Daniel Bowring3rd International Workshop on Thin Films

July 22, 2008

Molecular Dynamics Simulations of Thin

Film Growth

1Tuesday, July 22, 2008

Overview

• Why simulate film growth?

• Overview of MD

• Features of this model

• Future work

2Tuesday, July 22, 2008

Motivation

• Grain boundaries have an effect on surface resistance.

• Film quality is dependent on deposition technique:

• surface roughness

• defect density

• Backsputtering from energetic condensation

3Tuesday, July 22, 2008

Motivation (cont’d.)

Parameter space for film deposition is large:

• deposition energy

• substrate temperature

• substrate structure (amorphous, polycrystalline, single-crystal)

• bias voltage effects

These properties can all be simulated!

4Tuesday, July 22, 2008

Molecular Dynamics

• Integrate Newton’s laws of motion for many particles, watch system evolve.

• F2 are two-body forces, F3 are three-body. Many-body interactions also possible (jellium, EAM, etc.).

mid!vi

dt=

!

j

F2 (!ri,!rj) +!

j

!

k

F3 (!ri,!rj ,!rk) + · · ·

d!ri

dt= !vi

5Tuesday, July 22, 2008

Molecular Dynamics (cont’d.)

• Computationally intensive:

• For single processors, MD viable for N~104, total time ~ ns.

• Integrating Newton’s laws takes 2-3% of simulation time.

• Atom-by-atom interatomic potentials are the real computational burden.

6Tuesday, July 22, 2008

LAMMPS

• Open-source MD code developed by S.J. Plimpton at Sandia National Labs

• LAMMPS = Large-scale Atomic/Molecular Massively Parallel Simulator

S.J. Plimpton. Fast Parallel Algorithms for Short-Range Molecular Dynamics.J. Comp. Phys. 117 (1995) 1-19.

http://lammps.sandia.gov/index.html

7Tuesday, July 22, 2008

Interatomic Potential

• This analysis uses the embedded atom method (EAM) potential:

Fi = embedding energy

Φ = short-range pair potential

ρ = host density at i

Rij = distance between atoms i,j.

Etot =!

i

Fi (!h,i) +12

!

i !=j

"ij (Rij)

Pair interaction

Implantation energy

M.S. Daw, M.I. Baskes. Phys. Rev. B. 29 (1984) 12.

8Tuesday, July 22, 2008

Interatomic Potential (cont’d.)

• To our knowledge, no EAM potential has been developed yet that agrees with empirically-observed properties of Nb.

• The complicated electronic structure of transition metals makes an analytic determination of such a potential non-trivial.

• More on this shortly.

9Tuesday, July 22, 2008

Simulations in Development

• surface self-diffusion

• competitive grain growth

• defect density

• backsputtering

• preferential sputtering rates

10Tuesday, July 22, 2008

Some Preliminary Work

• LAMMPS-based simulation of Cu self-diffusion on a substrate with (110) and (111) grains.

• Substrate held at some constant temperature, consistent with the canonical ensemble.

• Movies produced using AtomEye, an atomistic configuration viewer developed by Ju Li at U. Penn.J. Li. Modeling Simul. Mater. Sci. Eng. 11 (2003) 173.

11Tuesday, July 22, 2008

Self Diffusion: Cu at 50 K

12Tuesday, July 22, 2008

Self Diffusion: Cu Atoms at 40 K

13Tuesday, July 22, 2008

Why Copper?

• These movies illustrate a proof-of-concept model.

• Cu very well understood.

• Modeling transition elements (like Nb) is non-trivial due to resonances in the electron density.

14Tuesday, July 22, 2008

Role of Electron Density

• How to approach an N-body quantum-mechanical problem?

• QM wavefunction has 4N degrees of freedom (position + spin).

• W. Kohn et al. mapped ground-state w.f. to the electron density:

• All material properties (e.g. specific heat) obtained from electron density!

c.f. W. Kohn, L.J. Sham. Phys. Rev. 140 (1965) 1133-1138.

15Tuesday, July 22, 2008

Role of Electron Density (cont’d.)

s-band (simple metals)superimposed d-band (transition metals)

dens

ity o

f sta

tes

energy

• Uniform density approximations (e.g. jellium) suitable for simple metals.

• Transition metals are complicated: d-band resonance invalidates many LDAs.

• Analytic approaches are not generally applied to the electron density of bcc transition metals.

16Tuesday, July 22, 2008

Nb interatomic potential from force-matching method

Implementation of parallel computing resources at JLAB

Future Work

17Tuesday, July 22, 2008

Ab Initio Force-Matching Method

• Possible to develop an EAM potential for Nb using empirical data.

• c.f. F. Ercolessi, J.B. Adams. Europhys. Lett. 26 (1994) 8.

• Similar to the least-squares kinematic fit procedure used in high-energy physics.

18Tuesday, July 22, 2008

Force-Matching Method (cont’d.)

• Electron density ρ(r) is approximated as a set of points in α-dimensional parameter space.

• Objective function Z(α) characterizes the mean square fitting error in ρ(r), using an ab initio force database as reference.

• Z(α) is minimized with respect to constraints on parameter space (e.g. stacking fault energy, elastic constants)

19Tuesday, July 22, 2008

Parallel Processing

• Practically, simulations on a single desktop are limited to:

- 104 atoms

- one nanosecond

• Complex (i.e. interesting) simulations require parallel computing platforms.

• This analysis can be easily ported to JLAB’s parallel computing farm via MPI.

20Tuesday, July 22, 2008

Acknowledgements

• Larry Phillips

• Xin Zhao

• David Srolovitz

• Jerry Floro

• Stephen Plimpton

21Tuesday, July 22, 2008