Pattern Formation via BLAG

Mike Parks & Saad Khairallah

Outline Simulate laboratory experiments

If successfully simulated, proceed to new computer experiments.

Phase 1: Deposition

Substrate

Xenon

T=20K

Gold particles incoming onto the surface from a heat sourceThe

particles will not move much at T=20K

Phase 2: Desorbtion

Substrate

Xenon particles desorbing

T>20K

Thin xenon film acts as timer

Gold particles walk randomly

With a sticking probability of one they form clusters when colliding

Final State: Clusters

SubstrateT>>20K

Final Equilibrium State: clusters on substrate(abrupt interface)

Control Parameters Parameters for Cluster Creation:

The thickness of the xenon layer acts as a timer

Sticking probability coefficient ~1 (DLCA) Surface coverage External potential (???)

No need to satisfy thermodynamics constraints: surface free energy and the three growth

modes

Results to simulate… Weighted cluster size grows as

S~t2 Density decays as N~t-2. Fractal dimension according to

DLCA size ~ (average radius)^Dimension.

…our contribution: Charge the particles Apply electric field perturbation

+-

Uniform E

-- -+

++

Simulation Start with uncharged particles interacting on a

square lattice with Lennard-Jones potentials. When two atoms become adjacent, they bond to

form a cluster. Update simulation time as

t = (# Atoms Moved)/(# Atoms), i.e. diffusion does not depend on time.

Simple metropolis algorithmNo KMC: 1. We are not describing the dynamics on the surface. 2. Pattern formation via BLAG does not depend on

time explicitly.

Implementation Issues: Need to efficiently

determine when to merge clusters

Use bounding boxes on clusters and check for adjacent atoms only when boxes overlap

Linked-cell method implemented for L-J potentials

The SIMULATIONS Performed

1. Uncharged particles: mimic experiment

2. Charged particles: uniformly distributed

3. Charged particles with uniform electric field: weak and strong

Results (Uncharged)

Initial Configuration

Final Configuration

Power Law Dependence(uncharged)

Experiment:

1.9 +/- 0.3

Simulation:

2.00 +/- 0.03

Agreement!

Fractal Dimension(uncharged)

Agreement!

Modification : Add Charge Add a positive or negative charge of

magnitude 1.6e-19 Coulombs to all atoms, such that the net charge is zero.

Distribute the charged particles uniformly over the lattice.

Clusters that form as to have no net charge interact only with L-J potential.

Results (Charged Particles)

Final Configuration

Fractal Dimension(charged plus charged with e-field)

Fractal:

New results. We see same dimension as with no charging.

Power law : Size~t2

coverage

Exp. No charge

Charge Charge with

Efield

21%

1.9 0.3

1.99 0.03 1.98 0.02 1.97 0.00

19%2.01 0.02 1.76 0.01 1.91 0.00

11%1.97 0.03 1.50 0.01 1.66 0.00

Interpretation…

The effect of charging subsides according to coverage:

1. Fast decay if high coverage: particles neutralize each other quickly

2. Slow decay if low coverage: particles neutralize each other slowly

Interpretation…

•When charging effect subsides fast, L-J takes over giving close results to exp.

•When charging effect subsides slow, Coulomb potential acts longer altering results from exp..

•So what does the electric field do?

Electric Field Effect… The electric field accelerates the

process of particles neutralizing each other making the charge effect decay fast.

We expect L-J to dominate on the long run

Hence results closer to experiment

Future work… The model, DLCA based on sticking

probability coefficient ~1: so change that number allowing for non-sticking collisions.

Have a metallic substrate to alter the potential with an image potential

Apply varying electric field More complicated: 3D clusters.