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ME6750Thermoelectrics Design and Materials
HoSung Lee, PhD
Professor of Mechanical and Aerospace Engineering
Western Michigan University
July 2, 2017
1
Outline
• Part I• Design of Thermoelectric Generators and Coolers
• Part II• Thermoelectric Materials
2
3
PART IDesign
--
-
-
---
-
-
- Room temperatureRoom temperature
Material
Cold Hot
I
- --
-
- --
--
V
E
Thermoelectric Phenomena
• Free electrons
• Coulomb force• Diffusion
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𝑉 = 𝛼𝐴𝐵∆𝑇Seebeck effect (1821)
Wire A
Wire B
I
Wire B+_
ThTc
Wire A
Wire B
I
Wire B +_
THTL
QThomson,A
.
QPeltier,AB
.
QThomson,B
.
QPeltier,AB
.
Peltier effect (1834)
Thomson effect (1854)
ሶ𝑄𝑇ℎ𝑜𝑚𝑠𝑜𝑛 = −𝜏𝐴𝐵𝐼𝛻𝑇
ሶ𝑄𝑃𝑒𝑙𝑡𝑖𝑒𝑟 = 𝜋𝐴𝐵𝐼
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6
Thomson Effect
ሶ𝑄𝑇ℎ𝑜𝑚𝑠𝑜𝑛 = −𝜏𝐴𝐵𝐼𝛻𝑇
TjE
TkjTq
Electric Field
Heat Flow
02 TjdT
dTjTk
dT
dT
:Thomson coefficient
Gov. equation
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Ideal (Standard) Equation
Assumptions• Thomson effect is negligible• Contact Resistances are negligible• Heat losses are negligible
chhh TTKRIITnQ 2
2
1
Thermoelectric effect
Joule heating
Thermal conduction
Load resistance
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p
n
p
n
np
p
pn
Positive (+)
Negative (-)
Heat Absorbed
Heat Rejected
Electrical Conductor (copper)Electrical Insulator (Ceramic)
p-type Semiconcuctor
n-type Semiconductor
Thermoelectric Module
9
h
ch
c
T
TTZ
TZ
T
T
1
111max
Conversion Efficiency
𝑍 =𝛼2
𝜌𝑘=
𝛼2𝜎
𝑘
where = Seebeck coefficient, mV/ K;
= electrical resistivity, Wcm
s = 1/ = electrical conductivity (Wcm)-1
k = thermal conductivity, W/mK
:Figure of merit (1/K)
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:Dimensionless figure of merit
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
2.7
3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1DT/DTmax = 0
DT/DTmax = 0
0.1
0.1
0.2
0.2
0.3
0.4
COP 0.3 0.5 Qc/Qcmax
0.6
0.4
0.5 0.8
0.6
0.8
I/Imax
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1
2
1
2
1
max
TZ
T
TTZ
TT
TCOP c
h
ch
c
Maximum Coefficient of Performance
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Materials (Lee,2016)
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Applications (TEG)
