THE SEEBECK COEFFICIENT
Anthony Rice
MTRL 286K
12/15/14
Outline
• The Seebeck coefficient is a property dependent on the
electronic structure near the fermi-level and is sensitive to
things including effective mass, carrier concentration, and
band shape
• Seebeck measurements may be used to further elucidate
basic electronic properties through a transition
• NaCo2O4 is a high-Seebeck metal, with possible
explanations including configurational entropy and
peculiar band shape
The Seebeck Effect
∆𝑉
𝑆=−
∆𝑇
μ𝑉
[
𝐾
“Power Factor”
]
-Direct Eg, Parabolic bands
J. Solyom. Fundamentals of the Physics of Solids
A. Shakouri. Annu. Rev. Mater. Res. 2011. 41:399–431
Typical Metallic Values
Sign determines whether dominant conduction occurs below or above fermi level
J. Solyom. Fundamentals of the Physics of Solids
“Mott Formula”
For a Metal/degenerate-semiconductor:
M. Cutler, N.F. Mott. Phys. Rev. 181, 1336 (1969)
Generalized For a Semiconductor:
τ-carrier lifetime
v-group velocity
ε-band dispersion
A- material dependent constant
J. Solyom. Fundamentals of the Physics of Solids
H. Fritzsche,Solid State Commun.9, 1813 (1971)
Pisarenko Plots
• Seebeck vs. n plot, generally log-log
• Should be a universal relationship for
a given band-structure/material
• Slope ~200 μ𝑉/k for a parabolic band
insulator
• k/e∗ln(10)
B. Jalan, S. Stemmer. Appl. Phys. Lett. 97, 042106 (2010)
PbTe:Tl
Solid line-calculated/published to date
Dots-Current study
J.P. Heremans. V. Jovovic. E.S. Toberer. A. Saramat. K. Kurosaki. A. Charoenphakdee.
S. Yamanak, G.J. Snyder. Science 25 July 2008: Vol. 321 no. 5888 pp. 554-557
V1-XWxO2: TMI vs. Ts
T. Katase, K. Endo, and H. Ohta. Phys. Rev. B 90, 161105(R) (2014)
V1-XWxO2:Parabolic Bands?
T. Katase, K. Endo, and H. Ohta. Phys. Rev. B 90, 161105(R) (2014)
Magnetite at the Verwey Transition
•
•
Oxidation varied-A least oxidized, E most
Above ~120K-independent of oxidation
-Provides a probe of carrier type without B-field
A.J.M. Kuipers and V.A. Brabers. Phys. Rev. B. 14, 1401 (1976)
Thermopower in the Correlated Hoping Regime
• Seebeck governed by entropy change due
to addition of one more carrier in cases of
interacting carriers at high temperatures
“Heikes formula”
P.M. Chaikin, G. Beni. Phys. Rev. B. 13, 647 (1975)
NaCo2O4
• Na/CoO2 Layered Structure
• At stoichiometry, Co valence +3.5
I. Terasaki, Y. Sasago and K. Uchinokura.
Phys. Rev. B 56, R12 685 (1997)
Initial explanation- Hopping due to degeneracy
g3, g4.-# of configurations for each valence
x-ratio of 3+/4+ states (depends on xna)
Degeneracy, plus 3d correlation effects
causes large S
W. Koshibae, K. Tsutsui, S. Maekawa. Phys. Rev. B. 62, 6869 (2000)
ARPES Results
Missing crossings near K point
Na0.7CoO2
D.J. Singh. Phys. Rev. B. 13397 (2000)
H.-B. Yang et al. Phys. Rev. Lett. 92, 246403 (2004)
Na0.6CoO2
M. Z. Hasan et at. Phys. Rev. Lett. 92, 246402 (2004)
“Pudding mold” Bands
K. Kuroki, R. Arita. J. Phys. Soc. Jpn. 76, 083707 (2007)
Fe(As1-xSex)2
Pnnm (no. 58)
H. Usui, K. Suzuki, K. Kuroki, S. Nakano, K. Kudo, M. Nohara. Phys. Rev. B. 88,
075140 (2013)
Summary
• The Seebeck coefficient provides useful information
beyond resistivity for basic electronic studies
• Metal-insulator studies may be further enhanced by using
thermopower measurements
• A number of materials with unique band-structure may be
potential candidates for further thermoelectric study
CuAlO2-Proposed Hole-doped TE
K. Mori, H. Sakakibara, H. Usui, K. Kuroki. Phys. Rev. B. 88, 075141 (2013)