Unification of step bunching phenomena on vicinal surfaces

We unify step bunching (SB) instabilities occurring under various conditions on crystal surfaces below roughening. We show that when attachment-detachment of atoms at step edges is the rate-limiting process, the SB of interacting, concentric circular steps is equivalent to the commonly observed SB of interacting straight steps under deposition, desorption, or drift. We derive a continuum Lagrangian partial differential equation, which is used to study the onset of instabilities for circular steps. These findings place on a common ground SB instabilities from numerical simulations for circular steps and experimental observations of straight steps.

[1]  Navot Israeli,et al.  PROFILE OF A DECAYING CRYSTALLINE CONE , 1999 .

[2]  Nano-scale equilibrium crystal shapes , 2004, cond-mat/0501003.

[3]  S. Stoyanov,et al.  Properties and dynamic interaction of step density waves at a crystal surface during electromigration affected sublimation , 1998 .

[4]  Scaling properties of step bunches induced by sublimation and related mechanisms , 2004, cond-mat/0409013.

[5]  E. Williams,et al.  Step Dynamics in 3D Crystal Shape Relaxation , 2001 .

[6]  F. Hudda,et al.  Atomic View of Surface Self‐Diffusion: Tungsten on Tungsten , 1966 .

[7]  M. Uwaha,et al.  Wandering and Bunching Instabilities of Steps Described By Nonlinear Evolution Equations , 1998 .

[8]  Highly regular self-organization of step bunches during growth of SiGe on Si(113) , 1998 .

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

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

[11]  S. Stoyanov.  Electromigration Induced Step Bunching on Si Surfaces – How Does it Depend on the Temperature and Heating Current Direction? , 1991 .

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

[13]  Z. Suo,et al.  Persistent step-flow growth of strained films on vicinal substrates. , 2005, Physical review letters.

[14]  Zangwill,et al.  Morphological equilibration of a corrugated crystalline surface. , 1990, Physical review. B, Condensed matter.

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

[16]  M. Uwaha,et al.  Growth law of step bunches induced by the Ehrlich–Schwoebel effect in growth , 2001 .

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

[18]  Williams,et al.  Size Scaling in the Decay of Metastable Structures. , 1996, Physical review letters.

[19]  T. Ogino,et al.  SUBLIMATION OF A HEAVILY BORON-DOPED SI(111) SURFACE , 1998 .

[20]  M. Uwaha,et al.  Decay of an Island on a Facet via Surface Diffusion , 2000 .

[21]  Kandel,et al.  Step bunching as a chaotic pattern formation process. , 1992, Physical review letters.

[22]  H. Stone,et al.  Continuum approach to self-similarity and scaling in morphological relaxation of a crystal with a facet , 2005 .

[23]  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.

[24]  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.

[25]  J. Oshinowo,et al.  In situ fabrication of self‐aligned InGaAs quantum dots on GaAs multiatomic steps by metalorganic chemical vapor deposition , 1995 .

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