient Integral Charge Control Relation—A Novel Formulation of the Currents in a Bipolar Transistor. I.E.E.E. Trans. Electr. Dev. ED-34, 1090 (1987).CrossRefGoogle Scholar
  41. [3.41]
    P. B. Weil, L. P. McNamee: Simulation of Excess Phase in Bipolar Transistors. I. E.E.E. Trans. CAS-25, 114 (1978).Google Scholar
  42. [3.42]
    J. J. H. van den Biesen: A Simple Regional Analysis of Transit Times in Bipolar Transistors. Solid-State Electr. 29, 529 (1986).CrossRefGoogle Scholar
  43. [3.43]
    R. G. Meyer, R. S. Mullen Charge-Control Analysis of the Collector-Base Space- Charge-Region Contribution to Bipolar Transistor Time Constant T T. I. E.E.E. Trans. Electr. Dev. ED-34, 450 (1987).CrossRefGoogle Scholar
  44. [3.44]
    J. A. Pals: On the Noise of a Transistor with d. c. Current Crowding. Philips Res. Rep. 26, 91 (1971).Google Scholar
  45. [3.45]
    J. L. Plumb, E. R. Chenette: Flicker Noise in Transistors. I.E.E.E. Trans. Electr. Dev. ED-10, 304(1963).CrossRefGoogle Scholar
  46. [3.46]
    J. M. C. Stork et al.: High Performance Operation of Silicon Bipolar Transistors at Liquid Nitrogen Temperatures. IEDM Techn. Digest 405 (1987).Google Scholar
  47. [3.47]
    J. W. Slotboom, H. C. de Graaff: Bandgap Narrowing in Silicon Bipolar Transistors. I.E.E.E. Trans. Electr. Dev.ED-24, 1123 (1977).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1990

Authors and Affiliations

  • Henk C. de Graaff
    • 1
  • François M. Klaassen
    • 1
  1. 1.Philips Research LaboratoriesEindhovenThe Netherlands

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