Thermal unobtainiums?The perfect thermal conductor andthe perfect thermal insulatorDavid G. CahillMaterials Research Lab and Department of MaterialsScience and Engineering, U. of IllinoisGratefully acknowledge support from ONR and AFOSR
Outline—toward perfect thermal conductors• Conventional conduction of heat in solids byphonons and electrons– phonon scattering mechanisms in dielectriccrystals– metals• Examples of unconventional heat conduction– Poiseuille flow of heat– ambipolar heat conduction• Heat conduction in Bose condensates– electronic superconductors– superfluid helium– Bose condensate of magnons
Outline—toward perfect thermal insulators• Einstein and minimum thermal conductivity• Localization of lattice vibrations by disorder• Beating the minimum with anisotropicdisordered materials: disordered layeredcrystalsConclude with some thoughts on promising,high-risk, research directions
Gas kinetic equation is a good place to start• Anharmonicity (high Tlimit)τ− 1∝ ω2 T• Point defect scatteringτ− 1 4∝ω• Boundary scatteringτ − 1∝1/dCahill and Pohl, Ann. Rev. Phys. Chem. 39, 93 (1988)
Peak occurs at T ∼ Θ Debye /30 in typical crystals• Anharmonicitycontrols conductivitynear roomtemperature.– k is not a perfectquantum number• Not possible (?) toeliminateanharmonicities evenin a computer model.
Thermal resistance is created by Umklappscattering (U-process)• Illustration gives examples of:N-process T+L → LU-process T+T → L• Considerations of symmetry anddimensionality are subtle and complex, seeHerring Phys. Rev. (1954).Peierls, Ann. Phys. 3, 1055 (1929)
Isotopes contribute to thermal resistance• Isotopically pure diamond has highest thermalconductivity of any materialWei et al., PRL 70, 3764 (1993)
Carbon nanotubes• Evidence for the highest thermal conductivityany material (higher conductivity thandiamond)Yu et al. (2005)Maruyama (2007)
High Debye temperature also produceshigh conductivity in metals• Phonons disrupt theperiodicity of thelattice– k is not a goodquantum number• Pure metals havehigh conductivity atlow temperaturesΛ=LσTMueller et al., APL 57, 240 (1990)
Unconventional heat conduction: Poiseuilleflow of phonons• Counter-intuitive:strong N-processesscreen the interactingphonon gas from theboundaries of thecrystal.• RequireslUlNrrLimited to He crystals(?)Hogan, Guyer, and Fairbank, PR 185, 356 (1969)
Ambipolar diffusion contributes to heatconduction.• In an intrinsicsemiconductor, e-h pairsdiffuse from hot-to-cold,driven by theconcentration gradient.• Each pair carriers theband-bap energy (but nocharge).Glassbrenner and Slack, PR 134, A1058 (1964)
Superconductors are an effective heat switch• Strong magnetic fieldsquenchessuperconductivity.• Normal electrons carryheat but Cooper pairsdo not.Schubert, RSI 55, 1486 (1984)
But unconventional metals show avariety of behaviorYBCO B-field dependenceMgB 2Schneider et al.,Physica C 363, 6 (2001)Peacor, Cohn, Uher, PRB 43, 8721 (1991)
Superfluid He near T c has a conductivitycomparable to Si at room temperature• Counter-flow of normal fluid and superfluidThermometer spacing is 1.6 cm2.2 mW/cm 28.8 mW/cm 2Leiderer and Pobell, JLTP 3, 577 (1970).
Could a solid-state Bose condensate showthis superfluid behavior?• magnons (quantizedspin waves) arebosons.• Do magnons Bosecondense in anapplied field?Kudo et al., JMMM 272, 214 (2004)
Produce low conductivity withnanoscale boundary scattering
Nanoscale boundary scattering reducesthe thermal conductivityCompilation of data for Sinanowires and thin films• Debye-Callaway-Morelli model• Length-scale thatreduces Λ by x2– Si: 300 nm– InGaAs: 200 nm– PbTe (predicted):15 nmKoh and Cahill, unpublished
Etched (rough) nanowires showanomalously low conductivity
Disorder creates localization in 1D1D crystalMass disorderHe and Maynard, PRL 57, 3171 (1986)
Einstein (1911)• coupled the Einsteinoscillators to 26neighbors• heat transport as arandom walk ofthermal energybetween atoms; timescale of ½ vibrationalperiod• did not realize waves(phonons) are thenormal modes of acrystal
Works well for homogeneousdisordered materialsamorphousdisordered crystalCahill, Watson, and Pohl, PRB (1991)
Time domain thermoreflectance since 2003• Improved optical design• Normalization by out-ofphasesignal eliminatesartifacts, increases dynamicrange and improvessensitivity• Exact analytical model forGaussian beams andarbitrary layered geometries• One-laser/two-colorapproach tolerates diffusescattering, see Kang et al.,RSI (2008)Clone built at Fraunhofer Institute forPhysical Measurement, Jan. 7-8 2008
Layered disordered crystals: WSe 2 by“modulated elemental reactants”• Deposit W and Selayers at roomtemperature on Sisubstrates• Anneal to removeexcess Se andimprove crystallinity• Characterize by RBS,x-ray diffraction (labsources and AdvancedPhoton Source) andTEMD. Johnson and co-workers
Cross-sectional TEM of 60 nm thick WSe 2Kim, Zuo et al., JMR (2008)
Thermal conductivity of WSe 2• 60 nm film has the lowestthermal conductivity everobserved in a fully densesolid. Only twice the thermalconductivity of air.• A factor of 6 less than thecalculated amorphous limitfor this material.Chiritescu et al., Science 315, 351 (2007)
Conclusions from theoretical work(Hu and Keblinski, unpublished)• Analysis of the participation ratio: phononlocalization is not significant.• Analysis of mode polarization: incoherent grainboundaries create diffusive but non-propagatingvibrational modes. (stacking faults are notsufficient)• Key to ultralow thermal conductivity is disorder incombination with anisotropy, i.e., an “anisotropicglass”.• Interface resistance between 2D crystallinesheets? Lowering of the effective density ofstates for modes diffusing perpendicular to thesheets?
Back to experiment: Can we lower theconductivity even further?• Synthesize misfitlayered compounds byelemental reactantsmethod (Johnson andco-workers)– WSe 2 /PbTe– MoSe 2 /PbTe• Interface density doesnot matter. Conductivitydetermined bycomposition notinterface density.Chiritescu et al., JAP (2008)
Conclusions and research directions• Hard for me to see a promising path toward“ultrahigh” thermal conductivity (conductivityhigher than diamond at room temperature)• But we could think outside-the-box about…– design of molecular structure to provideultrahigh conductivity polymers– searching for superfluid-type heat conduction insolid-state Bose condensates• Ultralow conductivity (conductivity lower thanaccepted minimum) has been demonstrated.– extend and ehance this physics for thermalbarriers and thermoelectrics– need to understand the physics of roughnanowires; localization in 1D?
Research directions• Passive and active control of heat conduction– Thermal regulator, thermal switch, thermalrectifier– Phase transformations are (to me) mostpromising route– Applications for passive temperature control;electrocaloric cooling; thermal protection
Extras slides start hereV. Narayanamurti and R. C. Dynes, PRL 28, 1461, (1972).