[Pw_forum] Fail to predict semiconductor

Giuseppe Mattioli giuseppe.mattioli at ism.cnr.it
Thu Jan 24 12:40:28 CET 2013

Dear Alexey
I do not agree with your analysis. GGA is indeed affected by the well known, bloody delocalisation 
error, which leads (among other, several, painful problems) to an underestimation of the band gap of 
insulators and semiconductors. This said, the Ti-->Zn substitution in the ZnO lattice seems to be 
characterized by a quite peculiar behaviour that, in my opinion, may be only partly accountable for 
the above delocalisation (or double counting, self interaction, call it as you like...:-)) error. A 
DFT+U correction, by the way, is often able to cure a vast majority of the symptoms of 
delocalisation errors, but, like all drugs, must be carefully used in the best way. A substitutional 
Ti atom has two excess electrons with respect to the Zn one. In Iwan's calculation they are 
accommodated in a hugely k-dispersed (i.e., highly delocalized) band which falls about 1.2 eV above 
the valence band maximum at Gamma, and cross the conduction band minimum in some regions of the 
Brillouin zone. A gap of about 3.0 eV, obtained by "pushing down" the Zn 3d orbitals with a 7.0 eV U 
correction and, therefore, by disentangling the narrow 3d band from the broader O 2p band is quite 
similar to the optical 3.2~3.4 gap of ZnO, even if the Zn 4s nature (and potential energy) of the 
conduction band minimum is nearly unaffected by the correction. In my experience, a "conventional" 
behaviour of a GGA calculation of Ti doped ZnO would be represented by one of the following 

a) the two excess electron populate the conduction band minimum of ZnO

b) the two excess electrons are localized on atomic-like d orbitals of Ti

The 5.5 eV correction applied to the Ti 3d shell should favour b), but the actual results seem to be 
a curious mixing of a) and b). On the ground of such an analysis, I would suggest to perform an 
nspin=2 calculation because:

a) Ti(3+) ions are often reported in the case of n-type doping of TiO2, at variance with Ti(2+). I 
suspect that Ti cannot accommodate more than 1 excess electron in a 3d-like small polaron.

b) Iwan's results seems to suggest that the first excess electron could be accommodated in a single-
occupied, k-narrow, deep in the band gap Ti 3d orbital, while the second one could be accommodated 
in the k-dispersed conduction band minimum.

c) If I'm right, I expect to be mentioned in the acknowledgment section of Iwan's thesis...:-)



P.S. It is not really polite to mention it, but it may be useful to Iwan to grab my recent 
publications on DFT+U calculations applied to TiO2 and ZnO...

On Wednesday 23 January 2013 21:53:37 Alexey Akimov wrote:
> Dear Iwan,
> The pure DFT is known to underestimate the band gaps, eventually making
> semiconductor material to appear as a metal in your calculations. This
> problem arises because of the double-counting in exchange terms. The
> problem solved with the hybrid functionals, such as PBE0. The GGA
> approximation and even +U correction terms provide only small improvement
> over LDA. So this may not be enough to make your system to be
> semiconductor (computationally). To summarize,the problem is inherently
> with the DFT methododology.
> Good luck,
> Alexey
> ----- Original Message -----
> From: "Iwan Darmadi" <iwan_darmadi at rocketmail.com>
> To: "pw forum" <pw_forum at pwscf.org>
> Sent: Wednesday, January 23, 2013 12:50:35 AM
> Subject: [Pw_forum] Fail to predict semiconductor
> Dear all,
> I have calculated electronic structure of Ti doped ZnO in both GGA and
> GGA+U scheme. Both scheme predicts Ti doped ZnO is metallic. In contrary,
> Ti doped ZnO is well known as semiconductor experimentally. At first
> glance, I thought it was local minimum problem of DFT+U (like FeO problem
> in Mr. Himmetoglu's tutorial). Then I try to copy Mr. Himmetoglu's trick
> to override a "suspected" fully occupied orbitals of Ti. Sadly, nothing
> change, it's still a metallic.
> Now, I am confused whether this is a really local minimum problem or
> intrinsic limitation of DFT it self.
> Do anyone here have suggestions so I can get semiconductor Ti doped ZnO in
> the calculation ?
> Ps.
> I have also attached my input and output file.
> ***
> Iwan Darmadi
> Undergrad.Student - Department of Physics
> Universitas Indonesia
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