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Steady-State Examples

  • Richard Ghez
Chapter

Abstract

This chapter introduces the notion of steady state through several physically significant examples. Indeed, there exist many time-dependent problems, among which are problems of phase growth, whose solution can be “almost” at steady state. Such is the case for oxidation kinetics, precipitate growth, and crystal growth under conditions of constant supersaturation. Along the way, the equilibrium properties of binary systems and of “small” phases will be reviewed.

Keywords

Crystal Growth Thermal Oxidation Parent Phase Critical Radius Parabolic Rate Constant 
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.

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References

  1. 1.
    R. P. Smith, “The Diffusivity of Carbon in Iron by the Steady-State Method, ” Acta Met. 1, 578 (1953).CrossRefGoogle Scholar
  2. 2.
    H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed., pp. 188–193 (Oxford University Press, London, 1959).zbMATHGoogle Scholar
  3. 3.
    W. G. Oldham, “The Fabrication of Microelectronic Circuits, ” Scientific American 237, pp. 110–128 (September 1977). [That whole issue is devoted to microelectronics. The reader can gauge the accelerating pace of technological change, since then by consulting the October 1986, February 1990, and June 1993 issues of Physics Today.]CrossRefGoogle Scholar
  4. 4.
    B. E. Deal and A. S. Grove, “General Relationship for the Thermal Oxidation of Silicon, ” J. Appl. Phys. 36, 3770 (1965).ADSCrossRefGoogle Scholar
  5. 5.
    E. Rosencher, A. Straboni, S. Rigo, and G. Amsel, “An 18O Study of the Thermal Oxidation of Silicon in Oxygen, ” Appl. Phys. Lett. 34, 254 (1979).ADSCrossRefGoogle Scholar
  6. 6.
    U. R. Evans, The Corrosion and Oxidation of Metals (Edward Arnold Ltd., London, 1960).Google Scholar
  7. 7.
    E. A. Irene and Y. J. van der Meulen, “Silicon Oxidation Studies: Analysis of SiO2 Film Growth Data, ” J. Electrochem. Soc. 123, 1380 (1976).CrossRefGoogle Scholar
  8. 8.
    E. A. Irene and D. W. Dong, “Silicon Oxidation Studies: The Oxidation of Heavily B- and P-Doped Single Crystal Silicon, ” J. Electrochem. Soc. 125, 1146(1978).Google Scholar
  9. 9.
    K. J. Laidler, Chemical Kinetics, 2nd ed. (McGraw-Hill, New York, 1965).Google Scholar
  10. 10.
    R. Ghez and Y. J. van der Meulen, “Kinetics of Thermal Growth of Ultra-thin Layers of SiO2 on Silicon. Part II: Theory” J. Electrochem. Soc. 119, 1100(1972).Google Scholar
  11. 11.
    E. A. Irene, “Evidence for a Parallel Path Oxidation Mechanism at the Si-SiO2 Interface, ” Appl. Phys. Lett. 40, 74 (1982).ADSCrossRefGoogle Scholar
  12. 12.
    H. Z. Massoud, J. D. Plummer, and E. A. Irene, “Thermal Oxidation of Silicon in Dry Oxygen: Growth-Rate Enhancement in the Thin Regime, Parts I and II, ” J. Electrochem. Soc. 132, 2685 and 2693 (1985).CrossRefGoogle Scholar
  13. 13.
    E. Bassous, H. N. Yu, and V. Maniscalco, “Topology of Silicon Structures with Recessed SiO2, ” J. Electrochem. Soc. 123, 1729 (1976).ADSCrossRefGoogle Scholar
  14. 14.
    R. B. Marcus and T. T. Sheng, “The Oxidation of Shaped Silicon Surfaces, ” J. Electrochem. Soc. 129, 1278 (1982).CrossRefGoogle Scholar
  15. 15.
    L. O. Wilson, “Numerical Simulation of Gate Oxide Thinning in MOS Devices, ” J. Electrochem. Soc. 129, 831 (1982).CrossRefGoogle Scholar
  16. 16.
    Proceedings of “Workshop on Oxidation Processes, ” Phil. Mag. 55, February and June issues (1987).Google Scholar
  17. 17.
    J. W. Gibbs, “On the Equilibrium of Heterogeneous Substances, ” Trans. Conn. Acad. (1875–1878). [Reprinted in Scientific Papers, Vol. 1 (Dover, New York, 1961).]Google Scholar
  18. 18.
    R. Defay and I. Prigogine, Tension Superficielle et Adsorption (Editions Desoer, Liège 1951). [Engl. transl. by D. H. Everett (John Wiley, New York, 1966).]Google Scholar
  19. 19.
    F. P. Buff, “The Theory of Capillarity, ” in Handbuch der Physik, Vol. 10, pp. 281–304 (Springer Verlag, Berlin, 1960).Google Scholar
  20. 20.
