Seebeck coefficient

[sayantanu]

Dear ATK users,
I was going through the following piece.

https://docs.quantumwise.com/tutorials/phonon_calcs/phonon_calcs.html

Here transmission near the Fermi level is zero and as a result transmission gradient at the Fermi level should also be zero. Then why Seebeck coefficient is not zero as Seebeck coefficient is directly proportional to the transmission gradient at the Fermi level?

[Petr Khomyakov]

I guess that is because it is computed at non-zero temperature, i.e., there are charge carriers, electrons and holes, populating the conduction band and the valence band, respectively, see the definition of S at https://en.wikipedia.org/wiki/Seebeck_coefficient, which is given by an integral over the entire conduction and valence band energy range.