Obtaining Thermodynamic Information from Kinetic Measurements: Island Shape, Evaporation, and Coarsening

  • Horia I. Metiu
Part of the NATO ASI Series book series (NSSB, volume 360)


Atoms deposited on a solid surface at sufficiently high temperature diffuse, meet, aggregate, and form many one-atom-high islands. During and after deposition the edge atoms move around the islands or “evaporate” onto the substrate, and the islands capture atoms from the gas surrounding them. These processes change the sizes and the shapes1–27 of the islands and lead to coarsening.28–32 In this lecture we examine some aspects of island-shape thermodynamics and its equilibrium with a two-dimensional gas, and the kinetics of evaporation. In addition we propose a fast method for atomic-level simulations of coarsening. We focus on recent work at Santa Barbara and some of the classic work needed to place it in proper context. We do not attempt a comprehensive review of important work by others.


Evaporation Rate Single Atom External Variable Equilibrium Shape Straight Edge 
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.


  1. 1.
    B. S. Swartzentruber and M. Schacht, Surface Sci. 322, 83 (1995).ADSCrossRefGoogle Scholar
  2. 2.
    R. M. Tromp and M. C. Reuter, Phys. Rev. Lett. 68, 820 (1992).ADSCrossRefGoogle Scholar
  3. 3.
    N. C. Bartelt, J. L. Goldberg, T. L. Einstein, et al., Surface Sci. 273, 252 (1992).ADSCrossRefGoogle Scholar
  4. 4.
    N. C. Bartelt, J. L. Goldberg, T. L. Einstein, et al., Phys. Rev. B 48, 15453 (1993).ADSCrossRefGoogle Scholar
  5. 5.
    N. C. Bartelt, R. M. Tromp, and E. D. Williams, Phys. Rev. Lett. 73, 1565 (1994).MathSciNetCrossRefGoogle Scholar
  6. 6.
    N. C. Bartelt, T. L. Einstein, and E. D. Williams, Surface Sci. 312, 411 (1994).ADSCrossRefGoogle Scholar
  7. 7.
    M. Giesen-Seibert, R. Jentjens, M. Poensgen, et al., Phys. Rev. Lett. 71, 3521 (1993).ADSCrossRefGoogle Scholar
  8. 8.
    M. Giesen-Seibert and H. Ibach, Surface Sci. 316, 205 (1994).ADSCrossRefGoogle Scholar
  9. 9.
    J. Jacobsen, K. W. Jacobsen, P. Stoltze, et al., Phys. Rev. Lett. 74, 2295 (1995).ADSCrossRefGoogle Scholar
  10. 10.
    J. Jacobsen, K. W. Jacobsen, and J. K. Norskov, Surface Sci. 359, 37 (1996).ADSCrossRefGoogle Scholar
  11. 11.
    N. Kitamura, B. S. Swartzentruber, M. G. Lagally, et al., Phys. Rev. B 48, 5704 (1993).ADSCrossRefGoogle Scholar
  12. 12.
    L. Kuipers, L. M. S. Hoogeman, and J. W. M. Frenken, Phys. Rev. Lett. 71, 3517 (1993).ADSCrossRefGoogle Scholar
  13. 13.
    R. Kunkel, K. L. Poelsema, L. K. Verheij, et al., Phys. Rev. Lett. 65, 733 (1990).ADSCrossRefGoogle Scholar
  14. 14.
    S. Liu, Z. Zhang, G. Comsa, et al., Phys. Rev. Lett. 71, 2967 (1993).ADSCrossRefGoogle Scholar
  15. 15.
    Y. W. Mo, B. S. Swartzentruber, R. Kariotis, et al., Phys. Rev. Lett. 63, 2393 (1989).ADSCrossRefGoogle Scholar
  16. 16.
    Y. W. Mo, R. Kariotis, and B. S. Swartzentruber, J. Vacuum Sci. Tech. 8, 201 (1990).ADSCrossRefGoogle Scholar
  17. 17.
    K. Morgenstern, G. Rosenfeld, and G. Comsa, Phys. Rev. Lett. 76, 2113 (1996).ADSCrossRefGoogle Scholar
  18. 18.
    V. V. Pai, N. C. Bartelt, and J. E. Reutt-Robey, Phys. Rev. B 53, 15991 (1996).ADSCrossRefGoogle Scholar
  19. 19.
    M. Poensgen, J. F. Wolf, J. Frohn, et al., Surface Sci. 274, 430 (1992).ADSCrossRefGoogle Scholar
