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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 • Motivation • NEMD Approach • Single Interfaces • Size effects • Comparison with theoretical models • Defects, temperature • Nanostructures (Si-Ge) • Summary and Future Plans
Macroscale 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 • 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 *kagakukan.toshiba.co.jp Superlattice 1-100 nm * Berkeley Nano Engineering Research Program
Other Applications • 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 Rq = Ratio of Film to Substrate Debye temperatures
Computational Molecular Dynamics Approach • 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.
Molecular Dynamics Issues • 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 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 • Lennard-Jones potential with cutoff at 2.5s. • Interfaces are oriented on the FCC (100) plane.
Errors, BC, and Size Effects • 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 Results are similar to NEMD approach, but there is difficulty in defining thermal mass.
Modeling Real Structures (Si-Ge) 4,000 atoms LJ Potential Pair-wise potential 100,000 atoms SW Potential 3 body potential
LAMMPS • 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) • 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) 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
Summary and Future Plans • 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 • 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
Transmission Coefficient-DMM Interface scattering with no memory: Principle of detailed balance: = Debye Model: