Size effect on thermal conductivity of thin films

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Size effect on thermal conductivity of thin films

• Guihua Tang, Yue Zhao, Guangxin Zhai, Zengyao Li,
  Wenquan Tao
• School of Energy Power Engineering,
• Xian Jiaotong University, China

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Outline
Results 1 Local thermal conductivity distribution
Results 2 Overall thermal conductivity
Conclusions
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1. Background

• Boundary or interface scattering becomes
  important when the characteristic length (film
  thickness, wire diameter) is comparable with the
  mean free path.
• The thermal conductivity (as well as other
  transport coefficients, viscosity) becomes size
  dependent.
• Numerous important applications of nanoscale
  thermal conduction (electronic devices cooling,
  thermal insulator, thermalelectric conversion,
  etc.)

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• Specific heat of solid Lattice vibration in
  solids.

Harmonic oscillator model of an atom

• Conduction in insulators is dominated by lattice
  waves or phonons.
• Simple expression of thermal conductivity based
  on the kinetic theory

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• Classical size effect based on geometric
  consideration (1)

• In the ballistic transport limit, LltltLb, the MFP
  is L
• LgtgtLb, the MFP is the bulk mean free path Lb
• Intermediate region

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• Classical size effect based on geometric
  consideration (2)

• When LltltLb, assuming that all the energy carriers
  originate from the boundary surface

• LgtgtLb, the MFP is the bulk mean free path Lb

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• Classical size effect based on geometric
  consideration (3)

• The direction of transport was not considered and
  the anisotropic feature cannot be captured
• Filk and Tien employed a weighted average of the
  mean free path components in the parallel and
  normal directions of a thin film

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• Classical size effect based on geometric
  consideration (4)

A thin circular wire for paths originated from
the centre
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• Classical size effect based on Boltzmann
  Transport Equation (BTE)

• The relaxation time approximation was adopted.
• The distribution function was assumed to be not
  too far away from equilibrium.

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2. Local mean free path method

• For an unbounded phonon gas, the probability of a
  phonon gas can travel between two consecutive
  collisions with other phonons at location x and
  xdx would be of the form

The probability of a phonon gas having a free
path between x and xdx

• When the gas is bounded, a number of phonons will
  be terminated by the boundary, thus effective
  MFP lt Lb

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Semi-infinite film
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Thin film
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3. Results
Local thermal conductivity distribution in a
semi-infinite film
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Local thermal conductivity distribution in a thin
film
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Overall thermal conductivity in a thin film VS Kn
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4. Conclusions

• An equation to calculate the size-dependent film
  thermal conductivity has been derived. No
  Matthiessens rule No interpolation
• Local thermal conductivity distribution in the
  thin film has been obtained.
• The present solution seems to overpredicts
  reduction in thermal conductivity compared to the
  data in references when Knudsen number is larger
  than 1.
• More cases are needed for further validation and
  extension to complicated geometric structures.

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Thanks for your attention!
09/07/2010