IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 56, NO. 3, JUNE 2009 949
First Principles Calculations for Scintillation inCe-Doped Y and La Oxyhalides
Anurag Chaudhry, Student Member, IEEE, Andrew Canning, Member, IEEE, Rostyslav Boutchko, Member, IEEE,Yetta Denise Porter-Chapman, Edith Bourret-Courchesne, Stephen E. Derenzo, Fellow, IEEE, and
Niels Grønbech-Jensen
Abstract—This work presents the results of first principles elec-tronic structure calculations for Cerium (Ce) doped Yttrium (Y)and Lanthanum (La) oxyhalides performed using the pseudopo-tential method based on the local density approximation in thedensity functional theory. The relative position of the Ce 4f and5d levels in the energy gap of the host are determined from theground-state density of states for the Ce-doped material. Localiza-tion of the excited electron is determined from the calculations ofthe ������ excited state. A qualitative prediction of Ce-activatedscintillation is made based on these theoretical calculations. Ourapproach indicates that Ce-doped Y and La oxyhalides show pro-gressively better luminescence as we move down the periodic tablefrom oxyfluorides to oxyiodides. These families of materials havebeen synthesized and the experimental results agree qualitativelywith our calculations.
Index Terms—Cerium-doped, first-principles, oxyhalides, scin-tillators.
I. INTRODUCTION
T HE process of scintillation has been employed for radia-tion detection for more than a century [1]. Interest in inor-
ganic scintillators has been intense during the past few decadeswith research and development efforts driven by applications inhigh-energy physics, medical imaging, homeland security andother scientific and industrial research areas. Cerium-activatedhost crystals, notably halide scintillators ,have received a lot of attention because of their fast decay time,excellent light output and energy resolution [2]. But these lan-thanide halides are known to be hygroscopic in nature which
Manuscript received July 14, 2008; revised October 20, 2008. Current versionpublished June 10, 2009. This work was supported by the U. S. Department ofHomeland Security and carried out at the Lawrence Berkeley National Labora-tory under U. S. Department of Energy Contract DE-AC02-05CH11231.
A. Chaudhry is with the Department of Electrical and Computer Engineering,University of California, Davis, CA 95616 USA and Life Sciences Division,Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA (e-mail:[email protected]).
A. Canning is with Computational Research Division, Lawrence BerkeleyNational Laboratory, Berkeley CA USA 94720 (e-mail: [email protected]).
N. Grønbech-Jensen is with the Department of Applied Science, Universityof California, Davis, CA 95616 USA and with Computational ResearchDivision, Lawrence Berkeley National Laboratory, Berkeley CA USA 94720(e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TNS.2009.2013856
Fig. 1. Schematic diagram of the position of the Ce �� and �� levels rela-tive to the conduction and valence band of the host material for a Ce activatedscintillator.
makes them difficult to handle. Recently, microcrystals of rare-earth oxyhalide compounds doped with Cerium were synthe-sized and investigated for their scintillation properties [3]. This,in part, was motivated by the understanding that metal oxidescintillators are generally more stable. The aim of this studyis to employ the set of our theoretical prediction guidelines [4]proposed for the prediction of new Ce-activated scintillators tothese families of rare-earth oxyhalides and compare with theexperimental results. This theoretical work is part of a largerproject “High-throughput discovery of improved scintillationmaterials” which aims to discover new scintillation radiation de-tector materials [5].
II. THEORETICAL BACKGROUND
Scintillation in Ce doped materials corresponds to a radiativetransition from the Ce excited state , usually re-ferred to as , to the ground state level(Fig. 1). Our theoretical approach for the prediction of candi-date scintillator materials is based on the calculation of the Ce
and levels relative to the valence and conduction bands ofthe host material [4]. The and levels must lie in the gapof the host material for the compound to be a Ce scintillator.
The theoretical approach we use to determine the energylevels and the wavefunctions is the Kohn-Sham formalism[6], [7] of the Density Functional Theory (DFT), where thewavefunctions of the electrons satisfy
(1)
where is the charge density, is the energy, is the nuclearcoordinate and is the nuclear charge. is the Local Den-sity Approximation (LDA) of the exchange-correlation poten-
950 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 56, NO. 3, JUNE 2009
Fig. 2. Representative crystal structures for (a) oxyfluorides and (b) oxychlo-rides, oxybromides and oxyiodides of Y and La. The oxyfluorides crystallizein the rhombohedral space group while the other oxyhalides have a tetragonalstructure. Y or La ions are in green, oxygen in orange and the halide in red.
tial. The wavefunctions are expanded in plane-waves to a cutoffin energy. The nucleus and core electrons are replaced by anionic pseudopotential so that only the valence electrons are in-volved in the calculation. The Kohn–Sham equations are usuallysolved by minimizing the total energy with an iterative scheme,such as conjugate gradient for a fixed charge density, and thenupdating the charge density until self-consistency is achieved.Forces can also be calculated within the Kohn-Sham formalismso that atomic relaxation as well as molecular dynamics can beperformed. A review of this pseudopotential plane-wave tech-nique for density functional calculations has been presented byPayne et al. [8].
