[Wien] Seebeck coefficient_Boltztrap

[Fecher, Gerhard]

Hallo Hannan,
there seems to be a big confusion about the terms Fermi energy and chemical potential
(unfortunately sometimes this happens already in text books)

What quantity do you call "Fermi energy", "chemical potential", or most undefined "Femi level" ?

Fermi energy is by definition the energy of the highest occupied state at T=0, in semi-conductors this is the top of the valence band.
Chemical potential is something different, for the here used context (otherwise see textbooks) it defines the middle of the Fermi-Dirac distribution,
For undoped, intrinsic semiconductors, the position of the chemical potential will be somewhere in the band gap but its exact energy position depends on the temperature 
(even though it is haphazardly set very often into the middle of the band gap of semiconductors).

If you take the Fermi energy from the scf2 file as Zero of the chemical potential (at what temperature ?) you make a mistake if you calculate for a semiconductor
(most often this is fine for metals, where it is rather independent on temperature).

I suggest to read the book "Electrons and Phonons" by Ziman
or have a look into one of my recent reviews in physica status solidi (a) 213 (2016), Pages: 716–731 and the references there  (http://onlinelibrary.wiley.com/doi/10.1002/pssa.201532595/abstract)

Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Inorganic and Analytical Chemistry
Johannes Gutenberg - University
55099 Mainz
and
Max Planck Institute for Chemical Physics of Solids
01187 Dresden
________________________________________
Von: wien-bounces at zeus.theochem.tuwien.ac.at [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Hannan.Sadek at uv.es [Hannan.Sadek at uv.es]
Gesendet: Dienstag, 5. April 2016 21:11
An: A Mailing list for WIEN2k users
Betreff: Re: [Wien] Seebeck coefficient_Boltztrap

Dear Gerhard;
I subtracted the value of the Fermi energy that is corresponding to this case(the value of the Fermi energy in the case.scf file) from each values in the column of the chemical potential, and then I got the zero at one of them. As I understand it should be done in that way, doesn't it?

But there is something that I don't understand, in the case.intrans file I assigned the value of efcut=0.15(the energy range of the chemical potential around efermi) even though in the case.trace file I see that the calculations have been run by using chemical potential over the range 0.1 lower than the Fermi energy till 0.2 higher than the Fermi energy(not 0.15 in both sides)

I expected that the seebeck is symmetric around zero chemical potential just because in almost all the articles that I have read about the boltztrap calculations, the seebeck coefficient is symmetric around zero chemical; they got the p-type at the negative values of the chemical potential and the n-type at the positive one. In my case, I got the n and p type at the positive values of the chemical potential.

Best regards
Hannan


why do you expect that the Seebeck is symmetric arround zero chemical potential (whatever you assume to be the Zero)
is your density of states symmetric with respect to the middle of the band gap ?

Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Inorganic and Analytical Chemistry
Johannes Gutenberg - University
55099 Mainz
and
Max Planck Institute for Chemical Physics of Solids
01187 Dresden
________________________________________
Von: wien-bounces at zeus.theochem.tuwien.ac.at [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Hannan.Sadek at uv.es [Hannan.Sadek at uv.es]
Gesendet: Montag, 4. April 2016 06:34
An: A Mailing list for WIEN2k users
Betreff: [Wien] Seebeck coefficient_Boltztrap

Dear Wien2k users;
I'm using the boltztrap code to study the thermoelectric properties of some semiconducting materials.
I run the process and I got the results. But I have a problem; when I drew the figure that represents the Seebeck coefficient as a function of the chemical potential, I didn't get the curve symmetric around zero chemical potential. I got the curve at the right of the zero chemical potential.
Also I tried to reproduce the examples that are given in the package like Bi2te3, to know if it is happened only with these materials, and I had the same problem.
What could be the mistake that I did in the calculations?
Best regards
Hannan

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