**At-a-Glance**

*MedeA*^{®}[1] *Electronic Transport* calculates the electronic
contributions to the electric and thermal conductivity, the thermoelectric
power, and related functions, as based on semiclassical Boltzmann theory.

**Key Benefits**

- Straightforward set up of the calculation
- Automated distribution over a large number of tasks enables quick calculation
- Accessible range of chemical potentials within a rigid-band scheme
- Straightforward adaptation of fundamental band gap for refined calculation of transport properties
- All quantities displayed as a function of temperature, chemical-potential shift (rigid-band doping), or carrier density

The early attempts at the end of the 19th century to understand the extraordinary transport properties of metals may be well regarded as the outset of solid state theory [2]. In particular, Drude’s theory of metals aimed at describing their high electrical and thermal conductivites [3], which about 50 years before, had been closely tied by the Wiedemann-Franz law. However, it was not before the advent of quantum theory that Sommerfeld was able to devise the first satisfactory theory of the solid state. Even around 100 years later, the calculation of transport properties remains a challenge, which is due in part to the close connection between the electronic and vibrational contributions to transport phenomena.

*MedeA Electronic Transport* captures the electronic contributions with
the help of the semiclassical Boltzmann theory, where the electron
dynamics are accounted for by classical equations of motion, while the
electronic states and their velocities are taken from first-principles
calculations [5] [6] [7].

As an example, the calculated electrical resistivities of several
ordered and quasi-disordered structures of Cu_{1-x}Au_{x}alloys as taken from the literature, the cluster expansion as
implemented in *MedeA UNCLE*, and *MedeA*’s builder of special quasirandom
structures (SQS), respectively, and as displayed in the figure below, reveal a
striking influence of the microscopic local environment of the atoms on
the transport properties. In particular, the ordered structures show
systematically reduced electrical resistivities, whereas the resistivities
of the disordered structures form a dome, with a maximum at equal
concentration of Cu and Au, which is in very good agreement with experimental
findings.

MedeA Electronic Transport captures the electronic contributions with the help of the semiclassical Boltzmann theory.

*MedeA Electronic Transport*computes the electronic contributions to the electrical and thermal conductivities, thermoelectric power (Seebeck coefficient), electronic specific heat, Pauli paramagnetic susceptibility, and Hall coefficient- All quantities can be displayed as a function of temperature, chemical potential (rigid-band doping), or carrier density
- An intuitive user interface allows completely automated setup, execution, and processing of the background jobs required to calculate isosurfaces of the electronic energies and the corresponding effective masses
*MedeA VASP*computes electronic eigenvalues- Full integration into the MedeA Environment allows you to take advantage
of
*MedeA*’s robust JobServer and TaskServer Infrastructure

- Electrical conductivity, thermal conductivity
- Thermoelectric power (Seebeck coefficient)
- Electronic specific heat
- Pauli paramagnetic susceptibility
- Hall coefficient

The calculated Seebeck coefficient of Bi_{2}Te_{3}at room
temperature is displayed in Figure 3 as a function of doping, as mimicked
by rigid shifts of the chemical potential. It agrees well with the experimental
values, which for the bulk material range from -250 μV/K (at an n-type
doping concentration of 7.4 × 10^{18} cm^{-3}) to +260 \(\mu V/K\)
(at a p-type doping concentration of 4 × 10^{18} cm^{-3})
[8] [9].

*MedeA Environment**MedeA VASP*

Learn more about MedeA Electronic Transport on Materials Design Application Notes:

- Thermoelectric Properties of Bi
_{2}Te_{3}as calculated using*MedeA Electronics*.

Check out the closely related datasheet on MedeA Special Quasirandom Structures

[1] | MedeA and Materials Design are registered trademarks of Materials Design, Inc. |

[2] | N. W. Ashcroft and N. D. Mermin, “Solid State Physics”, (Holt, Rinehart and Winston, New York 1976) |

[3] | P. Drude,
Annalen Phys. 306, 566 (1900)
(DOI),
ibid. 308, 369 (1900)
(DOI) |

[4] | A. R. Mackintosh,
Sci. Am. 209, 110 (1963)
(DOI) |

[5] | T. J. Scheidemantel, C. Ambrosch-Draxl, T. Thonhauser,
J. V. Badding, and J. O. Sofo,
Phys. Rev. B 68, 125210 (2003)
(DOI) |

[6] | G. K. H. Madsen and D. J. Singh,
Comp. Phys. Commun. 175, 67 (2006)
(DOI) |

[7] | V. Eyert,
Lect. Notes Phys. 849 (Springer, Berlin Heidelberg 2013)
(DOI) |

[8] | R. Sehr and L. R. Testardi,
J. Phys. Chem. Solids 23, 1219 (1962)
(DOI) |

[9] | H. J. Goldsmid, (Springer, New York, 1964) (DOI) |

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