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

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 ● Medicine ● Biological systems J.W. Abraham, CAU Kiel

(Metal-Polymer) Nanocomposites ● Optics (surface plasmon resonances) ● Electronics ● Food packaging ● Medicine ● Biological systems Nacre, source: wikipedia 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? 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 J.W. Abraham, CAU Kiel

Motivation by Experiments J.W. Abraham, CAU Kiel

(Co-)Deposition 1 1 M. Bonitz et al., Contrib. Plasma Phys. 52 , 890 (2012) J.W. Abraham, CAU Kiel

(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? J.W. Abraham, CAU Kiel

Surface vs. Bulk Diffusion Au-trimethylcyclohexane- polycarbonate interface 1 1 C. Bechtolsheim et al., Appl. Surf. Sci. 151 , 119 (1999) J.W. Abraham, CAU Kiel

From Low to High Filling Factors TEM micrographs of Nylon-Ag nanocomposites 1 1 H. Takele, H. Greve, C. Pochstein, V. Zaporojtchenko, F. Faupel, Nanotechnology 17 , J.W. Abraham, CAU Kiel 3499 (2006)

Controlling Electronic Properties Au-Teflon AF nanocomposite 1 1 H. Takele et al., Eur. Phys. J. Appl. Phys. 33 , 83 (2006) J.W. Abraham, CAU Kiel

Metallic Nanocolumns 1 Vapor-phase co-deposition Metal Polymer Fe-Ni-Co Teflon rates Self-organization of nanocolumnar structures 1 H. Greve et. al, Appl. Phys. Lett. 88 , 123103 (2006) J.W. Abraham, CAU Kiel

Theory J.W. Abraham, CAU Kiel

Probability Theory Physical Stochastic behavior process J.W. Abraham, CAU Kiel

Probability Theory Physical Stochastic behavior process Example: random walk with jumps at discrete time points J.W. Abraham, CAU Kiel

Random Variable sample space state space Random variable for a two-jump process J.W. Abraham, CAU Kiel

Random Variable sample space state space Random variable for a two-jump process J.W. Abraham, CAU Kiel

Stochastic Process family of random variables J.W. Abraham, CAU Kiel

Markov chain past Stochastic process “without memory“ J.W. Abraham, CAU Kiel

Time Homogeneity J.W. Abraham, CAU Kiel

Transition Times Jump rate Keep the rate, but allow random GOAL transition/holding times. J.W. Abraham, CAU Kiel

Transition Times What are the transition/holding times of continuous-time Markov chains? J.W. Abraham, CAU Kiel

Transition Times ● Time homogeneity Exponential distribution of ● Markov property transition times Exponential probability density function J.W. Abraham, CAU Kiel

Transition Times ● Time homogeneity Exponential distribution of ● Markov property transition times Exponential probability density function J.W. Abraham, CAU Kiel

Master Equation J.W. Abraham, CAU Kiel

Simulations J.W. Abraham, CAU Kiel

Workflow Physical Reality Experimental observations Exact microscopic calculations J.W. Abraham, CAU Kiel

Workflow Physical Reality Experimental observations Comparison Exact microscopic calculations Modeling Idealized processes Rates Simulations (KMC) Statistical results Solution of the master equation J.W. Abraham, CAU Kiel

Algorithmic Constructions 1 ● Variable Step Size Method ● Random Selection Method ● First Reaction Method . . . 1 A.P.J. Jansen, An Introduction to the Kinetic Monte Carlo Simulations of Surface J.W. Abraham, CAU Kiel Reactions, Springer (2012)

First Reaction Method 1 1 M. Bonitz et al. (Eds.), Complex Plasmas: Scientific Challenges and Technological J.W. Abraham, CAU Kiel Opportunities, Springer Series on Atomic, Optical, and Plasma Physics, Volume 82 (2014)

