thermoelectric power

7/29/2019 Thermoelectric Power

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for Radioisotope Thermoelectric Generators (RTGs)

by Bhaskar Bhattacharjee

Si-Ge Thermoelectrics

16. January 2013 | Materials Science Institute | Seminar Research Topics in Materials Science 2012/13| Bhaskar 1


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Why Thermoelectrics?


EnergyWaste

Reduction in Solar Flux+ Long Mission Times

Solar Panels Ineffective

Need Internal EnergySource (e.g. Pu-238)

Heat Electricityusing Thermoelectrics

MOTIVATIONS

UnmannedDeep SpaceMissions [2]

~ 40 %Efficient

[1]

~ 25 %Efficient

[1]


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Reduction in solar radiant flux with increasing distance from sun [2]


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Beyond 4 AU, radioisotope power systems more mass efficient than solar power [2]

MMRTG ~6.3%



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Content Overview

Fundamentals (F):

The Seebeck Effect Thermoelectric Power Generation

The Figure of Merit (zT)

Electron-Crystal, Phonon-Glass About Si-Ge Thermoelectrics

Si-Ge and the Problem of Segmentation

Improving zT

Si-Ge Thermoelectrics Research (R)

Conclusion



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Fundamentals

Of Thermoelectrics



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(F): The Seebeck Effect


Consider an n-type As doped Si1-xGex semiconductor subjected to a temperaturegradient:

+

Deep Space Pu-238 Pellet

Cold Hot

+

+

++

+

+

Electron Diffusion

Electron Drift

Electric FieldT (K)

x

Exposed As+donors

dV

dx

-++++

----

+

dT

dV=

Seebeckcoefficient

e- with energykTEK 2

3=

VT

SeebeckVoltage

=H

C

T

TdTV

Explanation of Seebeck effect [3]


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(F): Derivation of for n-type Semiconductor[3]

(Exaggerated) Schematic energy band diagram of a semiconductor in a temperature gradient [3]

Consider small distance dx at distance x from hot region where temperature is dT:

( ) kTEE FC 23+

Electrical work to move e- across dx: -edV

e- energy at x when measured from EF:

PE KE

Across dT: ( ) kdTEEdFc 2

3+

(EC-EF) with T, change in energy across dT from -edV: ( ) kdTEEdedV Fc 23+=

( ) ( )

+=+

=

dT

EEdk

ek

dT

EEd

dT

dVe Fcn

Fc

2

31

23

( )( )

( )2

lnexpk

T

EE

dT

EEd

nN

kTEEkT

EENn FcFccFc

Fcc +

=

=

=

*

+=kT

EE

e

kFC

n2

Seebeck coefficient forn-type semiconductor*



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(F): Thermoelectric Power Generation

Consider now that hot ends of n-type As doped Si1-xGex and p-type B doped Si1-xGex are

electrically connected in series and a load is connected across the cold ends:


R Spacecraft Load

n - type

p - type

e-

h+

e-

e-

h+

h+

i+

i+

Metal Interconnect

Cold Hot

Other Unicouples

Other UnicouplesV ( )

++

H

C

T

Tl

p

p

n

nnp R

A

l

A

lIdTnV

Electrical power @ RSpacecraft Load for n number of thermoelectric couples:LoadSpacecraftR

VP

2

=

Adapted from [4]


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(F): The Figure of Merit(zT)[5]


Maximum efficiency of thermoelectric generator:

H

CH

CH

T

TTZ

TZ

T

TT

++

+

=

1

11max

=

HH

CH

T

T

T

TTCarnot efficiency

Efficiency of thermoelectric generator:JunctionHotatAbsorbedHeat

LoadtoSuppliedPower=

+

= 2CH TT

T Average temperature( )

( ) ( )

+

=

2

2

1

2

1

2

ppnn

np TTZ

Figure of merit of thermoelectric generator

Thermoelectric material figure of merit:

TTzT

22

==

electrical resistivity, electrical conductivity, thermal conductivity,T operating temperature

Power factor= 22

Describes materials efficiencyto convert heat electricity


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(F): Electron-Crystal, Phonon-Glass


Electron-Crystal, Phonon Glass: e-free to transport charge and heat but phonons impeded fromtransporting heat [4]

Objectives

Large zT

High TLarge T

High electricalconductivity ()

Large Seebeckcoefficient ()

Low thermalconductivity ()

Large PowerFactor (2)


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(F): Electron-Crystal, Phonon-Glass Large 2


Power factor 2maximizes for carrier densities between1019 to 1021 cm-3or ~ 0.1% doping [4,5]

