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 ID: 806945
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Slide1
Thermoelectrics:The search for better materials
Jorge O. SofoDepartment of Physics,Department of Materials Science and Engineering,andMaterials Research InstitutePenn State
Slide2The basics
Abram F.
Ioffe
Slide3The devices
Slide4The performance
T
1T2
Slide5The materials
n-typep-type
J.-P. Fleurial, DESIGN AND DISCOVERY OF HIGHLY EFFICIENT THERMOELECTRIC MATERIALS Download Design and Discovery, Jet Propulsion Laboratory/California Institute of Technology, 1993.
Slide6Conductivity 101
Drude et al.
k-q
q
k
Slide7k
x
k
y
Conductivity 101
Slide8Slide9Slide10Slide11Slide12Slide13Slide14Slide15Slide16Slide17Slide18Slide19Slide20Slide21Slide22Slide23Transport distribution
Slide24“The best thermoelectric,” G. D. Mahan and J. O. Sofo
Proc. Nat. Acad. Sci. USA,
93
, 7436 (1996)
Slide25The “Best” Thermoelectric
Slide26Limitations of the Boltzman Equation Method
Also known as the Kinetic Method because of the relation with classical kinetic theoryAccording 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
Slide27Using 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)
Slide28First Born Approximation
Defect scattering
Crystal defectsImpuritiesNeutral
IonizedAlloyCarrier-carrier scatteringLattice scattering
Intravalley
Acoustic
Deformation potential
Piezoelectric
Optic
Non-polar
Polar
Intervalley
Acoustic
Optic
Slide29B. R. Nag - 1980 - Electron Transport in
Compound Semiconductors
Slide30B. R. Nag - 1980 - Electron Transport in
Compound Semiconductors
Slide31Slide32T. 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
Slide33Slide34Georg Madsen’s
Slide35Relaxation time from e-p interaction
Slide36Deformation Potential CalculationsVan de
Walle, Chris G. “Band Lineups and Deformation Potentials in the Model-solid Theory.” Phys. Rev. B 39, 1871–1883 (1989).
Bardeen, J., and W. Shockley. “Deformation Potentials and Mobilities in Non-Polar Crystals.” Phys. Rev. 80, 72–80 (1950).
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): 081406.
Slide37Careful…Doping: rigid bandGap problem
Temperature dependence of the electronic structure.Alloys. Single site approximations do not work.Many k-pointsCorrelated materials?Connection with magnetism and topology?
Slide38Linear Response Theory (Kubo)Valid only close
to equilibrium HoweverDoes not need well defined energy “bands”It is easy to incorporate most low energy excitations of the solidAmenable to diagrammatic expansions and controlled approximationsEquivalent to the Boltzmann equation when both are valid.
Slide39Summary
Tool to explore new compounds, pressure, “negative” pressure.Prediction of a new compound by G. Madsen.Easy to expand adding new Scattering MechanismsLimited to applications on “non-correlated” semiconductors.QuestionsShould 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…