mysovsky rpc2006

Theoretical modelling of the photoconversion and aggregation of

oxygen centres in calcium fluoride

A.S. Mysovsky, E.A. Radzhabov

Institute of Geochemistry SB RAS

1a Favorsky Street, 664033 Irkutsk, Russia

M. Reichling, J. Sils

Universität Osnabrück, Fachbereich Physik

Barbarastraße 7, D-49069 Osnabrück, Germany

A.L. Shluger, P.V. Sushko

University College London, Department of Physics & Astronomy

Gower Street, London WC1E 6BT, UK

Outline

1. Calculation technique2. Overview of possible defect species3. F-centre

Ground stateOptical absorption

4. O ion5. Oxygen-vacancy dipole

Optical absorption & luminescenceReorientation

6. F- and F2A

+ centres perturbed with oxygen7. Photodissociation and recombination mechanism Conclusion

Calculation technique

GUESS calculations(P.V. Sushko, A.L. Shluger and C.R.A. Catlow, Surface Science 450, 153 (2000))

Quantum region (QM):

– modified B3LYP functional (40% HF exchange + 60% Becke).

– Basis set: 6-31G + 2 additional d-functions on calcium ions

– TD DFT for optical absorption calculations

Classical region: shell model & pair potentials (A.M. Stoneham, Handbook of interatomic potentials, AERE Harwell (1981))

Region of fixed point charges

Molecular dynamics (MD)To study the reorientation of oxygen-vacancy dipoles we used classical MD without shells.

Possible defects

VA F F

(VA)

2F

2+ F

+ e

+ VA

F

+ e

O O2

O VA

O2 VA

F O2 F O2

O VA)

2O2 V

A)

2F

2O2 F

2O2 F

2O2

Not necessarily all these defects really exist, it's just a way to build all possible species.

+ VA

+ VA

+ e

cluster Ca4F7 Ca16F33 Expt. *

F(100) || 89.29 88.15 79.0759.5 64.5 58

F(110) || - 6.24 5.14- 4.3 3.2

F(111) || - 9.63 9.75- 5.9 6.5

F(11-1) || - 1.69 1.97- 1.2 1.0

F(200) || - 2.04 1.68- 1.1 0.91

*Hayes & Stott, Proc. Roy. Soc. A 301, 313 (1967)

F-centre hyperfine couplings (G)

F(100) F(110) F(111) F(11-1) F(200)

Theory* 87.6 3.87 7.61 1.33 1.16

Expt. 65.1 5.85 0.83 0.83 0.17

Another calculation (isotropic part of hyperfine tensor, G)Stoneham, Hayes, Smith & Stott, Proc. Roy. Soc. A 306, 369 (1968)

Cluster Ca4F7 Ca4F27 Ca4F27 Ca16F33 Ca16F33 Expt.Method MP2 HF MP2 B3LYP B3LYP

Basis set 6-311G 6-311G 6-311G LANL2 6-31GF(100) || 77.6 96.7 73.2 113.3 88.15 79.07

51 71 51 87 64.5 58

F(110) || - 7.1 4.2 9.9 6.24 5.14- 4 2.1 7.1 4.3 3.2

F(111) || - 1.4 3.4 4.1 9.63 9.75- 0.4 1.8 2.1 5.9 6.5

F(11-1) || - 1 1.3 3.4 1.69 1.97- -0.15 0.3 2.3 1.2 1.0

F(200) || - - - 2.6 2.04 1.68- - - 1.5 1.1 0.91

F-centre hyperfine couplings (G) with different methods

F-centre optical absorption

Transition E, eV fosc IRREP

1s 2p 3.23 0.133 T2

1s 2s 3.48 A1

1s 3p 4.27 0.012 T2

1s 3d 4.74 E

1s ? 4.95 0.000 ?

1s 3d 5.02 T2

Delta-SCF (with symmetry constraint)E(1s 2p) = 3.12 eV

Experimental absorption band at 3.3 eV

O ion

Affinity with respect to CBE

A=3.86 eV

Hyperfine couplings of O

This work Expt.*

atom A, G axis A, G axis

O (0 0 0) -116.43 <0 0 1> 97.8 <0 0 1>

7.68 9 6

F (0 0 1) 63.79 <0 0 1> 63.6 <0 0 1>

20.69 <1 1 0> 15.4 0.5

20.39 <1 -1 0> 15.4 0.5

F (1 0 0) -3.98 <1 0 0> 3.6 0.5 <1 0 0>

-2.24 <0, 0.87, -0.49> 3.4 0.5 <0 0 1>

-2.04 <0, 0.49, 0.87> 1.2 0.8 <0 1 0>

*Bill & Silsbee, PRB 10, 2697 (1974)

Optical absorption of O ion

Hole transition to other to 2p-states of oxygenE=0.4 eV

Hole transition to VBE=7.06 eV, f=0.076

Experimental evidence of O- ion absorption is absent at present moment. It can be done if it will be possible to establish correlation between EPR signal of O- ion and some absorption band in VUV

Calcium below the plane

Calcium above the plane

Vacancy

O - ion

Energy, eV

1 – luminescence2 – excitation of the luminescence3 – absorption4 – creation5 – absorption of pure crystal6 – photodissociation spectra

Two distinct absorption bands at 6.7 and 8.5 eVThe luminescence band at 2.6 eV.E. Radzhabov, P. Figura, pss(b) 136, K55 (1986); E. Radzhabov, pss(b)136, K149 (1986)

Oxygen-vacancy dipole

2px-y

(O) 2pz(O)2p

x+y(O)

1(V)=1s(V)

2(V)

Optical absorption of the dipole

(V)

Transition E, eV fosc

2px-y(O) 1s(V) 6.38 0.019

2px+y(O) 1s(V) 6.48

2pz(O) 1s(V) 6.63 0.084

2px-y(O) 2(V) 8.10

2px+y(O) 2(V) 8.22 0.018

2pz(O) 2(V) 8.22

2pz(O) (V) 8.38 0.006

2px-y(O) (V) 8.38 0.007

8.66 0.029

8.69 0.005

8.71 0.005

8.76 0.019

8.81 0.015

One-electron

interpretation

impossible

9.00 0.021

Luminescence of the dipole

Triplet absorptionE

SCF= 6.23 eV

Triplet luminescenceE

SCF= 1.71 eV

TDDFT in the geometry of relaxed triplet1.99 eV f=0.00142.23 eV f=0.00123.00 eV f=0.1162

?

