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Monte Carlo Simulation of SrTiO3Thin Film Growth
Carolyn Worley, Alexander ZakjevskiiAdvisor: Dr. Anter El-Azab
Department of Scientific ComputingFlorida State University
Pulsed Laser Deposition• Thin film deposition technique• Applications: Complex oxide thin film growth
(P. R. Willmott 2004)
Four Steps in PLD
• Laser ablation of target
• Plasma plume formation and propagation
• Deposition of material onto substrate
• Nucleation and island growth
PLD Thin Film Growth Process
1. Molecules arrive on surface2. 2D diffusion3. Collisions -> Nucleation4. Island and layer growth
PLD Growth Modes
• Ideal Layer-by-layer (LBL) Growth▫ One layer complete before next layer begins growing▫ High incident kinetic energy▫ Low laser repetition rate▫ Theoretical limit – cannot be achieved experimentally
• 3D Growth▫ Many layers grow simultaneously▫ Low incident kinetic energy▫ High laser repetition rate
Project Goals
• Model PLD thin film growth of STO• Use Monte Carlo algorithm• Model individual STO building blocks• Show nucleation & island growth process
z = 1
z = 2
z = 3
PLD
Monte Carlo Method
• MC methods rely on repeated random sampling
• Well suited for modeling complex physical phenomena▫ Too complex for deterministic models
• Categories of MC methods useful for thin film models▫ Metropolis Algorithm▫ Kinetic Monte Carlo Algorithm
Application of MC to Thin Film Growth
• MC methods are useful for modeling thin film diffusion and growth
• 3 types of MC events▫ Deposition▫ Diffusion▫ Chemical Reactions (model assumes no reactions)
• Collisions lead to island formation• Applied periodic boundary conditions
Algorithm (1) - Deposition• Deposition: n STO molecules
instantaneously deposited on random (x,y) coordinates of L x L lattice.
n is determined by instantaneous flux Fi
where, tp = pulse duration
Substrate
Plume
Algorithm (2) - Diffusion
• Diffusion: If there are no nearest neighbors, move the molecule based on Boltzmann probabilities and hopping rates.
(Q. Zhang 2006)
, where i refers to a specific direction
If the layer below has an open space, then automatically move down.
Algorithm (3) – Diffusion Parameters
• Change in energy given by
where, Esurf = surface diffusion activation energyEbond = bond energyN2, N1 = number of final & initial bonds
• Esurf = 0.3 eVEbond = 0.5 eV (Q. Zhang 2006)
Algorithm (4) – Island & Layer Growth
• Upon collision molecules form islands. No further diffusion for an island.
• Collision occurs when the distance between molecules = 1 lattice unit, and the molecules move for minimizing energy outcome
• Note: Upper layers tend to form islands when coverage of previous layer > 0.5
Algorithm (5) – Time Dependence• At the end of diffusion, compute time step
∆1∑
• Increment by time step• If t reaches pulse time ts, another deposition occurs• Repeat algorithm until desired coverage is reached.
t
Inci
den
t F
lux
tp
diffusion
tp tp
t = ts t = 2ts
Deposition events
Block Diagram of Algorithm
One iteration of entire algorithm
Results – Single layer growth progression
t = 10-5 s t = 0.010 s t = 0.026 s
t = 0.059 s t = 0.155 s t = 0.251 s
Results – First Layer
Single layer growth, 30% coveraget = 0.191 s
Formation of z = 2 islands at θ1 ≈ 0.5t = 0.326 s
Results – Subsequent Layers
Formation of z = 3 islandst = 0.888 s
z = 2 islands ripening;z = 1 nearly filled t = 0.626 s
Results – Deposition Animation
Simulation of deposition process from start to beginning of third layer growth
Future Work
• Extend code to model SrO & TiO2 molecules, rather than just STO units
• Increase simulation speed & efficiency▫ Vectorize MATLAB code▫ Use faster language
z = 1
z = 2
z = 3
Green = SrORed = TiO2
Acknowledgements
• Zhang Q., Vacuum 81 (2006) 539-544• Wilmott PR, Prog. Surf. Sci. 76 (2004) 163-217• Yu G., Integr. Ferroelectr. 78 (2006) 85-92
• Dr. Anter El-Azab• Srujan Rokkam• Ryan Deskins• NSF REU Program
References