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Volumn 214, Issue 1, 2006, Pages 187-208

Surface evolution of elastically stressed films under deposition by a diffuse interface model

Author keywords

Adaptive finite elements; Anisotropy; Diffuse interface models; Surface evolution

Indexed keywords

ASYMPTOTIC ANALYSIS; FINITE ELEMENT METHOD; INTERFACES (MATERIALS);

EID: 33644508961     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.09.013     Document Type: Article
Times cited : (128)

References (60)
  • 1
    • 51249188112 scopus 로고
    • Interface morphology development during stress-corrosion cracking. 1. via surface diffusion
    • R. Asaro W.A. Tiller Interface morphology development during stress-corrosion cracking. 1. via surface diffusion Metall. Trans. 2 1972 1789
    • (1972) Metall. Trans. , vol.2 , pp. 1789
    • Asaro, R.1    Tiller, W.A.2
  • 2
    • 0000281044 scopus 로고
    • Instability of interface between nonhydrostatically stressed elastic body and melts
    • M.A. Grinfeld Instability of interface between nonhydrostatically stressed elastic body and melts Doklady Akademii Nauk SSSR 290 1986 1358-1363
    • (1986) Doklady Akademii Nauk SSSR , vol.290 , pp. 1358-1363
    • Grinfeld, M.A.1
  • 3
    • 0024611337 scopus 로고
    • On the stability of surfaces of stressed solids
    • D.J. Srolovitz On the stability of surfaces of stressed solids Acta Metall. 37 1989 621-625
    • (1989) Acta Metall. , vol.37 , pp. 621-625
    • Srolovitz, D.J.1
  • 4
    • 6744224411 scopus 로고    scopus 로고
    • Surface roughening of heteroepitaxial thin films
    • H.J. Gao W.D. Nix Surface roughening of heteroepitaxial thin films Ann. Rev. Mater. Sci. 29 1999 179-209
    • (1999) Ann. Rev. Mater. Sci. , vol.29 , pp. 179-209
    • Gao, H.J.1    Nix, W.D.2
  • 6
    • 0000173136 scopus 로고
    • Dynamics of phase-separation of crystal-surfaces
    • F. Liu H. Metiu Dynamics of phase-separation of crystal-surfaces Phys. Rev. B 48 1993 5808-5817
    • (1993) Phys. Rev. B , vol.48 , pp. 5808-5817
    • Liu, F.1    Metiu, H.2
  • 7
    • 0000755219 scopus 로고
    • Spinodal decomposition of a crystal-surface
    • J. Stewart N. Goldenfeld Spinodal decomposition of a crystal-surface Phys. Rev. B 46 1992 6505-6512
    • (1992) Phys. Rev. B , vol.46 , pp. 6505-6512
    • Stewart, J.1    Goldenfeld, N.2
  • 8
    • 0001087994 scopus 로고    scopus 로고
    • A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth
    • A.A. Golovin S.H. Davis A.A. Nepomnyashchy A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth Physica D 118 1998 202-230
    • (1998) Physica D , vol.118 , pp. 202-230
    • Golovin, A.A.1    Davis, S.H.2    Nepomnyashchy, A.A.3
  • 10
    • 0037446088 scopus 로고    scopus 로고
    • Coarsening dynamics of the convective Cahn-Hilliard equation
    • S.J. Watson F. Otto B.Y. Rubinstein S.H. Davis Coarsening dynamics of the convective Cahn-Hilliard equation Physica D 178 2003 127-148
    • (2003) Physica D , vol.178 , pp. 127-148
    • Watson, S.J.1    Otto, F.2    Rubinstein, B.Y.3    Davis, S.H.4
  • 11
    • 15844381930 scopus 로고    scopus 로고
    • Facet formation and coarsening modeled by a geometric evolution law for epitaxial growth
    • F. Haußer A. Voigt Facet formation and coarsening modeled by a geometric evolution law for epitaxial growth J. Cryst. Growth 275 2005 e47-e51
    • (2005) J. Cryst. Growth , vol.275
    • Haußer, F.1    Voigt, A.2
  • 12
    • 33644537569 scopus 로고    scopus 로고
    • Numerical simulation of anisotropic surface diffusion with curvature-dependent energy
    • M. Burger Numerical simulation of anisotropic surface diffusion with curvature-dependent energy J. Comput. Phys. 52 2005 311-337
    • (2005) J. Comput. Phys. , vol.52 , pp. 311-337
    • Burger, M.1
  • 13
    • 0036627609 scopus 로고    scopus 로고
    • Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: Interface-controlled evolution, phase transitions, epitaxial growth of elastic films
    • M.E. Gurtin M.E. Jabbour Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: Interface-controlled evolution, phase transitions, epitaxial growth of elastic films Arch. Ration. Mech. Anal. 163 2002 171-208
    • (2002) Arch. Ration. Mech. Anal. , vol.163 , pp. 171-208
    • Gurtin, M.E.1    Jabbour, M.E.2
  • 14
    • 0001776828 scopus 로고
    • Continuum models of crystal growth from atomic-beams with and without desorption
    • J. Villain Continuum models of crystal growth from atomic-beams with and without desorption J. Phys. 1 1991 19-42
    • (1991) J. Phys. , vol.1 , pp. 19-42
    • Villain, J.1
  • 15
    • 5844271216 scopus 로고
    • Slope selection and coarsening in molecular-beam epitaxy
    • M. Siegert M. Plischke Slope selection and coarsening in molecular-beam epitaxy Phys. Rev. Lett. 78 1994 3705-3708
    • (1994) Phys. Rev. Lett. , vol.78 , pp. 3705-3708
    • Siegert, M.1    Plischke, M.2
  • 16
    • 0001446318 scopus 로고
    • Growth instabilities induced by elasticity in a vicinal surface
    • C. Duport P. Politi J. Villain Growth instabilities induced by elasticity in a vicinal surface J. Phys. I 5 1995 1317-1350
    • (1995) J. Phys. I , vol.5 , pp. 1317-1350
    • Duport, C.1    Politi, P.2    Villain, J.3
  • 17
    • 0036706326 scopus 로고    scopus 로고
    • Derivation of a continuum model for epitaxial growth with elasticity on vicinal surface
    • Y. Xiang Derivation of a continuum model for epitaxial growth with elasticity on vicinal surface SIAM J. Appl. Math. 63 2002 241-258
    • (2002) SIAM J. Appl. Math. , vol.63 , pp. 241-258
    • Xiang, Y.1
  • 18
    • 1442350650 scopus 로고    scopus 로고
    • Misfit elastic energy and a continuum model for epitaxial growth with elasticity on vicinal surfaces
    • Y. Xiang W. E Misfit elastic energy and a continuum model for epitaxial growth with elasticity on vicinal surfaces Phys. Rev. B 69 2004 035409
    • (2004) Phys. Rev. B , vol.69 , pp. 035409
    • Xiang, Y.W.E.1
  • 19
    • 0036721970 scopus 로고    scopus 로고
    • A continuum description of the energetics and evolution of stepped surfaces in strained nanostructures
    • V.B. Shenoy L.B. Freund A continuum description of the energetics and evolution of stepped surfaces in strained nanostructures J. Mech. Phys. Solids 50 2002 1817-1841
    • (2002) J. Mech. Phys. Solids , vol.50 , pp. 1817-1841
    • Shenoy, V.B.1    Freund, L.B.2
  • 20
    • 33644942921 scopus 로고    scopus 로고
    • A unified treatment of evolving interfaces accounting for small deformations and atomic transport with emphasis on grain-boundaries and epitaxy
    • E. Fried M.E. Gurtin A unified treatment of evolving interfaces accounting for small deformations and atomic transport with emphasis on grain-boundaries and epitaxy Adv. Appl. Mech. 40 2005
    • (2005) Adv. Appl. Mech. , vol.40
    • Fried, E.1    Gurtin, M.E.2
  • 21
    • 0343494921 scopus 로고    scopus 로고
    • Numerical simulations of island formation in a coherent strained epitaxial thin film system
    • Y.W. Zhang A.F. Bower Numerical simulations of island formation in a coherent strained epitaxial thin film system J. Mech. Phys. Solids 47 1999 2273-2297
    • (1999) J. Mech. Phys. Solids , vol.47 , pp. 2273-2297
    • Zhang, Y.W.1    Bower, A.F.2
  • 22
    • 0037460303 scopus 로고    scopus 로고
    • Morphological evolution driven by strain induced surface diffusion
    • Y.W. Zhang A.F. Bower P. Liu Morphological evolution driven by strain induced surface diffusion Thin Solid Films 424 2003 9-14
    • (2003) Thin Solid Films , vol.424 , pp. 9-14
    • Zhang, Y.W.1    Bower, A.F.2    Liu, P.3
  • 23
    • 3142603571 scopus 로고    scopus 로고
    • Three-dimensional simulations of self-assembly of hut-shaped Si-Ge quantum dots
