Introduction of Nano Science and Tech. Thermal and Electric Conduction in Nanostructures. Nick Fang
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1 Introduction of Nano Science and Tech Thermal and Electric Conduction in Nanostructures Nick Fang Course Website: nanohub.org Compass.illinois.edu ME Nick Fang, University of Illinois. All rights reserved. 1
2 First Midterm Friday, Sept PM Coverage: Scaling Quantum Effects Molecular Dynamics of Transport Nanoscale Solid Mechanics A Review Lecture on Monday, Sept 21 ME Nick Fang, University of Illinois. All rights reserved. 2
3 Back to Constitutive Equations Hooke s Law Fourier s Law = q = -k Fick s Law of Diffusion J = -DC Newton s law on shear stress = -du/dy) Ohm s Law J= How are they correlated in the nanoscale? ME Nick Fang, University of Illinois. All rights reserved. 3
4 Calculating Current Density Current = # electrons through A per second I e n( r, k) Adr / dt Average number of electrons Average velocity Current density: J e n( r, k) v( r, k) Power density: Q E( r, k) n( r, k) v( r, k) ME Nick Fang, University of Illinois. All rights reserved. 4
5 Net Charge/Energy Flux In order to find the net charge/energy flux (net current/power density), we need to consider all possible states at thermal equilibrium J e n( r, k) v( r, k) dk k Q E( r, k) n( r, k) v( r, k) dk k Note: n( r, k) dk D( r, k) p( r, k) dk Density of States Boltzmann Distributions ME Nick Fang, University of Illinois. All rights reserved. 5
6 Boltzmann Transport Equation t r r F p v r p k p h Convection Acceleration So how to estimate reaction? Locally, the system that is away from thermal equilibrium has a tendency to relax toward equilibrium state: t p p p 0 Equilibrium Distribution ME Nick Fang, University of Illinois. All rights reserved. 6
7 Current Density and Mobility J e n( r, k) v( r, k) dk k r r F p0 J e D( r, E) v( r, E) ( v ( r p0 )) de h E E Assume F along z direction, we find: kbtne ene J ( e ) Fz z m m Electron diffusion Migration under external field ME Nick Fang, University of Illinois. All rights reserved. 7
8 Coupled Heat and Electron Conduction Seebeck effect (1821) T 2 T 1 (Heat to electricity) + V S V T [V/ K] 2 T 1 Peltier effect (1834) Heat Q Heat Q (Electric cooling) I Q I ME Nick Fang, University of Illinois. All rights reserved. 8
9 Thermoelectric Cooling No moving parts Environmentally friendly No loss of efficiency with size reduction Can be integrated with electronic circuits (e.g. CPU) Localized cooling with rapid response Koolatron Kool Sport Cooler ME Nick Fang, University of Illinois. All rights reserved. 9
10 Major Opportunities in Energy Industry Large scale waste heat recovery of industrial processes Benefit from higher energy costs and reduction of fossil fuel pollution Hybrid low cost power sources Hybrid solar cell/thermoelectric/battery Day & night operation Flexible, easy deployment Industrial Waste Heat Recovery > 15 kw waste heat Automobile Exhaust Waste Heat Recovery ME Nick Fang, University of Illinois. All rights reserved. 10
11 Principle of Thermoelectric Effect Electron Current by BTE: J k E e T ln n B e e e e e Thermoelectricity: k e B E T e ln n e Seebeck coefficient: S E k B E a ln n0 T e kbt 86V/K - Density of electrons (n) - Activation energy (Ea) ME Nick Fang, University of Illinois. All rights reserved. 11
12 Thermoelectric Figure of Merit Electronic current Electronic current J ( E ST ) e e J T E T ( ST ) E Q Seebeck Coefficient Conductivity Temperature Figure of Merit ZT S 2 T Thermal Conductivity (from electron+phonon) ME Nick Fang, University of Illinois. All rights reserved. 12
