[QE-users] Fermi level and energy difference between identically charged cells

[Julien Barbaud]

Dear users,

 

I am getting confused over some pretty basic questions, when it comes to
comparing the energy of two charged supercells.

When we want to compute the formation energy of a charged defect (let's say
a +1 charged vacancy), we use the following:

Ef= E(vac)-[E(bulk)-mu-Efermi]

We substract from the bulk term the chemical potential mu of the vacant
species, and also the Fermi level, which is pretty much another kind of
chemical potential for the missing electron at 0K. This way, we discard the
energy difference that stems from taking out an electron from the arbitrary
Fermi level.

 

Does that mean that I have to take this Fermi level into account when
comparing the energy of two identically charged cells as well? For examples,
let's say I have the same compound in two different phases (A and B), both
with the same +1 vacancy. The Fermi energies that I get from a scf
calculation are significantly different. If I want to calculate the delta_E
between both charged defective cells, I should not do dE=E_B(vac)-E_A(vac),
but:

dE=[E_B(vac)+Efermi_B]-[E_A(vac)+Efermi_A] ?

This would discount the difference in energy that arises from taking out an
electron from each system at different fermi levels. That would be more
consistent with the above definition of vacancy formation energy for both A
and B.

 

Is it a correct way to compare both, or am I way off track?

 

Thanks in advance

Julien

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