Review of Last Lecture
T
I
M
,
⎛ ndΦ ⎞
⎛
dT ⎞
⎛ dΦ ⎞
⎛ dT ⎞
J
=
L
−
+
L
⎟ o ⎜
−
⎟
⎜
J = L ⎜−
⎟
⎟ + L ⎜−
e
h
⎝ dxl ⎠t
⎝ dx ⎠
⎝ dx ⎠
⎝ dx ⎠
C
a
g
m
r
n
Onsager Relation:
L =TL
e
a
h
G /T ion
r
s
2t ©
a
r
l
e
2o ∂ f o e
h
L11 = σ =ri−g ∫ vS τ nvD(E ) dE
t
o
y
3
E
∂
c
p
C
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i
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9
9
9
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.
.
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i
o
r
F Lc22t = − 1 ∫ (E − E f )2 v2 τ ∂f o D(E)dE
e
l
3T
∂E
E
ex
11
12
qx
21
21
12
22
–WARREN M. ROHS
ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
MIT
Property Examples
T
I
M
,
n o
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t
h
l
C
a
g rm
n
e
a
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G /T ion
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i
S
n
r
t
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c
p
C
e
o
r
i
y
C
g
D
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r
σ = ∫ τv7D(E)( −∂f7/∂E)dE e • Optimal thermoelectric materials
n
9
399
are usually degenerate
9
E
.
.
l
• Multiband transport important at
2
2
⎛ Ea
⎞
−
μ
⎟⎟
∝ (k T )or exp⎜⎜ −ic
high temperatures, leading to
r
k
T
⎠
F c⎝t
decreasing Seebeck coefficient
For nondegenerate
e
with increasing temperature
El
Images removed due to copyright restrictions.
Please see Fig. 2a, b in Poudel, Bed, et al.
"High-Thermoelectric Performance of Nanostructured Bismuth
Antimony Telluride Bulk Alloys." Science 320 (May 2, 2008): 634-638.
2
2
eq
γ +3 / 2
c
B
B
semiconductor only
–WARREN M. ROHS
ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
MIT
Phonon Heat Conduction
T
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,
•
•
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•
•
e
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Temperature
Gradient
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n [hωf (T )v ]
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o
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2
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o
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D
ω
r
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ek = 1 v τhω ∂f D(ω )dω
7
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9
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9
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E
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3
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l
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a
c
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x
x
x
x
kx
ky
x
x−vx τ
x
kz
kx
ky
x+vx τ
kz
max
2
0
max
3
0
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Typical Behavior of
T
I
Phonon Thermal Conductivity
M
,
n
e
o
h
Holland (1964) l t
C
a
Amith
et al. (1965)
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a
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10 2
THERMAL CONDUCTIVITY (W/cm.K)
Boundary
Scattering
Dominant
k~T3
10 1
10 0
10 -1
10 0
10 1
10 2
Impurity
Scattering
Dominant
PhononPhonon
Scattering
Dominant
k~1/Tn,
n=1-1.5
10 3
TEMPERATURE (K)
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Combined Electronic and Phononic
T
I
Thermal Conductivity
M
,
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e
o
2h σ aσtb
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7
7
n
9
9
9
9
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i
o
r
F ct
e
l
E
Image removed due to copyright restrictions.
Please see Fig. 4 in Poudel, Bed, et al. "High-Thermoelectric
Performance of Nanostructured Bismuth Antimony Telluride
Bulk Alloys." Science 320 (May 2, 2008): 634-638.
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Thermoelectric Figure of Merit
IT
M
,
2
2
2n
e
S
S
σS T
o
t
h
l
=
=C
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a
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m
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r
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+ a
+
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© −8lar rs
t
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S~10 μV/K
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D
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r
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9
9
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Good
Thermoelectric
Materials
.
.
l
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i
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t
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~
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e
8
−8
−
l
5
2.45 ×10 + 3 ×10
E
σ~10 S/m
p
–WARREN M. ROHS
ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
MIT
Properties vs. Carrier Density
T
I
M
,
n o
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t
h
l
C
a
g rm
n
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a
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G /T ion
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t
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7
7
n
9
9
9
9
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2. r 2. cal
i
o
r
F ct
e
l
E
Image removed due to copyright restrictions.
