Thermal Energy Transport in Nanostructured t and Complex Crystals

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1 Thermal Energy Transport in Nanostructured t and Complex Crystals Li Shi Department of Mechanical Engineering & Texas Materials Institute The University of Texas at Austin

2 BMW Wins ÿkoglobe 2008 Award for Thermoelectric Generator com/2008/09/25/bmw-wins-koglobe-2008-award-for-thermoelectric-generator/ wins generator/ g g g pp for-reducing-fuel-consumption-and-co2-new-ther.html#more 2

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

4 ZT Progress and Materials Issues ZT enhancement in complex or nanostructured bulk materials is caused by lattice thermal conductivity suppression. Peak ZT Thallium (Tl) doping in PbTe increases S 2 σ and ZT. Bi2Te3 SiGe Complex crystals Nano bulk telluride Tl doped PbTe 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.

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

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

7 Thermal Measurement of Individual NWs T T h T h Ts I T s x T h T s I T T h T h s T s T 0 Q R C1 R NW R C2 R Beams

8 Contact Thermal Resistance and Seebeck Measurements T T h T h Ts I V 14 T s x Mavrokefalos et al., Rev. Sci. Instr. 78, (2007): V 23 / V 14 (T h -T s )/ (T h -T s ) T h T s S V 14 /(T h -T s ) I V 23 Electrical contact was made between the NW and the pre-patterned Pt electrodes via annealing in hydrogen. T T h T h s T s T 0 R C1 R NW R C2 R Beams Q

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

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

11 n = 4 π (2m h Electron Concentration (n) and Mobility (μ) 4 3/ ) 2 3 ekbt F1/ 2 e σ = neμ + e ( ζ ) ~0 for the highly doped E F peμ h μ = σ / e / ne The measured σ can only be 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.

12 Electronic and Lattice Thermal Conductivity (κ e & κ l ) κ e calculated from the W-F law Symbols: κ l =κ κ e Lines: Callaway model For the polycrystalline NW 2, κ < κ bulk mainly because of κ e suppression. 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 il in the 50-nm diameter Bi 2 Te 3 NW.

13 μ of the NW is close to bulk values along the same direction. Hole effective mass m*= 5m 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.

14 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 found in two NWs of <100 nm diameter mainly because of the slightly suppressed κ without mobility reduction. κ l suppression in a NW is rather small unless d the umklapp scattering m.f.p. (l u ).

15 Complex Silicide Nanowires of Large Effective Mass A Mn 27 Si HRTEM MnSi nanowires C Novotony Chimney Ladder phases of MnSi 1.75 B (004) (112) 5 nm Mn 15 Si nm Mn 11 Si 19 5 nm Selected Area Electron Diffraction Mn 4 Si 7 J. M. Higgins, A. Schmitt, S. Jin, JACS (2008) Large unit cell size (c) along the c axis of a MnSi 1.75 NW 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.

16 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. 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 dis reduced dby diffuse surface scattering in the nanostructure.

17 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. 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 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 as κ l suppression.

18 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: 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 a Qi Ye (NASA) Natalio Mingo (CEA-Grenoble) Derek Stewart (Cornell) Heiner Linke, Kimberley Thelander, Jessica, Ann Persson, Linus Fröberg, Lars Samuelson (Lund) Research Sponsors:

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

20 S σ E D ( E ) E E E F Thallium (Tl) doping in PbTe distorts t the density of states, t increasing i S 2 σ and ZT.

21 Monte Carlo phonon transport simulation. Diffuse surface limit for random surface roughness: l d = 22 nm δ 1 d θ 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)

22 κ l << κ α has been demonstrated. The question is how much κ l can be lowered without considerable reduction of the charge mobility. We use nanowires as model systems to investigate this question because of the simple and well-characterized structure and interface.

23 Seebeck Coefficient and Fermi Level (E F ) Hall measurements cannot be used to obtain carrier concentration & mobility in NWs. Two-band model: S = S eσ e + S hσ σ +σ Single conduction band model: 5 ( re + ) F k r + 3 ( ζ e) B e S = 2 2 e ζ e e 3 ( re + ) F r + 1 (ζ e) 2 e 2 e h h ξ e = E F F k B T Relaxation time: τ =τ 0 E r e r e = -0.5 for phonon and boundary scattering

24 Structural &Thermal Characterization of MnSi 1.75 NWs Mn 39 Si 68 nanoribbon (NR) c 17 nm Growth direction perpendicular p to {121} planes, or 63 o from the c axis

25 Two-Dimensional Phonons in MnSi 1.75 NWs? If the c axis is along a radial direction, 2c <λ c = 2d /n < 2d: only one or several phonon wavevectors allowed in the c direction. modulation in d and thus in λ c can enhance phonon scattering. κ is reduced.

26 50 nm 2nm NW growth direction found to be <0001>

27 Thermoelectric Energy Conversion Waste Heat Recovery Thermoelectric Generator Heat Source I n p - + I Seebeck coefficient Figure of Merit (ZT) ZT 2 S σ T κ Electrical conductivity Thermal conductivity I Heat Sink I