L20

ME 381R Lecture 20: Nanostructured Thermoelectric Materials

Dr. Li Shi Department of Mechanical Engineering The University of Texas at Austin Austin, TX 78712 www.me.utexas.edu/~lishi [email protected] 1

Thermoelectrics 250C

• Thermocouple:

• Thermoelectric (Peltier) cooler:

250C

• Seebeck effect: ∆V S= ∆T

T1

T2 Bi, Cr, Si… Pt Pt

Metal

Cold

V

I

• Thermoelectric refrigeration: no toxic CFC, no moving parts • Electronics

Q

• Optoelectronic s

• Automobile

p

n

I

Hot

2

Thermoelectric Cooling Performance Metal

Cold

p

I

Q

n

Venkatasubramanian et al. Nature 413, 597

Nanostructured thermoelectric materials

I

2.5-25nm

Bi2Te3/Sb2Te3 Superlattices

Harman et al., Science 297, 2229

Hot

Quantum dot superlattices

• Coefficient of Performance (COP≡ COP

2

Q/IV)

CFC unit

1 0

Bi2Te3 0

1

2

3

4

5

ZT

• ZT: Figure of Merit

Seebeck coefficient Electrical conductivity S 2σ

ZT ≡

κ

T

Thermal conductivity

3

Thin Film Superlattice Thermoelectric Materials Thin superlattice 

film

• Phonon (lattice vibration wave) transmission at an interface Incident Reflection phonons Interface Transmission

 Approaches to improve Z ≡ S2σ/κ : --Frequent phonon-boundary scattering: low κ

Barrier (larger Eg)

Quantum well (smaller Eg)

--High density of states near EF: high S2σ in QWs

4

Electronic Density of States in 3D • Each state can hold 2 electrons of opposite spin(Pauli’s principle) • Number of states with wavevectore
2D projection of 3D k space

ky

( 4πk 3 3) k 3 N = 2⋅ = V

dk k

( 2π L ) 3

kx 2π/L

E =

2

k

2

3π 2

/ 2m

•Number of states with energy<E: N= Density of States

dN De ( E ) = dE = V

m 2 2

π

2mE 2

V 3π 2

(

2mE 2

)3 / 2

Number of k-states available between energy E and E+dE 5

Electronic Density of States in 2D 2D k space (kz = 0) ky

dk

• Each state can hold 2 electrons of opposite spin(Pauli’s principle) • Number of states with wavevectore
N = 2⋅

k kx 2π/L

πk 2

=

( 2π L ) 2

E =

2

k

2

k2

A

2π

/ 2m

•Number of states with energy<E: Density of States

dN m De ( E ) = dE = 2 A π

N=

mE

π

2

Number of k-states available between energy E and E+dE

A 6

Electronic Density of States in 1 D ψ k ( x ) ∝ eikx ψ(x+L) = ψ(x)

k = 2nπ/L; n = ±1, ± 2, ± 3, ± 4, …..

1D k space (ky = kz =0)

-6π/L -4π/L -2π/L

0

2π/L

4π/L

k

• Each state can hold 2 electrons of opposite spin(Pauli’s principle) • Number of states with wavevectore
N = 2⋅

k

( 2π L )

E = •Number of states with energy < E: Density of States

dN m dE De ( E ) = = L 2 Eπ

2

k

2

/ 2m

2mE N= L π

Number of k-states available between energy E and E+dE

7

Electronic Density of States

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

8

Low-Dimensional Thermoelectric Materials Thin

Film Superlattices of

Bi2Te3,Si/Ge, GaAs/AlAs

Nanowires

of

Bi, BiSb,Bi2Te3,SiGe Al2O3 template

Top View

Nanowire

Barrier Quantum well

Ec

E x

Ev 9

Potential Z Enhancement in Low-Dimensional Materials

•Increased Density of States near the Fermi Level: high S2σ (power factor) •Increased phonon-boundary scattering: low κ

 high Z = S2σ/κ:

10

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

11

Z Enhancement in Nanowires Experiment

Theory

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

Nanowire Heremans et at, Phys. Rev. Lett. 88, 216801 12

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

Imbedded Nanostructures in Bulk Materials •Nanodot Superlattice InGaAs

Data from A. Majumdar et al.

0.8ML

ErAs

5x1018 Si-doped InGaAs

0.6ML 0.4ML

Si-Doped ErAs/InGaAs SL (0.4ML)

0.2ML

Undoped ErAs/InGaAs SL (0.4ML)

Plan View

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

[11

0] 100 nm

Cross-section

•Bulk materials with embedded nanodots

10 nm

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

AgPb18SbTe20 ZT = 2 @ 800K

AgSb rich 13

Phonon Scattering with Imbedded Nanostructures Frequency, ω

LO

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

TO

LA

0

TA

Wave vector, K

π/a

v

eb

Phonon Scattering Nanostructures Atoms/Alloys

Frequency, ω

ωmax

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

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

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