Skip to main content
SpringerLink
Log in

Phase-field crystal modeling of shape transition of strained islands in heteroepitaxy

  • Article
  • Published:
Science China Physics, Mechanics and Astronomy Aims and scope Submit manuscript

Abstract

The phase-field crystal (PFC) model is employed to study the shape transition of strained islands in heteroepitaxy on vicinal substrates. The influences of both substrate vicinal angles β and the lattice mismatch ζ are discussed. The increase of substrate vicinal angles is found to be capable of significantly changing the surface nanostructures of epitaxial films. The surface morphology of films undergoes a series of transitions that include Stranski-Krastonov (SK) islands, the couple growth of islands and the step flow as well as the formation of step bunching. In addition, the larger ζ indicates an increased strained island density after coarsening, and results in the incoherent growth of strained islands with the creation of misfit dislocations. Coarsening, coalescence and faceting of strained islands are also observed. Some facets in the shape transition of strained islands are found to be stable and can be determined by β and crystal symmetry of the film.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zhu R, Pan E, Chung P W. Fast multiscale kinetic Monte Carlo simulations of three-dimensional self-assembled quantum dot islands. Phys Rev B, 2007, 75: 205339

    Article  ADS  Google Scholar 

  2. Tromp R M, Ross F M, Rerter M C. Instability-driven SiGe island growth. Phys Rev Lett, 2000, 84: 4641–4644

    Article  ADS  Google Scholar 

  3. Spencer B J, Blanariu M. Shape and composition map of a prepyramid quantum dot. Phys Rev Lett, 2005, 95: 206101

    Article  ADS  Google Scholar 

  4. Li A, Liu F, Lagally M G. Equilibrium shape of two-dimensional islands under stress. Phys Rev Lett, 2000, 85: 1922–1925

    Article  ADS  Google Scholar 

  5. Tersoff J, Tromp R W. Shape transition in growth of strained islands: Spontaneous formation of quantum wires. Phys Rev Lett, 1993, 70: 2782–2785

    Article  ADS  Google Scholar 

  6. Li W X, Zhang J, Shen T H, et al. Magnetic nanowires fabricated by anodic aluminum oxide template—a brief review. Sci China-Phys Mech Astron, 2011, 54(7): 1181–1189

    Article  ADS  Google Scholar 

  7. Chen D, Xiong S, Ran S H, et al. One-dimensional iron oxides nanostructures. Sci China-Phys Mech Astron, 2011, 54(7): 1190–1199

    Article  ADS  Google Scholar 

  8. Huang Z F, Elder K R. Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude-equation analysis of the phase-field-crystal model. Phys Rev B, 2010, 81: 165421

    Article  ADS  Google Scholar 

  9. Tersoff J, Spencer J, Rastelli A, et al. Barrierless formation and faceting of SiGe islands on Si(001). Phys Rev Lett, 2002, 89: 196104

    Article  ADS  Google Scholar 

  10. Sutter P, Lagally M G. Nucleationless three-dimensional island formation in low-misfit heteroepitaxy. Phys Rev Lett, 2000, 84: 4637–4640

    Article  ADS  Google Scholar 

  11. Floro J A, Sinclair M B, Chason E, et al. Novel SiGe island coarsening kinetics: ostwald ripening and elastic interactions. Phys Rev Lett, 2000, 84: 701–704

    Article  ADS  Google Scholar 

  12. Guyer J E, Voorhees P W. Morphological stability of alloy thin films. Phys Rev Lett, 1995, 74: 4031–4034

    Article  ADS  Google Scholar 

  13. Hankea M, Schmidbauer M, Kohler R, et al. Lateral short range ordering of step bunches in InGaAs/GaAs superlattices. J Appl Phys, 2004, 95: 1736–1739

    Article  ADS  Google Scholar 

  14. Wang Z M, Shultz J L, Salamo G J. Morphology evolution during strained (In,Ga) as epitaxial growth on GaAs vicinal (100) surfaces. Appl Phys Lett, 2003, 83: 1749–1751

    Article  ADS  Google Scholar 

  15. Eggleston J J, Voorheesa P W. Ordered growth of nanocrystals via a morphological instability. Appl Phys Lett, 2002, 80: 306–308

    Article  ADS  Google Scholar 

  16. Tu Y H, Tersoff J. Coarsening, mixing, and motion: The complex evolution of epitaxial islands. Phys Rev Lett, 2007, 98: 096103

    Article  ADS  Google Scholar 

  17. Chiu C, Poh C T. Strain energy of nanoislands on strained film-substrate systems. Phys Rev B, 2005, 71: 045706

    Article  ADS  Google Scholar 

  18. Lung M T, Lam C H, Sander L M. Island, pit, and groove formation in strained heteroepitaxy. Phys Rev Lett, 2005, 95: 086102

