materials for thermoelectric applications jorge o. sofo department of physics, department of...
TRANSCRIPT
Materials for Thermoelectric Applications
Jorge O. SofoDepartment of Physics,
Department of Materials Science and Engineering,and
Materials Research InstitutePenn State
Thermoelectricians at work
2S
Z
Thermoelectricians at work
Conductivity 101
m
ne2Drude et al.
k-q
q
k
00 kk
k vfeJ 0 kk
k vfeJ
kx
ky
Conductivity 101
k k k k
coll
f f f fdr dk
t dt r dt tk
k k k k
coll
f f f fdr dk
t dt r dt tk
0kf
t
0k
f
r
k k
coll
f fdk
dt tk
k k
coll
f fdk
dt tk
1dk dp eE
dt dt
1dk dp eE
dt dt
0 0 0k kk
kk k
f f fv
k k
k k
coll
f fdk
dt tk
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
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
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
00 ( )
k k k kk
ff f e v E
00 ( )
k k k kk
ff f e v E
k kk
J e f v
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
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�
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
�
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
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
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)
The “Best” Thermoelectric
)()( kkk
kk vv
)()()( 2 vN
)()( 0 Cbest TkB4.20
k
dSN
1)(
kv )(
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)
Careful…
• Doping: rigid band• Gap problem• Temperature dependence of the electronic
structure.• Alloys. Single site approximations do not work.• Many k-points
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
Bismuth
Why is Bi so good?
Bi vs. Bi2Te3
Improved thermoelectric devices using bismuth alloysT. Thonhauser, T. J. Scheidemantel, J. O. Sofo, Appl. Phys. Lett. 85, 588 (2004)
Is there any hope?
Courtesy of Georg Madsen
A Program by Georg Madsen and David Singh
Courtesy of Georg Madsen
Georg Madsen’s
Opals
• Different scattering for phonons and electrons.
• Work done for Allied Signal Corp.
• Not an alternative…
•
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…
