M. V. Lalic and S. O. SouzaM. V. Lalic and S. O. Souza

Universidade Federal de SergipeUniversidade Federal de Sergipe

Aracaju, BrazilAracaju, Brazil

Scintillators: convert the energy of incoming radiation into emission of light.

Used as detectors in:

scientific research: high energy and

nuclear physics industry: quality control, oil

exploration, airport security…

medicine: positron emission tomography (PET), computer

tomography…

The process of detection of the radiationThe incident radiation energy is converted into excitation energy of atoms, creating a large number of electron-hole pairs in the material.The electron-hole pairs recombine, transferring the energy to the luminescent ion which is promoted to excited state.The luminescent ion returns to the ground state, emitting a radiation in the visible or the UV range.The emitted radiation is detected by the photodiode or photomultiplier.

Photomultiplier tube

Anode

Desired characteristics of the scintillators:

transparency high density radiation hardness large light output short decay time

3 aspects of the scintillation process to understand :

1.) Absorption of the incoming radiation2.) Transfer of the absorbed energy to the luminescent

centers3.) Emission process

Discovered by Weber, Discovered by Weber, Monchamp 1973Monchamp 1973Main component of high Main component of high resolution positron resolution positron emission tomography (PET)emission tomography (PET)Used in the largest Used in the largest electromagnetic calorimeter electromagnetic calorimeter in the world (CERN – in the world (CERN – Geneva)Geneva)

BiBi33GeGe44OO12 12 – – Bismuth orto Bismuth orto

germanate (BGO)germanate (BGO)

BGO: Good characteristicsBGO: Good characteristicsHigh density (7,13 g/cmHigh density (7,13 g/cm33))Short radiation lengthShort radiation lengthLarge light output (9000 photons/MeV)Large light output (9000 photons/MeV)Large hardness (5 Mohs)Large hardness (5 Mohs)Low afterglowLow afterglowAbsence of hygroscopicity and cleavageAbsence of hygroscopicity and cleavageCrystal growth refined to a high degree of perfectionCrystal growth refined to a high degree of perfection

BGO: drawbacksBGO: drawbacksLong decay time (~300ns) Long decay time (~300ns) speed too slow for some speed too slow for some applicationsapplicationsRadiation hardness not sufficient in some applicationsRadiation hardness not sufficient in some applicationsHigh cost due to GeHigh cost due to Ge

BiBi33SiSi44OO1212 – Bismuth orto silicate (BSO) – Bismuth orto silicate (BSO) The same crystal structure as BGO, SiThe same crystal structure as BGO, SiGeGe

Much faster response (~100ns)Much faster response (~100ns)

Lower costLower cost

But:But:

smaller light output (1/5 of the BGO)smaller light output (1/5 of the BGO)

Other characteristics very similar to the BGOOther characteristics very similar to the BGO

BSO can substitute the BGO in some BSO can substitute the BGO in some applicationsapplications

BGO and BSO luminescence: state of knowledgeBGO and BSO luminescence: state of knowledge

A lot of experimental workA lot of experimental workAlmost no theoretical studiesAlmost no theoretical studies

Both are intrinsic scintillators

Emission assigned to Bi3+ ion: 3P11S0 transition (Weber, 1973)(Weber, 1973)

Transparent from ~300 to 6000nmTransparent from ~300 to 6000nm

M. Cobayashi et al, Nucl. Instr. And Meth. 372 (1996) 45-50

Emission spectra:

1. wide, due to extensive Stokes shift of the Bi

2. Peak maximum at 480nm (blue light)

Transmission spectraTransmission spectra

Ishii et al. Optical Materials 19 (2002) 201–212

Absorption edge: 286 nm

Band gap Eg = 4,34 eV

P. Kozma et al, Nucl. Instr. and Meth. A 501 (2003) 499

Absorption edge: 300 nm

Band gap Eg = 4,13 eV

Absorption spectraAbsorption spectra

Weber et al. J. Appl. Phys. 44 (1973) 5495

BGO BSO

?

