Dynamics of crystal steps

Abstract 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. To cite this article: O. Pierre-Louis, C. R. Physique 6 (2005).

[1]  John D. Weeks,et al.  CURRENT-INDUCED STEP BENDING INSTABILITY ON VICINAL SURFACES , 1998 .

[2]  Crystal symmetry, step-edge diffusion, and unstable growth , 1999, cond-mat/9908152.

[3]  Maria R. D'Orsogna,et al.  The Kink Ehrlich-Schwoebel Effect and Resulting Instabilities , 1999 .

[4]  Joachim Krug,et al.  Four lectures on the physics of crystal growth , 2002 .

[5]  B. Lundqvist,et al.  ISLAND MIGRATION CAUSED BY THE MOTION OF THE ATOMS AT THE BORDER : SIZE AND TEMPERATURE DEPENDENCE OF THE DIFFUSION COEFFICIENT , 1998 .

[6]  A. Pimpinelli,et al.  Steady-state motion of silicon islands driven by a DC current , 1999 .

[7]  Eshel Ben-Jacob,et al.  Dynamics of Interfacial Pattern Formation , 1983 .

[8]  Wolf,et al.  Attractive interaction between steps. , 1991, Physical review letters.

[9]  M. Murty,et al.  Instability in Molecular Beam Epitaxy due to Fast Edge Diffusion and Corner Diffusion Barriers , 1999 .

[10]  F. Much,et al.  Simulation of wetting-layer and island formation in heteroepitaxial growth , 2003 .

[11]  A. Karma,et al.  Quantitative phase-field modeling of dendritic growth in two and three dimensions , 1996 .

[12]  Alain Marty,et al.  Instabilities in crystal growth by atomic or molecular beams , 2000 .

[13]  A. Chernov Notes on interface growth kinetics 50 years after Burton, Cabrera and Frank , 2004 .

[14]  A. Saúl,et al.  Experimental evidence for an Ehrlich-Schwoebel effect on Si(111) , 2002 .

[15]  T. Einstein,et al.  Brownian motion and shape fluctuations of single-layer adatom and vacancy clusters on surfaces: Theory and simulations. , 1996, Physical review. B, Condensed matter.

[16]  I. Maksimov,et al.  ERRATUM: Mean-field theory of kinetic smoothening of growth steps , 2000 .

[17]  N. Bartelt,et al.  Terrace-width distributions on vicinal Ag(110) : evidence of oscillatory interactions , 1994 .

[18]  C. Misbah,et al.  Unstable step meandering with elastic interactions. , 2001, Physical review letters.

[19]  J. Métois,et al.  Impact of the growth on the stability–instability transition at Si (111) during step bunching induced by electromigration , 1999 .

[20]  Evans,et al.  Surface unwetting during growth of Ag on Si(001). , 1996, Physical Review B (Condensed Matter).

[21]  Kuo-Jen Chao,et al.  Formation of Atomically Flat Silver Films on GaAs with a "Silver Mean" Quasi Periodicity , 1996, Science.

[22]  Power-law behavior of step roughening with surface diffusion , 1997 .

[23]  Misbah,et al.  Pulses and disorder in a continuum version of step-bunching dynamics. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Richard L. Schwoebel,et al.  Step Motion on Crystal Surfaces. II , 1966 .

[25]  L. Douillard,et al.  WAVELENGTH SELECTION IN UNSTABLE HOMOEPITAXIAL STEP FLOW GROWTH , 1999 .

[26]  Yukio Saito,et al.  New Nonlinear Evolution Equation for Steps during Molecular Beam Epitaxy on Vicinal Surfaces , 1998 .

[27]  W. K. Burton,et al.  The growth of crystals and the equilibrium structure of their surfaces , 1951, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[28]  M. Uwaha,et al.  Growth of step bunches formed by the drift of adatoms , 1999 .

[29]  W. L. Williams,et al.  COLLISIONAL QUENCHING OF METASTABLE HYDROGEN. , 1973 .

[30]  P. Stoltze Simulation of surface defects , 1994 .

[31]  P. Peyla,et al.  Elastic Interaction between Surface Defects in Thin Layers , 1999 .

[32]  Liu,et al.  Stability and kinetics of step motion on crystal surfaces. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[33]  J. Villain,et al.  Physics of crystal growth , 1998 .

[34]  Zangwill,et al.  Morphological equilibration of a facetted crystal. , 1992, Physical review. B, Condensed matter.

[35]  When does coarsening occur in the dynamics of one-dimensional fronts? , 2003, Physical review letters.

[36]  Y. Homma,et al.  Morphological instability of atomic steps observed on Si(111) surfaces , 2001 .

[37]  B. Merriman,et al.  Kinetic model for a step edge in epitaxial growth. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[38]  J. Krug,et al.  On the microscopic origin of the kinetic step bunching instability on vicinal Si(0 0 1) , 2002 .

[39]  Feng Liu,et al.  SELF-ORGANIZATION OF STEPS IN GROWTH OF STRAINED FILMS ON VICINAL SUBSTRATES , 1998 .

