Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechanical ...
drag is an increase in the effective
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different element ...
of
conduction electron
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies ...
s or valence
holes
A hole is an opening in or through a particular medium, usually a solid body. Holes occur through natural and artificial processes, and may be useful for various purposes, or may represent a problem needing to be addressed in many fields of en ...
due to interactions with the
crystal lattice
In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by
: \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n ...
in which the electron moves. As an electron moves past atoms in the lattice its charge distorts or polarizes the nearby lattice. This effect leads to a decrease in the electron (or hole, as may be the case)
mobility
Mobility may refer to:
Social sciences and humanities
* Economic mobility, ability of individuals or families to improve their economic status
* Geographic mobility, the measure of how populations and goods move over time
* Mobilities, a conte ...
, which results in a decreased conductivity. However, as the magnitude of the
Seebeck coefficient
The Seebeck coefficient (also known as thermopower, thermoelectric power, and thermoelectric sensitivity) of a material is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material ...
increases with phonon drag, it may be beneficial in a
thermoelectric
The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa via a thermocouple. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when ...
material for direct energy conversion applications. The magnitude of this effect is typically appreciable only at low temperatures (<200 K).
Phonons are not always in local thermal equilibrium; they move against the thermal gradient. They lose momentum by interacting with electrons (or other carriers) and imperfections in the crystal. If the phonon-electron interaction is predominant, the phonons will tend to push the electrons to one end of the material, losing momentum in the process. This contributes to the already present thermoelectric field. This contribution is most important in the temperature region where phonon-electron scattering is predominant. This happens for
:
where ''θ''
D is the
Debye temperature
In thermodynamics and solid-state physics, the Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat (Heat capacity) in a solid. It treats the vibrations of the atomic lattice (hea ...
. At lower temperatures there are fewer phonons available for drag, and at higher temperatures they tend to lose momentum in phonon-phonon scattering instead of phonon-electron scattering.
This region of the Seebeck coefficient-versus-temperature function is highly variable under a magnetic field.
References
Kittel, Charles (1996)
Introduction to Solid State Physics
''Introduction to Solid State Physics'', known colloquially as ''Kittel'', is a classic condensed matter physics textbook written by American physicist Charles Kittel in 1953. The book has been highly influential and has seen widespread adoption ...
, 7th Ed., John Wiley and Sons, Inc.
Electron
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