  20. 20.
    H. Shao, S. Liu, and H. Metiu, Phys. Rev. B 51, 7827 (1995).ADSCrossRefGoogle Scholar
  21. 21.
    H. Shao, P. C. Weakliem, and H. Metiu, Phys. Rev. B 53, 16041 (1996).ADSCrossRefGoogle Scholar
  22. 22.
    D. S. Sholl and R. Skodje, Phys. Rev. Lett. 75, 3158 (1995).ADSCrossRefGoogle Scholar
  23. 23.
    J. Tersoff and E. Pehlke, Phys. Rev. Lett. 68, 816 (1992).ADSCrossRefGoogle Scholar
  24. 24.
    W. Theis, N. C. Bartelt, and R. M. Tromp, Phys. Rev. Lett. 75, 3328 (1995).ADSCrossRefGoogle Scholar
  25. 25.
    S. C. Wang and G. Ehrlich, Surface Sci. 239, 301 (1990).ADSCrossRefGoogle Scholar
  26. 26.
    J.-M. Wen, S.-L. Chang, J. W. Burnett, et al., Phys. Rev. Lett. 73, 2591 (1994).ADSCrossRefGoogle Scholar
  27. 27.
    J.-K. Zuo and J. F. Wendelken, Phys. Rev. Lett. 70, 1662 (1993).ADSCrossRefGoogle Scholar
  28. 28.
    P. Wynblatt and N. A. Gjostein, in Progress in Solid State Chemistry, edited by J. O. McCaldin and G. Somorjai (Pergamon, Oxford, 1975), Vol. 9, p. 21.Google Scholar
  29. 29.
    M. Zinke-Allmang, L. C. Feldman, and M. H. Grabow, Surface Sci. Rep. 16, 377 (1992).ADSCrossRefGoogle Scholar
  30. 30.
    C. Wagner, Z. Electrochem. 65, 581 (1961).Google Scholar
  31. 31.
    B. K. Chakraverty, J. Phys. Chem. Solids 28, 2401 (1967).ADSCrossRefGoogle Scholar
  32. 32.
    W. Ostwald, Z. Phys. Chem.(Leipzig) 34, 495 (1900).Google Scholar
  33. 33.
    B. Krishnamachari, J. McLean, B. Cooper, et al., Phys. Rev. B, to appear (1996).Google Scholar
  34. 34.
    D. R. Peale and B. H. Cooper, J. Vac. Sci. Tech. A 10, 2210 (1992).ADSGoogle Scholar
  35. 35.
    M. Bartelt and J. W. Evans, Phys. Rev. B 46, 12675 (1992).ADSCrossRefGoogle Scholar
  36. 36.
    M. Bartelt and J. W. Evans, Surface Sci. 298, 421 (1993).ADSCrossRefGoogle Scholar
  37. 37.
    G. S. Bales and D. C. Chrzan, Phys. Rev. B 50, 6057 (1994).ADSCrossRefGoogle Scholar
  38. 38.
    J. A. Venables, G. D. Spiller, and M. Hanbüken, Rep. Prog. Phys. 47, 399 (1984).ADSCrossRefGoogle Scholar
  39. 39.
    A. F. Voter, Phys. Rev. B 34, 6819 (1986).ADSCrossRefGoogle Scholar
  40. 40.
    J. M. Soler, Phys. Rev. B 50, 5578 (1994).ADSCrossRefGoogle Scholar
  41. 41.
    K. Morgenstern, G. Rosenfeld, B. Poelsema, et al., Phys. Rev. Lett. 74, 2058 (1995).ADSCrossRefGoogle Scholar
  42. 42.
    S. V. Khare, N. C. Bartelt, and T. L. Einstein, Phys. Rev. Lett. 75, 2148 (1995).ADSCrossRefGoogle Scholar
  43. 43.
    N. C. Bartelt, R. M. Tromp, and E. D. Williams, Phys. Rev. Lett. 73, 1656 (1994).ADSCrossRefGoogle Scholar
  44. 44.
    G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures (Halsted Press, New York, 1988).Google Scholar
  45. 45.
    C. Weisbuch and B. Binter, Quantum Semiconductor Structures (Academic Press, New York, 1991).Google Scholar
  46. 46.
    P. C. Weakliem, H. Shao, and H. Metiu, in preparation (1966).Google Scholar
  47. 47.
    K. A. Fichthorn and W. H. Weinberg, J. Chem. Phys. 95, 1090 (1991).ADSCrossRefGoogle Scholar
  48. 48.
    D. T. Gillespie, J. Comp. Phys. 22, 403 (1976).MathSciNetADSCrossRefGoogle Scholar
  49. 49.
    D. T. Gillespie, J. Stat. Phys. 16, 311 (1977).MathSciNetADSCrossRefGoogle Scholar
  50. 50.
    D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977).CrossRefGoogle Scholar
  51. 51.
