Advertisement

Journal of Nanoparticle Research

, Volume 2, Issue 4, pp 333–344 | Cite as

Forces that Drive Nanoscale Self-assembly on Solid Surfaces

  • Z. Suo
  • W. Lu
Editorial Commentary

Abstract

Experimental evidence has accumulated in the recent decade that nanoscale patterns can self-assemble on solid surfaces. A two-component monolayer grown on a solid surface may separate into distinct phases. Sometimes the phases select sizes about 10 nm, and order into an array of stripes or disks. This paper reviews a model that accounts for these behaviors. Attention is focused on thermodynamic forces that drive the self-assembly. A double-welled, composition-dependent free energy drives phase separation. The phase boundary energy drives phase coarsening. The concentration-dependent surface stress drives phase refining. It is the competition between the coarsening and the refining that leads to size selection and spatial ordering. These thermodynamic forces are embodied in a nonlinear diffusion equation. Numerical simulations reveal rich dynamics of the pattern formation process. It is relatively fast for the phases to separate and select a uniform size, but exceedingly slow to order over a long distance, unless the symmetry is suitably broken.

nanostructure epitaxtial film self-assembly surface stress phase separation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ball P., 1999. The Self-Made Tapestry. Oxford University Press, UK.Google Scholar
  2. Böhringer M.K.,W.-D. Morgenstern, R. Schneider, F. Berndt, A. Mauri, De Vita & R. Car, 1999. Two dimensional self-assembly of supramolecular clusters and chains. Phys. Rev. Lett. 83, 324–327.Google Scholar
  3. Brune H., M. Giovannin, K. Bromann & K. Kern, 1998. Self-organized growth of nanostructure arrays on strain-relief patterns. Nature 394, 451–453.Google Scholar
  4. Cahn J.W., 1961. On spinodal decomposition. Acta Metall. 9, 795–801.Google Scholar
  5. Cahn J.W. & J.E. Hilliard, 1958. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258–267.Google Scholar
  6. Cammarata R.C., 1994. Surface and interface stress effects in thin films. Prog. Surf. Sci. 46, 1–38.Google Scholar
  7. Chen L.-Q. & A.G. Khachaturyan, 1993. Dynamics of simultaneous ordering and phase separation and effect of long-range coulomb interactions. Phys. Rev. Lett. 70, 1477–1480.Google Scholar
  8. Chen L.-Q. & J. Shen, 1998. Applications of semi-implicit Fourier-spectral method to phase field equations. Computer Physics Communications 108, 14–158.Google Scholar
  9. Chen L.Q. & Y. Wang, 1996. The continuum field approach to modeling microstructural evolution. JOM 48 (December Issue), 13–18.Google Scholar
  10. Chou S.Y. & L. Zhuang, 1999. Lithographically-induced self-assembly of periodic polymer micropillar arrays. J. Vac. Sci. Tech. B 17, 3197–3202.Google Scholar
  11. Clark P.G. & C.M. Friend, 1999. Interface effects on the growth of cobalt nanostructures on molybdenum-based structures. J. Chem. Phys. 111, 6991–6996.Google Scholar
  12. Giess E.A., 1980. Magnetic-bubble materials. Science 208, 938–943.Google Scholar
  13. Ibach H., 1997. The role of surface stress in reconstruction, epitaxtial growth and stabilization of mesoscopic structures. Surf. Sci. Rep. 29, 193–263.Google Scholar
  14. Johnson K.L., 1985. Contact Mechanics. Cambridge University Press, UK.Google Scholar
  15. Kern K., H. Niebus, A. Schatz, P. Zeppenfeld, J. George & G. Comsa, 1991. Long range spatial self-organization in the adsorbate-induced restructuring of surfaces: Cu{110}-(2 x 1)O. Phys. Rev. Lett. 67, 855–858.Google Scholar
  16. Lu W. & Z. Suo, 1999. Coarsening, refining, and pattern emergence in binary epilayers. Zeitschrift fur Metallkunde, 90, 956–960.Google Scholar
  17. Lu W. & Z. Suo, 2001. Dynamics of nanoscale pattern formation of an epitaxtial monolayer. Prepared for a special issue of Journal of the Mechanics and Physics of Solids dedicated to Professors of J.W. Hutchinson and J.R. Rice on the occasion of their 60th birthdays.Google Scholar
  18. Martin J.W., R.D. Doherty & B. Cantor, 1997. Stability of Microstructure in Metallic Systems. 2nd edn. Cambridge University Press, UK.Google Scholar
  19. Murray C.B., C.R. Kagan & M.G. Bawendi, 2000. Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies. Annu. Rev. Mater. Sci. 30, 545–610.Google Scholar
  20. Narasimhan S. & D. Vanderbilt, 1992. Elastic stress domain and herringbone reconstruction on Au (111). Phys. Rev. Lett. 69, 1564–1567.Google Scholar
  21. Ng K.-O. & D. Vanderbilt, 1995. Stability of periodic domain structures in a two dimensional dipolar model. Phys. Rev. B 52, 2177–2183.Google Scholar
  22. Park M., C. Harrison, P.M. Chaikin, R.A. Register & D.H. Adamson, 1997. Block copolymer lithography: periodic arrays of ~1011 holes in 1 square centimeter. Science 276, 1401–1404.Google Scholar
  23. Parker T.M., L.K. Wilson & N.G. Condon, 1997. Epitaxy controlled by self-assembled nanometer-scale structures. Phys. Rev. B 56, 6458–6461.Google Scholar
  24. Pohl K., M.C. Bartelt, J. de la Figuera, N.C. Bartelt, J. Hrbek & R.Q. Hwang, 1999. Identifying the forces responsible for self-organization of nanostructures at crystal surfaces. Nature 397, 238–241.Google Scholar
  25. Röder H., R. Schuster, H. Brune & K. Kern, 1993. Monolayer-confined mixing at the Ag-Pt(111) interface. Phys. Rev. Lett. 71, 2086–2089.Google Scholar
  26. Seul M. & D. Andelman. Domain shapes and patterns: the phenomenology of modulated phases. Science 267, 476–483.Google Scholar
  27. Su C.H. & P.W. Voorhees, 1996. The dynamics of precipitate evolution in elastically stressed solids. Acta Mater 44, 1987–2016.Google Scholar
  28. Suo Z., 2000. Evolving materials structures of small feature sizes. Int. J. Solids Structures. 37, 367–378.Google Scholar
  29. Suo Z. & W. Lu, 2000a Composition modulation and nanophase separation in a binary epilayer. J. Mech. Phys. Solids. 48, 211–232.Google Scholar
  30. Suo Z. & W. Lu, 2000b. Self-organizing nanophases on a solid surface. In: ChuangT.J., ed. Multi-Scale Deformation and Fracture in Materials and Structures. A book dedicated to Professor James R. Rice on the occasion of his 60th birthday. (to be published by Kluwer Academic Publishers)Google Scholar
  31. Timoshenko S.P. & J.N. Goodier, 1970. Theory of Elasticity. McGraw-Hill Book Company, New York.Google Scholar
  32. Vanderbilt D., 1997. Ordering at surfaces from elastic and electrostatic interactions. Surface Rev. Lett. 4, 811–816.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Z. Suo
    • 1
  • W. Lu
    • 2
  1. 1.Department of Mechanical and Aerospace Engineering, Princeton Materials InstitutePrinceton UniversityPrincetonUSA
  2. 2.Department of Mechanical and Aerospace Engineering, Princeton Materials InstitutePrinceton UniversityPrincetonUSA

Personalised recommendations