Monte Carlo phonon transport at nanoscales

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Monte Carlo phonon transport at nanoscales

• Karl Joulain, Damian Terris,
• Denis Lemonnier

Laboratoire détudes thermiques, ENSMA,
Futuroscope France
David Lacroix
LEMTA, Univ Henri Poincaré, Nancy, France
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Random walk and diffusion equation
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RW and diffusion equation
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RW and diffusion equation
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RW and diffusion equation
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Nanoscale conductive heat transfer
Distribution function
Boltzmann Equation
Relaxation time approximation
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Boltzmann equation resolution methods

• Kinetic theory
• Radiative transfer equation methods
• P1
• Discrete ordinate
• Monte Carlo methods
• Advantages
• Geometry
• Separation of relaxation times

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Monte Carlo simulation
Earlier work Peterson (1994), Mazumder and
Majumdar (2001)
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Initialization
Polarization
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Drift and scattering
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Boundary conditions
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Transient results in bulk
Bulk simulation specular reflection at
boundaries
Diffusion regime
Phys. Rev. B, 72, 064305 (2005)
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Results in bulk
Diffusion balistic regime transtion
Ballistic regime
Phys. Rev. B, 72, 064305 (2005)
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Nanowires
Boundary collisions purely diffuse
Appl. Phys. Lett, 89, 103104 (2006)
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Perspectives
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Perspectives

• 1D kinetic theory.
• 1D direct integration of Boltzmann equation.
• 1D Monte Carlo simulations.
• 3D integration of Boltzmann equation by discrete
  ordinate method.