ab initio Peter Deák , Bálint Aradi, and Thomas Frauenheim
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Transcript ab initio Peter Deák , Bálint Aradi, and Thomas Frauenheim
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
Peter Deák
[email protected]
Challenges for ab initio defect modeling. EMRS Symposium I, 2008
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George D Watkins
Richard P Messmer
control
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How good is defect theory today?
Challenging some illusions!
James W Corbett
Peter Deák
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“State of the art”
• Supercell:
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QuickTim e™ and a
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QuickTim e™ and a
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QuickTim e™ and a
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QuickTim e™ and a
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QuickTim e™ and a
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QuickTim e™ and a
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QuickTim e™ and a
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QuickTim e™ and a
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QuickTim e™ and a
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Nr. of Atoms
64
128
216
256
Nr. of k points
43
23
1
1
• Plane Waves (with UPP or PAW ) up to ~240 eV.
• DFT-GGA: (PBE functional)
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WHAT COULD POSSIBLY GO WRONG?
BAND GAP & GAP STATES!
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“the scissor”
eC
eV
Shishkin&Kresse, PRB 75, 235102 (2007)
Peter Deák
eC
??
eV
Scissor works only for defects in the high electron density region of the perfect crystal.
Deák et al.. PRB 75, 153204 (2007)
[email protected]
Challenges for ab initio defect modeling. EMRS Symposium I, 2008
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Popular misapprehensions
1.
2.
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.
Considering vertical transitions (no relaxation of ions) as in optical absorption experiments:
0
I eC eD Eg eD eV
eC
E
I Egexptl ED ED0 E perf E 0perf
eD
g
eV
Kohn-Sham levels (w.gap error)
Total energies (w.o. gap error)
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).
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).
SiC:VSi
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The total energy is not affected by the “gap error”!
Cancellation??
Peter Deák
Etot ni ei Edc
E BE
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Challenges for ab initio defect modeling. EMRS Symposium I, 2008
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Hybrid functionals as etalon
1.
2.
3.
M. Städele et al., PRB 59, 10031 (1999): “most of the gap error disappears when using exact exchange in DFT”.
A. D. Becke, JCP 107, 8554 (1997): “mixing HF-exchange to DFT improves calculated molecular properties”
J. Muscat et al, Chem. Phys. Lett. 342, 397 (2001): “in solids the gap improves as well”.
4.
M. Marsman et al., J. Phys.: Condens. Matter. 20, 064201 (2008):
LATTICE CONSTANT
1 HF
4
+
3 PBE
4
= PBE0
hybrid exchange
BAND GAP
Present:
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BULK MODULUS
0.12HF + 0.88PBE
Exptl.
Eg
1.16
1.17
G25’-G2’
4.21
4.19
VB
12.65
12.6
a0
5.466
5.431
Eb
4.95
4.75
B
0.99
0.99
Defect levels
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COHESIVE ENERGY
Peter Deák
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eD-eV
LDA
G0W0
Hybrid
Si: HBC (0)
+0.61
+1.05
+1.08
Si: HAB (-)
-0.07
+0.10
+0.05
4H-SiC: HAB (-)
+0.50
+0.62
+0.54
3C-SiC: BSi+2Ci (+)
-0.12
+0.04
+0.10
3C-SiC: BSi+2Ci (-)
+0.18
+0.26
+0.29
Challenges for ab initio defect modeling. EMRS Symposium I, 2008
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Examples
Neutral BI in Silicon
Oi diffusion in Silicon
Si64; 222; 21G* (0.12HF + 0.88PBE)
Si64; 444; 21G* (0.12HF + 0.88PBE)
OY
Oi
Oi
Hybr.
Hybr.
GGA
eD-eV)
Etot(Oy)-[Etot(Oi)+ZPE]
2.62
2.30
GGA
Hybrid
GGA
C3v
C1h
0.64
0.36
Experiment (270-700 °C): 2.53 eV
Stavola et al., APL. 42, 73 (1983); Takeno et al., JAP 84, 3113 (1998).
GGA
Hybrid
Expt.a)
Stable (0)
C3v
C1h
C1h
E(+/0)
0.66
0.94b)
0.99
E(0/-)
0.55
0.66b)
0.75
a) Watkins et al. PRB 12, 5824 (1975); 36, 1094 (1987)
b) GGA EBE corrected with gap level positions in Hybrid.
VSi metastability in 4H-SiC
Si64C64; 444; 21G* (0.2HF + 0.8PZ)
CB
e
VB a
a
LDA
e
a
3V
Si
occupation
E(3VSi) - E(VC+Csi)
LDA
Hybrid
GW
a(1), e(1)
e(2), a(0)
e(2), a(0)
2.25
1.19
a
Peter Deák
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Challenges for ab initio defect modeling. EMRS Symposium I, 2008
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An approximate correction
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!
VB
Etot nD D nii
12 VH rrdr E XC r VXC rrdr
i
E dc
E BE
HF or GW
GGAor LDA
D DHF or GW VBM
DGGAor LDA VBM
LDA or GGA
HF or GW
Total Energy
Difference
LDA
“Marker”
HF-corrected
LDA
Hybrid
Exptl.a)
Seems to work well for
charge transition levels!
Si: HBC(+/0)
+0.54
+0.83
+0.98
+0.94
+0.94
Si: BI (+/0)
+0.66
a) K. B. Nielsen et al., PR B 65, 075205 (2002). b) Watkins
GOOD CANCELLATION
+0.94
+0.99
et al. PRB 12, 5824 (1975); 36, 1094 (1987)
SMALL CHANGES IN:
Peter Deák
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Challenges for ab initio defect modeling. EMRS Symposium I, 2008
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Cancellation when the configuration changes??
VB
Etot nD D nii 12 VH rrdr E XC r VXC rrdr EBE Edc
i
Si64
a-b
E
a
b
EBE
EBE
a
dc
b
Edc
a
b
Etot
Etot
e
nDa eDa eDa
nDb
b
D
eDb
Si64C64
HBC(0) – HAB(0)
OY(0) –Oi(0)
-0.04
+0.51
+1.08
+0.05
-0.21
-1.83
+0.01
+0.30
-0.75
+0.19
+0.27
-1.89
3V (0)
Si
– VC+CSi(0)
CONCLUSIONS:
1. LDA or GGA give rise to an error
in the band energy EBE (“gap
error”), which is defect dependent.
2. The error in EBE is 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!
6. There are catastrophe cases (e.g., TiO2:VO)!
Peter Deák
At least checks with hybrid functionals are recommended!
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Challenges for ab initio defect modeling. EMRS Symposium I, 2008
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