[Pw_forum] reference energy of eigenvalue of Kohn-Sham equation

[Stefano Baroni]

On Feb 18, 2010, at 6:46 AM, yukihiro_okuno at fujifilm.co.jp wrote:

> 
> Dear PWSCF users.

Hi, Yiukihiro:

> I want to calculate the band off set of semiconductor's hetero junction.
> (semiconductor A/B junction)
> In order to calculate the band offset value of valence band at the
> interface,
> I knew  the average potential of electrostatic potential, must be
> calculated
> in the super cell calculation of A/B hetero junction.
> (Baldereschi, et al  Phys. Rev. Lett vol61 734 ) and the eigenvalue of
> valence band top of semiconductors A and B, independently.
> The band offset is defined by
> 
> Band offset of valence band = (Ea-Eb)+(delta V),
> 
> where Ea and Eb is the eigenvalue of the valence band top of the K.S.eq and
> deltaV is
> the difference of the average of the electrostatic potential of bulk like
> region of
> A and B semiconductor in the supercell.
> 
> By the way, why the  reference energy of the eigenvalue of the Kohn-Sham
> equation
> is the average of electro static potential ?

because that average (which is ill-defined) is arbitrarily set to zero in PWscf (or at least it used to be so when the above mentioned paper was written).

>  Where in the formalism, the
> K.S eq  refers
> the average of the electro static potential ?

nowhere, explicitly. it is just the G=0 component of the potential. being ill-defined (as said), it is set to zero. *HENCE* the eigenvalues are referred to it (if you shift the average, the eigenvalues are all shifted accordingly).

hope this is clear enough

Stefano

---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
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