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Thermal Transport in NanoStructures A review of Quantized Heat Transfer . Patrick Miller April 12, 2006. 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 transport in nanostructures a review of quantized heat transfer

Thermal Transport in NanoStructuresA review of Quantized Heat Transfer

Patrick Miller

April 12, 2006

outline
Outline
  • Thermal Conductivity
  • Phonon
  • Quantum of Thermal Conductance
  • Thermal Conductance Theory
    • Fundamental Relation
  • Conditions for Quantum Thermal Conductance
  • Future issues
thermal conductivity
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.
thermal conductivity cont
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.
phonon
Phonon
  • What is a Phonon?
  • Quanta of lattice vibrations
  • Can’t 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.
quantum of thermal conductance qtc
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.
thermal conductance theory
Thermal Conductance Theory
  • Landauer Formula used as a starting point

General Landauer Formula

  • Landauer derived to describe limiting value of energy transport.
fundamental relation
Fundamental Relation
  • Dependent only on temperature
  • Represents the maximum possible value of energy transported per Phonon mode

Units of W/K

criteria for qtc
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

discretized transport
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
applications
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.
bibliography
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/story/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.