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