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

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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p g g g g ppfor-reducing-fuel-consumption-and-co2-new-ther.html#more

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)

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.

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.

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

Thermal Measurement of Individual NWsT Th Th’

xTs

ThTs’

II

TTh Ts

Th Ts T0Ts’Th’I

RNW

h s

RC2RC1

T0

RBeams

Qsh

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.

Single-crystal NW• Polycrystalline NW

• Majority of the NW oriented within 3o along the binary direction

003

Seebeck Coefficient and Fermi Level (EF)

• Hall measurements cannot be used to obtain carrier concentration & mobility in NWs.& mobility in NWs.

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.

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

• 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.

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)

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.

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.

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.

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:

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)

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.

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)

• 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.

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

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

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.

50 nm

2 nm

• NW growth direction found to be <0001>

2 nm

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