Exhaust Waste Heat Recovery
Radioisotope Thermoelectric Generator (RTG)on Mars Rover
Solar Thermoelectric Generator
Low Grade Waste Energy Recovery
Medicine (Wearable Electronics)
Micro robots or devices
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Applications (TEC)
Car Seat Climate Control
Telecom Laser for Optic Fibers
Microprocessor Cooling
Automotive Air Conditioner (Zonal Cooling)
Medical Instrument
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Electrical contact resistance
Ceramic thermal resistance
Electrical contact resistance
Micro and Macro Analytical ModelingIncluding Ceramic and Electrical Contact Resistance
𝑄1 =𝑛𝐴𝑒𝑘𝑐𝑙𝑐
𝑇1 − 𝑇1𝑐
𝑄1 = n 𝛼𝐼𝑇1𝑐 −1
2𝐼2
𝜌𝑙𝑜𝐴𝑒
+𝜌𝑐𝐴𝑒
−𝐴𝑒𝑘
𝑙𝑜𝑇2𝑐 − 𝑇1𝑐
𝑄2 = n 𝛼𝐼𝑇2𝑐 +1
2𝐼2
𝜌𝑙𝑜𝐴𝑒
+𝜌𝑐𝐴𝑒
−𝐴𝑒𝑘
𝑙𝑜𝑇2𝑐 − 𝑇1𝑐
𝑄2 =𝑛𝐴𝑒𝑘𝑐𝑙𝑐
𝑇2𝑐 − 𝑇2
𝐼 =𝛼 𝑇1𝑐 − 𝑇2𝑐
𝑅𝐿𝑛 +
𝜌𝑙𝑜𝐴𝑒
+𝜌𝑐𝐴𝑒
Lee (2016)-book
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0 20 40 60 80 1000
0.5
1
1.5
2
2.5
3
Theory with l = 1.14 mm
Theory with l = 1.52 mm
Theory with l = 2.54 mm
CP1.4-127-045L, l = 1.14 mm
CP1.4-127-06L, l = 1.52 mm
CP1.4-127-10L, l = 2.54 mm
Temperature Difference (K)P
ow
er O
utp
ut (W
)
Micro TEG (4.2 mm x 4.2 mm) Macro TEG (38 mm x 38 mm)
Lee (2016)-book
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Micro TEG (4.2 mm x 4.2 mm) Macro TEG (38 mm x 38 mm)
Lee (2016)-book
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ANSYS Numerical Simulations (TEG)-This work
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0 100 200 300 400 5000
2
4
6
8
10
12
Prediction
Experiment, Salvador et al. (2013)
T (K)
Max
. P
ow
er O
utp
ut (W
)
Description Value Description Value
Seebeck coefficient 𝛼𝑛 = −160 Τ𝜇𝑉 𝐾 Seebeck coefficient 𝛼𝑝 = 160 Τ𝜇𝑉 𝐾
Electrical resistivity 𝜌𝑛 = 0.45 × 10−3Ω𝑐𝑚 Electrical resistivity 𝜌𝑝 = 1.27 × 10−3Ω𝑐𝑚
TE thermal conductivity 𝑘𝑛 = 3.7 Τ𝑊 𝑚𝐾 TE thermal
conductivity
𝑘𝑝 = 2.75 Τ𝑊 𝑚𝐾
Ceramic thermal
conductivity for AlN
𝑘𝐴𝑙𝑁 = 180 Τ𝑊 𝑚𝐾 Ceramic thermal
conductivity for
Al2O3
𝑘𝐴𝑙2𝑂3 = 25 Τ𝑊 𝑚𝐾
Electrical contact
resistance
𝜌𝑐 = 1.6 × 10−6Ω𝑐𝑚2 Cross-sectional area
of TE element
𝐴𝑒 = 2 × 2 = 4 𝑚𝑚2
Thickness of ceramic plate
(assumed)
𝑙𝑐 = 1.5 𝑚𝑚 Leg length of TE
element
𝑙𝑜 = 4 𝑚𝑚
Number of thermocouples 𝑛 = 32
GM DOE Projects (2005-2016,$26 million) – JPL, ORNL
Purdue, U OF M, MSU, Marlow, Delphi, Fraunhofer, etc.