Conduction band

Valence band

Electronic transition studied so far:Electronic transition studied so far:

Valence band – impurity levelsValence band – impurity levels

Valence band – exciton levelsValence band – exciton levels

Missing:Missing:

Valence band – conduction band Valence band – conduction band

electronic transitionselectronic transitions

This work:This work:

Theoretical study of the BGO and BSO electronic structureTheoretical study of the BGO and BSO electronic structure

Calculation of their optical properties determined by valence band – Calculation of their optical properties determined by valence band –

conduction band electronic transitionsconduction band electronic transitions

OutlineOutline

Basics about the calculation methodBasics about the calculation method

Results of the calculations and conclusionsResults of the calculations and conclusions

Possible improvement of the theoretical descriptionPossible improvement of the theoretical description

TheoryTheory

How to solve the quantum How to solve the quantum many-body problem?many-body problem?

Complete: non-relativistic Hamiltonian: impossible to

solve! What to do?

nnnnr ΨEΨH

n21n21n R,...,R,R,r,...,r,rΨ

Seek for Seek for approximate approximate

solutions!solutions!

non-relativisticnon-relativisticHamiltonianHamiltonian

nreH

Sucessive approximations:Sucessive approximations:

full relativisticfull relativisticHamiltonianHamiltonian

fixedfixednucleinuclei

One electron One electron HamiltonianHamiltonian

Grond stateGrond stateElectronicElectronicstructurestructure

RelativisticRelativisticeffectseffects

NuclearNuclearmotionmotion

Higher-orderHigher-ordereffectseffects

ExcitedExcitedstatesstates

rH nrH nreH ih

Born – OpenheimerApproximation

One-electronapproximation

One-electron approximation:

-- constructs an effective potential for each individual electron in solid

-- many-body Hamiltonian is replaced by a set of Hamiltonians

describing non-interacting particles

i

inre hH

effr

2i

2

i V2m

h

Hartree-Fock Theory (HFT)

Density Functional Theory (DFT)

Green-function technique

Realized by:

description of the electronic

ground state

Perturbationtheory

Partial recuperation of the neglected effects (nuclear

motion, spin orbit, …)

,

1

DFT: Two theorems of Hohenberg and KohnDFT: Two theorems of Hohenberg and Kohn

ρ00 EΨHΨE

Electronic ground

state density

1 : 1 Potential of the nuclei

Vext

Total ground-state energy

is unique functional of !

2 ρE reaches its minimum when is the true ground-state density

ConsequencesConsequences

zy,x,ρR,...,R,r,...,rΨ M1N1o

2

The enables the application of the variation principle

Introducing a set of one-electron orbitals

and varying E with respect to

rψi

i

2

i rψrρ

rψεrψV2m iii

effr

22

Kohn-Sham

Equations

rxcrceffr VVV

How to solve Kohn-Sham equations?How to solve Kohn-Sham equations?

rext0

rc V´rd´rr

´rρ

4π

1V

Hartree + Electron-ion

potentials

: exchange – correlation potential unknownxcV

Approximated by the Vxcof homogeneous electron gas

(Local Density Approximation – LDA)

(Generalized Gradient Approximation – GGA)

Problem: VProblem: Veffeff depends on depends on ii

Solution: self-consistency!Solution: self-consistency!

Veff=Vc+Vxc

kj

kj ψ,ε

constructin

Converged ?

out

in

Mixin and out

NoDone

Yes

occ

kj,

2kj

out ψρ

inxc ρV

inc

2 8πV Poisson:

LDA:

kj

kj

kj

eff2 ψεψV Kohn-Sham:

Methods based on DFT:Methods based on DFT:– (L)APW: (linear) Augmented Plane Wave(L)APW: (linear) Augmented Plane Wave– LMTO: Linear Muffin Tin OrbitalLMTO: Linear Muffin Tin Orbital– KKR: Korringa Kohn RostokerKKR: Korringa Kohn Rostoker– PseudopotentialsPseudopotentials– ……

First Principle methodsFirst Principle methods Input: crystal structure, atom typesInput: crystal structure, atom types Output: ground-state properties of a solidOutput: ground-state properties of a solid

This workThis work

FP-LAPW methodFP-LAPW method

WIEN2K codeWIEN2K code

BGO, BSO PURE CRYSTALSBGO, BSO PURE CRYSTALS

TO STUDY THEIR ELECTRONICTO STUDY THEIR ELECTRONIC

AND OPTICAL PROPERTIESAND OPTICAL PROPERTIES

applied toapplied to

Valence statesValence states

8383Bi: Bi:

[Xe]4f[Xe]4f14145d5d10106s6s226p6p33

3232Ge: [Ar]3dGe: [Ar]3d10104s4s224p4p22

1414Si: [Ne]3sSi: [Ne]3s223p3p22

0808O: [He]2sO: [He]2s222p2p44

Calculation details -- Atomic sphere radii:

BGO BSO

Bi: 2.3 a.u. Bi: 2.3 a.u.Ge:1.8 a.u. Si: 1.6 a.u.O: 1.45 a.u. O: 1.4 a.u.

RKmax = RMT x Kmax = 7.0 for both compounds

Gmax = 14 ; LM expansion for O is limited up to L=4.

Matrix sizes: 7971 (BGO) ; 8277 (BSO)

6k-points in IBZ (80 in the whole BZ)

Exchange and correlation: GGA96

Crystal structureCrystal structureCubic; space group I-43d (No. 220)

Conven. unit cell: 4 formula units (76 atoms)Primitive unit cell: 2 formula units (38 atoms)

No inversion symmetry ! complex calculations!

-- Bi surrounding

6 O arranged in a strongly distorted octahedron

-- Ge (Si) surrounding

4 O arranged in a tetrahedron

Relaxation of the lattice parameter

BGO BSO

Experiment: a = 10,524 Å(a) a = 10,278 Å (b) Theory: a = 10,594 Å a = 10,379 Å

-6 -4 -2 0 2 4 6 8

Ene

rgy

[Ry]

Volume increase [%]

BGO

-2 0 2 4 6

Ene

rgy

[Ry]

Volume increase [%]

BSO

(a) S.F. Radaev et al, Kristallografiya 35 (1990) 361 (b) J. Barbier et al, Europ. J. of Solid State In. Chem. 27 (1990) 855

BGO BSO

All atomic positions: optimized!

BGOBi – O : 2,221 (3)

Bi – O : 2,584 (3)

Bi – Ge : 3,661

Bi – Bi : 3,944

BSOBi – O : 2,212 (3)

Bi – O : 2,595 (3)

Bi – Si : 3,586

Bi – Bi : 3,873

Atomic distances (in Å):

CONCLUSIONS:

1) The octahedron of oxygens around the Bi is more distorted in BSO than in BGO

2) The tetrahedron of Si is more compact around Bi in BSO than in BGO

-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,00

200

400

600

800Bi,Si,O: s,p mixture

Bi 6sO 2s2Bi 5d10

BSO

DO

S (

sta

tes/

cell)

Energy [Ry]

-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,00

200

400

600

800 Bi,Ge,O: s,p mixture

Bi 6s

O 2s2Bi 5d10

Ge 3d10

BGO

DO

S [

stat

es/c

ell]

Energy [Ry]

BGO

BSO

-12 -8 -4 0 4 8 12 160

5

10

Bi total Bi p Bi s

DO

S [

sta

tes/e

V/c

ell]

Energy [eV]

-12 -8 -4 0 4 8 12 160

10

20

30

40

DO

S [

sta

tes/e

V/c

ell]

Energy [eV]

O total O p O s

-10 -5 0 5 10 150

20

40

60 BGO total O Bi Ge

DO

S [

stat

es/R

y/ce

ll]Energy [eV]

BGODensity of

states

-10 -5 0 5 10 150

10

20

30 O total O p O s

DO

S [s

tate

s/eV

/cel

l]

Energy [eV]

-12 -8 -4 0 4 8 12 160

5

10

15 total

Bi p Bi s

DO

S [s

tate

s/eV

/cel

l]

Energy [eV]

-10 -5 0 5 10 150

10

20

30

40

50

60BSO total

O Bi Si

DO

S [

stat

es/R

y/ce

ll]

Energy [eV]

BSODensity of

states

BGO BSO

Band gap: Band gap: 3,54 eV3,54 eV

Indirect!Indirect!

Experim.: Experim.: 4,13 eV4,13 eV

Band gap: Band gap: 4,04 eV4,04 eV

Indirect!Indirect!

Experim.: Experim.: 4,34 eV4,34 eV

Band structure around

the band gap

BGOBGOPredominant Band Characters around the gap

totaltotal Bi-pBi-p O-pO-p

totaltotal Bi-pBi-p O-pO-p

BSOBSOPredominant Band Characters around the gap

ωkEkEδPP2π

2dk

ωm

e4πωε Im if

fi,ikαfk

BZ

ikβfk322

22

αβ

ik|

fk|

filled initial state of energy Ei(k)

empty final state of energy Ef(k)

Linear optics

RPA approximation

Inter-band electronic transitions

P: electronic momentum operator

: frequency of the incoming radiation

Optics: How does the solid respond to external electromagnetic field?

This information is contained in complex dielectric tensor of the material!

Re Kramers-Kronig relation

Connection between the electromagnetism and the optics:

N2 = (Maxwell)

Complex refraction index: N()=n()+ik()

n: “normal” refraction index (changes phase velocity and propagation angle of radiation in the material)

k: extinction (damping) coefficient (describes a rate of atenuation of radiation in the material)

: absorption coefficient (the inverse of the characteristic penetration depth of radiation, in which the intensity decreases 1/e times)

R: reflection index ( probability of the radiation reflection)

Knowing all the optical “constants” can be calculated !

Calculated optical absorption spectra of BGO(Imaginary part of dielectric tensor ε)

0 200 4000

2

4

6

8

10BGO

abso

rptio

n [a

.u.]

[nm]

total

0 200 4000

2

4

6

8

10

abso

rptio

n [a

.u.]

[nm]

total Bi-s --> Bi-p

0 200 4000

2

4

6

8

10

abso

rptio

n [a

.u.]

[nm]

total O-p --> the rest Bi-s --> Bi-p

0 200 4000

2

4

6

8

10

abso

rptio

n [a

.u.]

[nm]

total O-p --> Bi-p O-p --> the rest Bi-s --> Bi-p

Conclusion: Optical absorption in BGO is dominated by O-p -> Bi-p electronic transitions!

0 200 4000

2

4

6

8

10

ab

so

rpti

on

[a

.u.]

[nm]

total

0 200 4000

2

4

6

8

10

ab

so

rpti

on

[a

.u.]

[nm]

total Bi-s --> Bi-p

0 200 4000

2

4

6

8

10

Bi-s -> Bi-p

O-p -> the rest

ab

so

rpti

on

[a

.u.]

[nm]0 100 200 300 400 500

0

2

4

6

8

10

BSO

Bi-s -> Bi-p

O-p -> the rest O-p -> Bi-p

ab

so

rpti

on

[a

.u.]

[nm]

Calculated optical absorption spectra of BSO(Imaginary part of dielectric tensor ε)

Conclusion: Optical absorption in BSO is also dominated by

O-p -> Bi-p electronic transitions!

