[Wannier] Boltzwann problem order of magnitude electrical conductivity

[Giovanni Pizzi]

Dear Robert,
Just a quick comment.

Are you looking just at the maximum of the curve? Did you check at which chemical potential this value occurs?
If you move the chemical potential well inside the conduction or valence band, the material will behave as a metal.
But to do this, you need a *huge* doping.

You should instead check in the band structure, e.g. for p-doping, where the top of the valence band is, and then integrate the valence DOS to find where the chemical potential will be (at a given temperature) for the value of the doping of interest.

(Or, if you are interested in the non-doped material, you should still compute the position of the Fermi energy, at charge neutrality, at a given finite temperature, that will be very close to the gap).

If you check the value of the expected doping when mu is 1eV into the valence band, which I let you do it as an exercise, you will get that you are removing almost 1 electron (or even more) per unit cell, which is not realistic (please compare with typical doping of silicon).

I hope these comments will help you.

Best,
Giovanni



--
Giovanni Pizzi
Theory and Simulation of Materials and MARVEL, EPFL
http://people.epfl.ch/giovanni.pizzi
http://nccr-marvel.ch/en/people/profile/giovanni-pizzi

On 3 Sep 2020, at 19:12, Robert Benda <robert.benda at enpc.fr<mailto:robert.benda at enpc.fr>> wrote:

Dear all Wannier users,

I am quite new to Wannier90 and I am mostly performing electrical conductivity calculations using the BoltzWann module. I have followed the tutorial (example 16) on the computation of Boltzmann conductivity tensor for Silicon.

I attached the results I obtained for a 10 fs relaxation time as 'boltz_relax_time' Boltzwann parameter.

The order of magnitude of the largest conductivity component is 10^5 to 10^7 S/m, if I was not mistaken in the previous calculations using Quantum Espresso (I used the default parameters  provided in the example16/ repository as input filesfor SCF and NSCF calculations).

I am very surprised, as I was expecting something of order 10^{-3}  S/m, for the conductivity of Silicon, which is a semiconductor. Increasing more the relaxation time to 100 fs roughly produces a tenfold increase, accordingly to the scaling factor of the relaxation time, on the conductivity, which happens to be even larger, or order 10^8 S/m ; and farther away from the experimental conductivity.

In all cases, as far as I know, relaxation times in most solids (metals/semiconductors) range from a few fs to about 1000 fs -- that high, at low temperature and for some low dimensional materials--  and in this range I cannot reproduce a conductivity of order 10^{-3}, about 10 orders of magnitude smaller than what I found.

Also for a carbon nanotube (which I am interested in in the end, comparing the BoltzWann room T conductivity for defected CNTs / CNTs with adsorbed ions, to the conductivity of the perfect, pristine CNT) provided in example15, I obtain the same order of magnitude for the Boltzmann conductivity of the (5,5) metallic CNT of about 10^6 S/m.(while rather expecting from 0.5-5 * 10^{2} S/m).

Most probably I am missing a very basis subtlety in the input parameters or the code using, that prevents me from recovering the correct orders of magnitude. That is why I kindly request your help.

Thank you very much for your help,
Best regards,

Robert BENDA
PhD student, CERMICS (ENPC) and Ecole Polytechnique (FRANCE)


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