III. COMPUTATIONAL METHOD
The ab initio calculations of Ce-doped Y and La oxyhalideswere carried out using density functional theory as implementedin the ABINIT code [9], [10]. The exchange-correlation energyfunctional was evaluated within the local density approximationusing Ceperley-Alder homogeneous electron gas data [11], [12]and electronic wave functions were expanded in plane waves upto a kinetic energy cutoff of 60 Hartrees. Self-consistency wasachieved using a mesh of k points centered at the pointin reciprocal space. Brillouin zone integrations were carried outusing the tetrahedron method [13]. We used norm conservingTroullier-Martins pseudopotentials [14].
The computational procedure used for these calculations is asfollows:
a) The atomic positions and crystal symmetry group of thehost crystal were extracted from the Inorganic CrystalStructure Database (ICSD) [15], [16]. Since the primi-tive cell of Y and La oxyhalides consists of 6 atoms weused the supercell approach in order to minimize the in-teraction of with its periodic images. From compu-tational considerations, the supercell was chosen to be a
version of the primitive cell giving a 48 atomsupercell. By comparing with smaller cell sizes, this size
of cell was found to give reasonably well converged re-sults for the properties studied. A recent study on Ceriumdoped lanthanum halide compounds also used asupercell which the authors state is sufficient for properembedding of the dopant atom [17].
b) Atomic positions and cell size of the host material arerelaxed to their equilibrium values.
c) The host material is doped with a single Ce atom in thesupercell and the atomic positions are relaxed until themaximum component of forces acting on any atom is lessthan 1 mH/Bohr. A ion replaces 1 in 16 ions of
in the doped cell.d) A ground state band structure calculation is performed to
determine the position of the Ce level with respect tothe valence band maximum (VBM) of the host material.
e) A constrained LDA calculation for the stateis performed by setting the occupancy of the Cestates to zero. From this calculation we determine theposition of the state relative to the conductionband maximum (CBM) as well as the localization of theexcited state on the Ce atom by measuring the percentageof this state surrounding the Ce atom. This is done byconstructing a Voronoi type polyhedra centered on eachion and integrating the portion of charge density withinthis volume. Localization ratio is computed as the ratioof the excited state surrounding the Ce ion to that aroundone of the host ions (we select the host ion with thehighest integral), usually one of the trivalent ions,or . Our studies have indicated a localization ratiogreater than 1.1 yields consistent predictions.
This last step in the procedure is a simple way to characterizea material as a good candidate for a bright Ce activated scin-tillator and has been verified by studies of known Ce-activatedscintillators like and non-scintillators like [4]. Itshould be noted that we do not model any competing processeson the host material such as self-trapped excitons or defects thatcan reduce the brightness.
IV. RESULTS AND DISCUSSION
A. Crystal Structure
The Y and La oxyhalides studied in this work crystallize ineither the rhombohedral or tetragonal phases (Fig. 2) [3], [16].YOF and LaOF crystallize in the rhombohedral space groupR-3m with rare earth site symmetry of . Each RE ion coor-dinates to 4 O ions and 4 F ions in a bi-capped trigonal antipris-matic arrangement. REOX ( , Br, I) have a tetragonalstructure, space group P4/nmm. The rare earth cation in thesestructures has a coordination of in a distorted squareantiprismatic arrangement, forming overall layered structures.There was no entry for YOBr and YOI in the ICSD. The atomicpositions and cell size for these compounds were determinedby starting with an initial guess from an isostructural compound(e.g., taking YOCl atomic positions as an initial guess for YOBrsince they crystallize in the same space group) followed by com-plete relaxation of the cell and atomic parameters.