    D. T. Gillespie, J. Comp. Phys. 28 (1978).Google Scholar
  52. 52.
    P. A. Maksym, Semicond. Sci. Technol. 3, 594 (1988).ADSCrossRefGoogle Scholar
  53. 53.
    F. Liu and H. Metiu, Phys. Rev. B 48, 5808 (1993).ADSCrossRefGoogle Scholar
  54. 54.
    J. Villain, J. Phys. I(France) 1, 19 (1991).CrossRefGoogle Scholar
  55. 55.
    J. W. Gibbs, The Scientific Papers of J. W. Gibbs (Dover Publications, New York, 1961).Google Scholar
  56. 56.
    R. Defay and I. Prigogine, Surface Tension and Absorption (Longmans Green, London, 1966).Google Scholar
  57. 57.
    J. Cahn and J. E. Hilliard, J. Chem. Phys. 28, 258 (1958).ADSCrossRefGoogle Scholar
  58. 58.
    J. S. Rowlinson and B. Widom, Molecular Theory of Capilarity (Clarendon Press, Oxford, 1989).Google Scholar
  59. 59.
    G. Wulff, Z. Kristallogr. Mineral 34, 449 (1901).Google Scholar
  60. 60.
    I. V. Markov, Crystal Growth for Beginners (World Scientific, Singapore, 1995).Google Scholar
  61. 61.
    P. Noziere, in Solids Far From Equilibrium, edited by C. Godrèche (University Press, Cambridge, 1992).Google Scholar
  62. 62.
    L. Möllnitz, J. Jacobsen, J. Norskov, et al., in preparation (1996).Google Scholar
  63. 63.
    P. Curie, Bull. Soc. Miner. France 8, 195 (1885).Google Scholar
  64. 64.
    T. L. Hill, An Introduction to Statistical Thermodynamics (Dover Publications, Inc., New York, 1986).Google Scholar
  65. 65.
    R. C. Nelson, T. L. Einstein, S. V. Khare, et al., Surface Sci. 295, 462 (1993).ADSCrossRefGoogle Scholar
  66. 66.
    P. Stoltze, J. Phys. Cond. Matter 6, 9495 (1994).ADSCrossRefGoogle Scholar
  67. 67.
    L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon Press, New York, 1986).Google Scholar
  68. 68.
    J. Villain and A. Pimpinelli, Physique de la Croissance Crystalline (Eirolles, Paris, 1995).Google Scholar
  69. 69.
    M. A. van Hove, R. J. Koestner, P. C. Stair, et al., Surface Sci. 103, 189; ibid. 218 (1981).Google Scholar
  70. 70.
    K. H. Rieder, T. Engel, R. H. Swedsen, et al., Surface Sci. 127, 223 (1983).ADSCrossRefGoogle Scholar
  71. 71.
    G. K. Binnig, H. Rohrer, C. Gerber, et al., Surface Sci. 144, 321 (1984).ADSCrossRefGoogle Scholar
  72. 72.
    K. Yamazaki, K. Takayanagi, Y. Tanishiro, et al., Surface Sci. 199, 595 (1988).ADSCrossRefGoogle Scholar
  73. 73.
    S. Günter, E. Kopatzki, M. C. Bartelt, et al., Phys. Rev. Lett. 73, 553 (1994).ADSCrossRefGoogle Scholar
  74. 74.
    L. Bönig, S. Liu, and H. Metiu, Surface Sci. 365, 87 (1996).CrossRefGoogle Scholar
  75. 75.
    L. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961).ADSCrossRefGoogle Scholar
  76. 76.
    N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1990).Google Scholar
  77. 77.
    H. Metiu and G. Rosenfeld, Surface Sci. Lett., submited (1996).Google Scholar
  78. 78.
    M. C. Bartelt and J. W. Evans, Surface Sci. 298, 421–431 (1993).ADSCrossRefGoogle Scholar
  79. 79.
    J. A. Venables, G. D. Spiller, and M. Handbücken, Report. Prog. Phys. 47, 399 (1984).ADSCrossRefGoogle Scholar
  80. 80.
    S. Liu, L. Bönig, and H. Metiu, in preparation (1996).Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Horia I. Metiu
    • 1
  1. 1.Departments of Chemistry and Physics, and the Center for Quantized Electronic StructuresUniversity of CaliforniaSanta BarbaraUSA

Personalised recommendations