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To compare the band structure difference of a pure and doped stucture, I need to calculate the band structure of supercell. But i heard the calculation of this kind had some difference from the primitive cell. And i find some questions as follow is similar to me, but I am not clear yet.

http://cms.mpi.univie.ac.at/vasp-forum/ ... php?4.2764
http://cms.mpi.univie.ac.at/vasp-forum/ ... php?4.4162
http://cms.mpi.univie.ac.at/vasp-forum/ ... php?4.4040

The admin had fingured out the BZ of supercell need to unfold(http://cms.mpi.univie.ac.at/vasp-forum/ ... ic.php?4.7), I want to know how to do that.

Other question, to supercell, the BZ need to special setting for some important K points is folded. But doped structure no longer a supercell structure, and how to compare their band structure.

sincerely
Thanks

please read some solid state physics textbook concerning the electronic structure of repeated unit cells (e g J. Ziman, The Principles of the Theory of Solids, you will find an example of a linear chain there)
For doped structures the size of the primitive cell of course has to be a multiple of the un-doped cell, depending on the dopant concentration. (i.e. if you simulate eg a dopant concentration of 0.8% (at/at) of a system with a primitive lattice having 1 atom, the 5x5x5 supercell with 1 dopant atom is your primitive cell.

But if the concentration of defects/dopants is small, you can consider them as small perturbations to the original structure. From this perspective, it does make sense to unfold the band structure as if the supercell was a perfect repetition of the original primitive cell. I've posted a reply to a related question at a more recent thread http://cms.mpi.univie.ac.at/vasp-forum/ ... hp?4.13079
I've written a code to do that using VASP. See Phys. Rev. B 89, 041407(R) (2014) for the method. The code is available online at http://www.ifm.liu.se/theomod/compphys/band-unfolding