Effect of nonparabolicity described by the fivaz model on the electrical resistance of thermoelectric material-metal contact
Keywords:
Fivaz model, superlattice, Fermi energy, miniband, degree of nonparabolicity, thermoelectric material–metal contact, electrical contact resistance of transient layer, deviation of thermoelectric material surface from the ideal plane, steady-state diffusion, intensity of metal particles entering semiconductor, clustersAbstract
The temperature dependences of thermoelectric material-metal electrical contact resistance were investigated in the case when a band spectrum of free charge carriers in material is described by the Fivaz model. A transient contact layer formed by the deviation of the surface of superlattice semiconductor thermoelectric material (SL TEM) from the ideal plane and transient contact layers with and without clusters formed in the process of steady-state diffusion of metal particles in SL TEM were considered. It was established that contact resistance drastically decreases with increase in the degree of nonparabolicity of SL TEM band spectrum, which is determined as the ratio of the Fermi energy of ideal two-dimensional electron (hole) gas with a quadratic dispersion law to the miniband width describing translation motion of charge carriers in the direction perpendicular to the plane of layers. This decrease is explained by blocking of free carrier scattering in the direction perpendicular to the plane of layers. It is shown that in the range of degrees of nonparabolicity K from 0.1 to 10, transient layer thicknesses from 20 to 150 µm, dimensionless intensities of metal atoms entering the volume of transient layer A from 0 to 1 and temperatures from 200 to 400 K, the electrical contact resistance of transient layer due to the deviation of SL TEM surface from the ideal plane varies from 8·10-9 to 1.9·10-7Ohm·сm2, transient layer due to steady-state diffusion of metal into SL TEM without formation of clusters – from 8·10-9 to 4·10-7 Ohm·сm2, transient layer due to steady-state diffusion of metal in SL TEM with formation of clusters – from 8·10-9 to 4.5·10-7 Ohm·сm2.
References
Fivaz R.F. (1967). Theory of layered structures. J. Phys. Chem. Sol., 28 (5), 839-845.
Gorskyi P.V. (2019). The effect of nonparabolicity described by Fivaz model on the “thermoelectric material - metal” electrical contact resistance. In: Physics and Technology of Thin Films and Nanosystems. XVII Freik International Conference. Abstract book (Ivano-Frankivsk, Ukraine, May 20 – 25, 2019).
Gorskyi P.V. (2018). Estimation of the electrical and thermal contact resistances and thermoEMF of “thermoelectric material-metal” transient contact layer due to semiconductor surface roughness. J.Thermoelectricity, 4, 5-13.
Vikhor L. N., Anatychuk L.I., Gorskyi P.V. (2019). Electrical resistance of metal contact to Bi2Te3 based thermoelectric legs. J. Appl. Phys., 126, 64503-1 – 164503-8. Available at: https://doi.org /10.1063/1.5117183.
Zaiman G. (1982). Models of disorder. Moscow: Mir.
Snarskii A.O., Zhenirovskii M.I., Bezsudnov I.V. (2006). The law of Wiedemann-Franz in thermoelectric composites. J.Thermoelectricity, 3, 59-65.
