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Applicable Analysis
An International Journal
Volume 83, 2004 - Issue 10
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Original Articles

Phase-field model for island dynamics in epitaxial growth

Pages 1015-1025 | Received 02 Jun 2003, Accepted 01 May 2004, Published online: 22 Aug 2006

References

  • Bales , GS and Zangwill , A . 1990 . Morphological instability of a terrace edge during step-flow growth . Phys. Rev. B , 41 ( 9 ) : 5500 – 5508 .
  • Bänsch , E , Haußer , F , Lakkis , O , Li , B and Voigt , A . 2004 . Finite element method for epitaxial growth with attachment-detachment kinetics . Journal of Computational Physics , 194 : 409 – 434 .
  • Barabási A-L Stanley HE 1995 Fractal Concepts in Surface Growth, Cambridge University Press Cambridge
  • Burton , WK , Cabrera , N and Frank , FC . 1951 . The growth of crystals and the equilibrium of their surfaces . Phil. Trans. Roy. Soc. London Ser. A , 243 ( 866 ) : 299 – 358 .
  • Caginalp , G and Chen , X . 1998 . Convergence of the phase field model to its sharp interface limits . European J. Appl. Math. , 9 ( 4 ) : 417 – 445 .
  • Caginalp , G and Fife , PC . 1988 . Dynamics of layered interfaces arising from phase boundaries . SIAM J. Appl. Math. , 48 ( 3 ) : 506 – 518 .
  • Caginalp , G . 1986 . An analysis of a phase field model of a free boundary . Arch. Rational Mech. Anal. , 92 ( 3 ) : 205 – 245 .
  • Caginalp , G . 1989 . Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations . Phys. Rev. A (3) , 39 ( 11 ) : 5887 – 5896 .
  • Weinan , E and Kwan Yip , ANung . 2001 . Continuum theory of epitaxial crystal growth . 1. J. Stat. Physics. , 104 : 221 – 253 .
  • Fife PC Penrose O 1995 Interfacial dynamics for thermodynamically consistent phase-field models with nonconserved order parameter Electron. J. Differential Equations pages No. 16, approx. 49 pp. (electronic)
  • Fife PC 1979 Mathematical Aspects of Reacting and Diffusing Systems Lecture Notes in Biomathematics 28 Springer-Verlag Berlin
  • Ghez , R , Cohen , HG and Keller , JB . 1993 . The stability of growing or evaporating crystals . J. Appl. Phys.. , 73 : 3685 – 3693 .
  • Ghez , R and Iyer , SS . 1988 . The kinetics of fast steps on crystal surfaces and its application to the molecular beam epitaxy of silicon . IBM J. Res. Develop. , 32 : 804 – 818 .
  • Karmia , A and Plapp , M . 1998 . Spiral surface growth without desorption . Phys. Rev. Lett.. , 81 : 4444 – 4447 .
  • Keller , JB , Cohen , HG and Merchant , GJ . 1993 . The stability of rapidly growing crystals . J. Appl. Phys. , 73 : 3694 – 3697 .
  • Kohn , R , Lo , TS and Kwan Yip , ANung . 2002 . Continuum limit of a step flow model . Materials Research Society Symposium Proceedings , 696 : T1.7.1–T.1.7.7
  • Krug J 2002 Four lectures on the physics of crystal growth Physica A 0206401
  • Liu , F and Metiu , H . 1994 . Stability and kinetics of step motion on crystal surfaces . Phys. Rev. E , 49 : 2601 – 2616 .
  • Li B Rätz A Voigt A 2002 Stability of a circular epitaxial islands Physica D (Submitted)
  • Osher , S and Fedkiw , RP . 2001 . Level-set method: an overview and some resent results . Journal of Computational Physics , 169 : 463 – 502 .
  • Pimpinelli A Villain J 1998 Physics of Crystal Growth, Cambridge University Press Cambridge
  • Ratsch , C , Gyure , MF , Caflisch , RE , Gibou , F , Petersen , M , Kang , M , Garcia , J and Vvedensky , DD . 2002 . Level-set method for island dynamics in epitaxial growth . Physical Review B. , 65

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