[40]  Osipov,et al.  Morphological stability of islands upon thin-film condensation. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[41]  N. Bartelt,et al.  Step Permeability and the Relaxation of Biperiodic Gratings on Si(001) , 1997 .

[42]  Karma,et al.  Competition between noise and determinism in step flow growth. , 1993, Physical review letters.

[43]  M. Giesen Step and island dynamics at solid/vacuum and solid/liquid interfaces , 2001 .

[44]  M. Sato,et al.  Step Bunching as Formation of Soliton-Like Pulses in Benney Equation , 1995 .

[45]  J. Tersoff,et al.  Barrierless formation and faceting of SiGe islands on Si(001). , 2002, Physical review letters.

[46]  Absence of a step-edge barrier on a polar semiconductor surface with reconstruction , 2000 .

[47]  D. Spanjaard,et al.  The phonon spectra and vibrational thermodynamical properties of Cu vicinal surfaces , 2002 .

[48]  K. Kassner,et al.  Interrupted coarsening of anisotropic step meander. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  S. Stoyanov Heating Current Induced Conversion between 2×1 and 1×2 Domains at Vicinal (001) Si Surfaces–Can it be Explained by Electromigration of Si Adatoms? , 1990 .

[50]  O. Pierre-Louis Step bunching with general step kinetics: stability analysis and macroscopic models , 2003 .

[51]  Z. Zhang,et al.  Crystal growth. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[52]  P. Nozières On the motion of steps on a vicinal surface , 1987 .

[53]  K. Kassner,et al.  Peculiar effects of anisotropic diffusion on dynamics of vicinal surfaces. , 2004, Physical Review Letters.

[54]  W. Kohn,et al.  Elastic interaction of two atoms adsorbed on a solid surface , 1976 .

[55]  G. Caginalp,et al.  Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations. , 1989, Physical review. A, General physics.

[56]  Misbah,et al.  Nonlinear evolution of a terrace edge during step-flow growth. , 1993, Physical review. B, Condensed matter.

[57]  Irreversible nucleation in molecular beam epitaxy: From theory to experiments , 2002, cond-mat/0209609.

[58]  Ellen D. Williams,et al.  Steps on surfaces: experiment and theory , 1999 .

[59]  Hamers,et al.  Finite-temperature phase diagram of vicinal Si(100) surfaces. , 1990, Physical review letters.

[60]  Zangwill,et al.  Morphological instability of a terrace edge during step-flow growth. , 1990, Physical review. B, Condensed matter.

[61]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[62]  Infinite family of persistence exponents for interface fluctuations. , 2003, Physical review letters.

[63]  Dietrich E. Wolf,et al.  Diffusion on strained surfaces , 1997 .

[64]  T. Ogino,et al.  Step wandering induced by homoepitaxy on Si() during “1×1”–7×7 phase transition , 2003 .

[65]  R. Ferrando,et al.  Collective and single particle diffusion on surfaces , 2002 .

[66]  Felix Otto,et al.  A diffuse-interface approximation for step flow in epitaxial growth , 2004 .

[67]  Villain,et al.  New instability in molecular beam epitaxy. , 1995, Physical review letters.

[68]  Zhang,et al.  Dynamic scaling of growing interfaces. , 1986, Physical review letters.

[69]  R. Caflisch,et al.  Level-set method for island dynamics in epitaxial growth , 2002 .

[70]  O Pierre-Louis,et al.  Phase field models for step flow. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[71]  Da‐Jiang Liu,et al.  Sintering of two-dimensional nanoclusters in metal(100) homoepitaxial systems: Deviations from predictions of Mullins continuum theory , 2002 .

[72]  A. Latyshev,et al.  Transformations on clean Si(111) stepped surface during sublimation , 1989 .

[73]  Metiu,et al.  Evaporation of single atoms from an adsorbate island or a step to a terrace: Evaporation rate and the underlying atomic-level mechanism. , 1996, Physical review. B, Condensed matter.

[74]  Alain Karma,et al.  Spiral Surface Growth without Desorption , 1998, cond-mat/9809358.

[75]  O Pierre-Louis Continuum model for low temperature relaxation of crystal steps. , 2001, Physical review letters.

[76]  Scaling and universality of self-organized patterns on unstable vicinal surfaces. , 2002, Physical review letters.

[77]  Politi,et al.  Ehrlich-Schwoebel instability in molecular-beam epitaxy: A minimal model. , 1996, Physical review. B, Condensed matter.

[78]  M. Uwaha,et al.  Change of wandering pattern with anisotropy in step kinetics , 1999 .

[79]  Zhenyu Zhang,et al.  Island Diffusion and Coarsening on Metal (100) Surfaces , 1997 .

[80]  Zhenyu Zhang,et al.  ``Electronic Growth'' of Metallic Overlayers on Semiconductor Substrates , 1998 .

[81]  Z. Csahók,et al.  A class of nonlinear front evolution equations derived from geometry and conservation , 1999 .

[82]  M. Ichikawa,et al.  Size-scaling exponents of current-induced step bunching on silicon surfaces , 1999 .

[83]  W. Mullins Theory of Thermal Grooving , 1957 .