[Pw_forum] fermi level

Eyvaz Isaev eyvaz_isaev at yahoo.com
Thu Aug 14 20:35:46 CEST 2008

Dear Vega,

> How about the case for semi-conductors like TiO2? When
> calculations for TiO2 was achieved, I can't find any > information about Fermi energy in my output file.

Let me resend you my reply to almost the same question of Padmaja Patnaik. Please see below.


--- On Thu, 7/8/08, Eyvaz Isaev <eyvaz_isaev at yahoo.com> wrote:
From: Eyvaz Isaev <eyvaz_isaev at yahoo.com>
Subject: Re: [Pw_forum] doubt in occupations:2
To: "Padmaja Patnaik" <padmaja_patnaik at yahoo.co.uk>
Date: Thursday, 7 August, 2008, 4:52 AM

Dear Padmaja,

I have repeated your calculations and do not see any problem with them.

First of all I have to note that THERE IS NO FERMI LEVEL FOR SEMICONDUCTORS AND INSULATORS. Why, please read a textbook, say Kittel, Ashcroft&Mermin, etc. 
For them we can consider only the top of the valence bands and the bottom of the conductivity bands.

As the Fermi level is defined as \int_{e_min}^{e_F}n(E)dE=N, where e_F is the Fermi level, n(E) is the DOS and N is the number of valence electrons, it does not matter where you put the Fermi level in the band gap. Because the DOS for E>E_{top valence level} (but E<E_{bottom of conductivity levels}), i.e. inside the band gap, is zero.

So, even with the calculated Fermi level for semiconductor or insulator one can put it in the middle of the band gap (or everywhere you want!).

But the best choice is the top level of the valence bands which is well defined.  

1. Scf calculations do not give the Fermi level, because you use fixed occupations used by default for semiconductors (insulators). I.e. if nothing specified as occupations, your system is considered as a semiconductor
(insulator). In this case the number of bands treated is exactly half of the number of valence electrons, i.e. 4 in your case.

So, you do it correct, but the Fermi level should not be expected in this case.

2. As concerns the second remark, now it should be clear that you have to shift all your bands with respect to the highest filled band, 9.2464eV (the 4th band
at the Gamma point) in your particular case.
In this case there are no states at "the Fermi level".

3. Some additional remarks. 
a) as you use norm-conserving pseudopotentials there is no need to take ecutrho >4*ecutwf, even skip this keyword. 
b) Use more k-points for the DOS calculations.


-- On Tue, 8/5/08, Padmaja Patnaik <padmaja_patnaik at yahoo.co.uk> wrote:

> From: Padmaja Patnaik <padmaja_patnaik at yahoo.co.uk>
> Subject: Re: [Pw_forum] doubt in occupations:2
> To: eyvaz_isaev at yahoo.com
> Date: Tuesday, August 5, 2008, 6:16 PM
> Dear Sir
> Hope you remember our communication regarding the
> occupations and Fermi energy.
> I am here sending you the input and output file for > DOS plotting of SiC. Please have a look. The scf 
> calculations doesn't give Fermi energy. Am i doing 
> anything wrong again?
> Secondly, when plot the DOS, usually we take the Fermi
> energy as zero of the energy axis. So when i make > Fermi energy as zero(by subtracting the Fermi energy 
> from dos.out file, from the energy values of the 
> plot) then the valence band maximum is not at zero > but is less than zero. Why is this happening? 
> Attaching here both scf and dos files.
>  Regards
> Padmaja Patnaik
> Research Scholar
> Dept of Physics
> IIT Bombay 
> Mumbai, India

Prof. Eyvaz Isaev, 
Theoretical Physics Department, Moscow State Institute of Steel & Alloys, Russia, 
Department of Physics, Chemistry, and Biology (IFM), Linkoping University, Sweden 
Condensed Matter Theory Group, Uppsala University, Sweden 
Eyvaz.Isaev at fysik.uu.se, isaev at ifm.liu.se, eyvaz_isaev at yahoo.com

--- On Thu, 8/14/08, vega <vegalew at hotmail.com> wrote:

> From: vega <vegalew at hotmail.com>
> Subject: Re: [Pw_forum] fermi level
> To: "PWSCF Forum" <pw_forum at pwscf.org>
> Date: Thursday, August 14, 2008, 8:51 PM
> Dear all,
> > Fermi energy is written in output whenever it is
> calculated, that is in any scf calculations for metals.
> How about the case for semi-conductors like TiO2? When
> calculations for TiO2 was achieved, I can't find any > information about Fermi  energy in my output file.
> could anyone can help me.
> vega
> ==============================================================
> Vega Lew ( weijia liu)
> PH.D Candidate in Chemical Engineering
> State Key Laboratory of Materials-oriented Chemical
> Engineering
> College of Chemistry and Chemical Engineering
> Nanjing University of Technology, 210009, Nanjing, Jiangsu,
> China
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