Please see Fig. 3 in Minnich, A. J., et al.
"Bulknanostructured Thermoelectric Materials: Current Research
and Future Prospects." Energy and Environmental Science 2 (2009): 466-479.
–WARREN M. ROHS
ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
MIT
T
I
M
,
n o
e
t
h
l
C
a
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n
e
a
Classical Thermoelectric
h
n
G /T Materials
o
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C Dir rgy
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9
9
9
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.
.
l
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i
o
r
F ct
e
l
E
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Material ZT
T
I
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
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t
e
h
o
v
g
i
S
n
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c
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C
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7
7
n
9
9
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9
.
.
2 r 2 cal
i
o
r
t
F
c
Minnich et al.,
Energy and Environmental Sci., Aug. 2009
e
l
E
Image removed due to copyright restrictions.
Please see Fig. 1 in Minnich, A. J., et al.
"Bulk Nanostructured Thermoelectric Materials: Current
Rresearch and Future Prospects." Energy and Environmental Science 2 (2009): 466-479.
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
P-type and N-type
MIT
, n
he to
Image removed due to copyright restrictions.
Please see Fig. B2a,b in Snyder, G. Jeffrey, and Eric S. Toberer.
"Complex Thermoelectric Materials." Nature Materials 7
(February 2008): 105-114.
o
C Dir r
gy
e
7
7
n
9
9
9
9
E
2. r 2. cal
i
o
r
F ct
e
l
E
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Why Heavier Crystals? IT
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
o
y
c
p
C
e
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r
• Better mobility
C D i rg y
• Lower phonon
e
7
7
n
9
9
thermal conductivity
9
9
E
.
.
2 r 2 cal
i
o
r
F ct
From H.J. Goldsmid
E
104
InSb
Sn
Ge
InAs
GaAs
InP
GaSb
Si
(µe µh) 2 (cm2/V·s)
1
103
A1As
A1Sb
102
GaP
SiC
10
0
0.5
1.0
1.5
2.0
2.5
3.0
Eg (eV)
Figure by MIT OpenCourseWare.
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Unit CellIT
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
o
y
c
p
C
e
o
r
C D i rg y
e
7
7
n
9
9
9
9
E
2. r 2. cal
Huang and Kaviany, PRB,
i
o
r
77, 125209 (2008)
F ct
e
l
E
Image removed due to copyright restrictions.
Please see Fig. 1 (left) in Huang, Bao-Ling, and Massoud Kaviany.
"Ab initio and Molecular Dynamics Predictions for Electron and Phonon
Transport in Bismuth Telluride." Physical Review B 77 (2008): 125209.
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Electronic Band Structure IT
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
o
y
c
p
C
e
o
r
C D i rg y
e
7
7
n
9
9
9
9
E
2. r 2. cal
i
o
r
F ct
e
l
Larson et al., PRB, 61, 8261 (2000)
E
Images removed due to copyright restrictions.
Please see: Fig. 1 (right) in Huang, Bao-Ling, and Massoud Kaviany.
"Ab initio and Molecular Dynamics Predictions for Electron and Phonon
Transport in Bismuth Telluride." Physical Review B 77 (2008): 125209.
Fig. 4a in Larson, P., S. D. Mahanti, and M. G. Kanatzidis.
"Electronic Structure and Transport of Bi2Te3 and BaBiTe3."
Physical Review B 61 (March 2000): 8162-8171.
–WARREN M. ROHS
ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
MIT
Figure of Merit
T
I
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
o
y
c
p
C
e
o
r
C D i rg y
e
7
7
n
9
9
9
9
E
2. r 2. cal
i
o
r
F ct
e
l
E
Image removed due to copyright restrictions.
Please see Fig. 16 in Huang, Bao-Ling, and Massoud Kaviany.
"Ab initio and Molecular Dynamics Predictions for Electron and
Phonon Transport in Bismuth Telluride." Physical Review B 77 (2008): 125209.
