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Next: 8.8 Band decomposed chargedensity Up: 8 Special switches for Previous: 8.6 MonopoleDipole and

8.7 Dipole corrections for defects in solids

Similar to the case of charged atoms and molecules in a large cubic box also charged defects in semiconductors impose the problem of potentially slow convergence of the results with respect to the supercell size due to spurious electrostatic interaction between defects in neighboring supercells. Generally, the errors are less dramatic than for charged atoms or molecules since the charged defect is embedded in a dielectric medium (bulk) and all spurious interactions between neighboring cells are scaled down by the bulk dielectric constant tex2html_wrap_inline4765 . Hence, the total error might remain small (order of 0.1 eV) and one has not to worry too much about spurious electrostatic interactions between neighboring cells. However, there exist three critical cases where one should definitely start to worry (and to apply dipole corrections):

The worst case one can ever think of is that all three conditions mentioned above are fulfilled simultaneously. In this case the corrections can amount to the order of several eV (instead of the otherwise typical order of few 0.1 eV)!

In principle it is possible to apply the same procedure as in the case of charged atoms and molecules in vacuum. However, with the current implementation one has to care about following things and following restrictions apply:

Besides charged defects there's another critical type of defects which may cause serious trouble (and for which one should also apply dipole corrections): neutral defects or defect complexes of low symmetry. For such defects a dipole moment may occur leading to considerable dipole-dipole interactions. Though they fall off like tex2html_wrap_inline4373 they might not be negligible (even for somewhat larger cells!) if the induced dipole moment is rather large. The worst case that can happen is a defect complex with two (or more) rather distant defects (separated by distances of the order of nearest-neighbor bond lengths or larger) with a strong charge transfer between the defects forming the complex (e.g., one defect might possess the charge state 2+ and the other one the charge state 2-). This can easily happen for defect complexes representing acceptor-donor pairs. The most critical cases are again given for semiconductors with rather small lattice constants, rather small dielectric constants of for any defect complex causing strong charge transfers. Again the same restrictions and comments hold as stated above for charged cells: you may currently only use cubic cells, LDIPOL=.FALSE. and you have to rescale the correction printed in OUTCAR by the bulk dielectric constant tex2html_wrap_inline4765 (i.e., the printed energies are again meaningless and have to be corrected ``by hand''). There is only one point which might help: since in cubic cells any dipole moment can only be defect-induced no additional corrections are necessary (in contrast to the monopole-quadrupole energies of charged cells). However, the other bad news is: for such defect complexes it may sometimes be hard to find the correct ``center of mass'' (input DIPOL=... in INCAR!) for the defect induced charge perturbation (it's usually more easy for single points defect since usually DIPOL=position of the point defect is the correct choice). This introduces some uncertainties and one might try different values for DIPOL (the one giving the minimum correction should be the correct one). But also note: DIPOL is internally aligned to the position of the closest FFT-grid point in real space. Hence, the position DIPOL is only determined within distances corresponding to the FFT-grid spacing (controlled by NG*F). As an additional note this might also play a certain role if for charged single point defects the position of the defect is not chosen to be (0,0,0)! In this case DIPOL might correspond to a position lying slightly off the position of the defect what may also introduces inaccuracies in the calculation of the electrostatic interactions (i.e., apparent dipole moments may occur which should be zero if the correct position DIPOL would have been chosen). In this case you should whenever possible try to adjust your FFT-grid in such a way that the position of the defect matches exactly some FFT-grid point in real space or otherwise never use any other (point) defect position than (0,0,0) ... .

A final note has to be made: besides the electrostatic interactions there exist also spurious elastic interactions between neighboring cells which (according to a simple ``elastic dipole lattice model'') should scale like tex2html_wrap_inline4373 (leading order). Therefore, the corrected values may still show a certain variation with respect to the supercell size. One can check the relaxation energies (elastic energies) separately by calculating (and correcting) also unrelaxed cells (defect plus remaining atoms in their ideal bulk positions). If the k-point sampling is sufficient to obtain well-converged results (with respect to the BZ-integration) one might even try to extrapolate the elastic interaction energies empirically by plotting the relaxation energies versus tex2html_wrap_inline4373 (hopefully a linear function - if not try to plot it against tex2html_wrap_inline4793 and look whether it matches a linear function) and taking the value for tex2html_wrap_inline4795 (i.e. the axis offset). However, usually the remaining errors due to spurious elastic interactions can be expected to be small (rarely larger than about 0.1 eV) and the extrapolation towards tex2html_wrap_inline4908 may also be rather unreliable if the results are not perfectly converged with respect to the k-point sampling (though one should note that this may then hold for the electrostatic corrections too!).


next up previous contents
Next: 8.8 Band decomposed chargedensity Up: 8 Special switches for Previous: 8.6 MonopoleDipole and

MASTER USER VASP
Mon Mar 29 10:38:29 MEST 1999