[Analyse de lʼinfluence combinée du mouillage du substrat et de lʼélectromigration en surface sur la stabilité dʼune couche mince et les morphologies dynamiques]
Un modèle basé sur les équations aux dérivées partielles et qui combine lʼélectromigration de surface et le mouillage est developpé pour lʼanalyse de la stabilité morphologique de couches ultra-minces solides. La mobilité des adatomes est supposée anisotrope, et deux directions du champ électrique (parallèle et perpendiculaire à la surface) sont discutées et comparées. Des analyses de stabilité linéaire dʼéquations dʼévolution en approximation de petite inclinaison sont effectuées, suivies par des calculs dʼéquations dʼévolution complètement non linéaires et paramétriques, qui permettent des surplombs de surface. Les résultats révèlent des domaines de stabilité dans lʼespace des paramètres pour les couches mouillantes et non mouillantes, une intensité variable du champ électrique, des solutions non linéaires dʼéquilibre dans certains cas, ainsi quʼun comportement intéressant de grossissement pour les couches fortement mouillées.
A PDE-based model combining surface electromigration and wetting is developed for the analysis of morphological stability of ultrathin solid films. Adatom mobility is assumed anisotropic, and two directions of the electric field (parallel and perpendicular to the surface) are discussed and contrasted. Linear stability analyses of small-slope evolution equations are performed, followed by computations of fully nonlinear parametric evolution equations that permit surface overhangs. The results reveal parameter domains of instability for wetting and non-wetting films and variable electric field strength, nonlinear steady-state solutions in certain cases, and interesting coarsening behavior for strongly wetting films.
Mot clés : Électromigration, Mouillage, Dynamique des couches minces solides
Mikhail Khenner 1
@article{CRPHYS_2013__14_7_607_0,
author = {Mikhail Khenner},
title = {Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologies},
journal = {Comptes Rendus. Physique},
pages = {607--618},
publisher = {Elsevier},
volume = {14},
number = {7},
year = {2013},
doi = {10.1016/j.crhy.2013.06.009},
language = {en},
}
TY - JOUR AU - Mikhail Khenner TI - Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologies JO - Comptes Rendus. Physique PY - 2013 SP - 607 EP - 618 VL - 14 IS - 7 PB - Elsevier DO - 10.1016/j.crhy.2013.06.009 LA - en ID - CRPHYS_2013__14_7_607_0 ER -
%0 Journal Article %A Mikhail Khenner %T Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologies %J Comptes Rendus. Physique %D 2013 %P 607-618 %V 14 %N 7 %I Elsevier %R 10.1016/j.crhy.2013.06.009 %G en %F CRPHYS_2013__14_7_607_0
Mikhail Khenner. Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologies. Comptes Rendus. Physique, Volume 14 (2013) no. 7, pp. 607-618. doi : 10.1016/j.crhy.2013.06.009. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2013.06.009/
[1] Current-induced step bunching at vicinal surfaces during crystal sublimation, Surf. Sci., Volume 370 (1997), p. 345
[2] Current-induced step bending instability on vicinal surfaces, Phys. Rev. Lett., Volume 81 (1998), p. 2743
[3] Electromigration-induced step meandering on vicinal surfaces: Nonlinear evolution equation, Phys. Rev. B, Volume 75 (2007), p. 045413
[4] Birth and morphological evolution of step bunches under electromigration, Phys. Rev. Lett., Volume 96 (2006), p. 195901
[5] Local electromigration model for crystal surfaces, Phys. Rev. Lett., Volume 96 (2006), p. 135901
[6] Electromigration in macroscopic relaxation of stepped surfaces, Multiscale Model. Simul., Volume 8 (2010), p. 667
[7] Influence of electromigration field on the step bunching process on Si(111), Phys. Rev. B, Volume 82 (2010), p. 153301
[8] Current-induced faceting of crystal surfaces, Phys. Rev. Lett., Volume 73 (1994), p. 1947
[9] Surface electromigration as a moving boundary value problem, Phys. Rev. Lett., Volume 78 (1997), p. 278
[10] The influence of electric fields on nanostructures-simulation and control, Math. Comput. Simul., Volume 80 (2010), pp. 1449-1457
[11] Electromigration of single layer clusters, Phys. Rev. B, Volume 62 (2000), p. 13697
[12] Morphological stability of electromigration-driven vacancy islands, Phys. Rev. E, Volume 75 (2007), p. 046210