–WARREN M. ROHS
ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
MIT
SiGe Alloys
T
I
• Abeles Virtual Crystal Model M
,
n
e to
h
l
C
a
Rayleigh Scattering
g
m
r
n
e
a
h
G /T τio=nω δ Γ
© lar rs 4πv
t
e
h
o
v
g
i
S
n
r
t
o
y
c
Disorder Parameter
p
C
e
o
C D ir r g y
e
7
7
n
⎡⎛ ΔM ⎞
9
9
⎛ Δδ ⎞ ⎤
9
9
Γ
=
−
+
E
(
1
)
x
x
ε
⎟
⎜
⎟ ⎥
⎢⎜
M
δ
⎝
⎝
⎠
⎠ ⎥⎦
2. r 2. cal
⎣⎢
i
o
r
F ct
e
l
E
Image removed due to copyright restrictions.
Please see Fig. 2 in Abeles, B. "Lattice Thermal Conductivity
of Disordered Semiconductor Alloys at High Temperatures."
Physical Review 131 (September 1963): 1906-1911.
−1
p
4
3
3
2
2
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
T
I
Commercial Materials M
,
n
e to
h
l
C
a
• P-type: Bi2-xSbxTe
g 3 rm
n
e
a
h
• N-type: Bi2Sb
n
G 3-xSe
x
T
o
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i
r
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s
a
r
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• Dopinghtmainly
by
defects
e
o
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g
i
S
n
r
t
o
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–
antisites,
vacancies
c
p
C
e
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C D i rg y
7 97 ne
9
9
9
E
.
.
l
2 r 2 ca
i
o
r
F ct
e
l
E
–WARREN M. ROHS
ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
MIT
Oxides
T
I
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
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c
p
C
e
o
r
C D i rg y
e
7
7
n
9
9
9
9
E
2. r 2. cal
i
o
r
F ct
e
l
E
Images removed due to copyright restrictions.
Please see Fig. 2, 3 in Koumoto, Kunihito, Ichiro Terasaki,
and Ryoji Funahashi. "Complex Oxide Materials for Potential
Thermoelectric Applications." MRS Bulletin 31 (March 2006): 206-210.
–WARREN M. ROHS
ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
MIT
Half Heusler
T
I
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
o
y
c
p
C
e
o
r
C D i rg y
e
7
7
n
9
9
9
9
E
2. r 2. cal
i
o
r
F ct
e
l
E
Image removed due to copyright restrictions.
Please see Fig. 4 in Nolas, George S., Joe Poon, and Mercouri Kanatzidis.
"Recent Developments in Bulk Thermoelectric Materials."
MRS Bulletin 31 (March 2006): 199-205.
–WARREN M. ROHS
ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
MIT
Other Bulk Materials
T
I
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
o
y
c
p
C
e
o
r
C D i rg y
e
7
7
n
9
9
9
9
E
2. r 2. cal
i
o
r
F ct
e
l
E
Image removed due to copyright restrictions.
Please see Fig. 2 in Snyder, G. Jeffrey, and Eric S. Toberer.
"Complex Thermoelectric Materials." Nature Materials 7
(February 2008): 105-114.
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
All Classical Materials IT
M
,
Used Alloy Scattering
n
e to
h
l
C
a
g rm
n
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a
h
n
G Sb
Te
• Bi2Te3 with
T
o
2
3
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r
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a
r
t 2Se
l
and
Bi
e
h
o
3
v
g
i
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n
r
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•
pPbTe
PbSe
C
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e
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9
9
E
.
.
l
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E
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Institutional Method
T
I
Structure
x
M
Properties
,
n
Formula TPn
e
@ 300K
p-CoSbto p-IrSb
h
T = transition metal (Co,Ir,Rh,Fe,Ni)
l
C
a
S [μV/K]
138
72
Pn = pnicogen (P,As,Sb)
g
m
/V-s]
1944
1320
μ [cmn
r
space group Im3
e
p [ cma]
4.4 10
1.1x10
8 formula units/cell
h
n
G
ρ [mΩ-cm] /T
0.74
0.44
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i
r
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s
11.8
16.0
a
r
t
l
optical
gap [eV] e
0.5
1.4
h
o
v
g
i
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[nm]
0.9034
0.9250
n
r
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o
C Dir rgy
7 97 ne References
9
9
9
E
.
