1. Thermoelectrics: The search for better materials
Jorge O. Sofo
Department of Physics,
Department of Materials Science and Engineering,
and
Materials Research Institute
Penn State

2. The basics
Abram F. Ioffe

3. The devices

4. The performance T1 T2

5. The materials n-type p-type
J.-P. Fleurial, DESIGN AND DISCOVERY OF HIGHLY EFFICIENT THERMOELECTRIC MATERIALS
Download Design and Discovery, Jet Propulsion Laboratory/California Institute of Technology, 1993.

6. Conductivity 101
Drude et al.
k-q q k

7. Conductivity 101 ky kx

23. Transport distribution

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

25. The “Best” Thermoelectric

26. Limitations of the Boltzman Equation Method
Also known as the Kinetic Method because of the relation with classical kinetic theory
According to Kubo, Toda, and Hashitsume(1) cannot be applied when the mean free path is too short (e.g., amorphous semiconductors) or the frequency of the applied fields is too high.
However, it is very powerful and can be applied to non linear problems.
(1) R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Non-equilibrium Statistical Mechanics (Springer-Verlag, Berlin, 1991) p. 197

27. Using Boltzman with ab-initio
C. Ambrosch-Draxl and J. O. Sofo Linear optical properties of solids within the full-potential linearized augmented planewave method Comp. Phys. Commun. 175, 1-14 (2006)

28. First Born Approximation
Defect scattering
Crystal defects
Impurities
Neutral
Ionized
Alloy
Carrier-carrier scattering
Lattice scattering
Intravalley
Acoustic
Deformation potential
Piezoelectric
Optic
Non-polar
Polar
Intervalley

29. B. R. Nag - 1980 - Electron Transport in Compound Semiconductors

30. B. R. Nag - 1980 - Electron Transport in Compound Semiconductors

32. T. J. Scheidemantel, C. Ambrosch-Draxl, T. Thonhauser, J. V
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, (2003)
Bi2Te3

34. Georg Madsen’s

35. Relaxation time from e-p interaction

36. Deformation Potential Calculations
Bardeen, J., and W. Shockley. “Deformation Potentials and Mobilities in Non-Polar Crystals.” Phys. Rev. 80, 72–80 (1950).
Van de Walle, Chris G. “Band Lineups and Deformation Potentials in the Model-solid Theory.” Phys. Rev. B 39, 1871–1883 (1989).
Wagner, J.-M., and F. Bechstedt. “Electronic and Phonon Deformation Potentials of GaN and AlN: Ab Initio Calculations Versus Experiment.” Phys. Status Solidi (b) 234, 965–969 (2002)
Lazzeri, Michele, Claudio Attaccalite, Ludger Wirtz, and Francesco Mauri. “Impact of the Electron-electron Correlation on Phonon Dispersion: Failure of LDA and GGA DFT Functionals in Graphene and Graphite.” Physical Review B 78, no. 8 (August 26, 2008):

37. Careful… Doping: rigid band Gap problem
Temperature dependence of the electronic structure.
Alloys. Single site approximations do not work.
Many k-points
Correlated materials?
Connection with magnetism and topology?

38. Linear Response Theory (Kubo)
Valid only close to equilibrium
However
Does not need well defined energy “bands”
It is easy to incorporate most low energy excitations of the solid
Amenable to diagrammatic expansions and controlled approximations
Equivalent to the Boltzmann equation when both are valid.

39. 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.
Questions
Should we start the program of calculating all parameters from ab-initio?
What about an implementation based on the Kubo formula?
Where the “stochastization” will come from in a small periodic system? Remember that there should be an average somewhere to get irreversibility…