Thermoelectrics the search for better materials
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Thermoelectrics : The search for better materials. Jorge O. Sofo Department of Physics, Department of Materials Science and Engineering, and Materials Research Institute Penn State. The basics. Abram F. Ioffe. The devices. The performance. T 1. T 2. The materials. p -type. n -type.

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Thermoelectrics the search for better materials

Thermoelectrics:The search for better materials

Jorge O. Sofo

Department of Physics,

Department of Materials Science and Engineering,

and

Materials Research Institute

Penn State


The basics

The basics

Abram F. Ioffe


The devices

The devices


The performance

The performance

T1

T2


The materials

The materials

p-type

n-type

J.-P. Fleurial, DESIGN AND DISCOVERY OF HIGHLY EFFICIENT THERMOELECTRIC MATERIALS

Download Design and Discovery, Jet Propulsion Laboratory/California Institute of Technology, 1993.


Conductivity 101

k-q

q

k

Conductivity 101

Drude et al.


Conductivity 1011

Conductivity 101

ky

kx


Thermoelectrics the search for better materials

Transport distribution


Thermoelectrics the search for better materials

“The best thermoelectric,” G. D. Mahan and J. O. Sofo

Proc. Nat. Acad. Sci. USA, 93, 7436 (1996)


The best thermoelectric

The “Best” Thermoelectric


Limitations of the boltzman equation method

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


Using boltzman with ab initio

Using Boltzman with ab-initio

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)


Thermoelectrics the search for better materials

  • 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

      • Acoustic

      • Optic


Thermoelectrics the search for better materials

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


Thermoelectrics the search for better materials

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


Thermoelectrics the search for better materials

T. J. Scheidemantel, C. Ambrosch-Draxl, T. Thonhauser, J. V. Badding, and J. O. Sofo. “Transport Coefficients from First-principles Calculations.” Phys. Rev. B68, 125210 (2003)

Bi2Te3


Thermoelectrics the search for better materials

Georg Madsen’s


Relaxation time from e p interaction

Relaxation time from e-p interaction


Deformation potential calculations

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. B39, 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, LudgerWirtz, 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): 081406.


Careful

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?


Linear response theory kubo

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.


Summary

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…


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