1. Nanostructured Thermoelectric Materials
ME 381R Lecture 20:
Nanostructured Thermoelectric Materials
Dr. Li Shi
Department of Mechanical Engineering
The University of Texas at Austin
Austin, TX 78712

2. Thermoelectrics Seebeck effect: Thermoelectric (Peltier) cooler: Q p n
Metal
Cold
Hot
250C
Thermocouple:
250C
Seebeck effect: Pt
Bi, Cr, Si… V T1 T2
Electronics
Optoelectronics
Automobile
Thermoelectric refrigeration:
no toxic CFC, no moving parts

3. Coefficient of Performance (COPQ/IV)
Thermoelectric Cooling Performance Q p n I
Metal
Venkatasubramanian et al. Nature 413, 597
Cold
Nanostructured thermoelectric materials
2.5-25nm
Bi2Te3/Sb2Te3 Superlattices
Harman et al., Science 297, 2229
Hot
Quantum dot superlattices
Coefficient of Performance (COPQ/IV) 2
CFC unit
COP 1
Bi2Te3 1 2 3 4 5 ZT
ZT: Figure of Merit
Seebeck coefficient
Electrical conductivity
Thermal conductivity

4. Thin Film Superlattice Thermoelectric Materials
Incident phonons
Reflection
Transmission
Phonon (lattice vibration wave) transmission at an interface
Interface
Approaches to improve Z  S2s/k :
--Frequent phonon-boundary scattering: low k
--High density of states near EF: high S2s in QWs
Quantum well
(smaller Eg)
Barrier (larger Eg)

5. Electronic Density of States in 3D 2D projection of 3D k space
Each state can hold 2 electrons
of opposite spin(Pauli’s principle)
Number of states with wavevectore<k: ky dk k kx
2p/L
Number of states with energy<E:
Density of States
Number of k-states available between
energy E and E+dE

6. Electronic Density of States in 2D
2D k space (kz = 0)
Each state can hold 2 electrons
of opposite spin(Pauli’s principle)
Number of states with wavevectore<k: ky dk k kx
2p/L
Number of states with energy<E:
Density of States
Number of k-states available between
energy E and E+dE

7. Electronic Density of States in 1 D
(x+L) = (x)
k = 2np/L; n = ±1, ± 2, ± 3, ± 4, …..
2p/L
4p/L
-6p/L
-2p/L
-4p/L
1D k space (ky = kz =0) k
Each state can hold 2 electrons
of opposite spin(Pauli’s principle)
Number of states with wavevectore<k:
Number of states with energy < E:
Density of States
Number of k-states available between
energy E and E+dE

8. Electronic Density of States
Ref: Chen and Shakouri, J. Heat Transfer 124, p. 242 (2002)

9. Low-Dimensional Thermoelectric Materials
Thin Film Superlattices of
Bi2Te3,Si/Ge, GaAs/AlAs
Top View
Nanowire
Al2O3 template
Nanowires of
Bi, BiSb,Bi2Te3,SiGe
Barrier
Quantum well Ec E Ev x

10. Potential Z Enhancement in Low-Dimensional Materials
Increased Density of States near the Fermi Level:
high S2s (power factor)
Increased phonon-boundary scattering: low k
 high Z = S2s/k:

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

12. Z Enhancement in Nanowires
Experiment
Theory
Nanowire
Prof. Dresselhaus, MIT
Phys. Rev. B. 62, 4610
Heremans et at,
Phys. Rev. Lett. 88,
Challenge: Epitaxial growth of TE nanowires with a precise doping and size control

13. Imbedded Nanostructures in Bulk Materials
5x1018 Si-doped InGaAs
Si-Doped ErAs/InGaAs SL (0.4ML)
Undoped ErAs/InGaAs SL (0.4ML)
Nanodot Superlattice
Data from A. Majumdar et al.
AgPb18SbTe20
ZT = 800K
AgSb rich
Hsu et al., Science 303, 818 (2004)
Bulk materials with embedded nanodots
Images from Elisabeth Müller Paul Scherrer Institut Wueren-lingen und Villigen, Switzerland

14. Phonon Scattering with Imbedded Nanostructures
Atoms/Alloys
Nanostructures
Frequency, w
wmax eb v
Spectral distribution of phonon energy (eb) & group velocity (v) @ 300 K
Phonon Scattering
Long-wavelength or low-frequency phonons are scattered by imbedded nanostructures!

15. 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