Density functional theory calculations on the diamond ...
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Density functional theory calculations on the diamond nitrogen-vacancy center Robin L¨ ofgren, Ravinder Pawar, Sven ¨ Oberg and J. Andreas Larsson Applied Physics, Division of Materials Science, Department of Engineering Sciences and Mathematics, Lule˚ a University of Technology, SE-971 87 Lule˚ a, Sweden The diamond NV-center • Color center containing atomic nitrogen and a vacancy, situated on neighbouring vacancy positions. • Formed by irradiation (creating vacancies), followed by annealing (make vacancies move to nitrogens) • Can be in a neutral or negative state. The negative state is the most well researched and promising • Exhibits a zero-phonon line at 1.945 eV under optical excitation • The process of optical excitation and decay results in a preferential occupation of the S z = 0 ground state level • Have long spin lattice lifetime • The two previous properties makes the NV-center a promising candidate for quantum information applications Our research • Looking at how properties change by changing external conditions • Calculations on supercells and slabs • Comparing the hybrid HSE06 potential with the GGA potential PBE • Interested in applications like a qubit close to a surface, and the NV-center as a sensor close to a surface Distance to donor nitrogen in a supercell • How the electronic levels shift when varying the distance to the electron donator nitrogen • At what distance the NV-center is ”destroyed” (shifting more than 20 percent) • Placing donor N on the C 3 symmetry axis or perpendicular (on the side) to C 3 . Different types of surfaces and terminations • (001), (110) and (111) oriented surfaces investigated • Terminations include H, F, OH and clean • Reconstructed surfaces • Putting a molecule on surface HSE06 vs PBE • DFT underestimates the bandgap • Using HSE06 to widen the bandgap • Experimental bandgap of bulk diamond is 5.4 eV • PBE gives 4.171 eV • HSE06 gives 5.268 eV Conclusions and future work • N-N distance influence transition energies • Need to use HSE06 instead of PBE • Study the NV-center interaction with other diamond defects beside N • Study how the NV-center interact with different functionalizations of the surface Acknowledgements • Swedish Research Council • Swedish National Infrastructure for Computing (SNIC) I HPC2N I PDC I NSC NV-center in bulk diamond, supercell calculations Calculations on the diamond NV-center placed in a supercell, with a substitutional ni- trogen placed a distance from the NV-center, acting as an electron donor. Looking at how the transition energy between the v and e electronic levels are affected by placing the donor nitrogen at different dis- tances from the NV-center, as well as different orientations with respect to the C 3 symmetry axis. Computational method: • Vienna ab Initio Simulation Package (VASP) • PAW PBE potentials • Gamma centered k-point grid • 512 & 216 atom supercells Figure 1: Energy levels belonging to the NV-center 7 8 9 10 11 12 1.44 1.45 1.46 1.47 1.48 1.49 1.5 1.51 1.52 N-N distance (Å) Transition energy v-e (eV) NV-N NV - Figure 2: Transition energy between v and e levels for NV-N configuration in 512 atom supercell 20 30 40 50 60 70 1.46 1.48 1.5 1.52 1.54 1.56 1.58 Angle from C 3 axis (degrees) Transition energy v-e (eV) Symmetry br. NV - Figure 3: Transition energy between v and e levels for symmetry breaking in 216 atom supercell 3 A 2 3 E m s = 0 m s = +-1 u 2 v 2 e 2 u 2 v 1 e 3 m s = 0 m s = +-1 u 2 v 2 e 1 w 1 ZPL = 1.945 eV 1 E Figure 4: The groundstate 3 A 2 , the excited state 3 E, and the ZPL corresponding to the v-e transition 5 6 7 8 9 10 1.5 1.52 1.54 1.56 1.58 N-N distance (Å) Transition energy v-e (eV) N-NV NV - Figure 5: Transition energy between v and e levels for N-NV configuration in 512 atom supercell 3 4 5 6 7 8 9 10 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 N-N distance (Å) Transition energy v-e (eV) Side v-e 1 NV - Side v-e 2 Figure 6: Transition energy between v and e levels for side configuration in 512 atom supercell. Splitting of e-levels occurs because of the symmetry breaking 3 A 2 groundstate: u 2 v 2 e 2 3 E excited state