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
24-29 August 200824-29 August 2008
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