1 – luminescence2 – excitation of the luminescence3 – absorption

nonradiative transition

Reorientation/migration of the dipole

Example of <100>→<110> →<010>reorientation

Simultaneous jump of two fluorines

<100> → <200> →<100> process

Barrier for reorientationEB(<100> <110>)=0.64 eVBarrier for oxygen jumpED(O2--VA)=1.61 eV

FA(O2-)-centre


1s(V) 2px+y(V) 3.16 0.086

1s(V) 2pz(V) 3.43 0.150

1s(V) 2px-y(V) 3.46

EA=-0.49 eV

EI=4.69 eV

FA

(O2-)-centre


1s(V) 2px+y(V) 2.84 0.226

1s(V) 2pz(V) 2.93 0.116

1s(V) 2px-y(V) 3.06

EI=1.74 eV

Absorption of F2A

+-centres at4 – 130 K;1,5 – 230 K; 6 – 260 K;7 – 295 K;2,3 – after heating to 295 K

Temperature dependence of F2A

+ absorption band (3.4 eV) created by photodissociation

Photodissociation under irradiation in 2nd

band leads to the creation of FA

and F2A

+-centres.

Absorption of F2A

+ – 2.3-2.4 and 3.4 eV

Absorption of FA

– 2.8 and 3.2 eV

F2A

+(O2-)-centre

Two configurations denoted <100> and <110>In <110> spin density is completely localised on one vacancyIn <100> distributed over both vacancies.<100> configuration is energetically favourable, but not much

E=0.06 eV

e

e

<110> conf.E

A= 0.85 eV

EI = 5.98 eV

<110><100>

<100> conf.E

A= 1.45 eV

EI = 6.47 eV

2.76

6.05

ver

tica

l

ver

tica

l

ther

mal

0.86

3.38

5.31

2.03

1s(F ) 1s(VA)

Energy levels

1s(F)

EA

= Etot

(defect) – Etot

(defect + e ) – A(cryst.) (vertical affinity)E

I= E

tot(defect – e ) – E

tot(defect) – A(cryst.) (vertical ionization)

EI(thermal)= E

tot(defect – e relax.) – E

tot(defect) – A(cryst.)

A(cryst.) = Etot

(cryst.) – Etot

(cryst. + e ) (affinity of the crystal CB)

3.86

6.16

8.36

2p(O ) 2p(O2 )

10.24

4.69

-0.49

1.92

O2--VA

dipole

0.69

2p(O2-)

1s(VA)

FA(O2-)

1s(VA)

1.34

0.70

1s(VA)

FA

(O2-)

8.17

3.15

F2

+

6.47

1.45

F2A

+(O2-)

Energy levels (continued)

The photodissociation and “recombination”

The dissociation stage

The “recombination” stage

The photodissociation of dipoles is more or less clear. It occurs: 1) under irradiation in 8.4 or 9.2 eV bands 2) with higer energies (which leads to the creation of electron-hole pairs)3) under X-irradiation

The puzzling stage is «recombination».

Photodissociation occurs during irradiation in 2nd (8.4 eV) or 3rd (9.2 eV) OA bands. The mechanism includes following steps:1. Excitation from O2- to excited states of vacancy;2. Thermoionisation of electron;3. Dissociation of remaining O–VA centre;4. The electron (from step 2) is trapped on other O2--VA dipole;5. Finally the free vacancy (from step 3) is also trapped there.

Photodissociation mechanism

Conclusion

List of possible recombination channels.1. F

A(O2-) ==> F

A(O2-) + e thermoionization ( E

thermal= 0.70 eV)

2. Tunnelling recharging a) F

A(O2-) O ==> O2 V

A + O2-

Evertical

= -0.83 eV; Ethermal

= 4.24 eVb) F

A(O2-) F

2A+(O2-) ==> O2 V

A + F

2A(O2-)

Evertical


> -0.47 eVc) F

A(O2-) F

2+ ==> O2 V

A + F

2

Evertical


> 1.23 eVd) F

2A+(O2-) O ==> O2 V

A)

2 + O2-

Evertical


> 0.18 eVe) F

2A+(O2-) F

2+ ==> O2 V

A)

2 + F

2

3. Separation of vacancy from F2A

+(O2-) ?4. Migration of F

2A+(O2-) ?

Conclusion

1. Correct description of the F-centre excited and even ground states requires electronic correlation to be taken into account as well as tails of F-centre electronic density on the distances of several lattice constants from the defect. Using of B3LYP functional, all-electron basis set and relatively large quantum clusters allows to achieve qualitative and reasonable quantitative (with the relative error not more than 15% for hyperfine couplings).

2. TD DFT allows to calculate optical absorption energies with a precision of 0.1 eV (in the case of F-centre and oxygen-vacancy dipole). Such a good agreement with experiment is even suspicious, especially if we take into account that there is some controversy about TD DFT among theoreticians. However, we believe such a good precision can not be just a coincidence.

3. O ion should have an optical absorption band in VUV region about 7 eV.

4. Possible channels of oxygen-vacancy dipoles recombination are discussed.