associated with ZPL: u 2 v 1 e 3 V C 3 axis Figure 7: The diamond NV-center Surfaces, slab calculations Figure 8: (100), (110), and (111) surfaces Workfunction: Φ= E vac - f 0 50 100 Distance (Å) -20 -15 -10 -5 0 Electrostatic Potential (eV) Workfunction (eV) Figure 9: Workfunction for a small 16-carbon atom F-terminated (110)-slab Table 1: PBE Energies (eV), large diamond slabs with NV defect Surface Termination N-N dist. ( ˚ A) Energy gap v-e Workfunction (up) Workfunction (down) 100, Clean 4.2979 1.896 2.881 360 atoms, 5.0486 1.894 2.892 20 layers 8.8741 1.858 2.901 H term. 4.2979 3.150 1.501 2.023 1.965 5.0486 3.052 1.466 2.441 1.810 8.8741 3.076 1.377 1.992 1.997 F term. 4.2979 3.700 1.547 3.084 2.393 5.0486 3.922 1.497 2.866 2.615 8.874 3.6392 1.418 2.281 3.155 110, Clean 4.374 2.367 2.367 384 atoms, 5.052 2.345 2.377 14 layers 9.108 2.410 2.410 H term. 4.374 2.613 1.525 1.931 2.048 5.052 2.541 1.419 2.016 1.948 9.108 2.572 1.314 2.200 1.803 F term. 4.374 4.2432 1.667 3.128 2.623 5.052 4.2584 1.540 2.840 2.841 9.108 3.7304 1.458 2.191 3.379 111, Clean 4.950 4.839 4.780 384 atoms, 6.322 4.769 4.782 14 layers 7.695 4.764 4.944 H term. 4.950 2.948 1.636 1.445 1.565 6.322 2.918 1.419 1.308 1.348 7.695 2.919 1.427 1.391 1.431 F term. 4.950 3.494 1.723 4.409 5.859 6.322 3.775 1.413 5.183 6.080 7.695 3.755 1.427 5.143 6.012 References H. Pinto, R. Jones, D.W. Palmer, J.P. Goss, Amit K. Tiwari, P.R. Briddon, Nick G. Wright, Alton B. Horsfall, M.J Rayson, S. ¨ Oberg, Phys. Rev. B 86 045313 (2012) H. Pinto, R. Jones, D.W. Palmer, J.P. Goss, P.R. Briddon, S. ¨ Oberg, Phys. Status Solidi A 208 No. 9 2045-2050 (2011) J.A. Larsson, P. Delaney, Phys. Rev. B 77 165201 (2008)
Transcript of Density functional theory calculations on the diamond ...
Density functional theory calculations on thediamond nitrogen-vacancy center
Robin Lofgren, Ravinder Pawar, Sven Oberg and J. Andreas LarssonApplied Physics, Division of Materials Science, Department of Engineering Sciences and Mathematics, Lulea University of Technology, SE-971 87
Lulea, Sweden
The diamond NV-center
• Color center containing atomic nitrogenand a vacancy, situated on neighbouringvacancy positions.
• Formed by irradiation (creatingvacancies), followed by annealing (makevacancies move to nitrogens)
• Can be in a neutral or negative state. Thenegative state is the most well researchedand promising
• Exhibits a zero-phonon line at 1.945 eVunder optical excitation
• The process of optical excitation anddecay results in a preferential occupationof the Sz = 0 ground state level
• Have long spin lattice lifetime
• The two previous properties makes theNV-center a promising candidate forquantum information applications
Our research
• Looking at how properties change bychanging external conditions
• Calculations on supercells and slabs
• Comparing the hybrid HSE06 potentialwith the GGA potential PBE
• Interested in applications like a qubit closeto a surface, and the NV-center as asensor close to a surface
Distance to donor nitrogen in asupercell
• How the electronic levels shift whenvarying the distance to the electrondonator nitrogen
• At what distance the NV-center is”destroyed” (shifting more than 20percent)
• Placing donor N on the C3 symmetry axisor perpendicular (on the side) to C3.
Different types of surfaces andterminations
• (001), (110) and (111) oriented surfacesinvestigated
• Terminations include H, F, OH and clean
• Reconstructed surfaces
• Putting a molecule on surface
HSE06 vs PBE
• DFT underestimates the bandgap
• Using HSE06 to widen the bandgap
• Experimental bandgap of bulk diamond is5.4 eV
• PBE gives 4.171 eV
• HSE06 gives 5.268 eV
Conclusions and future work
• N-N distance influence transition energies
• Need to use HSE06 instead of PBE
• Study the NV-center interaction withother diamond defects beside N
• Study how the NV-center interact withdifferent functionalizations of the surface
Acknowledgements
• Swedish Research Council
• Swedish National Infrastructure forComputing (SNIC)
I HPC2N
I PDC
I NSC
NV-center in bulk diamond, supercell calculations
Calculations on the diamond NV-centerplaced in a supercell, with a substitutional ni-trogen placed a distance from the NV-center,acting as an electron donor.
