th le t tin ttd dthermal energy transport in ...€¦ · zt progress and materials issues • zt...
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Th l E T t i N t t d dThermal Energy Transport in Nanostructured and Complex Crystals
Li Shi
Department of Mechanical Engineering &Texas Materials Institute
The University of Texas at Austin
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BMW Wins ÿkoGlobe 2008 Award for Thermoelectric Generatorhttp://green autoblog com/2008/09/25/bmw-wins-koglobe-2008-award-for-thermoelectric-generator/http://green.autoblog.com/2008/09/25/bmw wins koglobe 2008 award for thermoelectric generator/
http://www.greencarcongress.com/2009/10/bmw-outlines-intelligent-heat-management-applications-
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Thermoelectric Energy ConversionWaste Heat Recovery
MetalSemi-conductor
Insulator
---
-n p
Waste Heat RecoveryHeat Source
EC
EF
-----n p- +
I I
S σ
EV + +II
Heat Sink
S σS2σ
Figure of Merit (ZT)Seebeck coefficient
Electrical conductivity
κ
TSZTκσ2
≡ κeκpκ
Thermal conductivity
p
Carrier concentration (n)
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ZT Progress and Materials Issues• ZT enhancement in complex or pnanostructured bulk materials is caused by lattice thermal conductivity suppression.
•Thallium (Tl) doping in PbTe increases S2σ and ZT.
2Bi2T 3
1.5
T
Bi2Te3SiGeComplex crystalsNano‐bulk telluride
1
Peak
ZT Nano bulk telluride
Tl doped PbTe
0
0.5
0
1950 1970 1990 2010Year•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.
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Thermal Conductivity (κ)+κ (W/m-K) @ 300 K κ ≈ κE+κl
Lattice vibration or phononElectronic
κ (W/m-K) @ 300 K
1000 Diamond, Graphene, CNTs, Graphite
100
Cu
Si imaxλ
Spectral specific heat Wavelength
100 Si
BiInAs
∑ ∫=i
iixili
i
dlvCmax,
min,
)()()( ,λ
λλλλκ
Alloy limit κalloy
10 BiCrSi2 Group velocity m.f.p.
λ
Polarizationsy alloy
Bi2Te3, PbTe, MnSi1.75
SiGe
Si
vx,i(λ) = speed of sound
li(λ) = λ/2
Amorphous limit κα1 α-Si
• κl << κα has been demonstrated in disordered, layered thin films.
0.1 PolymerAir
• The question is how much κl can be lowered without considerable reduction of the charge mobility.
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Nanowire Model Systems• Bi2Te3 NW Sample 3
210
- Electrodeposited- Single crystalline - Growth direction
003 <110>
[120] Zone Axis
B d tt i f• Boundary scattering m.f.p.:
0 for 11
→→−+
= pddpplb
• At 300 K, phonon wavelength (λ)
• Effective m.f.p.:
( ) 1111)(−−−− ++= biU llll ω
~1 nm ~ surface roughness (δ)
• Ziman’s surface specularity: dlvC iixilZBi
∑ ∫= )()()( , ωωωωκω
• Callaway-type model:
0)/16exp( 223 ≥−= λδπpdlbdiffuse
i
→→ when 0
,
κ
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Thermal Measurement of Individual NWsT Th Th’
xTs
ThTs’
II
TTh Ts
Th Ts T0Ts’Th’I
RNW
h s
RC2RC1
T0
RBeams
Qsh
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Contact Thermal Resistance and Seebeck MeasurementsT Th Th’
xTs
ThTs’
IIV14
TMavrokefalos et al., Rev. Sci.
Th TsV23 / V14
Instr. 78, 034901 (2007):
(Th’-Ts’)/ (Th-Ts)
S V /(T T )
Th Ts T0Ts’Th’IS ≈ V14/(Th-Ts) V23
• Electrical contact was made between
RNW
h s
RC2RC1
T0
RBeams
Qsh• Electrical contact was made between
the NW and the pre-patterned Pt electrodes via annealing in hydrogen.
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Single-crystal NW• Polycrystalline NW
• Majority of the NW oriented within 3o along the binary direction
003
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Seebeck Coefficient and Fermi Level (EF)
• Hall measurements cannot be used to obtain carrier concentration & mobility in NWs.& mobility in NWs.
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Electron Concentration (n) and Mobility (μ)
)()2(4 2/3 FTk ζπ ∗ )()2(42/1
2/33 eBe FTkm
hn ζπ ∗=
~0 for the highly doped EF
he pene μμσ +=
ne/σμ =
• The measured σ can only be fitted with the higher EF
nee /σμ =
fitted with the higher EF.
• 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 scatteringpartially specular electron-surface scattering.
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Electronic and Lattice Thermal Conductivity (κe & κl)
•For the polycrystalline NW 2, κ < κbulkmainly because of κ suppressionmainly because of κe suppression.
