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Further Time-Dependent Examples

  • Richard Ghez
Chapter

Abstract

The constructive (or synthetic) methods of Chaps. 4–6 often require considerable ingenuity. Solving a given diffusion problem depends on our ability to match certain known elementary solutions of the diffusion equation to the initial and boundary conditions. It thus requires detailed knowledge of the behavior of these solutions. In contrast, this last chapter describes deductive (or analytic) methods, based mainly on the Laplace transform, that can be applied with ease to a wide variety of problems.

Keywords

Integral Equation Diffusion Equation Laser Processing Diffusion Problem Skin Depth 
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.
    L. G. Pittaway, “The Temperature Distributions in Thin Foil and Semiinfinite Targets Bombarded by an Electron Beam, ” Brit. J. Appl. Phys. 15, 967 (1964).ADSCrossRefGoogle Scholar
  2. 2.
    D. Maydan, “Micromachining and Image Recording on Thin Films by Laser Beams, ” Bell Syst. Tech. J. 50, 1761 (1971).CrossRefGoogle Scholar
  3. 3.
    R. J. von Gutfeld and P. Chaudhari, “Laser Writing and Erasing on Chalcogenide Films, ” J. Appl. Phys. 43, 4688 (1972).ADSCrossRefGoogle Scholar
  4. 4.
    R. A. Ghez and R. A. Laff, “Laser Heating and Melting of Thin Films on Low-Conductivity Substrates, ” J. Appl. Phys. 46, 2103 (1975).ADSCrossRefGoogle Scholar
  5. 5.
    R. Srinivasan, “Ablation of Polymers and Biological Tissue by Ultraviolet Lasers, ” Science 234, 559 (1986).ADSCrossRefGoogle Scholar
  6. 6.
    J. Marshall, S. Trokel, S. Rothery, and R. P. Krueger, “Photoablative Reprofiling of the Cornea using an Eximer Laser, ” Lasers in Ophthalmology 1, 21 (1986).Google Scholar
  7. 7.
    I. W. Boyd and J. I. B. Wilson, “Laser Processing of Silicon, ” Nature 303, 481 (1983).ADSCrossRefGoogle Scholar
  8. 8.
    I. B. Khaibullin and L. S. Smirnov, “Pulsed Annealing of Semiconductors. Status Report and Unsolved Problems, ” Fiz. Tekh. Poluprovodn. 19, 569 (1985). [Engl. transl. in Sov. Phys. Semicond. 19, 353 (1985).]Google Scholar
  9. 9.
    D. Rosenthal, “The Theory of Moving Sources of Heat and its Application to Metal Treatments, ” Trans. ASME 68, 849 (1947).Google Scholar
  10. 10.
    H. E. Cline and T. R. Anthony, “Heat Treating and Melting with a Scanning Laser or Electron Beam, ” J. Appl. Phys. 48, 3895 (1977).ADSCrossRefGoogle Scholar
  11. 11.
    G. Ehrlich, “Kinetic and Experimental Basis of Flash Desorption, ” J. Appl. Phys. 32, 4 (1961).ADSCrossRefGoogle Scholar
  12. 12.
    P. A. Redhead, “Thermal Desorption of Gases, ” Vacuum 12, 203 (1962).CrossRefGoogle Scholar
  13. 13.
    Thermally Stimulated Relaxation in Solids, P. Bräunlich, Ed. (Springer-Verlag, Berlin, 1979).Google Scholar
  14. 14.
    G. Carter, B. J. Evans, and G. Farrell, “Gas Evolution from a Solid following De-trapping and Diffusion during Tempering, ” Vacuum 25, 197 (1975).CrossRefGoogle Scholar
  15. 15.
    M. A. Frisch, “Studies on Non-equilibrium Reactions by Knudsen Effusion Mass Spectrometry, ” in Adv. in Mass Spectrometry 8A, pp. 391–401, A. Quayle, Ed. (Heyden, London, 1980).Google Scholar
  16. 16.
    J. D. Fehribach, R. Ghez, and G. S. Oehrlein, “Asymptotic Estimates of Diffusion Times for Rapid Thermal Annealing, ” Appl. Phys. Lett. 46, 433 (1985).ADSCrossRefGoogle Scholar
  17. 17.
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Chap. 3 (Reprinted by Dover, New York, 1965).zbMATHGoogle Scholar
  18. 18.
    F. G. Tricomi, Integral Equations (Interscience, New York 1957). [Also reprinted by Dover, New York, 1987.]zbMATHGoogle Scholar
  19. 19.
    W. R. Mann and F. Wolf, “Heat Transfer between Solids and Gasses under Nonlinear Boundary Conditions, ” Quart. Appl. Math. 9, 163 (1951).MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    R. Ghez and J. S. Lew, “Interface Kinetics and Crystal Growth under Conditions of Constant Cooling Rate, ” J. Cryst. Growth 20, 273 (1973).ADSCrossRefGoogle Scholar
  21. 21.
    W. E. Olmstead and R. A. Handelsman, “Diffusion in a Semi-infinite Region with Nonlinear Surface Dissipation, ” SIAM Review 18, 275 (1976).MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    P. L. Chambré and A. Acrivos, “On Chemical Surface Reactions in Laminar Boundary Layers, ” J. Appl. Phys. 27, 1322 (1956).ADSCrossRefGoogle Scholar
  23. 23.
    C. Wagner, “On the Numerical Solution of Volterra Integral Equations, ” J. Math. & Phys. 32, 289 (1954).MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    P. Linz, “Numerical Methods for Volterra Integral Equations with Singular Kernels, ” SIAM J. Numer. Anal. 6, 365 (1969).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    J. C. Jaeger, “Conduction of Heat in a Solid with a Power Law of Heat Transfer at its Surface, ” Proc. Cambr. Phil. Soc. 46, 634 (1950).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    A. C. Norman, “Computing with Formal Power Series, ” ACM Trans. Math. Software 1, 346 (1975).CrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media New York 2001

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