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ME 381R Lecture 20:

Nanostructured Thermoelectric Materials

Dr. Li Shi

Department of Mechanical Engineering The University of Texas at Austin

Austin, TX 78712www.me.utexas.edu/~lishi

lishi@mail.utexas.edu

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250C

250C

Thermoelectrics

T

VS

• Seebeck effect:

PtBi, Cr, Si…

V

T1 T2

Pt

• Electronics

• Optoelectronics

• Automobile

• Thermoelectric refrigeration:no toxic CFC, no moving parts

• Thermocouple:• Thermoelectric (Peltier) cooler:

Q

p n II

MetalCold

Hot

3TS

ZT2

Seebeck coefficientElectrical conductivity

Thermal conductivity

• ZT: Figure of Merit

• Coefficient of Performance (COPQ/IV)

Bi2Te3

CFC unit

0

1

2

0 1 2 3 4 5ZT

CO

P

Harman et al., Science 297, 2229

Venkatasubramanian et al. Nature 413, 597

Bi2Te3/Sb2Te3 Superlattices2.5-25nm

Quantum dot superlattices

Thermoelectric Cooling Performance

Nanostructured thermoelectric materials

Q

p n II

MetalCold

Hot

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Thin Film Superlattice Thermoelectric Materials

Thin film superlattice

Approaches to improve Z S2/:

--Frequent phonon-boundary scattering: low --High density of states near EF: high S2 in QWsQuantum well

(smaller Eg)Barrier (larger Eg)

Incident phonons Reflection

Transmission

• Phonon (lattice vibration wave) transmission at an interface

Interface

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ky

kx

2/L

k

dk

• Each state can hold 2 electrons of opposite spin(Pauli’s principle)• Number of states with wavevectore<k:

Vk

L

kN

2

3

3

3

32

342

2/322

)2

(3

mEVN

Density of States

222

2

mEm

VdEdN

EDe

Number of k-states available betweenenergy E and E+dE

mkE 2/22

•Number of states with energy<E:

Electronic Density of States in 3D2D projection of 3D k space

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Electronic Density of States in 2D

ky

kx

2/L

k

dk

• Each state can hold 2 electrons of opposite spin(Pauli’s principle)• Number of states with wavevectore<k:

A

k

L

kN

222

2

2

2

AmE

N2

Density of States

2

m

AdEdN

EDe Number of k-states available betweenenergy E and E+dE

•Number of states with energy<E:

2D k space (kz = 0)

mkE 2/22

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Electronic Density of States in 1 D

• Each state can hold 2 electrons of opposite spin(Pauli’s principle)• Number of states with wavevectore<k: L

kN

22

LmE

N

2Density of States

E

m

LdEdN

EDe 2 Number of k-states available between

energy E and E+dE

mkE 2/22

•Number of states with energy < E:

1D k space (ky = kz =0)

ikxk ex

(x+L) = (x) k = 2n/L; n = ±1, ± 2, ± 3, ± 4, …..

0 2/L 4/L-6/L -2/L-4/Lk

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Electronic Density of States

Ref: Chen and Shakouri, J. Heat Transfer 124, p. 242 (2002)

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Low-Dimensional Thermoelectric MaterialsThin Film Superlattices of

Bi2Te3,Si/Ge, GaAs/AlAs

Ec

Ev

x

E

Quantum wellBarrier

Top View

Nanowire

Al2O3 template

Nanowires of

Bi, BiSb,Bi2Te3,SiGe

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Potential Z Enhancement in Low-Dimensional Materials

•Increased Density of States near the Fermi Level: high S2power factor)

•Increased phonon-boundary scattering: low

high Z = S2/:

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Thin Film Superlattices for TE CoolingVenkatasubramanian et al, Nature 413, P. 597 (2001)

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Z Enhancement in Nanowires

Heremans et at,Phys. Rev. Lett. 88, 216801

Prof. Dresselhaus, MIT Phys. Rev. B. 62, 4610

Theory Experiment

Challenge: Epitaxial growth of TE nanowires with a precise doping and size control

Nanowire

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5x1018 Si-doped InGaAs

Si-Doped ErAs/InGaAs SL (0.4ML)

Undoped ErAs/InGaAs SL (0.4ML)

Imbedded Nanostructures in Bulk Materials

10 nm

100 nm

Cross-section

Plan View

[110]

0.2ML

0.4ML

0.6ML

0.8ML

0.2ML

0.4ML

0.6ML

0.8MLInGaAs

ErAs

Images from Elisabeth Müller Paul Scherrer Institut Wueren-lingen und Villigen, Switzerland

Data from A. Majumdar et al.

AgPb18SbTe20

ZT = 2 @ 800KAgSb rich

Hsu et al., Science 303, 818 (2004)

•Nanodot Superlattice

•Bulk materials with embedded nanodots

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Phonon Scattering with Imbedded Nanostructures

Frequency, max

eb

v

Atoms/Alloys

Nanostructures

Phonon Scattering

Long-wavelength or low-frequency phonons are scattered by imbedded nanostructures!

Spectral distribution of phonon energy (eb) & group velocity (v) @ 300 K

Fre

quen

cy,

Wave vector, K0 /a

LATA

LO

TO

Fre

quen

cy,

Wave vector, K0 /a

LATA

LO

TO

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Challenges and Opportunities

• Designing interfaces for low thermal conductance at high temperatures

• Fabrication of thermoelectric coolers using low-thermal conductivity, high-ZT

nanowire materials

• Large-scale manufacturing of bulk materials with imbedded nanostructures

to suppress the thermal conductivity