• For the single crystal NW the obtained κ is
•κe calculated from the W-F law
• For the single-crystal NW, the obtained κl is suppressed by <20% because of the short Umklapp m.f.p. (lu~3 nm), so that the size ff d i il i h 50effects on κl and μ are similar in the 50-nm
diameter Bi2Te3 NW. • Symbols: κl =κ −κe
• Lines: Callaway modelLines: Callaway model
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• 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*= 5m0 large p & low bulk μ0
• 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.
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Thermal Conductivity and ZT of CrSi2 Nanowires
• Phonon m.f.p. in bulk CrSi2 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 reductionwithout mobility reduction.
• κl suppression in a NW is rather small unless d ≤ the umklapp scattering m.f.p. (lu). l pp pp g p ( u)
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Complex Silicide Nanowires of Large Effective MassA HRTEM MnSi1 75 nanowires C Mn27Si47A HRTEM MnSi1.75 nanowires C
NovotonyChimney Ladder
5 nm
phases of MnSi1.75
(004) (112)11.79
nm11.79
nm
Mn15Si26Mn15Si26
Mn11Si19Mn11Si19
B
5 nm5 nm
Mn Si
J. M. Higgins, A. Schmitt, S. Jin, JACS (2008)
Mn4Si7
Selected Area Electron Diffraction
• Large unit cell size (c) along the c axis of a MnSi1.75 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 MnSi1.75.
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Phonon-Glass Behavior in MnSi1.75 NRs and NWs
• For MnSi1.75 NWs and NRs, κ ~ κα = 0.7 W/m-K calculated with l = λ/2 and v = speed of
dsound.
• The group velocity of the numerous optical phonons is much smaller than the speed of sound.
Th f f ti h ld b till it l i b lk M Si d i d d b• The m.f.p. of acoustic phonons could be still quite long in bulk MnSi1.75, and is reduced by
diffuse surface scattering in the nanostructure.
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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 earthmass and abundant on earth.
• In such NWs, κl can be suppressed to κα via the combination of l l it ti l h ith ll f ti f tinumerous 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 , pas κl suppression.
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AcknowledgementCurrent 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:
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Power Factor (S2σ)• Electrical conductivity:
*mdEE ∝∫= σσConduction bandEFE∫
Differential conductivityValence EEffective mass
• Seebeck coefficient:
bandk
Seebeck coefficient: Th Tc
VS E∂Δ σ-
--- --
--
ΔVETVS E
∂∂
∝Δ
=σ
E E-
-
D(E)f(E) D(E)f(E)
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E EDS ⎟⎞
⎜⎛ ∂∂ )(σ
FE
EEE
S ⎟⎠⎞
⎜⎝⎛
∂∝
∂∝
)(
Th lli (Tl) d i i PbT di t t th d it f t t i i S2 d ZT•Thallium (Tl) doping in PbTe distorts the density of states, increasing S2σ and ZT.
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Diffuse surface limit for random surface roughness:
l d 22
• Monte Carlo phonon transport simulation.
δ1
d θ
δ1
d θ
l d = 22 nmtransport simulation.
δ2
d
δ2
θ
δ2
d
δ2
θ
Phonon backscattering at a sawtooth surface:
l < d
• κ can be decreased by the sawtooth roughness, but is still considerably higher than κα.
Johansson et al. Nature Nanotech 4, 50 (2009)
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• κl << κα has been demonstrated. • The question is how much κl 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.
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Seebeck Coefficient and Fermi Level (EF)• Hall measurements cannot be
hhee SSS σσ +
Hall measurements cannot be used to obtain carrier concentration & mobility in NWs.
he
hheeSσσ +
=• Two-band model:
• Single conduction band model:
⎟⎟⎟⎞
⎜⎜⎜⎛
−+
−=+
e
ereB
ee
FrkS ζζ
3
)()25(
23
Single conduction band model:
⎟⎟⎠
⎜⎜⎝
+ + eree
Fre ζ )()23(
21
EFξTkB
Fe =ξ
• Relaxation time:
erE0ττ =
Relaxation time:
re = -0.5 for phonon and boundary scattering
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Structural &Thermal Characterization of MnSi1.75 NWs
• Mn Si nanoribbon (NR)• Mn39Si68 nanoribbon (NR)• c ≈ 17 nm• Growth direction perpendicular to {121} planes, p p { } p ,or 63o from the c axis
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Two-Dimensional Phonons in MnSi1.75 NWs?
• If the c axis is along a radial direction, 2c <λc = 2d /n < 2d:only one or several phonon wavevectors allowed in the c direction.
d l ti i d d th i λ h h tt imodulation in d and thus in λc can enhance phonon scattering.κ is reduced.
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50 nm
2 nm
• NW growth direction found to be <0001>
2 nm
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Thermoelectric Energy ConversionWaste Heat RecoveryWaste Heat Recovery
Th l t i G t
n p
Thermoelectric GeneratorHeat Source
n p- +
I I
IIHeat Sink
S σ2Seebeck coefficient
Electrical conductivity
Figure of Merit (ZT)
TSZTκσ
≡Thermal conductivity