13 Comparison of Different Materials Material Metal Semicondu ctors Ionized Hydrogels Electrolyte Typical Seebeck Coefficient (µv/ K) < ~600 (Heavy Doping) 250~ (AgBr/CdBr 2 ) ZT 2 S T ME Nick Fang, University of Illinois. All rights reserved. 13
14 Challenges in Efficiency Existing thermo-electric devices operate in limited temperature range and suffer from lower efficiency 2 ZT S T 1 from G. Chen et al, JOURNAL OF HEAT TRANSFER, 2002(124) ME Nick Fang, University of Illinois. All rights reserved. 14
15 Nanoscale Thermoelectricity? Seebeck Coefficient Conductivity S ZT 2 T ZT ~ 3 for desired goal Temperature Thermal Conductivity Difficulties in increasing ZT in bulk materials: S S and A limit to Z is rapidly obtained in conventional materials So far, best bulk material (Bi 0.5 Sb 1.5 Te 3 ) has ZT ~ 1 at 300 K Low dimensions give additional control: Enhanced density of states due to quantum confinement effects Increase S without reducing Boundary scattering at interfaces reduces more than Possibility of materials engineering to further improve ZT ME Nick Fang, University of Illinois. All rights reserved. 15
16 New Directions for Nano- Thermoelectricity Electronic properties may be dramatically modified due to the electron confinement in nanostructures which exhibit low-dimensional behaviors D. O. S. D. O. S. D. O. S. D. O. S. insulator 3D E E 2D 1D Thermal conductivity can be significantly reduced by the preferential scattering of phonons at the interfaces conductor E 0D Predicted ZT E electron phonon ME Nick Fang, University of Illinois. All rights reserved. 16
17 State-of-the-Art in Thermoelectrics FIGURE OF MERIT (ZT) max PbSeTe/PbTe Quantum-dot Superlattices (Lincoln Lab) Bi 2 Te 3 /Sb 2 Te 3 Superlattices (RTI) Bi 2 Te 3 alloy PbTe alloy 0.5 Si 0.8 Ge 0.2 alloy Bi Nanowires YEAR AgPb m SbTe 2+m (Kanatzidis) Skutterudites (Fleurial) PbTe/PbSeTe Nano Bulk S 2 (W/cmK 2 ) k (W/mK) ZT (T=300K) Harman et al., Science (2003) Bi 2 Te 3 /Sb 2 Te 3 Nano Bulk S 2 (W/cmK 2 ) k (W/mK) ZT (T=300K) Venkatasubramanian et al., Nature, ME Nick Fang, University of Illinois. All rights reserved. 17
18 A Natural Thermo-electric Sensor in Shark Brown, Nature, 2003 Extreme sensitivity to temperature changes ~0.001 C!! 97% H2O Sulfated glycoprotein Na, Ca, Cl, and K ions. ME Nick Fang, University of Illinois. All rights reserved. 18
19 Hornet skin: a natural heat pump? IR image of the hornets Hornets keep their body temperature lower by 3-4 degrees when they are active outside the nest in daytime, where the ambient temperature can be as high as C. (Ishay et al, PRL, 2003) ME Nick Fang, University of Illinois. All rights reserved. 19
20 Hornet skin: a natural heat pump? 1um Indirect measurement suggests =0.16 S/m and S~ 2mV/K! ~ 0.01W/(mK) 1um Shimony and Ishay, J. Theo. Bio, 1981 ME Nick Fang, University of Illinois. All rights reserved. 20
21 Additional Readings G. Chen and A. Shakouri, Heat Transfer in Nanostructures for Solid-State Energy Conversion, JOURNAL OF HEAT TRANSFER, 2002(124) J.S. Ishay et al, Natural Thermoelectric Heat Pump in Social Wasps, Physical Review Letters, 2003 (90) Theme Issue, Harvesting Energy through Thermoelectrics: Power Generation and Cooling, MRS Bulletin, March 2006 (36). ME Nick Fang, University of Illinois. All rights reserved. 21
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