Tetragonal structured oxychlorides, oxybromides and oxyio-dides have similar lattice parameters for the axis [3]. The
CHAUDHRY et al.: FIRST PRINCIPLES CALCULATIONS FOR SCINTILLATION 951
Fig. 3. Total density of states (DOS) for (a) LaOX:Ce and (b) YOX:Ce family of Ce-doped oxyhalides. (c) Atom-projected partial DOS (PDOS) for YOBr:Ce.The Ce �� states are located inside the bandgap of the host crystals. Moving down the periodic table from F to I, a decreasing gap favors more electron hole pairsand migration of hole to Ce but the Ce �� states hybridize more with the host � states (�� for Y, �� for La). The Fermi level is set at zero.
cell lengthens along the direction ( axis) as the halide ionchanges from Cl to I. In the case of the oxyfluorides, the unit celldoubles in this direction. These structural differences compen-sate for the increases in size of the halide atoms moving downthe periodic table. In all cases, the rare earth cations are bondedto both oxide and halide ions.
B. Electronic Structure
Ordering of the electronic states of the Cerium doped Y andLa oxyhalides can be seen from the density of states (DOS) plot(Fig. 3). Also shown is the atom-projected partial DOS (PDOS)for YOBr:Ce (Fig. 3(c)). The lowest state of Ce is the highestoccupied state and the Fermi level is above this state and set tozero. It should be noted that the states above the Fermi levelare unoccupied and will change in energy for the excited statecalculation. This is because of the localized nature of thestates in these compounds. In particular for LaOBr and LaOI theempty Ce states move down below the La states when theCe state is excited to the Ce state. From the PDOS we cansee that the valence bands have the character of the p-states ofthe anion (predominantly O states), whereas the conductionbands have the character of the trivalent cation (Y or La )
-states hybridized with the Ce states.The oxyfluorides have the biggest bandgap in these families
of compounds which gradually decreases as we move down theperiodic table from fluoride to iodide. The number of electronhole pairs produced by an incident gamma ray is inversely pro-portional to the host bandgap and a smaller (VBM)- levelseparation favors transfer of the hole to the Ce level. We
observe that the Ce level is inside the host bandgap for allcompounds in these families of materials and the valence bandmaximum (VBM)-Ce gap decreases from oxyfluorides tooxyiodides. This indicates the possibility of Ce-activated scin-tillation since a level situated below the VBM precludes anypossibility of ionization hole capture by Cerium.
It is known that bandgaps are typically underestimated byLDA, but for the purposes of our calculations LDA does pro-vides useful trends in families of materials of interest. We aretherefore looking at relative rather than absolute numbers whereLDA can give good predictions, e.g., for relative positions ofbands of the same character etc. For example, in the case of Lacompounds the host conduction band is primarily composed ofLa states which are of the same character as the Ce statesso we believe the LDA-DFT error in placement of these stateswould be similar. Strongly correlated electrons are known tobe better described by the LDA+U approach [18]. We have per-formed LDA+U calculations using an appropriate U parameterto see if this results in major changes to the position of the oc-cupied levels. We found that it only results in changes of theorder of tenths of an eV. Furthermore, excited state calculationsto determine the localization have no filled states.
Studies on scintillation mechanism in have re-ported that there is an energy transfer from the self-trapped ex-citons (STEs) to the Ce ion which depends on the STE life-time, Ce concentration and temperature [19]. In this scenariothe -VBM gap may not provide direct information about thescintillation brightness. In this case, from a theory perspective,the relative localization of the excited state on the plays
952 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 56, NO. 3, JUNE 2009
Fig. 4. ��� � excited state for some members of the Y and La oxyhalide compounds doped with Ce. (a) YOF:Ce, (b) YOCl:Ce, (c) YOBr:Ce, (d) LaOF:Ce,(e) LaOBr:Ce, and (f) YOI:Ce. Blue is Ce, green is the trivalent Y or La ion, orange is O and red is the halide ion. The plots are charge density isosurfaces of the��� � state. Localization of the � state on the Ce atom compared to the host trivalent cation (� or �� ) is calculated as a ratio for qualitative predictions.
a more important role. This has been calculated in previousstudies of Ce-doped Lanthanum halide scintillators [4]. How-ever it should be noted that we are not aware of any bright scin-tillators with a large -VBM gap.
C. Constrained LDA
The atom-projected (DOS) indicates that the Ce statesare hybridized with the host d states of the conduction bandas shown in Fig. 3. Therefore to have a better measure of theprobability of scintillation for these compounds we measure thelocalization of the first excited state of the system on the Ceatom [4].
