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Challenges for ab initio defect modeling

Challenges for ab initio defect modeling. Peter De ák , Bálint Aradi, and Thomas Frauenheim. Bremen Center for Computational Materials Science, University of Bremen POB 330440, 28334 Bremen, Germany. Adam Gali. Dept. Atomic Physics, Budapest University of Technology & Economics

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Challenges for ab initio defect modeling

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  1. Challenges for ab initio defect modeling Peter Deák, Bálint Aradi, and Thomas Frauenheim Bremen Center for Computational Materials Science, University of Bremen POB 330440, 28334 Bremen, Germany Adam Gali Dept. Atomic Physics, Budapest University of Technology & Economics H-1521 Budapest, Hungary

  2. George D Watkins Richard P Messmer control James W Corbett How good is defect theory today? Challenging some illusions!

  3. BAND GAP & GAP STATES! “the scissor” eC eC eV eV Scissor works only for defects in the high electron density region of the perfect crystal. Shishkin&Kresse, PRB 75, 235102 (2007) Deák et al.. PRB 75, 153204 (2007) “State of the art” • Plane Waves (with UPP or PAW) up to ~240 eV. • DFT-GGA: (PBE functional) • commercial or public domain „turn-key“ package WHAT COULD POSSIBLY GO WRONG? ??

  4. Considering vertical transitions (no relaxation of ions) as in optical absorption experiments: 0 Kohn-Sham levels (w.gap error) eC Total energies (w.o. gap error) eD Eg eV Problem of charged supercells can be handled by the Makov-Payne correction [PRB 51, 4014 (1995)]. ASSUMPTIONS U. Gerstmann, P. Deák, et al. Physica B 340-342, 190 (2003). SiC:VSi The total energy is not affected by the “gap error”! Cancellation?? GGA is always successful in describing the ground state of a system. Internal ionization energies (charge transition levels) of defects can be calculated accurately as difference between total energies. Popular misapprehensions C.-O. Ambladh, U. von Barth, PRB 31, 3231 (1985) Using a correct asymptotic form of the exact exchange correlation potential it is shown that the eigenvalue of the uppermost occupied orbital equals the exact ionization potential of a finite system (atom, molecule, or a solid with a surface).

  5. LATTICE CONSTANT 4. M. Marsman et al., J. Phys.: Condens. Matter. 20, 064201 (2008): BAND GAP BULK MODULUS COHESIVE ENERGY 1. M. Städele et al., PRB 59, 10031 (1999): “most of the gap error disappears when using exact exchange in DFT”. 2. A. D. Becke, JCP 107, 8554 (1997): “mixing HF-exchange to DFT improves calculated molecular properties” 3. J. Muscat et al, Chem. Phys. Lett. 342, 397 (2001): “in solids the gap improves as well”. Hybrid functionals as etalon Present: Defect levels

  6. Neutral BI in Silicon Si64; 222; 21G* (0.12HF + 0.88PBE) Oi diffusion in Silicon Si64; 444; 21G* (0.12HF + 0.88PBE) OY Oi Oi Hybr. Hybr. GGA GGA C1h C3v eD-eV) Etot(Oy)-[Etot(Oi)+ZPE] Hybrid 0.64 2.62 0.36 2.30 GGA Experiment (270-700 °C): 2.53 eV Stavola et al., APL. 42, 73 (1983); Takeno et al., JAP 84, 3113 (1998). a) Watkins et al. PRB 12, 5824 (1975); 36, 1094 (1987) b) GGA EBEcorrected with gap level positions in Hybrid. VSi metastability in 4H-SiC Si64C64; 444; 21G* (0.2HF + 0.8PZ) LDA CB e a e a VB a a Examples

  7. LDA or GGA HF or GW SMALL CHANGES IN: GOOD CANCELLATION Implication of the previous examples: the error in energy differences between two configurations is related the error in the gap level position!Let us introduce a correction! An approximate correction Seems to work well for charge transition levels! a) K. B. Nielsen et al., PR B 65, 075205 (2002). b) Watkins et al. PRB 12, 5824 (1975); 36, 1094 (1987)

  8. CONCLUSIONS: 1. LDA or GGA give rise to an error in the band energy EBE(“gap error”), which is defect dependent. 6. There are catastrophe cases (e.g., TiO2:VO)! Cancellation when the configuration changes?? 2. The error in EBEis not – as a rule – compensated in the expression of the total energy Etot! 3. Calculated energy differences between different charge states are not – as a rule – correct! 4. If the bonding configuration does not change much, correction of the gap level in EBE is sufficient, but only then! 5. Total energy differences may be seriously wrong, for defects with different kinds of bonding configuration and levels in the gap.The ground state may not be predicted correctly! At least checks with hybrid functionals are recommended!

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