    • A. Ramasubramaniam V.B. Shenoy Three-dimensional simulations of self-assembly of hut-shaped Si-Ge quantum dots J. Appl. Phys. 95 2004 7813-7824
    • (2004) J. Appl. Phys. , vol.95 , pp. 7813-7824
    • Ramasubramaniam, A.1    Shenoy, V.B.2
  • 24
    • 0028409294 scopus 로고
    • Surface motion by surface-diffusion
    • J.W. Cahn J.E. Taylor Surface motion by surface-diffusion Acta Metall. 42 1994 1045-1063
    • (1994) Acta Metall. , vol.42 , pp. 1045-1063
    • Cahn, J.W.1    Taylor, J.E.2
  • 25
    • 21544450961 scopus 로고
    • Theory of thermal grooving
    • W.W. Mullins Theory of thermal grooving J. Appl. Phys. 28 1957 333-339
    • (1957) J. Appl. Phys. , vol.28 , pp. 333-339
    • Mullins, W.W.1
  • 26
    • 0030488511 scopus 로고    scopus 로고
    • The Cahn-Hilliard equation with a concentration dependent mobility: Motion by minus the Laplacian of the mean curvature
    • J.W. Cahn C.M. Elliott A. Novick-Cohen The Cahn-Hilliard equation with a concentration dependent mobility: Motion by minus the Laplacian of the mean curvature Eur. J. Appl. Math. 7 1996 287-301
    • (1996) Eur. J. Appl. Math. , vol.7 , pp. 287-301
    • Cahn, J.W.1    Elliott, C.M.2    Novick-Cohen, A.3
  • 27
    • 0030526461 scopus 로고    scopus 로고
    • On the Cahn-Hilliard equation with degenerate mobility
    • C.M. Elliott H. Garcke On the Cahn-Hilliard equation with degenerate mobility SIAM J. Math. Anal. 27 1996 404-423
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 404-423
    • Elliott, C.M.1    Garcke, H.2
  • 28
    • 4243457001 scopus 로고    scopus 로고
    • Quantitative phase-field modeling of dendritic growth in two and three dimensions
    • A. Karma W.J. Rappel Quantitative phase-field modeling of dendritic growth in two and three dimensions Phys. Rev. E 57 1998 4323-4349
    • (1998) Phys. Rev. E , vol.57 , pp. 4323-4349
    • Karma, A.1    Rappel, W.J.2
  • 29
    • 21844495223 scopus 로고
    • Linking anisotropic sharp and diffuse surface motion laws via gradient flows
    • J.W. Cahn J.E. Taylor Linking anisotropic sharp and diffuse surface motion laws via gradient flows J. Stat. Phy. 77 1994 183-197
    • (1994) J. Stat. Phy. , vol.77 , pp. 183-197
    • Cahn, J.W.1    Taylor, J.E.2
  • 31
    • 0038624024 scopus 로고    scopus 로고
    • Phase field simulations of faceted growth for strong anisotropy of kinetic coefficient
    • T. Uehara R.F. Sekerka Phase field simulations of faceted growth for strong anisotropy of kinetic coefficient J. Cryst. Growth 254 2003 251-261
    • (2003) J. Cryst. Growth , vol.254 , pp. 251-261
    • Uehara, T.1    Sekerka, R.F.2
  • 32
    • 15844383470 scopus 로고    scopus 로고
    • Analytical criteria for missing orientations on three-dimensional equilibrium shapes
    • R. Sekerka Analytical criteria for missing orientations on three-dimensional equilibrium shapes J. Cryst. Growth 2005
    • (2005) J. Cryst. Growth
    • Sekerka, R.1
  • 33
    • 33847303953 scopus 로고
    • Multiphase thermomechanics with interfacial structure. ii. evolution of an isothermal interface
    • S. Angenent M.E. Gurtin Multiphase thermomechanics with interfacial structure. ii. evolution of an isothermal interface Arch. Ration. Mech. Anal. 108 1989 323-391
    • (1989) Arch. Ration. Mech. Anal. , vol.108 , pp. 323-391
    • Angenent, S.1    Gurtin, M.E.2
  • 34
    • 0035276946 scopus 로고    scopus 로고
    • A phase-field model for highly anisotropic interfacial energy
    • J.J. Eggleston G.B. McFadden P.W. Voorhees A phase-field model for highly anisotropic interfacial energy Physica D 150 2001 91-103
    • (2001) Physica D , vol.150 , pp. 91-103
    • Eggleston, J.J.1    McFadden, G.B.2    Voorhees, P.W.3
  • 38
    • 29144514194 scopus 로고    scopus 로고
    • A phase-field formulation of the Willmore problem
    • Q. Du C. Liu X. Wang A phase-field formulation of the Willmore problem Nonlinearity 18 2005 1249-1267
    • (2005) Nonlinearity , vol.18 , pp. 1249-1267
