As we know, During the thermoelectric measurements at the hotter side of the material there is more variation in the energies of the charge carriers, compared to the colder side. This means that high energy levels have a higher carrier occupation per state on the hotter side, but also the hotter side has a lower occupation per state at lower energy levels. The high-energy carriers diffuse away from the hot end, and produce entropy by drifting towards the cold end of the device and at the same time low-energy carriers are drawn back towards the hot end of the device that decreases the thermoelectric (TE) emf.
TE emf and charge carriers mobility depend upon the scattering of charge carriers. If effective mass higher, Seebeck coefficient will higher but as a result lesser mobility obtained.I am little bit confused that how to relate mobility, seebeck coefficient and electrical conductivity.
Dear Kumar,
unfortunately there is no (exact and easy) answer to the question because the answer is related to the solution of the so called Mott's equation (Phys. Rev. 181, 1336 (1969)) to handle the equation you have to introduce some simplifications (given by your system of consideration) or use “brute force numeric s”. I can also recommend the book “Thermoelectrics Handbook – Macro to NANO” Edited by M.D. Rowe (CRC Press).
Regards
Ernst
Mobility enter in the calculation of the Seebeck coefficient only if there two types of carrier
This question is really nice and one should do some measurements on samples with same charge carrier concentration (n-type) but different values for mobility, to see, if there is an significant effect.
There is a very nice calculation for seebeck-coefficient in the book 'Halbleiterphysik' from Paul. As soon as possible I will look at my notices, but I think their is a dependency of the mobility.
In the book of Kirejev 'Physik der Halbleiter' the calculation of Seebeck-coefficient for the case of both types of carriers are involved (n + p-type) is wrong.
In the formula for the seebeck coefficient (one energy band contribution) given in the book of Kirejev there is the scattering parameter p. Therefore there is at least an influence to the seebeck-coeffiecient by the mobility.
Have a closer look to the dependency of the carrier concentration from the effective masses and the dependency of the mobility from that masses (which depends from the orientation of mobility) and you get a felling of that influence. First you should make you an idea what the effective masses describe, then you will get an idea of the density of states and how this effect the carrier concentartion and the fermi energy. Then make same ideas for mobility. At the end combine this knowledges.
As soon as I will find more time I will write it down.
Good luck
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