Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of...

41
Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research Institute Penn State

Transcript of Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of...

Page 1: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Materials for Thermoelectric Applications

Jorge O. SofoDepartment of Physics,

Department of Materials Science and Engineering,and

Materials Research InstitutePenn State

Page 2: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.
Page 3: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Thermoelectricians at work

Page 4: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

2S

Z

Thermoelectricians at work

Page 5: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Conductivity 101

m

ne2Drude et al.

k-q

q

k

Page 6: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

00 kk

k vfeJ 0 kk

k vfeJ

kx

ky

Conductivity 101

Page 7: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

k k k k

coll

f f f fdr dk

t dt r dt tk

Page 8: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

k k k k

coll

f f f fdr dk

t dt r dt tk

0kf

t

0k

f

r

Page 9: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

k k

coll

f fdk

dt tk

Page 10: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

k k

coll

f fdk

dt tk

1dk dp eE

dt dt

Page 11: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

1dk dp eE

dt dt

0 0 0k kk

kk k

f f fv

k k

k k

coll

f fdk

dt tk

Page 12: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

1dk dp eE

dt dt

0 0 0k kk

kk k

f f fv

k k

0k kk

coll k

f ff

t

k k

coll

f fdk

dt tk

Page 13: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

1dk dp eE

dt dt

0 0 0k kk

kk k

f f fv

k k

0k kk

coll k

f ff

t

k k

coll

f fdk

dt tk

00 ( )

k k k kk

ff f e v E

Page 14: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

1dk dp eE

dt dt

0 0 0k kk

kk k

f f fv

k k

0k kk

coll k

f ff

t

k k

coll

f fdk

dt tk

00 ( )

k k k kk

ff f e v E

Page 15: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

00 ( )

k k k kk

ff f e v E

Page 16: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

00 ( )

k k k kk

ff f e v E

k kk

J e f v

Page 17: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

00 ( )

k k k kk

ff f e v E

k kk

J e f v

2 0k k k

k k

fJ e v v E

Page 18: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

00 ( )

k k k kk

ff f e v E

k kk

J e f v

2 0k k k

k k

fJ e v v E

EJ�

Page 19: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

00 ( )

k k k kk

ff f e v E

k kk

J e f v

2 0k k k

k k

fJ e v v E

EJ�

2 0k k k

k k

fe v v

Page 20: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Q

J E S T

J S T E T

2 20k k

k k

fe v

20 kBk k

k Bk

fekS v

k T

2

2 20 kel B k k

k Bk

fk v

k T

2

0el ph

SZ

0 2el el S T

Page 21: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

2 2 20 0( )k k

k k

f fe v e d

20 0( )kB Bk k

k B Bk

f fek ekS v d

k T k T

2 2

2 2 20 0( )kel B Bk k

k B Bk

f fk v k d

k T k T

2( ) ( )k k k

k

v

Transport distribution

[ ] [ ]S

[ ]el

Page 22: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

max [ ] [ ]best bestZ Z

)()( 0 Cbest TkB4.20

2

0[ ]

el ph

SZ Z

2 0 ( )f

e d

0 ( )B

B

fkS d

k T

2

2 0 ( )el BB

fk d

k T

“The best thermoelectric,” G. D. Mahan and J. O. SofoProc. Nat. Acad. Sci. USA, 93, 7436 (1996)

Page 23: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

The “Best” Thermoelectric

)()( kkk

kk vv

)()()( 2 vN

)()( 0 Cbest TkB4.20

k

dSN

1)(

kv )(

Page 24: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Exciting Conductivity

kkkk

vvf

e�

0

2

kv

kk

1

kpm

1 kpk

mˆ1

k First Born Approximation

• Acoustic phonons

• Optical phonons (polar, non-polar)

• Ionized impurities

• Inter-valley scattering

• …

C. Ambrosch-Draxl and J. O. SofoLinear optical properties of solids within the full-potential linearized augmented planewave methodComp. Phys. Commun. 175, 1-14 (2006)

Page 25: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Careful…

• Doping: rigid band• Gap problem• Temperature dependence of the electronic

structure.• Alloys. Single site approximations do not work.• Many k-points

Page 26: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

T. J. Scheidemantel, C. Ambrosch-Draxl, T. Thonhauser, J. V. Badding, and J. O. Sofo. “Transport Coefficients from First-principles Calculations.” Phys. Rev. B 68, 125210 (2003)

Bi2Te3

Page 27: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.
Page 28: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Bismuth

Page 29: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Why is Bi so good?

Page 30: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Bi vs. Bi2Te3

Improved thermoelectric devices using bismuth alloysT. Thonhauser, T. J. Scheidemantel, J. O. Sofo, Appl. Phys. Lett. 85, 588 (2004)

Page 31: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Is there any hope?

Page 32: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Courtesy of Georg Madsen

A Program by Georg Madsen and David Singh

Page 33: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Courtesy of Georg Madsen

Page 34: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Georg Madsen’s

Page 35: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.
Page 36: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.
Page 37: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.
Page 38: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.
Page 39: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Opals

• Different scattering for phonons and electrons.

• Work done for Allied Signal Corp.

• Not an alternative…

Page 40: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.

Summary

• Tool to explore new compounds, pressure, “negative” pressure.

• Prediction of a new compound by G. Madsen.• Easy to expand adding new Scattering

Mechanisms• Limited to applications on “non-correlated”

semiconductors.• The search for the best material continues…

Page 41: Materials for Thermoelectric Applications Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research.