    • Du, Q.1    Liu, C.2    Wang, X.3
  • 39
    • 0000861083 scopus 로고
    • Crack-like surface instabilities in stressed solids
    • W.H. Yang D.J. Srolovitz Crack-like surface instabilities in stressed solids Phys. Rev. Lett. 71 1993 1593-1596
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 1593-1596
    • Yang, W.H.1    Srolovitz, D.J.2
  • 40
    • 0028517037 scopus 로고
    • Surface-morphology evolution in stressed solids - Surface-diffusion controlled crack initiation
    • W.H. Yang D.J. Srolovitz Surface-morphology evolution in stressed solids - surface-diffusion controlled crack initiation J. Mech. Phys. Solids 42 1994 1551-1574
    • (1994) J. Mech. Phys. Solids , vol.42 , pp. 1551-1574
    • Yang, W.H.1    Srolovitz, D.J.2
  • 41
    • 0028532637 scopus 로고
    • Nonlinear evolution of the stress-driven morphological instability in a 2-dimensional semiinfinite solid
    • B.J. Spencer D.I. Meiron Nonlinear evolution of the stress-driven morphological instability in a 2-dimensional semiinfinite solid Acta Metall. Mater. 42 1994 3629-3641
    • (1994) Acta Metall. Mater. , vol.42 , pp. 3629-3641
    • Spencer, B.J.1    Meiron, D.I.2
  • 42
    • 0015655431 scopus 로고
    • A linear theory of thermochemical equilibrium of solids under stress
    • F. Larché J.W. Cahn A linear theory of thermochemical equilibrium of solids under stress Acta Metall. 21 1973 1051-1063
    • (1973) Acta Metall. , vol.21 , pp. 1051-1063
    • Larché, F.1    Cahn, J.W.2
  • 43
    • 0000467453 scopus 로고    scopus 로고
    • Model of surface instabilities induced by stress
    • J. Muller M. Grant Model of surface instabilities induced by stress Phys. Rev. Lett. 82 1999 1736-1739
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 1736-1739
    • Muller, J.1    Grant, M.2
  • 44
    • 0033560197 scopus 로고    scopus 로고
    • A phase-field approach for stress-induced instabilities
    • K. Kassner C. Misbah A phase-field approach for stress-induced instabilities Europhys. Lett. 46 1999 217-223
    • (1999) Europhys. Lett. , vol.46 , pp. 217-223
    • Kassner, K.1    Misbah, C.2
  • 45
    • 0344874711 scopus 로고    scopus 로고
    • Phase field microelasticity modeling of surface instability of heteroepitaxial thin films
    • Y.U. Wang Y.M. Jin A.G. Khachaturyan Phase field microelasticity modeling of surface instability of heteroepitaxial thin films Acta Mater. 52 2004 81-92
    • (2004) Acta Mater. , vol.52 , pp. 81-92
    • Wang, Y.U.1    Jin, Y.M.2    Khachaturyan, A.G.3
  • 46
    • 0032010562 scopus 로고    scopus 로고
    • A diffuse interface model for microstructural evolution in elastically stressed films
    • P.H. Leo J.S. Lowengrub H.J. Jou A diffuse interface model for microstructural evolution in elastically stressed films Acta Mater. 46 1998 2113-2130
    • (1998) Acta Mater. , vol.46 , pp. 2113-2130
    • Leo, P.H.1    Lowengrub, J.S.2    Jou, H.J.3
  • 48
    • 0001540757 scopus 로고    scopus 로고
    • Asymptotic derivation of the glues-wetting layer model and contact angle condition for Stranski-Krastanow islands
    • B.J. Spencer Asymptotic derivation of the glues-wetting layer model and contact angle condition for Stranski-Krastanow islands Phys. Rev. B 59 1999 2557-2567
    • (1999) Phys. Rev. B , vol.59 , pp. 2557-2567
    • Spencer, B.J.1
  • 49
    • 0033246392 scopus 로고    scopus 로고
    • Spontaneous ordering of nanostructures on crystal surfaces
    • V.A. Shchukin D. Bimberg Spontaneous ordering of nanostructures on crystal surfaces Rev. Mod. Phys. 71 1999 1125-1171
    • (1999) Rev. Mod. Phys. , vol.71 , pp. 1125-1171
    • Shchukin, V.A.1    Bimberg, D.2
  • 50
    • 0041627429 scopus 로고    scopus 로고
    • Phase separation in heteroepitaxial thin-film growth
    • F. Leonard M. Laradji R.C. Desai Phase separation in heteroepitaxial thin-film growth Physica A 239 1997 129-136
