Monte Carlo approach to island formation during thermal treatment of thin films* Ann Marie Hardin December 6, 2006 *F. Lallet, R. Bachelet, A. Dauger, and N. Olivi-Tran, (2006) Physical Review B, 74
Outline Background Monte Carlo Simulation of Thin Films Simulation Results Extended Investigations Conclusions
Thin Film Applications Electronic semiconductor Optical coatings Corrosion, oxidation and wear resistance Computer memory Photovoltaic cells
Challenges Physics of thin films are not completely understood Dewetting Island formation Effect of substrate inpurities Film thickness control
Methods of manufacture Dip coating Spin coating Sputtering Chemical Vapor Deposition Sol-gel
Methods of Manufacture All methods require coating of substrate surface with polymer film and then curing to form stable film
Island Formation Accompanied by dewetting During thermal treatment, areas of increased height form spontaneously in film Initial flat surface is a strained fromation Film stabilizes to lowest-energy configuration
Island Formation Zhang, Y. W., Self-organization, shape transition, and stability of epitaxially strained islands., Physical Review B. 61(15):10388-10392
Simulation of Island Formation: a Monte Carlo Approach Surface modeled as array of square domains 500 1000 atoms per domain Initial film thickness is 1 nm Crystallographic orientation randomly assigned
Model Parameters Film thickness Crystallographic orientation related to inter-plane spacing Film energy Surface strain due to neighboring domains with different crystallographic orientation Interfacial energy between one domain and substrate Surface strain due to neighboring domains with different heights
Model Implentation Each domain owns three states Vertical interplane spacing (0.5 2.5) Horizontal interplane spacing (0.5 2.5) Domain height (0 4) Film energy given as sum of all domain state energies
Monte Carlo Algorithm Choose domain Propose new horizontal spacing Accept or reject proposed change Propose new vertical spacing Accept or reject proposed change
Monte Carlo Algorithm Choose neighbor of chosen domain Propose height exchange between two domains
Proposal Vertical and horizontal spacing Increase or decrease by 0.5 Bounded at 0.2 and 2.5 Reflect back to interior if at boundary. Domain height Target domain increased or decreased by 1 Neighbor changed by same amount but opposing direction
Acceptance criteria Calculate energy change associated with proposed configurational change E E E 2 1 Accept proposed change with probability P P 1, E 0 E kbt e, E 0
Calculation of Surface Energy E l B l c c l C l d d Dl h h 2 NN 2 NN NN i i i i j i i j i i j hi j 1 hi j 1 j 1 i 2 B scales interfacial energy between two domains C scales interfacial energy between a domain and the substrate D scales the surface strain between two neighboring domains of differing heights
Efficiency Chain requires 1 million steps 3 evaluations per step Effeciency is important Calculate energy only at affected domains, not entire film
Results
Island Formation z y x
Evolution of Film Thickness
Published evolution of domain height
Evolution of Interplane Spacing
Effect of various components Parameter B and C are symmetrical B scales horizontal effects C scales vertical effects Affect inter-plane spacing or crystallographic orientation D scales surface strain due to height differences Affects island height and formation
Effect of inter-plane surface strain
Effect of inter-plane surface strain
Effect of Surface Strain due to Height differences
Effect of Surface Strain due to Height differences B=C=10 5, D = 10-5 B=C= D=1
Effect of Curing Temperature on Film Thickness 6000 5000 Domains 4000 3000 2000 1000 0 h=0 h=1 h=2 h=3 h=4 500 1800 3000
Effect of Curing Temperature on Crystallographic Orientation 9000 9000 8000 7000 8000 7000 6000 6000 5000 5000 4000 4000 3000 3000 2000 1000 0 c=0.5 c=1.0 c=1.5 c=2.0 c=2.5 Temperature 2000 1000 0 d=0.5 d=1.0 d=1.5 d=2.0 d=2.5 Temperature
Effect of Initial Film Thickness Evolution of domain height Number of domains 0 2000 4000 6000 8000 10000 h=0 nm h=1 nm h=2 nm h=3 nm h=4 nm 0 e+00 2 e+05 4 e+05 6 e+05 8 e+05 1 e+06 Monte Carlo Steps
Conclusions Islands will form spontaneously during thermal annealing of thin films Monte Carlo simulations can be used to study island formation I was able to approximate but not replicated published results