    E. A. Guggenheim, Thermodynamics, An Advanced Treatment for Chemists and Physicists (North-Holland, Amsterdam, 1986).zbMATHGoogle Scholar
  21. 21.
    R. Ghez, “A Theoretical Crystal Grower’s View of Phase Equilibria, ” in Crystal Growth in Science and Technology, Proceedings of the International School of Crystallography, Erice, 1987, NATO Advanced Study Institute, Vol. B-210, pp. 1–26 (Plenum Publishing, New York 1989).Google Scholar
  22. 22.
    E. A. Guggenheim, Mixtures (Oxford University Press, London, 1952).zbMATHGoogle Scholar
  23. 23.
    A. S. Jordan and M. E. Weiner, “The Effect of the Heat Capacity of the Liquid Phase on the Heat of Fusion Liquidus Equation of Compound Semiconductors, ” J. Phys. Chem. Sol 36, 1335 (1975).ADSCrossRefGoogle Scholar
  24. 24.
    J. D. Honeycutt and H. C. Anderson, “Small System Size Artifacts in the Molecular Dynamics Simulation of Homogeneous Crystal Nucleation in Supercooled Atomic Liquids, ” J. Phys. Chem. 90, 1585 (1986).CrossRefGoogle Scholar
  25. 25.
    F. S. Ham, “Shape-Preserving Solutions of the Time-Dependent Diffusion Equation, ” Quart. Appl. Math. 17, 137 (1959).MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    R. F. Sekerka, “Morphologocal Stability, ” in Crystal Growth: An Introduction, pp. 403–443, P. Hartman, Ed. (North-Holland, Amsterdam 1973).Google Scholar
  27. 27.
    J. S. Langer, “Instabilities and Pattern Formation in Crystal Growth, ” Rev. Mod. Phys. 52, 1 (1980).ADSCrossRefGoogle Scholar
  28. 28.
    M. Kahlweit, “Precipitation and Aging, ” in Physical Chemistry, an Advanced Treatise, Vol. 10, pp. 719–759, H. Eyring, D. Henderson, and W. Jost, Eds. (Academic Press, New York, 1970).Google Scholar
  29. 29.
    I. M. Lifshitz and V. V. Slyozov, “The Kinetics of Precipitation from Supersaturated Solid Solutions, ” J. Phys. Chem. Sol. 19, 35 (1961).ADSCrossRefGoogle Scholar
  30. 30.
    C. Wagner, “Theorie der Alterung von Niederschlägen durch Umlösen, ” Zeitschr. für Elektrochemie 65, 581 (1961).Google Scholar
  31. 31.
    P. W. Voorhees, “The Theory of Ostwald Ripening, ” J. Stat. Phys. 38, 231 (1985).ADSCrossRefGoogle Scholar
  32. 32.
    B. Lewis and G. J. Rees, “Adatom Migration, Capture, and Decay among Competing Nuclei on a Substrate, ” Phil. Mag. 29, 1253 (1974).ADSCrossRefGoogle Scholar
  33. 33.
    J. A. Venables and G. L. Price, “Nucleation of Thin Films, ” in Epitaxial Growth, Part B, pp. 381–436, J. W. Matthews, Ed. (Academic Press, New York, 1975).CrossRefGoogle Scholar
  34. 34.
    W. K. Burton, N. Cabrera, and F. C. Frank, “The Growth of Crystals and the Equilibrium Structure of their Surfaces, ” Phil. Trans. Roy. Soc. (London) A243, 299 (1951).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    J. Frenkel, “On the Surface Motion of Particles in Crystals and the Natural Roughness of Crystalline Faces, ” J. Phys. USSR 9, 392 (1945).Google Scholar
  36. 36.
    M. Volmer, Kinetik der Phasenbildung (Th. Steinkopff Verlag, Dresden, 1939).Google Scholar
  37. 37.
    P. Bennema and G. H. Gilmer, “Kinetics of Crystal Growth, ” in Crystal Growth: An Introduction, pp. 263–327, P. Hartman, Ed. (North-Holland, Amsterdam, 1973).Google Scholar
  38. 38.
    A. A. Chernov, “The Spiral Growth of Crystals, ” Usp. Fiz. Nauk. 73, 277 (1961). [Engl. transl. in Sov. Phys. Usp. 1, 116 (1961).]CrossRefGoogle Scholar
  39. 39.
    A. A. Chernov, Modern Crystallography III: Crystal Growth (Springer-Verlag, Berlin 1984).CrossRefGoogle Scholar
  40. 40.
    R. Ghez and S. S. Iyer, “The Kinetics of Fast Steps on Crystal Surfaces and its Application to the Molecular Beam Epitaxy of Silicon, ” IBM J. Res. & Dev. 32, 804 (1988).CrossRefGoogle Scholar
  41. 41.
    G H. Gilmer, “Growth on Imperfect Crystal Faces, ” J. Cryst. Growth 35, 15 (1976).ADSCrossRefGoogle Scholar
  42. 42.
    G. H. Gilmer, “Computer Models of Crystal Growth, ” Science 208, 355 (1980).ADSCrossRefGoogle Scholar

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© Springer Science+Business Media New York 2001

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  • Richard Ghez

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