Question: vacancy formation energy with charged state

[fangyongxinxi]

Dear Sir,

I have a problem on how to calculate the formation energy of charged vacancy.

For this problem, I checked some papers, and found How other people did before.
Follow the description in this paper: Phys. Rev. B 68, 205213
First-principles study on structures and energetics of intrinsic vacancies in SrTiO3
The formation energy could be write as that in pic_1,
It conneted with:
Total energy of defective supercell with charge q, Etotal(defect:q)
Total energy of perfect supercell, Etotal(perfect:0)
atom chemical potential, eg. Oxygen vacancy, u(oxygen)
Femi energy, Ef
Energy of Valence-band maximum of defective supercell, E(VBM)
Average Potentials at a number of atomic sites in supercell, V(av)(defect/perfect)
Total energy of perfect supercell with charge q, Etotal(perfect:q)

I don know how to get these things in ATK:
u(oxygen),  Ef, and Average Potentials at a number of atomic sites in supercell, V(av)(defect/perfect)

In my case, I want to get the oxygen (Voxygen(+1)) formation energy in MgO,
Firstly, I make supercell, and calculate the total energy of supercell. E(total, perfect,q=0),
Next, I move away one oxygen atom, and set: Charge = +1, calculate total energy of the defective supercell, get E(total, defect,q=1),
Question is :
How to get the, oxygen chemical potential, Femi energy, and Average Potentials at a number of atomic sites in supercell, V(av)(defect/perfect) ?

So, could you give me an example on how to calculate the vacancy formation energy (with charge) in ionic crystal ?


There are two more papers talked about the formation energy of vacancy  (I did not get how they did in detail)
1. Ab initio calculation of the formation energy of charged vacancies in germanium
http://www.sciencedirect.com/science/article/pii/S0921452607006953?np=y

2. First-principles calculations for defects and impurities: Applications to III-nitrides
http://scitation.aip.org/content/aip/journal/jap/95/8/10.1063/1.1682673

Thanks.

[zh]

First of all, you have to understand the physics concept (or definition) of Fermi energy (or Fermi level, particularly for the Fermi energy of a semiconductor) and chemical potential of a gas molecule.

The average potential in your mentioned papers may be the average electrostatic potential.  This can be obtained by do a specific average of  the calculated ElectrostaticDifferencePotential.

The chemical potential of a gas molecule is usually  calculated based on the ideal-gas approximation.  You can refer to the following webpage, which gives nice explanation on the background of the calculation of chemical  potential of a gas molecule
https://wiki.fysik.dtu.dk/ase/ase/thermochemistry/thermochemistry.html

The Fermi energy in the formation energy of  a charged defect is indeed the chemical potential of electron reservoir. Its value in the range of valence band minimum (VBM) and  conduction band maximum (CBM) is more interesting to be studied.  The VBM could be chosen as a reference for the zero energy. This is why people plot the formation energy versus Fermi energy in the range of 0 and band gap.

[fangyongxinxi]

Thanks for your reply!

It is very good to see the vacancy formation energy calculation in ATK tutorial, it helps me alot.
http://quantumwise.com/publications/tutorials/item/864-calculation-of-formation-energies

However, I still do not know how to calculate the formation energy of charged vacancy.
hope to see related tutorial.

First of all, you have to understand the physics concept (or definition) of Fermi energy (or Fermi level, particularly for the Fermi energy of a semiconductor) and chemical potential of a gas molecule.

The average potential in your mentioned papers may be the average electrostatic potential.  This can be obtained by do a specific average of  the calculated ElectrostaticDifferencePotential.

The chemical potential of a gas molecule is usually  calculated based on the ideal-gas approximation.  You can refer to the following webpage, which gives nice explanation on the background of the calculation of chemical  potential of a gas molecule
https://wiki.fysik.dtu.dk/ase/ase/thermochemistry/thermochemistry.html

The Fermi energy in the formation energy of  a charged defect is indeed the chemical potential of electron reservoir. Its value in the range of valence band minimum (VBM) and  conduction band maximum (CBM) is more interesting to be studied.  The VBM could be chosen as a reference for the zero energy. This is why people plot the formation energy versus Fermi energy in the range of 0 and band gap.

[Umberto Martinez]

Indeed we are working on it for some time now.
A description of the methodology will be published soon.
Keep you posted!

[fangyongxinxi]

Happy to know that!