Nonlinear evolution of the step meandering instability of a growing crystal surface

Physica D: Nonlinear Phenomena

Volumn 235, Issue 1-2 SPEC. ISS., 2007, Pages 15-20

  Frisch, Thomas ^a   Verga, Alberto ^a  

^a CNRS   (France)

Author keywords

Burton Cabrera Frank equations; Crystal growth; Meandering instability; Molecular beam epitaxy; Step flow

Indexed keywords

ATOMS; BOUNDARY VALUE PROBLEMS; COARSENING; CRYSTALLINE MATERIALS; EVAPORATION; MOLECULAR BEAM EPITAXY; NONLINEAR ANALYSIS; NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES;

ATOM DIFFUSION; BURTON-CABRERA-FRANK EQUATIONS; GROWING CRYSTAL SURFACE; MEANDERING INSTABILITY;

CRYSTAL GROWTH;

EID: 35048893596     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2007.04.021     Document Type: Article

References (30)

1. Barabási A.-L., and Stanley H.E. Fractal Concept in Surface Growth (1995), Cambridge University Press
2. Stangl J., Holy V., and Bauer G. Structural properties of self-organized semiconductor nanostructures. Rev. Modern Phys. 76 3 (2004) 725-783
3. Pimpinelli A., and Villain J. Physics of Crystal Growth (1998), Cambridge University Press
4. Saito Y. Statistical Physics of Crystal Growth (1998), World Scientific
5. Néel N., Maroutian T., Douillard L., and Ernst H.-J. From meandering to faceting, is step flow growth ever stable?. Phys. Rev. Lett. 91 22 (2003) 226103-1-226103-6
6. Nita F., and Pimpinelli A. When smoothening makes it rough: Unhindered step-edge diffusion and the meandering instability on metal surfaces. Phys. Rev. Lett. 95 (2005) 106104-1-106104-4
7. Michely T., and Krug J. Island, Mounds and Atoms. Pattern and Processes in Crystal Growth Far from Equilibrium (2004), Springer
8. Jeong H.-C., and Williams E.D. Steps on surfaces: Theory and experiments. Surf. Sci. Rep. 34 (1999) 171-294
9. Politi P., Grenet G., Marty A., Ponchet A., and Villain J. Instabilities in crystal growth by atomic or molecular beams. Phys. Rep. 324 (2000) 271-404
10. Yagi K., Minoda H., and Degawa M. Step bunching, step wandering and faceting: Self-organization at Si surfaces. Surf. Sci. Rep. 43 (2001) 45-126
11. Shchukin V.A., and Bimberg D. Spontaneous ordering of nanostructures on crystal surfaces. Rev. Modern Phys. 71 4 (1999) 1125-1171
12. Brunner K. Si/Ge nanostructures. Rep. Prog. Phys. 65 (2002) 27-72
13. Bales G.S., and Zangwill A. Morphological instability of a terrace edge during step-flow growth. Phys. Rev. B 41 9 (1990) 5500-5508
14. Pimpinelli A., Elkinani I., Karma A., Misbah C., and Villain J. Step motion on high temperature vicinal surface. J. Phys.: Condens. Matter 6 (1994) 2661-2680
15. Bena I., Misbah C., and Valance A. Non-linear evolution of a terrace edge during step flow growth. Phys. Rev. B. 47 12 (1993) 7408-7419
16. Pierre-Louis O., Misbah C., Saito Y., Krug J., and Politi P. New nonlinear evolution equation for steps during molecular beam epitaxy on vicinal surfaces. Phys. Rev. Lett. 80 19 (1998) 4221-4224
17. Kallunki J., and Krug J. Asymptotic step profiles from a nonlinear growth equation for vicinal surfaces. Phys. Rev. E 62 (2000) 6229-6232
18. Gillet F., Pierre-Louis O., and Misbah C. New non-linear evolution of step meander during growth with no desorption. Eur. Phys. J. B 18 (2000) 519
19. Paulin S., Gillet F., Pierre-Louis O., and Misbah C. Unstable step meandering with elastic interactions. Phys. Rev. Lett. 86 24 (2001) 5538-5541
20. Danker G., Pierre-Louis O., Kassner K., and Misbah C. Interrupted coarsening of anisotropic step meander. Phys. Rev. E 68 (2003) 020601-1-020601-4
21. Danker G., Pierre-Louis O., Kassner K., and Misbah C. Peculiar effects of anisotropic diffusion on dynamics of vicinal surfaces. Phys. Rev. Lett. 93 18 (2004) 185504-1-185504-4
22. Frisch T., and Verga A. Effect of step stiffness and diffusion anisotropy on the meandering of a growing vicinal surface. Phys. Rev. Lett. 96 (2006) 166104-1-166104-4
23. Burton W.K., Cabrera N., and Frank F.C. The growth of crystals and the equilibrium structure of their surfaces. Philos. Trans. R. Soc. A 243 (1951) 199-358
24. Schwoebel R.L., and Shipsey E.J. Step motion on crystal surfaces. J. Appl. Phys. 37 (1966) 3682-3686
25. Pierre-Louis O. Step bunching with general step kinetics: Stability step analysis and macroscopic models. Surf. Sci. 529 (2003) 114-134
26. Frisch T., and Verga A. Kinetic step-bunching in surface growth. Phys. Rev. Lett. 94 (2005) 226102-1-226102-4
27. Liu D.-J., and Weeks J.D. Quantitative theory of current induced-step bunching on Si (111). Phys. Rev. B 57 23 (1998) 14891-14900
28. Pierre-Louis O., and Métois J.-J. Kinetic step pairing. Phys. Rev. Lett. 93 16 (2004) 165901-1-165901-4
29. Berbezier I., Ronda A., and Portavoce A. Si-Ge nanostructures: New insight into growth process. J. Phys.: Condens. Matter 14 (2002) 8283-8331
30. Xiang Y., and Misfit W.E. Elastic energy and a continuum model for epitaxial growth with elasticity on vicinal surfaces. Phys. Rev. B 69 (2004) 035409-1-035409-16