    Article  ADS  Google Scholar 

  19. Park Y, Tan W, Strachan A. Strain engineering via amorphization and recrystallization in Si/Ge heterostructures. Phys Rev B, 2011, 84: 125412

    Article  ADS  Google Scholar 

  20. Elder K R, Katakowski M, Haataja M, et al. Modeling elasticity in crystal growth. Phys Rev Lett, 2002, 88: 245701

    Article  ADS  Google Scholar 

  21. Elder K R, Grant M. Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals. Phys Rev E, 2004, 70: 051605

    Article  ADS  Google Scholar 

  22. Provatas N, Dantzig J A, Athreya B, et al. Using the phase-field crystal method in the multi-scale modeling of microstructure evolution. JOM, 2007, 59: 83–90

    Article  Google Scholar 

  23. Elder K R, Huang Z F, Provatas N. Amplitude expansion of the binary phase-field-crystal model. Phys Rev E, 2010, 81: 011602

    Article  ADS  Google Scholar 

  24. Huang Z F, Elder K R, Provatas N. Phase-field-crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures. Phys Rev E, 2010, 82: 021605

    Article  ADS  Google Scholar 

  25. Yu Y M, Backofen R, Voigt A. Morphological instability of heteroepitaxial growth on vicinal substrates: A phase-field crystal study. J Cryst Growth, 2011, 318: 18–22

    Article  ADS  Google Scholar 

  26. Teeffelen S, Backofen R, Voigt A, et al. Derivation of the phase-field-crystal model for colloidal solidification. Phys Rev E, 2009, 79: 051404

    Article  ADS  Google Scholar 

  27. Tegze G, Granasy L, Toth G I, et al. Tuning the structure of non-equilibrium soft materials by varying the thermodynamic driving force for crystal ordering. Soft Matter, 2011, 7: 1789–1799

    Article  ADS  Google Scholar 

  28. Greenwood M, Provatas N, Rottler J. Free energy functionals for efficient phase field crystal modeling of structural phase transformations. Phys Rev Lett, 2010, 105: 045702

    Article  ADS  Google Scholar 

  29. Wu K A, Voorhees P W. Phase field crystal simulations of nanocrystalline grain growth in two dimensions. Acta Mater, 2012, 60: 407–419

    Article  Google Scholar 

  30. Toth G I, Tegze G, Pusztai T, et al. Heterogeneous crystal nucleation: The effect of lattice mismatch. Phys Rev Lett, 2012, 108: 025502

    Article  ADS  Google Scholar 

  31. Tang S, Backofen R, Wang J C, et al. Three-dimensional phase-field crystal modeling of fcc and bcc dendritic crystal growth. J Cryst Growth, 2011, 334: 146–152

    Article  ADS  Google Scholar 

  32. Huang Z F, Elder K R. Mesoscopic and microscopic modeling of island formation in strained film epitaxy. Phys Rev Lett, 2008, 101: 158701

    Article  ADS  Google Scholar 

  33. Achim C V, Karttunen M, Elder K R, et al. Phase diagram and commensurate-incommsurate transitions in the phase field crystal model with an external pinning potential. Phys Rev E, 2006, 74: 021104

    Article  ADS  Google Scholar 

  34. Granasy L, Tegze G, Toth G I, et al. Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning. Philos Mag, 2011, 91: 123–143

    Article  ADS  Google Scholar 

  35. Elder K R, Provatas N, Berry J, et al. Phase field crystal modeling and classical density functional theory of freezing. Phys Rev B, 2007, 75: 064107

    Article  ADS  Google Scholar 

  36. Wise S M, Lowengrub J S, Kim J S, et al. Quantum dot formation on a strain-patterned epitaxial thin film. Appl Phys Lett, 2005, 87: 133102

    Article  ADS  Google Scholar 

  37. Teichert C. Self-organization of nanostructures in semiconductor heteroepitaxy. Phys Rep, 2005, 365: 335–432

    Article  ADS  Google Scholar 

  38. Spencer B J, Voorhees P W, Davis S H. Morphological instability in epitaxially strained dislocation-free solid films: Linear stability theory. J Appl Phys, 1993, 73: 4955–4970

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an, 710072, China

    Cheng Chen, Zheng Chen, Jing Zhang & XiuJuan Du

Authors
  1. Cheng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jing Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. XiuJuan Du
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cheng Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, C., Chen, Z., Zhang, J. et al. Phase-field crystal modeling of shape transition of strained islands in heteroepitaxy. Sci. China Phys. Mech. Astron. 55, 2042–2048 (2012). https://doi.org/10.1007/s11433-012-4896-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-012-4896-1

Keywords

Search

Navigation