Transport Coefficients with WIEN2k
Jorge O. SofoDepartment of Physics
Department of Materials Science and Engineering
Thermoelectrics
Thermoelectrics
2SZ
Conductivity 101
mne2Drude et al.
k-q
q
k
Conductivity 101
00 kk
k vfeJ 0 kk
k vfeJ
kx
ky
Conductivity 101
kk
k vfeJ
Evfeff kkkk
0
0 )(
EvvfeJ kkkk
02
EJ
Conductivity 2k
kkkk
vvfe
0
2kv
kk
1kp
m1
kpkm
ˆ1
k First Born Approximation
•Acoustic phonons
•Optical phonons (polar, non-polar)
•Ionized impurities
•Inter-valley scattering
•…
Careful…
• Doping: rigid band• Gap problem• Temperature dependence of the
electronic structure.• Alloys. Single site approximations do
not work.• Many k-points
For free…
kkkk
vvfe
0
2
Tk
vvfekSB
kkkk
k
B
0
202
Tkvvfk
B
kkkk
kBel
Q
J E S TJ STE T
Application to Thermoelectrics
phel
SZ
2
Transport Distribution0 0
2 2 ( )k k kk
f fe v v e d
0 0
( )kB Bk k k
k B B
ek ekf fS v v dk T k T
2 20 02 2 ( )k k
el B k k k Bk B B
f fk v v k dk T k T
Application to Thermoelectrics: The best thermoelectric
max [ ] [ ]best bestZ Z
)()( 0 Cbest
2
[ ]el ph
SZ Z
TkB4.20
Transport Distribution
)()( kkk
kk vv
)()()( 2 vN
)()( 0 Cbest TkB4.20
k
dSN
1)(
kv )(
Bi2Te3
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 applications to “non-correlated” semiconductors.
Collaborators
• Claudia Ambrosch-Draxl (UNI-GRAZ)• Georg Madsen• John Badding (Penn State)• Timo Thonhauser (Wake Forest)• Tom Scheidemantel (Penn State)With the always present coaching of Jerry Mahan.
Bismuth
Bi vs. Bi2Te3
Thonhauser, Scheidemantel, Sofo, Appl. Phys. Lett. 2004
Why is Bi so good?
Is there any hope?