How to calculate the defect charge formation energy for a metallic system (bulk/surface) using DFT?
The defect formation energy is calculated by the following formula
E_formation (D,q) = E (D,q) - E(host defect free) + Sum[n(i)*µ(i)] + q( Ev + delta E_F )+E_corr
E_formation (D,q) = formation energy of point defect D with supercell charge q
E (D,q) = total energy of the point defect D with supercell charge q
E(host defect-free) = E(host defect-free) = total energy of host supercell
containing an equivalent number of atoms as that of the
defect supercell
Sum[n(i)*µ(i)] = The growth conditions for the crystal are
incorporated through the chemical potentials µ(i)
of the elemental species with the number n(i) of atoms added
( n(i) negative) or removed ( n(i) positive) from the pure host
Ev + delta E_F: The Fermi level E_F is referenced with respect
to the valence band maximum Ev and is related to Ev as
Ev+ delta E_F (from pure host calculations)
E_corr is the correction term that accounts for finite k-point sampling in the case of shallow impurities, or for elastic and/or electrostatic interactions between supercells.
My question is specifically how to calculate the term Ev and deltaE_F term fro the metallic system? As there is a continuous density of states for a metallic system how to predict the valence band maxima?
Mohanned Alanber Sir, Do you have any general idea of how to calculate the defect formation energy for the metallic system.
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