Comptes Rendus
Dynamics of crystal steps
Comptes Rendus. Physique, Self-organization on surfaces, Volume 6 (2005) no. 1, pp. 11-21.

In this article, we wish to point out some of the recent advances in the study of step dynamics on crystal surfaces. We will first list some approaches to steps dynamics, based on irreversible thermodynamics, kinetic roughening concepts, and mass transport mechanisms. In a second part, we shall analyze step motion coupled to the diffusion of mobile atoms on terraces. A special focus will be given on pattern formation on vicinal surfaces and two-dimensional islands. Finally, we will report on the consequences of elastic and electronic relaxation on the dynamics of steps and adatoms.

Nous présentons quelques avancées récentes dans l'étude de la dynamique des marches cristallines. Nous mentionnerons tout d'abord différentes approches pour la modélisation de la dynamique des marches, basées sur la thermodynamique des processus irréversibles, les théories de rugosification, et le transport de masse. Dans une deuxième partie, nous analyserons le mouvement de marches couplées à la diffusion des atomes mobiles à la surface. Nous développerons particulièrement le cas des surfaces vicinales et des îlots bidimensionnels. Finalement, nous étudierons les conséquences de la relaxation élastique et électronique du solide sur la dynamique des marches et des adatomes.

Published online:
DOI: 10.1016/j.crhy.2004.11.005
Keywords: Crystal steps, Crystal growth, Electromigration, Step meandering, Step bunching, Nonlinear dynamics, Pattern formation
Mots-clés : Marche atomique, Croissance cristalline, Électromigration, Fluctuation de marche, Accumulation de marches, Dynamique non-linéaire, Auto-organisation

Olivier Pierre-Louis 1

1 Laboratoire de spectrométrie physique, 140, avenue de la physique, BP 87, 38402 Saint Martin d'Hères, France
@article{CRPHYS_2005__6_1_11_0,
     author = {Olivier Pierre-Louis},
     title = {Dynamics of crystal steps},
     journal = {Comptes Rendus. Physique},
     pages = {11--21},
     publisher = {Elsevier},
     volume = {6},
     number = {1},
     year = {2005},
     doi = {10.1016/j.crhy.2004.11.005},
     language = {en},
}
TY  - JOUR
AU  - Olivier Pierre-Louis
TI  - Dynamics of crystal steps
JO  - Comptes Rendus. Physique
PY  - 2005
SP  - 11
EP  - 21
VL  - 6
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crhy.2004.11.005
LA  - en
ID  - CRPHYS_2005__6_1_11_0
ER  - 
%0 Journal Article
%A Olivier Pierre-Louis
%T Dynamics of crystal steps
%J Comptes Rendus. Physique
%D 2005
%P 11-21
%V 6
%N 1
%I Elsevier
%R 10.1016/j.crhy.2004.11.005
%G en
%F CRPHYS_2005__6_1_11_0
Olivier Pierre-Louis. Dynamics of crystal steps. Comptes Rendus. Physique, Self-organization on surfaces, Volume 6 (2005) no. 1, pp. 11-21. doi : 10.1016/j.crhy.2004.11.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2004.11.005/

[1] W.K. Burton; N. Cabrera; F.C. Frank Philos. Trans. Roy. Soc. London Ser. A, 243 (1951), p. 299

[2] M. Ozdemir; A. Zangwill Phys. Rev. B, 45 (1992), pp. 3718-3729

[3] O. Pierre-Louis Phys. Rev. E, 68 (2003), p. 021604

[4] E. Ben-Jacob; N. Goldenfeld; J.S. Langer; G. Schön Phys. Rev. Lett., 51 (1983), p. 1930

[5] S. Tanaka; N.C. Bartelt; C.C. Umbach; R.M. Tromp; J.M. Blakely Phys. Rev. Lett., 78 (1997), p. 3342

[6] S. Stoyanov; J.-J. Métois; S. Stoyanov Surf. Sci., 29 (1990), p. L659

[7] O. Pierre-Louis; J.-J. Métois; O. Pierre-Louis Surf. Sci., 93 (2004), p. 165901

[8] T. Ala-Nissila; R. Ferrando; F.C. Ying; P. Stolze J. Phys. Cond. Matter, 51 (2002), p. 949

