scholarly journals Stochastic Models of Epitaxial Growth

2011 ◽  
Vol 1318 ◽  
Author(s):  
Dionisios Margetis ◽  
Paul N. Patrone ◽  
T. L. Einstein
Keyword(s):  
Kinetic Monte Carlo ◽  
Mean Field ◽  
Spatial Dimension ◽  
Stochastic Equations ◽  
Vicinal Surfaces ◽  
Field Approach ◽  
Material Deposition ◽  
Elastic Dipole ◽  
Kinetic Monte Carlo Simulations ◽  
Step Fluctuations

ABSTRACTWe study theoretical aspects of step fluctuations on vicinal surfaces by adding conservative white noise to the Burton-Cabrera-Frank model in one spatial dimension. We consider material deposition from above, as well as entropic and elastic-dipole step repulsions. Two approaches are discussed: (i) the linearization of stochastic equations when fluctuations are small, which captures correlations; and (ii) a mean field approach, which leaves out correlations but captures nonlinearities. Comparisons to kinetic Monte-Carlo simulations are presented.

Step-Edge Barriers on GaAs(001)

1995 ◽  
Vol 399 ◽  
Author(s):  
P. Šmilauer ◽  
D.D. Vvedensky
Keyword(s):  
Kinetic Monte Carlo ◽  
Step Edge ◽  
Layer By Layer ◽  
Vicinal Surfaces ◽  
Activation Barriers ◽  
Long Time ◽  
Kinetic Monte Carlo Simulations ◽  
Simulated Surface ◽  
Constant Slope ◽  
Surface Morphologies

ABSTRACTWe investigate growth of GaAs(001) using kinetic Monte Carlo simulations of a very simple atomistic solid-on-solid model. The key features of this model are a short-range incorporation process of freshly deposited atoms and additional activation barriers to interlayer transport. Both are required to obtain close agreement between measured electron-diffraction intensities and simulated surface step densities during growth and post-growth equilibration on vicinal surfaces. This model is used to study long-time evolution of the surface morphology. Large pyramid-like features develop during growth on a singular surface which coarsen in time while maintaining an approximately constant slope. Growth on a vicinal surface is also found to be unstable. Simulated surface morphologies are compared with recent work using atomic-force microscopy. Finally, we show how a suitably modified version of this model helps to explain the recently observed phenomenon of re-entrant layer-by-layer chemical-beam etching of a singular GaAs(001) surface. The central features responsible for this behavior are the site selectivity of the etching process combined with step-edge barriers to interlayer adatom migration.

Island Size and Environment Dependence of Adatom Capture: Cu/Co Islands on Ru(0001)

1998 ◽  
Vol 528 ◽  
Author(s):  
M.C. Bartelt ◽  
J.W. Evans ◽  
A.K. Schmid ◽  
R.Q. Hwang
Keyword(s):  
Kinetic Monte Carlo ◽  
Strong Dependence ◽  
Mean Field ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Island Size ◽  
Kinetic Monte Carlo Simulations ◽  
Environment Dependence ◽  
And Diffusion ◽  
Capture Rates

AbstractThe rate of capture by stable Co islands on Ru(0001) of additionally deposited Cu atoms is quantified using scanning tunneling microscopy, kinetic Monte Carlo simulations, and diffusion equation analyses. We find strong dependence of the capture rates on Co-island size, larger islands showing larger capture rates, qualitatively distinct from self-consistent mean-field predictions. The observed size dependence is shown to reflect larger island-free areas surrounding bigger islands, i.e., a strong correlation between island sizes and separations neglected in mean-field treatments.

scholarly journals Grain-boundary topological phase transitions

2020 ◽  
Vol 117 (52) ◽  
pp. 33077-33083
Author(s):  
Kongtao Chen ◽  
David J. Srolovitz ◽  
Jian Han
Keyword(s):  
Phase Transition ◽  
Grain Boundary ◽  
Grain Growth ◽  
Kinetic Monte Carlo ◽  
Mean Field Theory ◽  
Mean Field ◽  
Polycrystalline Materials ◽  
Topological Phase ◽  
Kinetic Monte Carlo Simulations ◽  
And Migration

The formation and migration of disconnections (line defects constrained to the grain boundary [GB] plane with both dislocation and step character) control many of the kinetic and dynamical properties of GBs and the polycrystalline materials of which they are central constituents. We demonstrate that GBs undergo a finite-temperature topological phase transition of the Kosterlitz–Thouless (KT) type. This phase transition corresponds to the screening of long-range interactions between (and unbinding of) disconnections. This phase transition leads to abrupt changes in the behavior of GB migration, GB sliding, and roughening. We analyze this KT transition through mean-field theory, renormalization group theory, and kinetic Monte Carlo simulations and examine how this transition affects microstructure-scale phenomena such as grain growth stagnation, abnormal grain growth, and superplasticity.

scholarly journals Crossover from Dimer Nucleation to Adatom Exchange During Submonolayer Epitaxy

1995 ◽  
Vol 399 ◽  
Author(s):  
G.S. Bales
Keyword(s):  
Kinetic Monte Carlo ◽  
Mean Field ◽  
Nucleation And Growth ◽  
Rate Equations ◽  
Number Density ◽  
Dimer Formation ◽  
Island Size ◽  
Self Consistent ◽  
Kinetic Monte Carlo Simulations ◽  
Increasing Temperature

ABSTRACTThe nucleation and growth of islands in the early stages of epitaxial growth is studied with kinetic Monte Carlo Simulations and self-consistent mean field rate equations. Specifically, adatom exchange and irreversible dimer formation are allowed to compete equally as the origin of two-dimensional islands. The island size distribution and number density are found to satisfy a dynamic crossover scaling form. The critical island size evolves from one to zero with increasing temperature, decreasing flux, and increasing coverage.

Effective Interactions Approach to Phase Stability in Alloys Under Irradiation

1998 ◽  
Vol 538 ◽  
Author(s):  
Raúl A. Enrique ◽  
Pascal Bellon
Keyword(s):  
Phase Diagram ◽  
Phase Stability ◽  
Kinetic Monte Carlo ◽  
Theoretical Frameworks ◽  
Effective Interactions ◽  
Dynamical Phase ◽  
Thermodynamic Potentials ◽  
Simple Kinetic Model ◽  
Kinetic Monte Carlo Simulations ◽  
Competing Dynamics

AbstractPhase stability in alloys under irradiation is studied considering effective thermodynamic potentials. A simple kinetic model of a binary alloy with phase separation is investigated. Time evolution in the alloy results from two competing dynamics: thermal diffusion, and irradiation induced ballistic exchanges. The dynamical (steady state) phase diagram is evaluated exactly performing Kinetic Monte Carlo simulations. The solution is then compared to two theoretical frameworks: the effective quasi-interactions model as proposed by Vaks and Kamishenko, and the effective free energy model as proposed by Martin. New developments of these models are proposed to allow for quantitative comparisons. Both theoretical frameworks yield fairly good approximations to the dynamical phase diagram.

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