Th Thermal Energy Transport in Nanostructured and l E T t i N t - PowerPoint PPT Presentation

Th Thermal Energy Transport in Nanostructured and l E T t i N t t d d Complex Crystals Li Shi Department of Mechanical Engineering & Texas Materials Institute The University of Texas at Austin

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Thermoelectric Energy Conversion Waste Heat Recovery Waste Heat Recovery Semi- Metal Insulator Heat Source conductor - - - - p p n n - - - - - E C - + I I E F Heat Sink E V + + I I S S σ σ S 2 σ Figure of Merit ( ZT ) Electrical Seebeck conductivity coefficient κ σ 2 S ≡ κ e ZT T κ κ κ p p Carrier concentration ( n ) Thermal conductivity

ZT Progress and Materials Issues • ZT enhancement in complex or p nanostructured bulk materials is caused by lattice thermal conductivity suppression. • Thallium (Tl) doping in PbTe increases S 2 σ and ZT . 2 Bi2T 3 Bi2Te3 SiGe 1.5 Complex crystals Nano bulk telluride Nano ‐ bulk telluride Peak ZT T Tl doped PbTe 1 0.5 0 0 1950 1970 1990 2010 Year • Tellurium and germanium are costly. Thallium is toxic. • Low-cost, abundant, and environmentally-friendly materials with ZT > 1.5 are needed for large-scale deployment of thermoelectric generators.

Thermal Conductivity ( κ ) κ (W/m-K) @ 300 K κ (W/m-K) @ 300 K κ ≈ κ E + κ l + Diamond, Graphene, CNTs, Graphite Electronic Lattice vibration or phonon 1000 Cu Spectral specific heat Wavelength λ Si Si 100 100 max max, i i κ = λ λ λ λ ∑ ∫ ( ) ( ) ( ) C v l d l i x , i i λ InAs i min, i Bi Bi Group velocity CrSi 2 Polarizations m.f.p. 10 Alloy limit κ alloy y alloy v x,i ( λ ) = speed of sound λ SiGe l i ( λ ) = λ /2 Bi 2 Te 3 , PbTe, MnSi 1.75 α -Si Si 1 Amorphous limit κ α • κ l << κ α has been demonstrated in disordered, layered thin films. • The question is how much κ l can be lowered without considerable Polymer 0.1 reduction of the charge mobility. Air

Nanowire Model Systems • Bi 2 Te 3 NW Sample 3 - Electrodeposited - Single crystalline 210 - Growth direction 003 <110> [120] Zone Axis • Boundary scattering m.f.p.: B d tt i f + 1 p = → → l b d d for p 0 − 1 p • Effective m.f.p.: ( ) − 1 − − − l ω = 1 + 1 + 1 ( ) l l l • At 300 K, phonon wavelength ( λ ) U i b ~1 nm ~ surface roughness ( δ ) • Callaway-type model: ω ZBi κ = ω ω ω ω ∑ • Ziman’s surface specularity: ∫ C ( ) v ( ) l ( ) d l i x , , i i i 0 = − π δ λ ≥ 3 2 2 p exp( 16 / ) 0 → κ → when l b d diffuse

Thermal Measurement of Individual NWs T h T T h ’ T h T s ’ T s x I T h T s I T s ’ T h ’ T h T s T 0 T 0 h s s h Q R C1 R NW R C2 R Beams

Contact Thermal Resistance and Seebeck Measurements T h T T h ’ T h T s ’ T s x I V 14 Mavrokefalos et al., Rev. Sci. Instr. 78, 034901 (2007): T h T T s V 23 / V 14 � ( T h ’-T s ’)/ ( T h -T s ) S ≈ V 14 /( T h -T s ) V /( T T ) S V 23 I T s ’ T h ’ T h T s T 0 T 0 • Electrical contact was made between • Electrical contact was made between h s s h Q the NW and the pre-patterned Pt electrodes via annealing in hydrogen. R C1 R NW R C2 R Beams

Single-crystal NW • Polycrystalline NW • Majority of the NW oriented within 3 o along the binary direction 003

Seebeck Coefficient and Fermi Level ( E F ) • Hall measurements cannot be used to obtain carrier concentration & mobility in NWs. & mobility in NWs.

Electron Concentration ( n ) and Mobility ( μ ) π π 4 4 ∗ ∗ = ζ ζ 3 3 / / 2 2 ( ( 2 2 ) ) ( ( ) ) n m k k T T F F e B 1 / 2 e 3 h ~0 for the highly doped E F σ = μ + μ ne pe e h μ = μ = σ σ / / ne ne e • The measured σ can only be fitted with the higher E F fitted with the higher E F . • The mobility of the single-crystal NW 3 is ~19% lower than the bulk value. • The electron m.f.p. is reduced from 60 nm in bulk to 40 nm in NW 3 because of partially specular electron surface scattering partially specular electron-surface scattering.

