Journal of Materials Science

, Volume 53, Issue 8, pp 5777–5785 | Cite as

Anisotropy effect on strain-induced instability during growth of heteroepitaxial films

  • X. Zhang
  • Y. Wang
  • W. Cai
Interface Behavior


The use of misfit strain to improve the electronic performance of semiconductor films is a common strategy in modern electronic and photonic device fabrication. However, pursuing a favorable higher strain could lead to mechanical instability, on which systematic and quantitative understandings are yet to be achieved. In this paper, we investigate the anisotropy effects on strain-induced thin-film surface roughening by phase field modeling coupled with elasticity. We find that compared with films grown along {111} and {100} surfaces, the instability of {110} film occurs at a much lower strain. Our simulations capture the evolution of interface morphology and stress distribution during the roughening process. Similar characterizations are performed for heteroepitaxial growth from a surface pit. Finally, from 3D simulations, we show that the surface roughening pattern on {110} film exhibits a clear in-plane orientation preference, consistent with experimental observations.



X. Zhang acknowledges supports from Samsung Semiconductor Inc. This work is partially supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-SC0010412 (W.C.).


  1. 1.
    Lee ML, Fitzgerald EA, Bulsara MT, Currie MT, Lochtefeld A (2005) Strained Si, SiGe, and Ge channels for high-mobility metal-oxide-semiconductor field-effect transistors. J Appl Phys 97(1):1CrossRefGoogle Scholar
  2. 2.
    Gao H, Nix WD (1999) Surface roughening of heteroepitaxial thin films. Annu Rev Mater Sci 29(1):173–209CrossRefGoogle Scholar
  3. 3.
    Ozkan CS, Nix WD, Gao H (1997) Strain relaxation and defect formation in heteroepitaxial \({\text{ Si }}_{1-x}{\text{ Ge }}_{x}\) films via surface roughening induced by controlled annealing experiments. Appl Phys Lett 70(17):2247–2249CrossRefGoogle Scholar
  4. 4.
    Asaro R, Tiller W (1972) Interface morphology development during stress corrosion cracking: part I. Via surface diffusion. Metall Trans 3(7):1789–1796CrossRefGoogle Scholar
  5. 5.
    Grinfeld M (1986) Instability of the interface between a nonhydrostatically stressed elastic body and a melt. Akad Nauk SSSR Doklady 290:1358–1363Google Scholar
  6. 6.
    Spencer B, Voorhees P, Davis S (1991) Morphological instability in epitaxially strained dislocation-free solid films. Phys Rev Lett 67(26):3696CrossRefGoogle Scholar
  7. 7.
    Srolovitz DJ (1989) On the stability of surfaces of stressed solids. Acta Metall 37(2):621–625CrossRefGoogle Scholar
  8. 8.
    Freund LB, Suresh S (2004) Thin film materials: stress, defect formation and surface evolution. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  9. 9.
    Ni Y, He L, Soh A (2005) Three-dimensional phase field simulation for surface roughening of heteroepitaxial films with elastic anisotropy. J Cryst Growth 284(1):281–292CrossRefGoogle Scholar
  10. 10.
    Wu KA, Voorhees PW (2009) Stress-induced morphological instabilities at the nanoscale examined using the phase field crystal approach. Phys Rev B 80(12):125408CrossRefGoogle Scholar
  11. 11.
    Huang ZF, Elder K (2008) Mesoscopic and microscopic modeling of island formation in strained film epitaxy. Phys Rev Lett 101(15):158701CrossRefGoogle Scholar
  12. 12.
    Ramachandramoorthy R, Wang Y, Aghaei A, Richter G, Cai W, Espinosa HD (2017) Reliability of single crystal silver nanowire-based systems: stress assisted instabilities. ACS Nano 11(5):4768–4776CrossRefGoogle Scholar
  13. 13.
    Wang Y, Ryu S, McIntyre PC, Cai W (2014) A three-dimensional phase field model for nanowire growth by the vapor–liquid–solid mechanism. Model Simul Mater Sci Eng 22(5):055005CrossRefGoogle Scholar
  14. 14.
    Wang Y, McIntyre PC, Cai W (2017) Phase field model for morphological transition in nanowire vapor–liquid–solid growth. Cryst Growth Des 17(4):2211–2217CrossRefGoogle Scholar
  15. 15.
    Jesson D, Pennycook S, Baribeau JM, Houghton D (1993) Direct imaging of surface cusp evolution during strained-layer epitaxy and implications for strain relaxation. Phys Rev Lett 71(11):1744CrossRefGoogle Scholar
  16. 16.
    Qin R, Bhadeshia H (2009) Phase-field model study of the effect of interface anisotropy on the crystal morphological evolution of cubic metals. Acta Mater 57(7):2210–2216CrossRefGoogle Scholar
  17. 17.
    Jaccodine RJ (1963) Surface energy of germanium and silicon. J Electronchem Soc 110:524–527CrossRefGoogle Scholar
  18. 18.
    Garcia N, Stoll E (1984) Monte Carlo calculation for electromagnetic-wave scattering from random rough surfaces. Phys Rev Lett 52(20):1798CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringStanford UniversityStanfordUSA
  2. 2.Research Laboratory of ElectronicsMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations