The refinement of self-trapped excitons

structure in CaF2 and SrF2 crystals: an ab initio study

Andrey S. Mysovsky, Evgeny A. Radzhabov

Vinogradov Institute of

Geochemistry SB RAS

1a Favorsky Street, 664033 Irkutsk, Russia

I. Motivation

Short-wave excitonic luminescence bands

Short-wave excitonic luminescence bands

Thermal quenching of the

new bands

Short-wave excitonic luminescence bands

Crystal Main bands New bands

BaF2 4.25 eV 5.05 eV

SrF2 4.4 eV 5.33 eV

CaF2 4.5 eV 5.66 eV

•New bands are not influenced by impurities in wide concentration

range (in contrast to the quenching of main bands)

•New bands disappear in temperature region 90-150K

•The exciton configuration responsible for these bands must have

the formation mechanism different from that of normal STE

II. Calculation method

Calculation method

Quantum cluster:

•BH&HLYP density functional

•6-31G basis set, +2d functions

on cations

Classical region:

•Buckingham pair potentials

Interface

•LANL1 ECPs on cations to avoid the distortions of electronic

density by positive point charges

Code

•Modified PC GAMESS 7.12

F-centre

CaF2 SrF2

Calc. Expt. Calc. Expt.

F(100) 65.4 65.14 44.0 43.39

F(110) 4.7 3.86 3.3 3.45

F(111) 7.8 7.61 10.4 10.58

F(11ī) 1.9 1.33 1.1 1.24

F(200) 1.4 1.16 0.6 0.69

Aiso - Isotropic Fermi contact couplings (G)

Spin density

VK-centre

Aiso for VK-centre (G)

CaF2 SrF2

Calc. Expt. Calc. Expt.

F(00½) 336 332.3 332.9 329

F(00 1½) 4.4 5-8 1.9 2-4

Experimental data where not explicitly cited is taken from

K.S. Song, R.T. Williams, Self-Trapped Excitons, Springer-

Verlag (1993)

III. Off-centre STE

Off-centre STE

M Adair, C H Leung, K S Song,

J. Phys. C: Solid State Phys. 18

(1985) L909-L913

I

III

II

IV

Off-centre STE

Conf. I II IV

Electron

MO

Hole

MO

E (eV)

CaF2

SrF2

0.00

0.00

0.23

0.28

0.40

0.36

Off-centre STE

Calculated Expt.

R(F2¯), Å Aiso, G Biso , G Aiso, G Biso , G

I 1.96 319 272

CaF2 II 1.95 404 291 386.7 314.3

IV 1.95 376 282

I 2.02 330 271

SrF2 II 1.96 385 298 409.7 318.3

IV 1.96 347 261

Aiso – hyperfine coupling for interstitial fluorine

Biso – for lattice fluorine bonded to interstitial

Ground state parameters

Off-centre STE

Luminescence energies

Triplet

lumin. (eV)

TDDFT

energy (eV)

fosc Expt.

lumin. (eV)

I 2.34 2.14 0.028

CaF2 II 3.62 3.73 0.004 4.5

IV 2.88 3.20 0.057

I 1.88 1.75 0.029

SrF2 II 3.24 3.44 0.002 4.4

IV 2.42 2.72 0.041

IV. On-centre STE

On-centre STE

K.Tanimura, Phys. Rev. B, 63, 184303, 2001

On-centre STE

Electron MO Hole MOC

aF

2S

rF2

On-centre STE

CaF2 SrF2

F(00½) 480 490

F(00 1½) 117 95

F(10½) 104 94

Formation

energy, eV

9.5 7.1

Luminescence

energy, eV

6.57 6.31

Aiso, G

V. Electron self-trappinghypothesis

Electron self-trapping

•First discussed in: C.R.A. Catlow, J. Phys. C: Solid State Phys.,

12, 969 (1979)

•Stable according to our calculations

Trigonal symmetry (C3V)

FI – vacancy distance = 2.32 Å

FI – central interstitial

position distance = 0.06 Å

9.1%

6.6%

5.1%

5.3%

6.6%

5.3%

9.1%

Electron self-trapping

•Self-trapping of electron is (according to calculations)

energetically favorable. The energy gain ≈ 0.3 eV

•This value may be within the calculation error and is not to be

taken as absolute truth

•The barrier for self-trapping EB ≈ 0.3 eV

•The existence of barrier and two minima (corresp. to conductive

band electron and self-trapped electron) has been checked in

several clusters.

Electron self-trapping

Hyperfine portrait (Aiso, G)

CaF2 SrF2

FI 61.5 52.9

F(100) 36.7 16.8

F(ī00) 112.0 96.4

Electron self-trapping

Conclusion

There is a new excitonic band in CaF2, SrF2 and BaF2 crystals about 1

eV higher the main band of STE luminescence.

Its intensity does not depend on impurities in wide range of impurity

concentration, in contrast to the quenching of main bands.

The defect specie responsible for this band must differ from usual off-

centre STE by the formation mechanism.

On-centre STE (VK+e) should have the luminescence sufficiently higher

then the energy of new band. Besides, on-centre STE is unstable and relaxes

into off-centre configuration after overcoming very small energy barrier.

It follows from calculation results that self-trapping of electron is possible

in CaF2 and SrF2 crystals. Self-trapped electron is a centre with trigonal

symmetry and can be considered as perturbed F-centre. There is a barrier

for self-trapping about 0.3 eV.

It can be tentatively suggested that self-trapped electrons are the

precursors of yet unknown excitonic configuration responsible for the new

luminescence bands.

Thank you!

Acknowledgements:

• Alex A. Granovsky (http://classic.chem.msu.su/gran/gamess/index.html) for the source code of PC GAMESS 7.12

• Institute of System Dynamics SB RAS for granting access to BLACKFORD supercomputer facility

• Alexandra Myasnikova for preparing nice schematic picture

• RBFR for the possibility to be here now (travel grant 09-02-09332-моб_з)