    • (1997) Physica A , vol.239 , pp. 129-136
    • Leonard, F.1    Laradji, M.2    Desai, R.C.3
  • 51
    • 0035894096 scopus 로고    scopus 로고
    • Morphological instability theory for strained alloy film growth: The effect of compositional stresses and species-dependent surface mobilities on ripple formation during epitaxial film deposition
    • B.J. Spencer P.W. Voorhees J. Tersoff Morphological instability theory for strained alloy film growth: The effect of compositional stresses and species-dependent surface mobilities on ripple formation during epitaxial film deposition Phys. Rev. B 64 2001 235318
    • (2001) Phys. Rev. B , vol.64 , pp. 235318
    • Spencer, B.J.1    Voorhees, P.W.2    Tersoff, J.3
  • 52
    • 0035451471 scopus 로고    scopus 로고
    • Dynamics of nanoscale pattern formation of an epitaxial monolayer
    • W. Lu Z. Suo Dynamics of nanoscale pattern formation of an epitaxial monolayer J. Mech. Phys. Solids 49 2001 1937-1950
    • (2001) J. Mech. Phys. Solids , vol.49 , pp. 1937-1950
    • Lu, W.1    Suo, Z.2
  • 53
    • 79956032946 scopus 로고    scopus 로고
    • Ordered growth of nanocrystals via a morphological instability
    • J.J. Eggleston P.W. Voorhees Ordered growth of nanocrystals via a morphological instability Appl. Phys. Lett. 80 2002 306-308
    • (2002) Appl. Phys. Lett. , vol.80 , pp. 306-308
    • Eggleston, J.J.1    Voorhees, P.W.2
  • 54
    • 9644302801 scopus 로고    scopus 로고
    • Efficient phase-field simulation of quantum dot formation in a strained heteroepitaxial film
    • S.M. Wise J.S. Lowengrub J.S. Kim W.C. Johnson Efficient phase-field simulation of quantum dot formation in a strained heteroepitaxial film Superlattice Microst. 36 2004 293-304
    • (2004) Superlattice Microst. , vol.36 , pp. 293-304
    • Wise, S.M.1    Lowengrub, J.S.2    Kim, J.S.3    Johnson, W.C.4
  • 56
    • 20344364819 scopus 로고    scopus 로고
    • AMDiS - Adaptive multidimensional simulations: Object oriented software concepts for scientific computing
    • S. Vey A. Voigt AMDiS - adaptive multidimensional simulations: Object oriented software concepts for scientific computing WSEAS Trans. Syst. 3 2004 1564-1569
    • (2004) WSEAS Trans. Syst. , vol.3 , pp. 1564-1569
    • Vey, S.1    Voigt, A.2
  • 57
    • 20344390525 scopus 로고    scopus 로고
    • AMDiS - Adaptive multidimensional simulations: Composite finite elements and signed distance functions
    • C. Stöcker S. Vey A. Voigt AMDiS - adaptive multidimensional simulations: Composite finite elements and signed distance functions WSEAS Trans. Circuit Syst. 4 2005 111-116
    • (2005) WSEAS Trans. Circuit Syst. , vol.4 , pp. 111-116
    • Stöcker, C.1    Vey, S.2    Voigt, A.3
  • 58
    • 0003435748 scopus 로고    scopus 로고
    • A Review of a Posteriori Error Estimation and Adaptive Mesh-refinement Techniques
    • Wiley-Teubner
    • R. Verfürth A Review of a Posteriori Error Estimation and Adaptive Mesh-refinement Techniques 1996 Wiley-Teubner
    • (1996)
    • Verfürth, R.1
  • 59
    • 10844272222 scopus 로고    scopus 로고
    • Surface diffusion of graphs: Variational formulation, error analysis, and simulation
    • (electronic)
    • E. Bänsch P. Morin R.H. Nochetto Surface diffusion of graphs: variational formulation, error analysis, and simulation SIAM J. Numer. Anal. 42 2 2004 773-799
    • (2004) SIAM J. Numer. Anal. , vol.42 , Issue.2 , pp. 773-799
    • Bänsch, E.1    Morin, P.2    Nochetto, R.H.3
  • 60
    • 2342502809 scopus 로고    scopus 로고
    • Finite element method for epitaxial growth with attachment-detachment kinetics
    • E. Bänsch F. Haußer O. Lakkis B. Li Finite element method for epitaxial growth with attachment-detachment kinetics J. Comput. Phys. 194 2004 409-434
    • (2004) J. Comput. Phys. , vol.194 , pp. 409-434
    • Bänsch, E.1    Haußer, F.2    Lakkis, O.3    Li, B.4


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