Refraction index

Exp: n(480nm)=2.15 ** Theory: 2.22 Exp: n(480nm)=2.06 ** Theory: 2.13

** M. Kobayashi, Nucl. Instr. And Meth. A 372 (1996) 45

0 100 200 300 400 500 6000

2

4

Ref

raci

on

ind

ex

[nm]

BGOBGO

0 100 200 300 400 500 6000

2

4

Ref

ract

ion

ind

ex

[nm]

BSOBSO

400 600 800 10002,0

2,5

3,0

Ind

ex o

f R

efra

ctio

n

Wavelength (nm)

ref. 1 ref. 2 ref. 3

calculated

[1] P. A., Williams et al. Applied Optics, 35 (1996) 3562

[2] R. Nitsche, J. Appl. Phys. 36 (1965) 2358

[3] G. Montemezzani et al. 9 (1992) 1110

Comparison between Comparison between Experimental and Theoretical Experimental and Theoretical Refraction index of the BGORefraction index of the BGO

0 100 200 300 400 500 6000,0

0,2

0,4

0,6

0,8

Ref

lect

ivit

y

[nm]

BGOBGO

0 100 200 300 400 500 6000,0

0,2

0,4

0,6

0,8

Ref

lect

ivit

y

[nm]

BSOBSO

Reflectivity

0 100 200 300 400 500 6000,0

0,5

1,0

1,5

2,0

exti

nct

ion

co

effi

cien

t

[nm]

BGOBGO

0 100 200 300 400 500 6000,0

0,5

1,0

1,5

2,0

exti

nct

ion

co

effi

cien

t [nm]

BSOBSOExtinctioncoefficient

Absorption coefficient

0 200 400 6000

50

100

150

200

250

abs.

coe

ff.

[104 1

/cm

]

[nm]

BGO

0 100 200 300 400 500 6000

50

100

150

200

250

abs.

co

eff.

[10

4 1/c

m]

[nm]

BSO

Conclusions Conclusions Electronic structureElectronic structure

– Band structures of BGO and BSO are very similar, except for some details in the Band structures of BGO and BSO are very similar, except for some details in the conduction band bottom (different arrangement of empty bands)conduction band bottom (different arrangement of empty bands)

– The valence band top is dominated by the O-p states and the conduction band The valence band top is dominated by the O-p states and the conduction band bottom by the Bi-p statesbottom by the Bi-p states→ principal physical and optical properties are → principal physical and optical properties are determined by these states determined by these states

– Band gaps in both compounds are indirectBand gaps in both compounds are indirect– The principle effect of substitution of Ge (BGO) for Si (BSO) is the change of The principle effect of substitution of Ge (BGO) for Si (BSO) is the change of

interatomic distances between Bi and O: octahedron around the Bi in BSO is interatomic distances between Bi and O: octahedron around the Bi in BSO is more distorted than in BGOmore distorted than in BGO

Optical absorptionOptical absorption

– The strongest absorption of the BGO is in the region of 160-300 nm and of the The strongest absorption of the BGO is in the region of 160-300 nm and of the BSO in the region of 160-230 nmBSO in the region of 160-230 nm

– In these regions, the BSO attenuates the radiation more efficiently than the BGO In these regions, the BSO attenuates the radiation more efficiently than the BGO → the BSO scintillator can be made thinner!→ the BSO scintillator can be made thinner!

– Refraction indices for both BGO and BSO decrease when the radiation energy Refraction indices for both BGO and BSO decrease when the radiation energy exceeds the gap energyexceeds the gap energy

– For a region of far-UV both BGO and BSO exhibit very strong reflection For a region of far-UV both BGO and BSO exhibit very strong reflection – Absorption process: the O atoms around the Bi absorb the energy of radiation Absorption process: the O atoms around the Bi absorb the energy of radiation

(through their p-electrons) and transfer the energy to the Bi ion (to its p-(through their p-electrons) and transfer the energy to the Bi ion (to its p-electrons).electrons).

What about the emission spectra? What about the emission spectra?

Precise description of the excited states are Precise description of the excited states are required !required !

Acknowledgements

ISNCS2007IV International Symposium on Non-Crystalline Solids

VIII Brazilian Symposium on Glass and Related Materials

Brazil- October 21-25, 2007Aracaju- Sergipe

International Scholl on Glasses, October 26-28

16th INTERNATIONAL CONFERENCE ON DEFECTS 16th INTERNATIONAL CONFERENCE ON DEFECTS IN INSULATING MATERIALSIN INSULATING MATERIALS

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