[9] K. Nishino; M. Uwaha; Y. Saito Surf. Sci., 374 (1997), p. 291

[10] O. Pierre-Louis; T.L. Einstein Phys. Rev. B, 62 (2000), p. 13697

[11] J. Villain J. Phys. (Paris) I, 1 (1991), p. 19

[12] G.S. Bales; A. Zangwill Phys. Rev. B, 41 (1990), p. 5500

[13] R.L. Schwoebel J. Appl. Phys., 40 (1969), p. 614

[14] O. Pierre-Louis; M.I. Haftel Phys. Rev. Lett., 87 (2001), p. 048701

[15] M. Giesen; H.-C. Jeong; E.D. Williams Surf. Sci. Rep., 68 (2001), p. 1

[16] W.W. Mullins J. Appl. Phys., 28 (1957), p. 333

[17] S. Khare; T.L. Einstein Phys. Rev. B, 54 (1996), p. 11752

[18] W.W. Pai; A.K. Swan; Z. Zhang; J.F. Wendelken Phys. Rev. Lett., 79 (1997), p. 3210

[19] A. Bogicevic; S. Liu; J. Jacobsen; B. Lundqvist; H. Metiu Phys. Rev. B, 57 (1998), p. R9459

[20] N. Combe; H. Larralde Phys. Rev. B, 62 (2000), p. 16074

[21] O. Pierre-Louis Phys. Rev. Lett., 87 (2001), p. 106104

[22] J. Kallunki; J. Krug Surf. Sci., 523 (2003), p. L53

[23] D.-J. Liu; J.W. Evans Phys. Rev. B, 66 (2002), p. 165407

[24] H. Shao; P.C. Weakliem; H. Metiu Phys. Rev. B, 53 (1996), p. 16041

[25] A.A. Chernov J. Crystal Growth, 264 (2004), p. 499

[26] M. Kardar; G. Parisi; Y.C. Zhang Phys. Rev. Lett., 56 (1986)

[27] R. Cafflish et al. Phys. Rev. B, 59 (1999), p. 6879

[28] M. Itoh; T. Ohno Phys. Rev. B, 62 (2000), p. 1889

[29] L.N. Balykov; M. Kitamura; I.L. Maksimov; K. Nishioka Europhys. Lett., 52 (2000), p. 692

[30] A. Pimpinelli; J. Villain Physics of Crystal Growth, Cambridge University Press, 1999

[31] I.L. Aleiner; R.A. Suris Sov. Phys. Sol. State, 34 (1992), p. 809

[32] O. Pierre-Louis; M.R. D'Orsogna; T.L. Einstein; M.V.R. Murty; B.H. Cooper Phys. Rev. Lett., 82 (1999), p. 3661

[33] M. Rusanen; I.T. Koponen; T. Ala-Nissila; C. Ghosh; T.S. Rahman Phys. Rev. B, 65 (2002), p. 041404

[34] P. Politi; J. Villain Phys. Rev. B, 54 (1996), p. 5114

[35] T. Maroutian; L. Douillard; H.-J. Ernst; N. Néel; T. Maroutian; L. Douillard; H.-J. Ernst Phys. Rev. Lett., 83 (1999), p. 4353

[36] P. Politi; J. Krug Surf. Sci., 446 (2000), p. 89

[37] G. Caginalp Phys. Rev. A, 39 (1989), p. 5887

[38] A. Karma; W.-J. Rappel Phys. Rev. E, 57 (1998), p. 4323

[39] F. Otto; P. Penzler; A. Rätz; T. Rump; A. Voigt Nonlinearity, 17 (2004), p. 477

[40] A. Karma; M. Plapp Phys. Rev. Lett., 81 (1998), p. 4444

[41] F. Liu; H. Metiu Phys. Rev. E, 49 (1997), p. 2601

[42] C. Ratsch et al. Phys. Rev. B, 65 (2002), p. 195403

[43] L. Proville Phys. Rev. Lett., 88 (2002), p. 046102

[44] C. Duport; P. Nozières; J. Villain Phys. Rev. Lett., 74 (1995), p. 134

[45] H. Hibino et al. Surf. Sci., 527 (2003), p. L222

[46] M. Sato; M. Uwaha; Y. Saito; Y. Hirose Phys. Rev. B, 65 (2002), p. 245427

[47] M. Degawa; H. Minoda; Y. Tanishiro; K. Yagi Phys. Rev. B, 63 (2001), p. 045309

[48] D.-J. Liu; J.D. Weeks; D. Kandel Phys. Rev. Lett., 81 (1998), p. 2743

[49] I. Bena; C. Misbah; A. Valance; O. Pierre-Louis; C. Misbah Phys. Rev. Lett., 47 (1993), p. 7408

[50] O. Pierre-Louis; C. Misbah; Y. Saito; J. Krug; P. Politi Phys. Rev. Lett., 80 (1998), p. 4221

[51] S. Paulin; F. Gillet; O. Pierre-Louis; C. Misbah Phys. Rev. Lett., 86 (2001), p. 5538

[52] G. Danker; O. Pierre-Louis; K. Kassner; C. Misbah; G. Danker; O. Pierre-Louis; K. Kassner; C. Misbah Phys. Rev. Lett., 68 (2003), p. 020601

