Critical Cluster Size: Island Morphology and Size Distribution in Submonolayer Epitaxial Growth

1994 ◽  
Vol 367 ◽  
Author(s):  
Jacques G. Amar ◽  
Fereydoon Family
Keyword(s):  
Epitaxial Growth ◽  
Size Distribution ◽  
Excellent Agreement ◽  
Bond Activation ◽  
Kinetic Monte Carlo ◽  
Analytic Form ◽  
Analytical Form ◽  
Island Size ◽  
Kinetic Monte Carlo Simulations ◽  
The One

AbstractThe island-size distribution scaling function fi (u) corresponding to submonolayer epitaxial growth with critical island size i is studied via kinetic Monte Carlo simulations for i = 0, 1, 2, and 3. An analytic form for fi (u) based on a conjecture for the small-u behavior is also presented. For i = 1, the scaled island-size distribution is found to depend on island morphology. In particular, for fractal islands with i = 1 there is excellent agreement with our analytical form as well as with experiments on low temperature Fe/Fe(100) deposition. However, for compact islands with i = 1, the scaled distribution is found to deviate slightly at small u. We also find excellent agreement between our analytical form, simulations, and experiment for i =- 2 and i = 3. Good agreement between our simulation results for i = 0 and recent experiments on Fe/Cu(100) deposition is also found. Results for the scaling of the island-density as well as crossover scaling forms for the transition from i = 1 to i = 2 and from i = 1 to i = 3 are also presented and used to determine the one-bond activation energy and critical island size transition temperature for Fe/Fe(100). The morphology of fractal islands for i = 2 is also studied and compared with experiments on Au/Ru(0001).

Effects of Crystalline Microstructure on Epitaxial Morphology

1995 ◽  
Vol 399 ◽  
Author(s):  
Fereydoon Family ◽  
Jacques G. Amar
Keyword(s):  
Crystal Structure ◽  
Epitaxial Growth ◽  
Large Scale ◽  
Kinetic Monte Carlo ◽  
Island Size ◽  
The Past ◽  
Stages Of Growth ◽  
Kinetic Monte Carlo Simulations ◽  
Crystalline Microstructure ◽  
Good Agreement

ABSTRACTIn the past simulations of epitaxial growth have used solid-on-solid (SOS) models to simulate the crystalline structure of both the substrate and the growing crystal. These models have produced results in the early stages of growth in good agreement with experiments for a number of different quantities, including the island density and the island size distribution. For multilayer growth, however, there exists a competition between microscopic effects such as the Ehrlich-Schwoebel step barrier and the crystalline microstructure. Therefore, the crystal structure and geometry are important in determining the dynamics and evolution of epitaxial structure and morphology. We present the results of large-scale realistic kinetic Monte-Carlo simulations of multilayer epitaxial growth on fcc(100) and bcc(100) surfaces. The influence of crystal structure on the formation and coarsening of mounds and facets is discussed. We also discuss and compare our results with recent experiments.

Analytic Form Solution of the Direct Position Analysis of a Wide Family of Three-Legged Parallel Manipulators

2005 ◽  
Vol 128 (1) ◽  
pp. 264-271 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Analytic Form ◽  
Parallel Manipulators ◽  
Analytical Form ◽  
Form Solution ◽  
Kinematic Chains ◽  
Position Analysis ◽  
In Series ◽  
The One ◽  
Generic Structures ◽  
Wide Family

A wide family of parallel manipulators (PMs) is the one that groups all PMs with three legs where the legs become kinematic chains constituted of a passive spherical pair (S) in series with either a passive prismatic pair (P) or a passive revolute pair (R) when the actuators are locked. The topologies of the structures generated by these manipulators, when the actuators are locked, are ten. Two out of these topologies are the SR-2PS topology (one SR leg and two PS legs) and the SP-2RS topology (one SP leg and two RS legs). This paper presents two algorithms. The first one determines all the assembly modes of the SR-2PS structures. The second one determines all the assembly modes of the SP-2RS structures. The presented algorithms can be applied without changes to solve, in analytical form, the direct position analysis (DPA) of all the parallel manipulators that generate a SR-2PS structure or a SP-2RS structure when the actuators are locked. In particular, the closure equations of two generic structures, one of type SR-2PS and the other of type SP-2RS, are written. The eliminants of the two systems of equations are determined and the solution procedures are presented. Finally, the proposed procedures are applied to real cases. This work demonstrates that (i) the DPA solutions of any PM that becomes a SR-2PS structure are at most eight, and (ii) the DPA solutions of any PM that becomes a SP-2RS structure are at most sixteen.

Kinetic Monte Carlo simulations of nanocolumn formation in two-component epitaxial growth

2010 ◽  
Vol 96 (7) ◽  
pp. 071913 ◽  
Author(s):  
Shu Zheng ◽  
Wenguang Zhu ◽  
Y. F. Gao ◽  
G. M. Stocks ◽  
Zhenyu Zhang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Epitaxial Growth ◽  
Kinetic Monte Carlo ◽  
Two Component ◽  
Kinetic Monte Carlo Simulations

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.

Scaling and Coarsening in Epitaxial Growth

1998 ◽  
Vol 528 ◽  
Author(s):  
Fereydoon Family ◽  
Jacques G. Amar
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Deposition Rate ◽  
Kinetic Monte Carlo ◽  
Realistic Model ◽  
Island Size ◽  
Island Nucleation ◽  
Homoepitaxial Growth ◽  
Coarsening Behavior ◽  
Kinetic Monte Carlo Simulations

AbstractThe results of recent theoretical and simulational studies of submonolayer and multilayer homoepitaxial growth are discussed. In the submonolayer regime, the results of kinetic Monte Carlo simulations are presented and shown to provide a quantitative explanation for the variation of the submonolayer island density, critical island size, island-size distribution and morphology as a function of temperature and deposition rate found in recent experiments. In multilayer growth, a realistic model for homoepitaxial growth on fcc and bcc lattices which takes into account the correct crystal structure is reviewed. The effects of instabilities which lead to mound formation and coarsening are discussed and a unified picture of the effects of attractive and repulsive interactions at ascending and descending steps on surface morphology and island nucleation is presented. An accurate prediction of the observed mound angle for Fe/Fe(100) deposition is obtained analytically and by kinetic Monte Carlo simulations. The general dependence of the mound angle, and mound coarsening behavior on temperature, deposition rate, and strength of the step barrier in bcc(100) and fcc(100) growth is also presented and compared with recent experiments.

Germanium Island Size Distribution by Atomistic Simulation

2003 ◽  
Vol 794 ◽  
Author(s):  
Richard J. Wagner ◽  
Erdogan Gulari
Keyword(s):  
Quantum Dots ◽  
Epitaxial Growth ◽  
Size Distribution ◽  
Atomistic Simulation ◽  
Chemical Potential ◽  
Gibbs Distribution ◽  
Nanometer Scale ◽  
Size Distributions ◽  
Island Size ◽  
Self Assembled

ABSTRACTStrained epitaxial growth of Ge on Si(001) produces self-assembled, nanometer scale islands, or quantum dots. We study this growth by atomistic simulation, computing the energy of island structures to determine when and how islanding occurs. The distribution of island sizes on a surface is determined by the relation of island energy to size. Applying the calculated chemical potential to the Boltzmann-Gibbs distribution, we predict size distributions as functions of coverage and temperature. The peak populations around 80 000 atoms (35 nm wide) compare favorably with experiment.

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