Q:Why does 2reach a maximum?A: Not all dopants ionizedcarrier density reaches

saturation

Q: Why cannot all dopants ionize?A: Heavy dopingdopants interact orbital overlap

to form narrow energy band that overlaps andbecomes part of CB

Q: What does this all mean?A: shift in E

C, E

G, E

Fin CB degenerate n-Sc

shift in EV, EG, EF in VB degenerate p-Sc

E

g(E)

CB

VB

EFp

EV

EC

EV

EFnEC

Impuritiesforming

band

Degenerate n-typesemiconductor [3]

Degenerate p-typesemiconductor [3]

CBGeneral implications [3]:

( )

/>

kT

EENnNn

FC

CCexp

+ kT

EE

e

k FCn 2Seebeck coefficient:

Metal-like properties: T

Specific Implication [4]:For maximized carrier densities, require EG to

be not too large nor too small


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(F): Electron-Crystal, Phonon-Glass Low

phonon

electron

total

InsulatorsSemiconductors Metals

Dependence ofon carrier density [4,5]

=electron+phonon

electronthroughWiedemann-Franz Law

minimized by phonon

A Primary Research Focus:

while maintaining if notsimultaneously 2


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About Si-Ge Thermoelectrics


Does Si-Ge alloy system satisfy the objectives?

n-type Si1-xGex p-type Si1-xGex

Large zT

High T

Large T

High zT thermoelectric materials [4]Si-Ge Unicouple used in Voyager I/II RTG [4]


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Si-Ge and the Problem of Segmentation


Recall the Objectives: Large zT, High T, Large T

Idealthermoelectric able to operate to over the widest possible temperature range

Reality:

, , T-dependent Optimal zTover

small T

High zTover largeT not possible

Solution

Segmentation

Schematic of Segmented Generator [4]

CompatibilityFactor, s[4]

T

zTs

11 +=

Relative CurrentDensity, u[4]

T

Ju

=

s should be < 2 for u throughsegmented element to be < 20 % [4] Si-Ge unsuited for segmentation [4]


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Why Continue with Si-Ge?

The only high T TE material capable of operating over relatively large T

Degradation by sublimation at


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Strategies for Improving zT


Producerattling

structures toscatter

phonons

Separatephonon glass

from electroncrystal

Yb, Sb (Ionic, doped)

MnSb4 (Covalent)

Scatter longmean-free-pathphonons atnanostructured

interfaces

Si95Ge5P2.5(GaP)1.5

Approach:

phonon

AlloysMultiphase

Nanocomposites

ComplexCrystals


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Si-Ge Thermoelectrics Research

Improving zT via Nanostructure Methods(MIT NASA JPL Boston College Partnership)


Synthesis ofNanoparticles

Inert GasCondensation

BallMilling

WetChemistry


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(R): Phonon Scattering in p-type Nanostructured Si80Ge20 Alloy


Fabrication: Starting MaterialsBall Mill

(10 60 hrs)DC Hot Press

(950 1200 C)

99.99 % B99.99 % Ge99.99% Si

Results:

Bulk

Bulk

Bulk

Comparison of T-dependence of2,, and zT in nanostructured bulk Si80Ge20 alloy and bulk RTG SiGe [6]

90%improvementin zT

Nano

Nano

Nano

Analysis: Increasedphonon scattering at nanostructure gbs, in phononby factor of 2 [6]


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Conclusion


Improve

zT

Find materialswith s


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References

Motivations[1] Thermoelectrics for Energy , 2013.

[2] Dr. Balint, Radioisotope Power System Candidates for Unmanned Exploration Missions, Utah, March4, 2005.

R. Abelson, Expanding Frontiers with Standard Radioisotope Power Systems, California, January 12,2005.

Fundamentals[3] S.O. Kasap, Principles of Electronic Materials and Devices ,3rd Ed., The McGraw Hill Companies,

Canada, 2006.

[4] The Science of Thermoelectrics, 2013.

[5] D.M. Rowe, Thermoelectric Power Generation, PROC. IEE, Vol. 125, No. 11R, November 1978,IEE REVIEWS.

L.E. Bell, Cooling, Heating, Generating Power, and Recovering Waste Heat with Thermoelectric

Systems, Science 321, 1457 (2008) Thermoelectrics Research

[6] G. Joshi et.al., Enhanced Thermoelectric Figure-of-Merit in Nanostructured p-type SiliconGermanium Bulk Alloys, Nano Lett., Vol. 8, No. 12, 2008.

Zhu, G. H. et al. Increased Phonon Scattering by Nanograins and Point Defects in Nanostructured Siliconwith a Low Concentration of Germanium. Physical Review Letters 102.19 , 2009



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for your time and attention

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