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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. Motivation

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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 l.jpg
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 nanoscale l.jpg
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 l.jpg
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 l.jpg
Thermoelectrics Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

*kagakukan.toshiba.co.jp

Superlattice

1-100 nm

* Berkeley Nano Engineering Research Program


Thermoelectric performance l.jpg
Thermoelectric Performance Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques


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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


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Motivation Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques

Rq = Ratio of Film to Substrate Debye temperatures


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Motivation Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques


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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.


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MD Approach Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques


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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.


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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.


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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.


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NEMD Approach Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques


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MDS Temperature Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques


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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.


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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.


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


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


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


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Lattice Mismatch Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques


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Mixed Interface Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques


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Temperature Dependence Nanostructured Materials Using Non-equilibrium Molecular Dynamics Techniques


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


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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


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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.


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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


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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


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


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


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


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


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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.


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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


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


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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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