[Pw_forum] Electronic band structure calculation of Si using supercell

Mon Mar 20 10:24:02 CET 2017

You are luck, because I already answered a similar question some years ago, so I’ve just needed the time
to find useful plots somewhere in my archives!!!

Your band structure is likely to be correct. One more thing you should consider when you
use non primitive cells is band folding. The simple cubic (SC) cell has a volume that is 4 times
that of the FCC cell, indeed you use 4 Si-Si formula units. That means that you get, for each fixed k,
4 times the number of bands with respect to the FCC calculation but the Brillouin zone (BZ) is 4 time smaller.

See the 1st attachment: the BZ of the SC crystal is contained WITHIN the BZ of the FCC crystal. The X point
at the boundary of the LARGER BZ has (in units 2*pi/a) coordinates (1,0,0). On the other hand, in the SMALLER
BZ the boundary along the <100> direction is (in the SAME units) at (1/2,0,0). That means that the 1st X_FCC point is,
in the SC system, equivalent to Gamma because they differ by a reciprocal vector of the SC system, (1, 0, 0).

In FCC the conduction band minimum is found at about 0.85 G-X_FCC segment.

In SC, the bands along G - X_FCC / 2 remain the same, whereas the X_FCC / 2 - X_FCC is folded back
with a sign inversion:
X_FCC / 2 equivalent to X_SC = (1/2,0,0)
X_FCC      equivalent to Gamma_SC = (0,0,0)

The conduction band minimum is thus obtained at (1-0.85) Gamma_SC - X_SC segment, so at about 0.15 * (2*pi/a, 0, 0)

If you look at the second attachment, this is exactly what you obtain, what was missing in your calculation is that you did not
include, in the SC calculation, the Gamma_SC - X_SC direction.

Giovanni

PS beware: in the second attachment the FCC and SC band structures of Si are compared with each other, but the X point
in the left graph IS NOT the same of the X point in the right one, one is X_SC = (pi/a, 0, 0), the other X_FCC = (2*pi/a, 0, 0)

> On 17 Mar 2017, at 17:55, phs157144 <phs157144 at iitd.ac.in> wrote:
> 
> Thank you so much Giovanni for your prompt response.
> I repeated the calculations using unshifted k-point grid  with the 
> k-path
> gamma-R-X-M-gamma as you instructed and got better result.( 
> https://www.dropbox.com/s/a3przkx0cl193ao/Si111r.pdf?dl=0 ). But still 
> the band gap seems to be direct.
> 
> 
> On 17.03.2017 16:37, Giovanni Cantele wrote:
>> Before answering your question about gaps, two minor remarks:
>> 
>> i) you’re using norm conserving pseudo potential, you do not need to
>> set ecutrho to a value
>> larger than 4*ecutwfc, use the default instead
>> 
>> ii) you are representing the Si crystal with a simple cubic supercell.
>> When you calculate the
>> band structure, you should use special points of the Brillouin zone of
>> a simple cubic crystal,
>> whereas as far as I understand you are using the special points of the
>> Brillouin zone of a
>> cubic fcc crystal. Of course you don’t get anything wrong (you can
>> diagonalise the Hamiltonian
>> at whatever point in k space you want), but this is not the way in
>> which the electronic structure of
>> a cubic crystal is usually represented.
>> 
>> 
>> This being said, you can easily understand that the DOS you compute is
>> INCOMPATIBLE
>> with the band structure you show, because slightly above -2 eV you get
>> an energy gap
>> in the DOS, whereas you see electronic states in the band structure.
>> So, either you are calculating
>> the DOS and band structure of two different systems, or the DOS
>> derives from a calculation where
>> the Brillouin zone has not been correctly sampled. The latter
>> explanation applies to your case.
>> Indeed, in the nscf calculation preceding the dos.x run you use
>> K_POINTS {automatic}
>>  8 8 8 1 1 1
>> that is, a shifted k-point grid that, as such, does not include gamma 
>> point.
>> From the band structure you see that the electronic states in the
>> energy window -2 : -1 eV are just
>> localised around Gamma, so if you get rid of Gamma point you just
>> obtain nothing in the DOS.
>> 
>> The shifted grid would return the correct result if you make it finer,
>> but it is anyway better to use an
>> unshifted grid.
>> 
>> 
>> Giovanni
>> 
>> 
>>> On 17 Mar 2017, at 07:35, phs157144 <phs157144 at iitd.ac.in> wrote:
>>> 
>>> 
>>> Hi every one ,
>>>   I am new to Quantum Espresso and using v.6.0 (svn rev. 13079). I 
>>> was
>>> doing the band structure calculation of Si using  supercell and 
>>> obtained
>>> the electronic band structure and DOS (
>>> https://www.dropbox.com/s/shh289r33uod32e/Si111.pdf?dl=0 ). The result
>>> is showing two band gaps,one at the fermi level and the other one is
>>> near -2 eV . The band gap at the fermi level  seems to be direct. Am I
>>> doing wrong? I have attached my input file:
>>> https://www.dropbox.com/s/vqml9lq6v4pnr1w/Si111.sh?dl=0
>>> Please comment.
>>> 
>>> --
>>> Ruhul Amin
>>> M.Sc,physics
>>> IIT Delhi
>>> _______________________________________________
>>> Pw_forum mailing list
>>> Pw_forum at pwscf.org
>>> http://pwscf.org/mailman/listinfo/pw_forum
>>> 
>> 
>> --
>> 
>> Giovanni Cantele, PhD
>> CNR-SPIN
>> c/o Dipartimento di Fisica
>> Universita' di Napoli "Federico II"
>> Complesso Universitario M. S. Angelo - Ed. 6
>> Via Cintia, I-80126, Napoli, Italy
>> e-mail: giovanni.cantele at spin.cnr.it
>> Phone: +39 081 676910
>> Skype contact: giocan74
>> 
>> ResearcherID: http://www.researcherid.com/rid/A-1951-2009
>> Web page: http://people.na.infn.it/~cantele
>> 
>> 
>> 
>> _______________________________________________
>> Pw_forum mailing list
>> Pw_forum at pwscf.org
>> http://pwscf.org/mailman/listinfo/pw_forum
> 
> -- 
> Ruhul Amin
> M.Sc,physics
> IIT Delhi
> 
> _______________________________________________
> Pw_forum mailing list
> Pw_forum at pwscf.org
> http://pwscf.org/mailman/listinfo/pw_forum

-- 

Giovanni Cantele, PhD
CNR-SPIN
c/o Dipartimento di Fisica
Universita' di Napoli "Federico II"
Complesso Universitario M. S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
e-mail: giovanni.cantele at spin.cnr.it
Phone: +39 081 676910
Skype contact: giocan74

ResearcherID: http://www.researcherid.com/rid/A-1951-2009
Web page: http://people.na.infn.it/~cantele

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20170320/0d0ee975/attachment.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Si_fcc_vs_sc_BS.png
Type: image/png
Size: 61350 bytes
Desc: not available
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20170320/0d0ee975/attachment.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Si_fcc_vs_sc.png
Type: image/png
Size: 55867 bytes
Desc: not available
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20170320/0d0ee975/attachment-0001.png>