Marlow fabricated module GM Suburban
DT= 450 K
Skuttarudite
Lee (2016)-book
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2010s 1950s
Suggested Design with Ceramic of Aluminum Nitride (AlN)
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PART II Materials
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𝑍𝑇 =𝛼2𝜎
𝑘𝑇 =
𝛼2𝜎
𝑘𝑒+𝑘𝑙
T
where = Seebeck coefficient, mV/ K;
s = electrical conductivity (Wcm)-1
ke = electronic thermal conductivity, W/mK
kl = lattice thermal conductivity, W/mK
:Dimensionless figure of merit (1/K)
Figure of Merit
Electrons: 𝛼2𝜎 (power factor), ke
Lattice (Phonons): klWiedemann-Franz law:
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3
e
k
T
kL Be
o
s
FEE
BEn
EgTk
e
m
m
1
3
22
m
s nem
ne
2
Difficulties
Mott formula
24
Hicks and Dresselhaus (1993)
Effect of Nanostructured Materials
Lee (2016)-book
Electron Relaxation time = constant Electron Relaxation time = function of energy
Energy Environ. Sci. 2014, 7, 251-268
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Two approaches to improve ZT
1. Electrons• Not satisfactory-the present work tries to improve using anisotropy of
materials
2. Phonons (Lattice)• Nanocomposite materials
• Nanostructures –quantum wells, nanowires, quantum dot superlattices(QDSL) etc.
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Science, 2008, 320, 634-638 (Poudel et al.)
Nanocomposite materials
Nature, 2008, 451,163-167 (Hochbaum et al.)
Nanostructured materials – nanowires
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Quantum Dot Superlattices (QDSL)-impractical
Growth rate is so slow (1.4 mm/h)
Nature (2001)
ZT = 2.6 at 300 K (Bi2Te3/Sb2Te3 QDSL)(record)
Theoretical Approaches for Thermoelectric Transport Properties
1. Classical and Semi-classical Theories• Parabolic Single Band Model
• Nonparabolic Two-Band Kane Model
2. First-Principles (ab initio) Calculations• Molecular Dynamics (MD) Simulations
• Density Functional Theory (DFT)
3. Monte Carlo Simulations
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31
k
E
0
Conduction Band
Valence Band
EC
EV
EgDoping level
Band gap
Valance electrons
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Nonparabolic Two-Band Kane Model (Lee, 2016)
: Density of States
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zyxd mmmm where : Density-of-states effective mass
: Fermi integral
gg
Bidiv
iE
E
E
EE
TkmNg
21
221
2
32
2123
,,
0
232
,0
,
21 dE
E
E
E
EEE
E
fF
m
gg
nl
i
im
il
n
33
ii
i
iiH
iHen
A
enR
,
,
1:Hall coefficient
21
,1
0
1
,0
01
,2
0
2)12(
)2(3,,
i
ii
KdFi
F
FF
K
KKAAnTEA
:Hall factor
where tl mmK Ak is the anisotropy factor
1
,1
0
3
,
2
23
,
2
,
3
2
i
ic
Bidiiv
i Fm
TkmeN
s : electrical conductivity
1213
tlc mmm 312 tld mmmwhere
F
i
B EF
F
e
k1
1,1
0
1
1,1
1
1
FgB EE
F
F
e
k1
2,1
0
1
2,1
1
2
2
s
ss 2211
: Seebeck coefficients
: total Seebeck coefficent
:conductivity effective mass : density-of-state effective mass
34
zx
y
HHi
ER
A magnetic field zH in the z-direction applied perpendicularly to an electric current xi in the x-
direction, will produce an electric field yE in the y-direction. Then the Hall coefficient HR is
defined by
Anisotropy Factor AK
12
3 32
K
K
m
mA
d
cK
tl mmK
1
,1
0
3
,
2
23
,
2
,
3
2
i
ic
Bidiiv
i Fm
TkmeN
s : electrical conductivity
Anisotropy factor
Lee (2016)
35
Comparison of the Present Model with Measurements of PbTe (Lee,2016)
36
Comparison of the Present Model with Measurements of Bi2Te3 (Lee, 2016)
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Nature (2014)
Tin Selenide (SnSe) ZT = 2.6 at 900 K (record)ZT = 0.3 at 600 K
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Comparison of the Present Model with Measurements of SnSe (Lee, 2016)
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Tin Selenide (SnSe) ZT = 2.2 at 733 KZT = 1.5 at 600 K
Nature Communication (2016)
Fabrication of Single Crystal
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Czochralski TechniquePlanetary Ball milling
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43
Thermoelectric Materials
End