Thermal Transport in NanoStructures A review of Quantized Heat Transfer

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Thermal Transport in NanoStructuresA review of
Quantized Heat Transfer

• Patrick Miller
• April 12, 2006

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Outline

• Thermal Conductivity
• Phonon
• Quantum of Thermal Conductance
• Thermal Conductance Theory
• Fundamental Relation
• Conditions for Quantum Thermal Conductance
• Future issues

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Thermal Conductivity

• What is Thermal Conductivity?
• Measure of how well a material transfers heat
• Usually discussed as a macroscopic parameter
• Apply Heat to one side and will flow to another.

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Thermal Conductivity (cont)

• Heat transfer involves Electrons (non-insulators)
  and/or phonons.
• For technologically important semiconductors
  acoustic phonons are the dominant carriers.
• Presentation will focus on mesoscopic scale,
  acoustic phonons, at low temperature.

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Phonon

• What is a Phonon?
• Quanta of lattice vibrations
• Cant vibrate independently
• Wavelike motion characterized by mass spring
  model (however phonons are massless)
• Small structures can only support one Phonon mode
  and have a fundamental limit for thermal
  conductivity
• Quantum of Thermal Conductance.

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Quantum of Thermal Conductance (QTC)

• What is Quantum of Thermal Conductance?
• When an object becomes extremely small, only a
  limited number of phonons remain active and play
  a significant role in heat flow within it.

http//pr.caltech.edu/media/Press_Releases/PR12040
.html

• As devices become smaller a strict limit exists
  for heat conduction
• Maximum Value is a Fundamental Law of Nature.
• Only way to increase thermal conductance is to
  increase the size.

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Thermal Conductance Theory

• Landauer Formula used as a starting point

General Landauer Formula

• Landauer derived to describe limiting value of
  energy transport.

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Fundamental Relation

• Dependent only on temperature
• Represents the maximum possible value of energy
  transported per Phonon mode

Units of W/K
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Criteria for QTC

• Ballistic phonon transport in 1D waveguide
  required
• Transmission coefficient must be close to unity
• Temperature bounded
• Low temp by transmission coefficient going to
  zero.
• Upper temp by onset of higher-energy modes

Need to be Close to 1
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Discretized transport.

• Strain map in structure. Interesting to note the
  blue areas on the bridges. Indicates discrete
  flow otherwise strain map would be a gradient

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Applications

• Importance for future of NanoScale devices
• represents max energy transfer per channel
  I.e there is a temp rise of one kelvin when a
  thousandth of a billionth of a watt is applied.

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Bibliography

• Rego and Kirczenow Quantized Thermal Conductance
  of Dielectric Quantum Wires Physical Review
  Letters Vol 81, Num 1, 232-235, 1998.
• Schwab et al Thermal Conductance through
  discrete quantum channels Physica E 60-68
  (2001).
• Kouwenhoven and Venema Heat Flow through
  nanobridges Nature Vol 404, 943-944, 27, April
  2000.
• Fresley Conductance ---the Landauer Formula
  http//www.utdallas.edu/frensley/technical/qtrans
  /node9.html 23, July 1995.
• Schwab et al Measurement of the quantum of
  thermal conductance Nature Vol 404, 974-977, 27,
  April 2000.
• Roukes Physicists observe the quantum of heat
  flow http//pr.caltech.edu/media/Press_Releases/
  PR12040.html 4/26/2000.
• Phonons and the Debye Specific Heat
  http//hyperphysics.phy-astr.gsu.edu/hbase/solids/
  phonon.html.
• Collins The Quantum of Heat Flow Physical
  Review Focus 9, July 1998 http//focus.aps.org/s
  tory/v2/st2
• Balandin Nanophononics Phonon Engineering in
  Nanostructures and Nanodevices Journal of
  Nanoscience and Nanotechnology Vol 5, 1-8, 2005.
• Tanaka et al Lattice thermal conductance in
  nanowires at low temperatures Physical Review B
  71, 205308, 2005.
• Wang and Yi Quantized phononic thermal
  conductance for one-dimensional ballistic
  transport Chinese Journal of Physics, Vol 41,
  No. 1, 92-99, 2005.