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Modeling Thermal Transport at Single Interfaces and in Nanostructured Materials Using Non-equilibrium Molecular Dynamics TechniquesPowerPoint Presentation

Modeling Thermal Transport at Single Interfaces and in Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

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### Modeling Thermal Transport at Single Interfaces and in Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Robert J. Stevens

Department of Mechanical Engineering

Rochester Institute of Technology

RIT Research Computing Tech Group

April 19, 2007

Outline Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

- Motivation
- NEMD Approach
- Single Interfaces
- Size effects
- Comparison with theoretical models
- Defects, temperature

- Nanostructures (Si-Ge)
- Summary and Future Plans

Macroscale Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques Nanoscale

Nanoscale thermal transport is important when either the individual energy carriers must be considered and/or when continuum models break down.

Bulk

Nanostructure

Thermal Boundary Resistance Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

- Mismatch in materials causes a resistance to heat flow across an interface.

10-9-10-7 m2K/W

~ 0.15-15 mm Si

~ 1-100 nm Si2O

Thermoelectrics Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

*kagakukan.toshiba.co.jp

Superlattice

1-100 nm

* Berkeley Nano Engineering Research Program

Thermoelectric Performance Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Other Applications Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

- Vertical Cavity Surface Emitting Lasers
- Optical storage
- Micro-bolometers
- Nanocomposites
and nanostructures

*Cahill, et al., 2002

*Li, et al., 2003

*Yang and Chen, 2004

Motivation Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Rq = Ratio of Film to Substrate Debye temperatures

Motivation Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Computational Molecular Dynamics Approach Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

- Numerically solve equation of motion for a system of interacting particles.
- Rules are set up about how atoms interact with one another.
- Precise knowledge and control over interface types.
- Ability to vary one parameter to study its impact on interfacial thermal conductance.
- Anharmonic potentials.
- Probing at high spatial resolution is not possible by traditional experiments.

MD Approach Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Molecular Dynamics Issues Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

- Choice of interatomic potential (approximates).
- Classical model, does not account for electron transport nor quantum effect of phonons.
- Limit on system size (< 1mm), atomic spacing ~1-2 Å, system sizes 104 – 107.
- Limit to short time scales (<100 ns), timesteps of ~1 fs.

y Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

x

z

NEMD: Non-Equilibrium Molecular Dynamics- Build crystal, periodic in x-y direction
- Either fixed or periodic in z direction
- Apply heating and cooling to bath atoms by velocity scaling, constant heat flux, or Gaussian thermostat method.
- System is allowed to come to steady state conditions and data collected over next ~5·106 time steps.
- Temperatures, energy flux, and pressures are monitored.

Fundamental Interface Study Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

- Lennard-Jones potential with cutoff at 2.5s.
- Interfaces are oriented on the FCC (100) plane.

NEMD Approach Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

MDS Temperature Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Errors, BC, and Size Effects Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

- Statistical errors due to system noise for 6 million time step simulations was ~6-8%.

- Crystal sizes of 5x5x40 were typically used, so size effect errors were less than statistical error.
- Negligible differences between different BC and temperature regulation methods.

Transient MDS Experiment Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Results are similar to NEMD approach, but there is difficulty in defining thermal mass.

Results for Perfect Interface with Mass Mismatch Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Fitting DMM to MDS Data Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Comparison with DMM Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Lattice Mismatch Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Mixed Interface Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Temperature Dependence Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Experimental Evidence of Temperature Dependence Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Modeling Real Structures (Si-Ge) Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

4,000 atoms

LJ Potential

Pair-wise potential

100,000 atoms

SW Potential

3 body potential

LAMMPS Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

- Large-scale Atomic/Molecular Massively Parallel Simulator
- Developed in the mid 1990’s at Sandia National Laboratories as an open source C++ code, funded by DOE. http://lammps.sandia.gov/
- Distributed-memory message-passing parallelism (MPI).
- Spatial decomposition of simulation domain using “ghost” atoms.
- Has been used to model atomic, biological, metallic, and granular systems based on classical molecular dynamics.
- Uses neighbor lists to reduce computational effort.
- Velocity-Verlet integrator, with constant NVE, NVT, or NPT.

Modeling Real Structures (Si-Ge) Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

- RIT Cluster
- 47 IBM Xseries 330 Servers 2-1.4GHZ Pentium 3 Xeon Processors
- 1 IBM Server for the Head Node 2-2.0GHZ Pentium 4 Xeon Processors

Modeling Real Structures (Si-Ge) Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Stillinger and Weber, Phys. Rev. B, 1985

Ding and Andersen, Phys. Rev. B., 1986

- Stillinger-Weber potential
- Mixing rules

Ethier and Lewis, J. Matr. Res., 1992

Crystal Size Impact Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Si-Ge Superlattices Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Si-Ge Superlattices Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Si-Ge Superlattices Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Summary and Future Plans Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

- NEMD is one means of exploring thermal transport at interfaces and nanostructured materials.
- For LJ interfaces with defects when compared to DMM, partially captures the trend seen in real interfaces.
- Thermal boundary conductance is linearly dependent with temperature in the classical limit, indicating potential role for inelastic scattering mechanisms for thermal transport at LJ interfaces.
- Stillinger-Weber potential with NEMD predicts bulk conductivity of Si well. Still need to confirm for Ge material using naturally occurring isotope breakdown.
- Reduced effective thermal conductivity for SiGe superlattice as period size is reduced. Results compare with existing experimental data on SiGe SL.
- Did not observe reduction in thermal conductivity when increasing superlattice period above 10 nm, as observed experimentally.
- Need to explore size impact on SiGe SL results.
- Expand simulations to examine nanocomposite materials.
- Temperature dependence in SL.

Acknowledgements Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

- Leonid Zhigilei, University of Virginia
- Patrick Hopkins, University of Virginia
- Rick Bohn and Gurcharan Khanna, RIT
- New Faculty Development Funds, RIT
- Steve Plimpton, Sandia National Lab, LAMMPS

DMM Calculations for Debye Approximation Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Transmission Coefficient-DMM Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Interface scattering with no memory:

Principle of detailed balance:

=

Debye Model:

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