*Vcd*) and Te-antisite (

*Tecd*) in CdTe, but I am struggling to get the expected formation energies in line with other works in the literature.

I want to ask what the fundamental steps are and the main points that must be considered in order to calculate the formation energy (as I feel that I must be missing something)?

What I am currently doing is as follows:

1. I assume a neutrally charged defect such that the formation energy (

*Ef*) is given by:

**Ef = Etot(D) - Etot + u(Cd) - u(Te)**

where

*Etot*is the total energy of the whole bulk system,

*Etot(D)*the energy of the total system that includes the single defect, and

*u(Cd)*and

*u(Te)*are the chemical potential energy of a single Cd atom and single Te atom respectively.

*u(Te)*is only subtracted in the case of the Te-antisite calculation of course.

2. I calculate

*Ef*using supercell sizes of 64, 216 and 512 atoms. Because of the spurious interaction between the defect in the repeating supercell due to the periodic boundary condition (PBC), the formation energy should change as a function of supercell size and reach its true value in the limit of an infinitely large supercell. Using these three points I should be able to through extrapolation approximate

*Ef*at an infinitely large supercell. Even if extrapolation is not possible, the

*Ef*obtained for a supercell of 512 atoms should be pretty close to its true value (within 0.1 eV).

3. For all total energy (

*Etot*) calculations, I relax the supercell structure until the stresses are below 10^-4 Ha/Bohr. This has proved to be a considerable challenge for the supercells containing the defect, where the difference in energy between the SCF iterations begins to increase (instead of decrease!) and the relaxation abruptly stops. I've had the most luck when I fix all of the atom positions except for the defect and its nearest neighbours and use ionmov 2 and optcell 0 (i.e. fixing the volume to that of the relaxed bulk structure and only allowing atoms which are not fixed to move).

4 a). How do you get the chemical potentials of the atoms,

*u(Cd)*and

*u(Te)*? This part I'm very unsure about (yet its something papers in the literature seem to skip over as being trivial). I believe that the condition

*u(Cd)*+

*u(Te)*=

*Etot(CdTe)*, where

*Etot(CdTe)*is the total energy of a CdTe pair, must be satisfied? Initially, for

*u(Cd)*for example, I would place a single isolated Cd atom in the middle of the unit cell with a volume fixed to that of the relaxed corresponding bulk supercell size. When I did this for Cd and Te, the condition above was not satisfied. Furthermore, for CdTe, defect formation energies are often given in terms of Cd-rich or Te-rich conditions. If I use the isolated atom approach to calculate the chemical potential energies, do I get the Cd-rich or Te-rich formation energies? Or neither?

4 b). In order to calculate the formation energy of the defects in Te-rich conditions, I determine

*u(Te)*from a calculation of bulk Te where I define a unit cell containing 3 Te atoms arranged in a trigonal lattice, and relax the structure. Then,

*u(Te)*=

*Etot(Te)*/3 and

*u(Cd)*=

*Etot(CdTe)*-

*u(Te)*. This of course satisfies the condition above.

Doing all this, the formation energies I obtain for

*Vcd*and

*Tecd*are still out by ~1-2 eV and neither is the relationship between

*Ef*and supercell size (which I plot as

*1/L*where

*L*is the cubic root of the number of atoms) linear - it appears more to plateau at the larger supercell sizes.

Some quick further questions: Am I correct in relaxing the supercell when I introduce the defect? Do I need to add a charge to the defect (and is this done using the charge variable)? Even in my current case of a neutrally charged defect am I correct in thinking there would still be spurious interaction between the supercells in the PBC due to valance electrons moving around the defect?

For context, I am using PAW datasets from the JTH table v1.1 with LDA.

Any help or tips from your own experience calculating formation energies would be greatly appreciated!

Cheers,

Kjell