[53] Z. Csahòk; C. Misbah; A. Valance Physica D, 128 (1999), p. 87

[54] P. Politi; C. Misbah Phys. Rev. Lett., 92 (2004), p. 090601

[55] F.C. Frank Perfection of Crystals, Wiley, NY, 1958, p. 411

[56] A.V. Latyshev et al. Surf. Sci., 213 (1989), p. 157

[57] D.-J. Liu; J.D. Weeks Phys. Rev. B, 57 (1998), p. 14891

[58] P. Politi; G. Grenet; A. Marty; A. Ponchet; J. Villain Phys. Rep., 324 (2000), p. 271

[59] G.B. Whitam Linear and Nonlinear Waves, Wiley, 1976

[60] S.P. Garcia; H. Bao; M.A. Hines J. Phys. Chem. B, 108 (2004), p. 6062

[61] M. Sato; M. Uwaha; Y. Saito; C. Misbah; O. Pierre-Louis Phys. Rev. E, 32 (1995), p. 639

[62] M. Sato; M. Uwaha J. Crystal Growth, 198 (1999), p. 38

[63] F. Gillet; Z. Csahok; C. Misbah Phys. Rev. B, 63 (2001), p. 241401

[64] J. Chang, O. Pierre-Louis, C. Misbah, unpublished

[65] A. Pimpinelli et al. Phys. Rev. Lett., 88 (2002), p. 206103

[66] P. Nozières; K. Fujita; M. Ichikawa; S. Stoyanov Phys. Rev. B, 48 (1987), p. 1605

[67] M. Sato; M. Uwaha Surf. Sci., 442 (1999), p. 318

[68] A. Pascale, PhD Thesis, Luminy, Marseille, 2003

[69] S.A. Kukushkin; A.V. Osipov Phys. Rev. E, 53 (1996), p. 4964

[70] Y. Homma; P. Finnie; M. Uwaha Surf. Sci., 492 (2001), p. 125

[71] A. Saul; J.-J. Métois; A. Ranguis; J.-J. Métois; J.-C. Heyraud; A. Pimpinelli Surf. Sci., 65 (2002), p. 075409

[72] K.H. Lau; W. Kohn Surf. Sci., 65 (1977), p. 607

[73] P. Peyla et al. Phys. Rev. Lett., 82 (1999), p. 787

[74] V.I. Marchenko; A.Y. Parshin Sov. Phys. JETP, 52 (1980), p. 129

[75] B. Houchmandzadeh; C. Misbah J. Phys. I (Paris), 5 (1995), p. 695

[76] O.L. Alerhand et al. Phys. Rev. Lett., 64 (1990), p. 2406

[77] F. Liu; J. Tersoff; M.G. Lagally Phys. Rev. Lett., 80 (1998), p. 1268

[78] C. Barreteau; F. Raouafi; M.C. Desjonquères; D. Spanjaard; S.L. Cunningham; L. Dobrzynki; A.A. Maradudin Phys. Rev. B, 519 (2002), p. 15

[79] M. Schroeder; D.E. Wolf Surf. Sci., 375 (1997), p. 129

[80] J. Tersoff; B.J. Spencer; A. Rastelli; H. von Känel Phys. Rev. Lett., 89 (2002), p. 196104

[81] J. Tersoff; J. Villain C. R. Acad. Sci. Paris, 87 (2001), p. 156101

[82] J. Villain Proceedings of the ICCG14, J. Crystal Growth (2004)

[83] F. Much; M. Biehl Europhys. Lett., 63 (2003), p. 14

[84] J.C. Glueckstein; M.M.R. Evans; J. Nogami Phys. Rev. B, 54 (1996), p. R11066

[85] T.L. Einstein Handbook of Surface Science, vol. 1, Elsevier Science, 1996

[86] J. Frohn et al. Phys. Rev. Lett., 67 (1991), p. 3543

[87] W.W. Pai et al. Surf. Sci., 307 (1994), p. 747

[88] Z. Zhang et al. Phys. Rev. Lett., 80 (1997), p. 5381

[89] A.R. Smith et al. Science, 273 (1996), p. 226

[90] Y. Saito, C. Misbah, O. Pierre-Louis, preprint

[91] Nozières; J. Krug Physica A, 313 (1991), p. 47

[92] M. Constantin; S. Das Sarma; C. Dasgupta; O. Bondarchuk; D.B. Dougherty; E.D. Williams Phys. Rev. Lett., 91 (2003), p. 086103

[93] A. Karma; C. Misbah Phys. Rev. Lett., 71 (1993), p. 3810

[94] P. Politi; C. Castellano Phys. Rev. B, 67 (2003), p. 075408

Cited by Sources:

Comments - Policy