M. V. Lalic and S. O. Souza

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The first principles study
of optical properties of
BGO and BSO scintillators

• M. V. Lalic and S. O. Souza
• Universidade Federal de Sergipe
• Aracaju, Brazil

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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

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The process of detection of the radiation

• The 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
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3 aspects of the scintillation process to
understand 1.) Absorption of the incoming
radiation 2.) Transfer of the absorbed energy to
the luminescent centers 3.) Emission process

• Desired characteristics of the scintillators
• transparency
• high density
• radiation hardness
• large light output
• short decay time

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

Bi3Ge4O12 Bismuth orto germanate (BGO)
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• BGO Good characteristics
• High density (7,13 g/cm3)
• Short radiation length
• Large light output (9000 photons/MeV)
• Large hardness (5 Mohs)
• Low afterglow
• Absence of hygroscopicity and cleavage
• Crystal growth refined to a high degree of
  perfection
• BGO drawbacks
• Long decay time (300ns) ? speed too slow for
  some applications
• Radiation hardness not sufficient in some
  applications
• High cost due to Ge

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• Bi3Si4O12 Bismuth orto silicate (BSO) The same
  crystal structure as BGO, Si?Ge
• Much faster response (100ns)
• Lower cost
• But
• smaller light output (1/5 of the BGO)
• Other characteristics very similar to the BGO
• ? BSO can substitute the BGO in some applications

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BGO and BSO luminescence state of knowledge

• A lot of experimental work
• Almost no theoretical studies

• Both are intrinsic scintillators
• Emission assigned to Bi3 ion 3P1?1S0
  transition (Weber, 1973)
• Transparent from 300 to 6000nm

• Emission spectra
• wide, due to extensive Stokes shift of the Bi
• 2. Peak maximum at 480nm (blue light)

M. Cobayashi et al, Nucl. Instr. And Meth. 372
(1996) 45-50
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Transmission spectra
Ishii et al. Optical Materials 19 (2002)
201212 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
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Absorption spectra
BGO
BSO
?
Weber et al. J. Appl. Phys. 44 (1973) 5495
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• Electronic transition studied so far
• Valence band impurity levels
• Valence band exciton levels
• Missing
• Valence band conduction band
• electronic transitions

• This work
• Theoretical study of the BGO and BSO electronic
  structure
• Calculation of their optical properties
  determined by valence band
• conduction band electronic transitions

Outline

• Basics about the calculation method
• Results of the calculations and conclusions
• Possible improvement of the theoretical
  description

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Theory

• How to solve the quantum many-body problem?

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Seek for approximate solutions!
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Sucessive approximations
non-relativistic Hamiltonian
full relativistic Hamiltonian
One electron Hamiltonian
fixed nuclei
Relativistic effects
Nuclear motion
Higher-order effects
Excited states
Born Openheimer Approximation
One-electron approximation
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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
,
description of the electronic ground state
Perturbation theory
Partial recuperation of the neglected effects
(nuclear motion, spin orbit, )

• Hartree-Fock Theory (HFT)
• Density Functional Theory (DFT)
• Green-function technique

Realized by
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DFT Two theorems of Hohenberg and Kohn
1 1
Potential of the nuclei Vext
Electronic ground state density

• Total ground-state energy
• is unique functional of ? !

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Consequences
Introducing a set of one-electron orbitals and
varying E with respect to ?
Kohn-Sham Equations
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• How to solve Kohn-Sham equations?

• Problem Veff depends on ?i

• Solution self-consistency!

