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

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-

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-

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- Room temperatureRoom temperature

Material

Cold Hot

I

- --

-

- --

--

V

E

Thermoelectric Phenomena

• Free electrons

• Coulomb force• Diffusion

4

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

5

6

Thomson Effect

ሶ𝑄𝑇ℎ𝑜𝑚𝑠𝑜𝑛 = −𝜏𝐴𝐵𝐼𝛻𝑇

TjE

TkjTq

Electric Field

Heat Flow

02 TjdT

dTjTk

dT

dT

:Thomson coefficient

Gov. equation

7

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

8

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)

10

:Dimensionless figure of merit

11

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

11

1

2

1

2

1

max

TZ

T

TTZ

TT

TCOP c

h

ch

c

Maximum Coefficient of Performance

12

Materials (Lee,2016)

13

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

14

Applications (TEC)

Car Seat Climate Control

Telecom Laser for Optic Fibers

Microprocessor Cooling

Automotive Air Conditioner (Zonal Cooling)

Medical Instrument

15

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

16

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

17

Micro TEG (4.2 mm x 4.2 mm) Macro TEG (38 mm x 38 mm)

Lee (2016)-book

18

ANSYS Numerical Simulations (TEG)-This work

19

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

20

2010s 1950s

Suggested Design with Ceramic of Aluminum Nitride (AlN)

21

PART II Materials

22

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:

22

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

25

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.

26

Science, 2008, 320, 634-638 (Poudel et al.)

Nanocomposite materials

Nature, 2008, 451,163-167 (Hochbaum et al.)

Nanostructured materials – nanowires

29

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

30

31

k

E

0

Conduction Band

Valence Band

EC

EV

EgDoping level

Band gap

Valance electrons

32

Nonparabolic Two-Band Kane Model (Lee, 2016)

: Density of States

31

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)

37

Nature (2014)

Tin Selenide (SnSe) ZT = 2.6 at 900 K (record)ZT = 0.3 at 600 K

38

Comparison of the Present Model with Measurements of SnSe (Lee, 2016)

39

Tin Selenide (SnSe) ZT = 2.2 at 733 KZT = 1.5 at 600 K

Nature Communication (2016)

Fabrication of Single Crystal

40

Czochralski TechniquePlanetary Ball milling

41

42

43

Thermoelectric Materials

End