Looking at how the transition energy betweenthe v and e electronic levels are affected byplacing the donor nitrogen at different dis-tances from the NV-center, as well as differentorientations with respect to the C3 symmetryaxis.
Computational method:
• Vienna ab Initio Simulation Package(VASP)
• PAW PBE potentials• Gamma centered k-point grid• 512 & 216 atom supercells
Figure 1: Energy levels belonging to the NV-center
7 8 9 10 11 121.44
1.45
1.46
1.47
1.48
1.49
1.5
1.51
1.52
N−N distance (Å)
Tra
nsiti
on e
nerg
y v−
e (e
V)
NV−N
NV−
Figure 2: Transition energy between v and e levels forNV-N configuration in 512 atom supercell
20 30 40 50 60 701.46
1.48
1.5
1.52
1.54
1.56
1.58
Angle from C3 axis (degrees)
Tra
nsiti
on e
nerg
y v−
e (e
V)
Symmetry br.
NV−
Figure 3: Transition energy between v and e levels forsymmetry breaking in 216 atom supercell
3A2
3E
ms = 0ms = +-1
u2v2e2
u2v1e3ms = 0ms = +-1 u2v2e1w1
ZPL = 1.945 eV
1E
Figure 4: The groundstate 3A2, the excited state 3E,and the ZPL corresponding to the v-e transition
5 6 7 8 9 10
1.5
1.52
1.54
1.56
1.58
N−N distance (Å)
Tra
nsiti
on e
nerg
y v−
e (e
V)
N−NV
NV−
Figure 5: Transition energy between v and e levels forN-NV configuration in 512 atom supercell
3 4 5 6 7 8 9 101.48
1.5
1.52
1.54
1.56
1.58
1.6
1.62
N−N distance (Å)
Tra
nsiti
on e
nerg
y v−
e (e
V)
Side v−e1
NV−
Side v−e2
Figure 6: Transition energy between v and e levels forside configuration in 512 atom supercell. Splitting ofe-levels occurs because of the symmetry breaking
3A2 groundstate: u2v2e2
3E excited state associated with ZPL: u2v1e3
V
C3 axis
Figure 7: The diamond NV-center
Surfaces, slab calculations
Figure 8: (100), (110), and (111) surfaces
Workfunction: Φ = E vac − εf
0 50 100Distance (Å)
-20
-15
-10
-5
0
Ele
ctro
stat
ic P
oten
tial (
eV)
Workfunction (eV)
Figure 9: Workfunction for a small 16-carbon atom F-terminated(110)-slab
Table 1: PBE Energies (eV), large diamond slabs with NV defect
Surface Termination N-N dist. (A) Energy gap v-e Workfunction (up) Workfunction (down)100, Clean 4.2979 1.896 2.881360 atoms, 5.0486 1.894 2.89220 layers 8.8741 1.858 2.901
H term. 4.2979 3.150 1.501 2.023 1.9655.0486 3.052 1.466 2.441 1.8108.8741 3.076 1.377 1.992 1.997
F term. 4.2979 3.700 1.547 3.084 2.3935.0486 3.922 1.497 2.866 2.6158.874 3.6392 1.418 2.281 3.155
110, Clean 4.374 2.367 2.367384 atoms, 5.052 2.345 2.37714 layers 9.108 2.410 2.410
H term. 4.374 2.613 1.525 1.931 2.0485.052 2.541 1.419 2.016 1.9489.108 2.572 1.314 2.200 1.803
F term. 4.374 4.2432 1.667 3.128 2.6235.052 4.2584 1.540 2.840 2.8419.108 3.7304 1.458 2.191 3.379
111, Clean 4.950 4.839 4.780384 atoms, 6.322 4.769 4.78214 layers 7.695 4.764 4.944
H term. 4.950 2.948 1.636 1.445 1.5656.322 2.918 1.419 1.308 1.3487.695 2.919 1.427 1.391 1.431
F term. 4.950 3.494 1.723 4.409 5.8596.322 3.775 1.413 5.183 6.0807.695 3.755 1.427 5.143 6.012
ReferencesH. Pinto, R. Jones, D.W. Palmer, J.P. Goss, Amit K. Tiwari, P.R. Briddon, Nick G. Wright, Alton B. Horsfall, M.J Rayson, S. Oberg, Phys. Rev. B 86 045313 (2012)H. Pinto, R. Jones, D.W. Palmer, J.P. Goss, P.R. Briddon, S. Oberg, Phys. Status Solidi A 208 No. 9 2045-2050 (2011)J.A. Larsson, P. Delaney, Phys. Rev. B 77 165201 (2008)
