# (Fundamental) difference of Seebeck effect for metals and semiconductors

In which way is the Seebeck effect different for semiconductors from metals and why is it greater? What is the difference in the underlying physical principle?

My knowledge so far is: Bring two materials in touch, doesn't matter which, their electrochemical potentials will align but the electrical potentials will differ which causes the generating voltage. I don't see how semiconductors are different here as it seems to be a very general principle.

• Your knowledge is wrong: the Seebeck effect does not depend on whether you have two materials or not. The thermoelectric voltage is distributed along the whole conductor, where there is a temperature gradient: it's a bulk effect. Different materials or, more generally, inhomogeneities along the circuit make the effect observable, but it does exist even in a homogeneous material. Commented Aug 24, 2020 at 5:39
• isn't that the thomson effect?
– Ben
Commented Aug 24, 2020 at 6:48
• No, really. Pay attention that there are many books out there, especially at the elementary level, that give a wrong description and explanation of the Seebeck effect, and of all the thermoelectric effects in general (something I discussed here). Sorry I don't have time to write an extensive answer. Commented Aug 24, 2020 at 7:01
• But I didn't say the seebeck effect is a result of contact potential.
– Ben
Commented Aug 24, 2020 at 7:03
• I would word it differently than Massimo. He is right that the Seebeck effect needs no pair of materials. A single chunk of metal would do, as long as there is a temperature gradient through it (i.e. apply a temperature difference between two points). If you want to measure the Seebeck voltage and be able to read anything different from 0V, then you will need to use a different material as probe. But the Seebeck effect takes place in a single material. Commented Aug 24, 2020 at 19:10

I think the answer has to do with the relation between the Seebeck coefficient and the electrical conductivity's dependence on energy, known as the Mott Formula (https://en.wikipedia.org/wiki/Thermopower#Mott_formula).

In short, the model that leads to the formula yields to a Seebeck coefficient that is proportional to -T for metals, with a very small factor (proportional to $$T/T_F$$ where the Fermi temperature is much bigger than the absolute temperature) and so yields low values.

However for semiconductors, one has to check the band structures according to the doping level and again how the electrical conductivity depends on the energy. It turns out that the prefactors in the different Mott formulae are not as small as in the case of a metal, apparently because transport does not occur near the Fermi level in this case.

• Thank you! But would you say it is a different principle then?
– Ben
Commented Aug 25, 2020 at 5:49
• I would say it is the same principle, generally. The big difference lies in the energy dependence of the conductivity because the density of states of the charge carriers differ greatly between metals and semiconductors. Commented Aug 25, 2020 at 7:43
• Thanks for clearifying!
– Ben
Commented Aug 25, 2020 at 10:46