.
l
2 r 2 ca
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r
F ct
e
l
E
3
Hall
3
3
18
19
2
-3
0
square array of Pn
(not to scale)
T
vacant
J-P Fleurial, T. Caillat and A. Borshchevsky, AIP Press,
40-44 (1995); J.-P. Fleurial, A. Borshchevsky, T. Caillat,
D. Morelli and G. P. Meisner, 15th International Conf.
on Thermoelectrics (1996) 91-95; G. A. Slack and
V.G. Tsoukala, J. Appl. Phys. 76 (1994) 1665.
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Phonon Rattlers
T
I
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
o
y
c
p
C
e
o
r
C D i rg y
e
7
7
n
9
9
9
9
E
2. r 2. cal
i
o
r
F ct
e
l
E
Images removed due to copyright restrictions.
Please see Fig. 3, 4, 6 in Sales, B. C., et al.
"Filled Skutterudite Antimonides: Electron Crystals and Phonon Glasses."
Physical Review B 56 (December 1997): 15081-15089
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
T
I
M
,
n o
e
t
h
l
C
a
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n
e
a
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G /T ion
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Nanostructuring
t
e
h
o
v
g
i
S
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r
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c
p
C
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C D i rg y
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9
9
9
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l
2 r 2 ca
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o
r
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E
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Nanoscale Effects for Thermoelectrics
T
I
M
,
n o
e
t
h
l
C
a
g
m
r
n
Phonons
Electrons
e
a
h
nm n
G Λ=10-100
Λ=10-100 nm
T
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λ=1
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Electron
l
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Interfaces that Scatter Phonons but not Electrons
Phonon
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Superlattice Structures with Enhanced ZT
T
I
M
,
n o
e
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C
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e
a
h
G /T ion
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e
PbTe/PbTeSeh
Quantum o
Dot
v
g
i
S
Superlattices
n
r
t
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y
c
p
C
e
Ternary:
ZT=1.3-1.6
o
r
i
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CQuaternary:
ZT=2
g
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T.C.
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Images removed due to copyright restrictions. Please see
Fig. 1 in Springholz, G., et al. "Self-Organized Growth of Three-Dimensional Quantum-Dot Crystals
with fcc-like Stacking and a Tunable Lattice Constant." Science 282 (October 23, 1998): 734-737.
Fig. 2 in Harman, T. C., et al. "Quantum Dot Superlattice Thermoelectric Materials and Devices."
Science 297 (September 27, 2002): 2229-2232.
Fig. 5a in Venkatasubramanian, Rama, et al. "Thin-film Thermoelectric Devices with High Room-temperature
Figures of Merit." Nature 413 (October 11, 2001): 597-602.
Fig. 4a in Venkatasubramanian, Rama, et al. "Low-temperature Organometallic Epitaxy and its
Applications to Superlattice Structures in Thermoelectrics." Applied Physics Letters 75 (August 1999): 1104-1106.
2
3
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Heat Conduction Mechanisms in Superlattices
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–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Nanocomposites ApproachIT
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Nanostructured Bi2Te3
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Fig. 3d in Wang, X. W., et al.
"Enhanced Thermoelectric Figure of Merit in
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Applied Physics Letters 93 (2008): 193121.
Poudel et al., Science, 320, 634, 2008
–WARREN M. ROHS
ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
Thermoelectric Properties: Bi2Te3
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–WARREN M. ROHS
ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
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ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
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Rhyee et al., Nature, 459,
965 (2009)
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ENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ROHSENOW
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Experimental Proof of Principle
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–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
Thermionic Emission and Energy Filtering
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D(E)
Moyzhes and Nemchinsky, Appl. Phys. Lett., 73,
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Shakouri and Bowers, Appl. Phys. Lett., 71,
1234 (1997).
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
MIT OpenCourseWare
http://ocw.mit.edu
2.997 Direct Solar/Thermal to Electrical Energy Conversion Technologies
Fall 2009
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