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?