Kinetic Monte Carlo Simulations of Nanofilm Formation South Orange, - - PowerPoint PPT Presentation

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Kinetic Monte Carlo Simulations of Nanofilm Formation South Orange, - - PowerPoint PPT Presentation

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Kinetic Monte Carlo Simulations of Nanofilm Formation South Orange, August 5, 2014 Jan Willem Abraham CAU Kiel J.W. Abraham, CAU Kiel (Metal-Polymer) Nanocomposites Optics (surface plasmon resonances) Electronics Food packaging

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J.W. Abraham, CAU Kiel

Kinetic Monte Carlo Simulations of Nanofilm Formation

South Orange, August 5, 2014

Jan Willem Abraham CAU Kiel

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J.W. Abraham, CAU Kiel

(Metal-Polymer) Nanocomposites

  • Optics (surface plasmon resonances)
  • Electronics
  • Food packaging
  • Medicine
  • Biological systems
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J.W. Abraham, CAU Kiel

(Metal-Polymer) Nanocomposites

  • Optics (surface plasmon resonances)
  • Electronics
  • Food packaging
  • Medicine
  • Biological systems

Nacre, source: wikipedia

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J.W. Abraham, CAU Kiel

Questions

  • How do KMC simulations work?
  • Is KMC exact?
  • What are the advantages/disadvantages of

the method?

  • How can the formation of nanofilms be

simulated with KMC?

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J.W. Abraham, CAU Kiel

Reference for Details

Complex Plasmas: Scientific Challenges and Technological Opportunities Michael Bonitz, Jose Lopez, Kurt Becker and Hauke Thomsen (Eds.), Springer Series on Atomic, Optical, and Plasma Physics, Volume 82 2014

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Motivation by Experiments

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(Co-)Deposition1

  • 1M. Bonitz et al., Contrib. Plasma Phys. 52, 890 (2012)
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(Co-)Deposition

Metal atoms (or clusters) are deposited on a polymer matrix, where they diffuse and form metallic structures. Or: Metal and polymer are deposited at the same time (co-deposition). What arrives at the substrate?

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Surface vs. Bulk Diffusion

Au-trimethylcyclohexane- polycarbonate interface1

  • 1C. Bechtolsheim et al., Appl. Surf. Sci. 151, 119 (1999)
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From Low to High Filling Factors

TEM micrographs of Nylon-Ag nanocomposites1

  • 1H. Takele, H. Greve, C. Pochstein, V. Zaporojtchenko, F. Faupel, Nanotechnology 17,

3499 (2006)

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Controlling Electronic Properties

Au-Teflon AF nanocomposite1

  • 1H. Takele et al., Eur. Phys. J. Appl. Phys. 33, 83 (2006)
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Metallic Nanocolumns1

Vapor-phase co-deposition

Metal Polymer Fe-Ni-Co Teflon

rates

  • 1H. Greve et. al, Appl. Phys. Lett. 88, 123103 (2006)

Self-organization of nanocolumnar structures

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Theory

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Probability Theory

Physical behavior Stochastic process

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Probability Theory

Physical behavior Stochastic process

Example: random walk with jumps at discrete time points

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Random Variable

sample space

Random variable for a two-jump process

state space

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Random Variable

sample space

Random variable for a two-jump process

state space

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Stochastic Process

family of random variables

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Markov chain

Stochastic process “without memory“

past

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Time Homogeneity

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Transition Times

Jump rate

Keep the rate, but allow random transition/holding times.

GOAL

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Transition Times

What are the transition/holding times of continuous-time Markov chains?

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Transition Times

Exponential probability density function

  • Time homogeneity
  • Markov property

Exponential distribution of transition times

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Transition Times

Exponential probability density function

  • Time homogeneity
  • Markov property

Exponential distribution of transition times

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Master Equation

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Simulations

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Workflow

Physical Reality

Experimental observations Exact microscopic calculations

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Workflow

Modeling

Idealized processes Rates

Physical Reality

Experimental observations Exact microscopic calculations

Simulations (KMC)

Statistical results Solution of the master equation Comparison

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Algorithmic Constructions1

  • Variable Step Size Method
  • Random Selection Method
  • First Reaction Method

1A.P.J. Jansen, An Introduction to the Kinetic Monte Carlo Simulations of Surface

Reactions, Springer (2012)

. . .

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First Reaction Method1

  • 1M. Bonitz et al. (Eds.), Complex Plasmas: Scientific Challenges and Technological

Opportunities, Springer Series on Atomic, Optical, and Plasma Physics, Volume 82 (2014)

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First Reaction Method1

  • 1M. Bonitz et al. (Eds.), Complex Plasmas: Scientific Challenges and Technological

Opportunities, Springer Series on Atomic, Optical, and Plasma Physics, Volume 82 (2014)

Skipped: competition theorem

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First Reaction Method1

Initialization Sample process times according to the exponential distribution f(t)=Ri exp(-Ri t) Monte Carlo step Execute process with the earliest time Update Advance the time Resample all affected processes Iterate

  • 1M. Bonitz et al. (Eds.), Complex Plasmas: Scientific Challenges and Technological

Opportunities, Springer Series on Atomic, Optical, and Plasma Physics, Volume 82 (2014)

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Why are we doing this?

Experiment

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Why are we doing this?

Experiment Model A Model B

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Is KMC exact?

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Is KMC exact?

Exact behavior as dictated by the corresponding master equation

But: systematic errors in the model

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Example: Diffusion & Drift

Master equation Fokker-Planck equation

KRAMERS-MOYAL EXPANSION

Langevin equation

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Example: Diffusion & Drift

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Example: Diffusion in 2D

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Example: Forces

19 charged particles in a 2D harmonic trap

  • 2

. 5

  • 2
  • 1

. 5

  • 1
  • .

5 . 5 1 1 . 5 2 2 . 5

  • 2

. 5

  • 2
  • 1

. 5

  • 1
  • .

5 0 0 . 5 1 1 . 5 2 2 . 5 y x

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Applications

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Simulation Model1,2

  • 1L. Rosenthal et al., J. Appl. Phys. 144, 044305 (2013)
  • 2L. Rosenthal et al., Contrib. Plasma Phys. 51, 971 (2011)

Processes with rates Growth mechanisms and trapping

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Metal-Polymer Interfaces

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Metal-Polymer Interfaces1

  • 1L. Rosenthal, PhD thesis, University of Kiel (2013)
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Metal-Polymer Interfaces1

  • 1L. Rosenthal, PhD thesis, University of Kiel (2013)
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Percolation1

  • 1L. Rosenthal, PhD thesis, University of Kiel (2013)
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Metallic Nanocolumns

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Metallic Filling Factor1,2

  • 1H. Greve et. al, Appl. Phys. Lett. 88, 123103 (2006)
  • 2L. Rosenthal et al., J. Appl. Phys. 144, 044305 (2013)
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Growth Mechanisms

N=50 N=100

Spherical growth Columnar growth

“liquid drop“ atom

critical nucleus size

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Video ...

cluster defect column

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Nucleation at Defect Sites

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Columnar Growth

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Results

Rdefect / Rm= 10-8

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Results

Rdefect / Rm= 10-8

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Results

Rdefect / Rm= 10-3

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Results

Rdefect / Rm= 10-3

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Extensions of the Model

Temperature dependence

  • f critical nucleus size1
  • 1F. Ding et al. Phys. Rev. B 70, 075416 (2004)
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Simulation vs. Experiment

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Summary

  • How do KMC simulations work?
  • Is KMC exact?
  • What are the advantages/disadvantages of

the method?

  • How can the formation of nanofilms be

simulated with KMC?

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Thank you!