Electronic and Lattice Thermal Conductivity ( κ e & κ l ) • For the polycrystalline NW 2 , κ < κ bulk mainly because of κ suppression mainly because of κ e suppression. • κ e calculated from the W-F law • For the single crystal NW the obtained κ is • For the single-crystal NW, the obtained κ l is suppressed by <20% because of the short Umklapp m.f.p. ( l u ~3 nm), so that the size effects on κ l and μ are similar in the 50-nm ff d i il i h 50 diameter Bi 2 Te 3 NW. • Symbols: κ l = κ −κ e • Lines: Callaway model Lines: Callaway model

• μ of the NW is close to bulk values along the same • μ of the NW is close to bulk values along the same direction. • Hole effective mass m *= 5 m 0 � large p & low bulk μ 0 • σ is high because of a large m* and p • μ and τ in NWs were dominated by acoustic phonon scattering instead of boundary scattering.

Thermal Conductivity and ZT of CrSi 2 Nanowires • Phonon m.f.p. in bulk CrSi 2 is less than 10 nm < d. • Compared to the hot pressed bulk powder sample small ZT enhancement was • Compared to the hot pressed bulk powder sample, small ZT enhancement was found in two NWs of <100 nm diameter mainly because of the slightly suppressed κ without mobility reduction without mobility reduction. • κ l suppression in a NW is rather small unless d ≤ the umklapp scattering m.f.p. (l u ). pp pp g p ( u ) l

Complex Silicide Nanowires of Large Effective Mass Mn 27 Si 47 A A C C HRTEM MnSi 1 75 nanowires HRTEM MnSi 1.75 nanowires Novotony Chimney Ladder phases of MnSi 1.75 5 nm Mn 15 Si 26 Mn 15 Si 26 B 11.79 11.79 (004) (112) nm nm Mn 11 Si 19 Mn 11 Si 19 5 nm 5 nm 5 nm 5 nm J. M. Higgins, A. Schmitt, S. Jin, JACS (2008) Mn Si Mn 4 Si 7 • Large unit cell size ( c ) along the c axis of a MnSi 1.75 NW Selected Area Electron Diffraction • Numerous phonon modes of low group velocity and enhanced phonon-phonon scattering results in low κ = 2−4 W/m-K and ZT = 0.7 at 800 K in bulk MnSi 1.75 .

Phonon-Glass Behavior in MnSi 1.75 NRs and NWs • For MnSi 1.75 NWs and NRs, κ ~ κ α = 0.7 W/m-K calculated with l = λ /2 and v = speed of sound. d • The group velocity of the numerous optical phonons is much smaller than the speed of sound. • The m.f.p. of acoustic phonons could be still quite long in bulk MnSi 1.75 , and is reduced by Th f f ti h ld b till it l i b lk M Si d i d d b diffuse surface scattering in the nanostructure.

Summary • It appears to be possible to achieve phonon-glass, electron-crystal behavior in silicide NWs of complex crystals that have a large effective mass and abundant on earth mass and abundant on earth. • In such NWs, κ l can be suppressed to κ α via the combination of numerous low-velocity optical phonons with a small fraction of acoustic l l it ti l h ith ll f ti f ti phonons of suppressed m.f.p. • While it remains to be verified, the large effective mass can potentially lead to large carrier concentration and low-medium bulk mobility that is not reduced much in a NW, so that the power factor is not reduced as much , p as κ l suppression.

Acknowledgement Current Graduate Students and Post-doc Fellows: Arden Moore, Jae Hun Seol, Michael Pettes, Yong Lee, JaeHyun Kim, Mir Mohammad Sadeghi, Patrick Jurney Alumni: Alumni: Anastassios Mavrokefalos, Feng Zhou, Choongho Yu, Jianhua Zhou, Sanjoy Saha, Huijun Kong Collaborations for Nanowire Studies: Jeremy Higgins, Jeannine Szczech, Song Jin (UW-Madison) Wei Wang, Xiaoguang Li (USTC) Laura Qi Ye (NASA) au a Q e (N S ) Natalio Mingo (CEA-Grenoble) Derek Stewart (Cornell) Heiner Linke, Kimberley Thelander, Jessica, Ann Persson, Linus Fröberg, Lars Samuelson (Lund) Research Sponsors:

Power Factor ( S 2 σ ) • Electrical conductivity: Conduction band σ = σ ∝ ∫ ∫ dE m * E F E E Differential conductivity E Valence Effective mass band k • Seebeck coefficient: Seebeck coefficient: T h T c - - - - Δ ∂ ∂ σ σ - - - - V V = ∝ E E S S Δ V Δ ∂ T E E E - - D ( E ) f ( E ) D ( E ) f ( E )

∂ σ ⎛ ∂ ⎛ ⎞ ⎞ D ( ( E ) ) ∝ ∝ ⎜ ⎜ ⎟ ⎟ E E S S ∂ ∂ ⎝ ⎠ E E E F • Thallium (Tl) doping in PbTe distorts the density of states, increasing S 2 σ and ZT . Th lli (Tl) d i i PbT di t t th d it f t t i i S 2 d ZT

Diffuse surface limit for • Monte Carlo phonon random surface roughness: transport simulation. transport simulation. l � d = 22 nm 22 l � d δ 1 δ 1 θ θ θ θ d d d d δ 2 δ 2 δ 2 δ 2 Phonon backscattering at a sawtooth surface: l < d • κ can be decreased by the sawtooth roughness, but is still considerably higher than κ α . Johansson et al. Nature Nanotech 4, 50 (2009)