Fig. 4 shows the charge density isosurface plots of thestate for a few representative systems in these families
of compounds. The ratio of concentration of this state on the
Ce atom, as compared to the host trivalent cation ( or), gives a qualitative measure of the localization of this
state on the Ce atom. A delocalized state would indicate no Cescintillation.
Table I summarizes the results of our calculations forCe-doped La and Y oxyhalides. YOCl:Ce and YOBr:Ce havethe same crystal structure but YOBr:Ce has a lower bandgap,smaller 4f-VBM separation and much better localization of theexcited state ( 3.3 for YOBr:Ce compared to 1.8 for YOCl:Ce)making YOBr a better candidate for bright Ce-activatedscintillation. YOF:Ce presents an interesting case where thelocalization appears rather good at 5.5, but a large bandgap(reducing the number of electron-hole pairs) and a large
-VBM gap (low hole capture probability) may lead to weakCe-activated scintillation. YOI:Ce shows good localization of
CHAUDHRY et al.: FIRST PRINCIPLES CALCULATIONS FOR SCINTILLATION 953
TABLE ITHEORETICAL RESULTS (LDA-DFT) FOR CE-DOPED Y AND LA OXYHALIDES
Data taken from [3]. Luminosities relative to YAP ����� � ��.
the excited state and its low bandgap indicates the possibility ofbright Ce-scintillation. The -VBM separation for LaOF:Ceis rather large ( 3.1 eV) and coupled with the fact that it hasa rather large bandgap, we expect it to have weak Ce-activatedscintillation. The LaOBr:Ce excited state plot indicates that thewavefunction has weak character in addition to the typestate on the Cerium ion and this was confirmed by an excitedstate projected DOS for this system. We get a similar weakmixing of the excited state for LaOCl:Ce. A lower bandgapand favorable positioning of the Ce state with respect tothe VBM indicate that LaOBr:Ce is a better candidate forCe-scintillation than LaOCl:Ce. The excited state calculationfor LaOI:Ce gives a localization ratio of 1.4 though we againsee mixed character in the excited state wavefunction. A de-tailed analysis to understand this observation for La oxyhalidesis ongoing. A favorable location of the Ce level in the hostbandgap ( -VBM separation of 0.5 eV) nonetheless indicatesthe possibility of bright Ce-scintillation for LaOI:Ce.
These materials have been synthesized in microcrystal formas a part of the project and experimental results will be presentedin detail elsewhere [3]. Table I also has a column of data fromthe preliminary measurements of luminosity of these Ce-dopedmaterials. We can see that the theoretical results are consis-tent with the experimental data in predicting Ce-activated scin-tillation for these families of compounds. YOBr:Ce shows thebrightest Ce-activated scintillation in the Y oxyhalide family.Based on our calculations we expect YOI:Ce also to be simi-larly bright but the synthesis results at present do not concur.A reduced luminosity could be due to some kind of quenchingmechanism involving defects the modeling of which is outsidethe scope of the work presented here. La oxyhalides are alsoincreasingly luminous going from LaOF:Ce to LaOI:Ce series.This agrees with our theoretical predictions.
V. CONCLUSION
First principles electronic structure calculations for Ce-dopedY and La oxyhalides were performed using the pseudopotentialmethod based on the local density approximation in densityfunctional theory. Qualitative predictions of the relative bright-ness of activated luminescence in doped materials were
made based on the calculation of the ground-state density ofstates for the Ce-doped material as well as the localization of the
excited state. These families of materials have beensynthesized and the experimental results agree qualitativelywith our calculations. This work demonstrates the utility ofour first-principles approach for prediction the of Ce-activatedscintillation in detector materials.
ACKNOWLEDGMENT
We want to thank Marvin J. Weber and Gregory Bizarri forinvaluable discussions and constructive criticism.
Disclaimer: This document was prepared as an account ofwork sponsored by the United States Government. While thisdocument is believed to contain correct information, neither theUnited States Government nor any agency thereof, nor The Re-gents of the University of California, nor any of their employees,makes any warranty, express or implied, or assumes any legal re-sponsibility for the accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed, or rep-resents that its use would not infringe privately owned rights.Reference herein to any specific commercial product, process,or service by its trade name, trademark, manufacturer, or other-wise, does not necessarily constitute or imply its endorsement,recommendation, or favoring by the United States Governmentor any agency thereof, or The Regents of the University of Cal-ifornia. The views and opinions of authors expressed herein donot necessarily state or reflect those of the United States Gov-ernment or any agency thereof, or The Regents of the Universityof California. Ernest Orlando Lawrence Berkeley National Lab-oratory is an equal opportunity employer.
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