[13] Complex shape evolution of electromigration-driven single-layer islands, Phys. Rev. Lett., Volume 94 (2005), p. 166105
[14] Nonlinear wavelength selection in surface faceting under electromigration, Phys. Rev. Lett., Volume 109 (2012), p. 056101
[15] Surface morphological response of crystalline solids to mechanical stresses and electric fields, Surf. Sci. Rep., Volume 66 (2011), pp. 299-346
[16] Current-induced stabilization of surface morphology in stressed solids, Phys. Rev. Lett., Volume 100 (2008), p. 036106
[17] Controlled electroplating and electromigration in nickel electrodes for nanogap formation, Nanotechnology, Volume 21 (2010), p. 445304
[18] Imaging electromigration during the formation of break junctions, Nano Lett., Volume 7 (2007), pp. 652-656
[19] Switchable nanometer contacts: Ultrathin Ag nanostructures on Si(100), Appl. Phys. Lett., Volume 89 (2006), p. 063120
[20] Size effect on the electron wind force for electromigration at the top metal-dielectric interface in nanoscale interconnects, Appl. Phys. Lett., Volume 101 (2012), p. 101601
[21] Adsorbate transport on graphene by electromigration, Phys. Rev. Lett., Volume 109 (2012), p. 095504
[22] Thin Films: Stresses and Mechanical Properties V (S.P. Baker et al., eds.), MRS Symp. Proc., vol. 356, Materials Research Society, Pittsburgh, USA, 1995, p. 33
[23] Epitaxial films stabilized by long-range forces, Phys. Rev. B, Volume 58 (1998), p. 5116
[24] A continuum model of kinetic roughening and coarsening in thin films, J. Mech. Phys. Solids, Volume 47 (1999), p. 697
[25] Morphological stability of epitaxial thin elastic films by van der Waals force, Arch. Appl. Mech., Volume 72 (2002), pp. 77-84
[26] Ordering of strained islands during surface growth, Phys. Rev. E, Volume 81 (2010), p. 021605
[27] Morphological evolution in a strained-heteroepitaxial solid droplet on a rigid substrate: Dynamical simulations, J. Appl. Phys., Volume 108 (2010), p. 063527
[28] Faceting instability in the presence of wetting interactions: A mechanism for the formation of quantum dots, Phys. Rev. B, Volume 70 (2004), p. 235342
[29] Self-assembly of quantum dots in a thin epitaxial film wetting an elastic substrate, Phys. Rev. B, Volume 75 (2007), p. 205312
[30] Nonlinear effect of stress and wetting on surface evolution of epitaxial thin films, Phys. Rev. B, Volume 74 (2006), p. 075413
[31] Asymptotic derivation of the glued-wetting-layer model and contact-angle condition for Stranski–Krastanow islands, Phys. Rev. B, Volume 59 (1999), p. 2011
[32] On the existence of a critical perturbation amplitude for the Stranski–Krastanov transition, Surf. Sci., Volume 602 (2008), p. 3560
[33] Stability of a strongly anisotropic thin epitaxial film in a wetting interaction with elastic substrate, Eur. Phys. Lett., Volume 93 (2011), p. 26001
[34] Comparative study of a solid film dewetting in an attractive substrate potentials with the exponential and the algebraic decay, Math. Model. Nat. Phenom., Volume 3 (2008), pp. 16-29
[35] Morphologies and kinetics of a dewetting ultrathin solid film, Phys. Rev. B, Volume 77 (2008), p. 245445
[36] Formation and stability of self-assembled coherent islands in highly mismatched heteroepitaxy, Phys. Rev. Lett., Volume 82 (1999), p. 4042
[37] Surface energetics and structure of the Ge wetting layer on Si(100), Phys. Rev. B, Volume 70 (2004), p. 205337
[38] A front-tracking method for the computations of multiphase flow, J. Comput. Phys., Volume 169 (2001), p. 708
[39] A review of recent numerical algorithms for hypersurfaces moving with curvature-dependent speed, J. Differ. Geom., Volume 31 (1990), p. 131
[40] Geometrical models of interface evolution, Phys. Rev. A, Volume 29 (1984), pp. 1335-1342
[41] Geometric evolution law for modeling strongly anisotropic thin-film morphology, Phys. Rev. E, Volume 84 (2011), p. 061606
[42] Solid surface morphologies governed by capillarity, Metal Surfaces: Structure, Energetics and Kinetics, American Society for Metals, Cleveland, OH, 1963, pp. 17-66
[43] Numerical simulation of grain boundary grooving by level set method, J. Comput. Phys., Volume 170 (2001), p. 764
[44] Electromigration-induced propagation of nonlinear surface waves, Phys. Rev. E, Volume 65 (2002), p. 036603
[45] Faceting of a growing crystal surface by surface diffusion, Phys. Rev. E, Volume 67 (2003), p. 021606
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