First Reaction Method 1 Skipped: competition theorem 1 M. Bonitz et al. (Eds.), Complex Plasmas: Scientific Challenges and Technological J.W. Abraham, CAU Kiel Opportunities, Springer Series on Atomic, Optical, and Plasma Physics, Volume 82 (2014)

First Reaction Method 1 Initialization Sample process times according to the exponential distribution f ( t )= R i exp(- R i t ) Monte Carlo step Execute process with the earliest time Iterate Update Advance the time Resample all affected processes 1 M. Bonitz et al. (Eds.), Complex Plasmas: Scientific Challenges and Technological J.W. Abraham, CAU Kiel Opportunities, Springer Series on Atomic, Optical, and Plasma Physics, Volume 82 (2014)

Why are we doing this? Experiment J.W. Abraham, CAU Kiel

Why are we doing this? Experiment Model A Model B J.W. Abraham, CAU Kiel

Is KMC exact? J.W. Abraham, CAU Kiel

Is KMC exact? Exact behavior as dictated by the corresponding master equation But: systematic errors in the model J.W. Abraham, CAU Kiel

Example: Diffusion & Drift Master equation KRAMERS-MOYAL EXPANSION Fokker-Planck equation Langevin equation J.W. Abraham, CAU Kiel

Example: Diffusion & Drift J.W. Abraham, CAU Kiel

Example: Diffusion in 2D J.W. Abraham, CAU Kiel

Example: Forces 2 . 5 2 19 charged 1 . 5 1 particles 0 . 5 y in a 2D 0 - 0 . 5 harmonic trap - 1 - 1 . 5 - 2 - 2 . 5 - 2 . 5 - 2 - 1 . 5 - 1 - 0 . 5 0 0 . 5 1 1 . 5 2 2 . 5 x J.W. Abraham, CAU Kiel

Applications J.W. Abraham, CAU Kiel

Simulation Model 1,2 Processes with rates Growth mechanisms and trapping 1 L. Rosenthal et al., J. Appl. Phys. 144 , 044305 (2013) J.W. Abraham, CAU Kiel 2 L. Rosenthal et al., Contrib. Plasma Phys. 51 , 971 (2011)

Metal-Polymer Interfaces J.W. Abraham, CAU Kiel

Metal-Polymer Interfaces 1 1 L. Rosenthal, PhD thesis, University of Kiel (2013) J.W. Abraham, CAU Kiel

Metal-Polymer Interfaces 1 1 L. Rosenthal, PhD thesis, University of Kiel (2013) J.W. Abraham, CAU Kiel

Percolation 1 1 L. Rosenthal, PhD thesis, University of Kiel (2013) J.W. Abraham, CAU Kiel

Metallic Nanocolumns J.W. Abraham, CAU Kiel

Metallic Filling Factor 1,2 1 H. Greve et. al, Appl. Phys. Lett. 88 , 123103 (2006) J.W. Abraham, CAU Kiel 2 L. Rosenthal et al., J. Appl. Phys. 144 , 044305 (2013)

Growth Mechanisms N =50 N =100 atom Spherical growth “liquid drop“ critical nucleus size Columnar growth J.W. Abraham, CAU Kiel

Video ... defect cluster column J.W. Abraham, CAU Kiel

Nucleation at Defect Sites J.W. Abraham, CAU Kiel

Columnar Growth J.W. Abraham, CAU Kiel

Results R defect / R m = 10 -8 J.W. Abraham, CAU Kiel

Results R defect / R m = 10 -8 J.W. Abraham, CAU Kiel

Results R defect / R m = 10 -3 J.W. Abraham, CAU Kiel

Results R defect / R m = 10 -3 J.W. Abraham, CAU Kiel

Extensions of the Model Temperature dependence of critical nucleus size 1 1 F. Ding et al. Phys. Rev. B 70 , 075416 (2004) J.W. Abraham, CAU Kiel

Simulation vs. Experiment J.W. Abraham, CAU Kiel

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? J.W. Abraham, CAU Kiel

Thank you! J.W. Abraham, CAU Kiel