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• Methods based on DFT
• (L)APW (linear) Augmented Plane Wave
• LMTO Linear Muffin Tin Orbital
• KKR Korringa Kohn Rostoker
• Pseudopotentials
• First Principle methods
• Input crystal structure, atom types
• Output ground-state properties of a solid

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This work

• FP-LAPW method
• WIEN2K code
• BGO, BSO PURE CRYSTALS
• TO STUDY THEIR ELECTRONIC
• AND OPTICAL PROPERTIES

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Calculation details

• Valence states
• 83Bi Xe4f145d106s26p3
• 32Ge Ar3d104s24p2
• 14Si Ne3s23p2
• 08O He2s22p4

-- Atomic sphere radii BGO
BSO Bi 2.3 a.u.
Bi 2.3 a.u. Ge1.8 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 L4. Matrix sizes 7971 (BGO)
8277 (BSO) 6k-points in IBZ (80 in the whole
BZ) Exchange and correlation GGA96
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Crystal structure
Cubic 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
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Relaxation of the lattice parameter
BSO
BGO
BGO
BSO Experiment a 10,524
Å(a) a 10,278 Å (b) Theory
a 10,594 Å a 10,379 Å

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

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All atomic positions optimized!
Atomic distances (in Å)

• BSO
• Bi O 2,212 (3)
• Bi O 2,595 (3)
• Bi Si 3,586
• Bi Bi 3,873

• BGO
• Bi O 2,221 (3)
• Bi O 2,584 (3)
• Bi Ge 3,661
• Bi Bi 3,944

• CONCLUSIONS
• The octahedron of oxygens around the Bi is more
  distorted in BSO than in BGO
• The tetrahedron of Si is more compact around Bi
  in BSO than in BGO

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BGO
BSO
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BGO Density of states
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BSO Density of states
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Band structure around the band gap
BGO
BSO
Band gap 3,54 eV Indirect! Experim. 4,13 eV
Band gap 4,04 eV Indirect! Experim. 4,34 eV
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BGO Predominant Band Characters around the gap
total
Bi-p
O-p
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BSO Predominant Band Characters around the gap
total
Bi-p
O-p
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Optics How does the solid respond to external
electromagnetic field? This information is
contained in complex dielectric tensor ? of the
material!
Linear optics RPA approximation Inter-band
electronic transitions
filled initial state of energy Ei(k)
empty final state of energy Ef(k)
P? electronic momentum operator ? frequency of
the incoming radiation
Re ??? ? Kramers-Kronig relation
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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 !
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Calculated optical absorption spectra of
BGO (Imaginary part of dielectric tensor e)
Conclusion Optical absorption in BGO is
dominated by O-p -gt Bi-p electronic transitions!
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Calculated optical absorption spectra of
BSO (Imaginary part of dielectric tensor e)
Conclusion Optical absorption in BSO is also
dominated by O-p -gt Bi-p electronic transitions!
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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
Comparison between Experimental and Theoretical
Refraction index of the BGO
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
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Reflectivity
Extinction coefficient
Absorption coefficient
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Conclusions

• Electronic structure
• Band structures of BGO and BSO are very similar,
  except for some details in the conduction band
  bottom (different arrangement of empty bands)
• The valence band top is dominated by the O-p
  states and the conduction band bottom by the Bi-p
  states? principal physical and optical properties
  are determined by these states
• Band gaps in both compounds are indirect
• 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 more distorted than in BGO
• Optical absorption
• The strongest absorption of the BGO is in the
  region of 160-300 nm and of the BSO in the region
  of 160-230 nm
• In these regions, the BSO attenuates the
  radiation more efficiently than the BGO ? the BSO
  scintillator can be made thinner!
• Refraction indices for both BGO and BSO decrease
  when the radiation energy exceeds the gap energy
• 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 (through their
  p-electrons) and transfer the energy to the Bi
  ion (to its p-electrons).

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• What about the emission spectra?
• Precise description of the excited states are
  required !

Acknowledgements
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ISNCS2007
IV International Symposium on Non-Crystalline
Solids VIII Brazilian Symposium on Glass and
Related Materials Brazil- October 21-25,
2007 Aracaju- Sergipe International Scholl on
Glasses, October 26-28
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16th INTERNATIONAL CONFERENCE ON DEFECTS IN
INSULATING MATERIALS 24-29 August 2008
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ARACAJU Capital of Sergipe State
Thank you for your attention!