Kinetic phase diagrams for island nucleation and growth using accelerated dynamics

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Kinetic phase diagrams for island nucleation and
growth using accelerated dynamics M. Basham and
P.A. Mulheran Department of Physics University of
Reading
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Simplistic Mesoscopic simulations (DDA)
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Scaling in the Island Size Distribution
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Capture Zones beyond mean field
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• Multiscale Modelling Cu/Cu(100)
• High i is preferable because it yields narrower
  size distributions (and better spatial
  organisation), which in turn influences the
  regularity of complete films and multilayer growth

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• Multiscale Modelling Cu/Cu(100)
• High i is preferable because it yields narrower
  size distributions (and better spatial
  organisation), which in turn influences the
  regularity of complete films and multilayer
  growth
• What influence do temperature and deposition rate
  have on i?

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• Multiscale Modelling Cu/Cu(100)
• High i is preferable because it yields narrower
  size distributions (and better spatial
  organisation), which in turn influences the
  regularity of complete films and multilayer
  growth
• What influence do temperature and deposition rate
  have on i?
• Atomistic modelling of island dynamics using
  saddle-point search methods

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• Multiscale Modelling Cu/Cu(100)
• High i is preferable because it yields narrower
  size distributions (and better spatial
  organisation), which in turn influences the
  regularity of complete films and multilayer
  growth
• What influence do temperature and deposition rate
  have on i?
• Atomistic modelling of island dynamics using
  saddle-point search methods
• Self-learning Kinetic Monte Carlo to access the
  long-timescale regime

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• Multiscale Modelling Cu/Cu(100)
• High i is preferable because it yields narrower
  size distributions (and better spatial
  organisation), which in turn influences the
  regularity of complete films and multilayer
  growth
• What influence do temperature and deposition rate
  have on i?
• Atomistic modelling of island dynamics using
  saddle-point search methods
• Self-learning Kinetic Monte Carlo to access the
  long-timescale regime
• Incorporate dynamics into MC simulations to
  address long lengthscales of film morphology

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Self-learning kinetic Monte Carlo simulation for
small island dynamics
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Island mobility parameters from self-learning KMC
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Some tetramer island dissociation pathways
discovered by the SL-KMC
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Island dissociation parameters from self-learning
KMC
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Enhanced DDA Simulation

• Lattice-based Monte Carlo simulation

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Enhanced DDA Simulation

• Lattice-based Monte Carlo simulation
• Deposition, Diffusion and Aggregation of monomers

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Enhanced DDA Simulation

• Lattice-based Monte Carlo simulation
• Deposition, Diffusion and Aggregation of monomers
• Island sizes slt9 can hop and dissociate according
  to activation energies and temperature

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Enhanced DDA Simulation

• Lattice-based Monte Carlo simulation
• Deposition, Diffusion and Aggregation of monomers
• Island sizes slt9 can hop and dissociate according
  to activation energies and temperature
• Islands grow when monomers or sub-critical
  islands diffuse onto them

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Enhanced DDA Simulation

• Lattice-based Monte Carlo simulation
• Deposition, Diffusion and Aggregation of monomers
• Island sizes slt9 can hop and dissociate according
  to activation energies and temperature
• Islands grow when monomers or sub-critical
  islands diffuse onto them
• Islands sgt8 are immobile and grow as compact
  circles

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Enhanced DDA Simulation

• Lattice-based Monte Carlo simulation
• Deposition, Diffusion and Aggregation of monomers
• Island sizes slt9 can hop and dissociate according
  to activation energies and temperature
• Islands grow when monomers or sub-critical
  islands diffuse onto them
• Islands sgt8 are immobile and grow as compact
  circles
• Can directly image the impact of the small island
  dynamics

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DDA simulations T300, D1/F 2e8
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DDA simulations T300, D1/F 2e8
Diffusion only
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DDA simulations T300, D1/F 2e8
Dissociation only
Diffusion only
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DDA simulations T600, D1/F 2e8
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DDA simulations T600, D1/F 2e8
Diffusion only
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DDA simulations T600, D1/F 2e8
Diffusion only
Dissociation only
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Kinetic Phase Diagram

• Can we predict what the dominant growth process
  is for a given temperature and deposition rate?

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Kinetic Phase Diagram

• Can we predict what the dominant growth process
  is for a given temperature and deposition rate?
• Start with mean-field rate equations for very
  small (point-like) islands

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Kinetic Phase Diagram

• Can we predict what the dominant growth process
  is for a given temperature and deposition rate?
• Start with mean-field rate equations for very
  small (point-like) islands
• The game is to decide
• which flux dominates when
• consequent scaling laws
• when transitions between regimes occur

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n1 is monomer density F is deposition rate N is
density of stable islands nj density if
subcritical islands size j Dj is diffusion rate
of island size j Kj is dissociation rate of
island size j Capture numbers O(1) neglected We
can assume terms always negligible
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• In general for critical island size i, islands
  si1 stable but smaller ones dissociate before
  they capture monomers

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• Consider the early stages of growth island and
  monomer density very low so i8
• At high enough F, the monomer density becomes
  high enough to make a smaller island size stable
• Here take theta 0.001 for nucleation regime

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• Consider the early stages of growth island and
  monomer density low so i8
• At high enough F, the monomer density becomes
  high enough to make a smaller island size stable
• Here take theta 0.001 for nucleation regime
• Alternatively perhaps the island mobility
  dominates

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• i3 -gt i1,2 use i3 density equation for N
• i3 -gt mobility scaling regime
• Dimer mobility -gt i1 regime

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Theory 2/5 3/5 8/10 1/3 3/5
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• Summary and Conclusions
• Multiscale modelling of Cu(100) homoepitaxy
• Self-learning KMC of small island dynamics
• Large-scale simulations of island nucleation and
  growth
• higher temperature yields larger critical island
  size
• Lower temperature growth can be dominated by
  dimer-island mobility
• Theory development Kinetic Phase Diagrams
• Thanks to Francesco Montalenti
• Work supported by EPSRC grant T18738/01

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Improving order in the JPD with temperature
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Variance of JPD with coverage test of scaling