Energy Levels and Optical Spectroscopy of Er3+ in Gd2O3

Jun 26, 2007 - Judd–Ofelt analysis of powder samples: LiNbO3:Er3+ submicron-sized particles as a model case. Eugenio Cantelar ... Şerban Georgescu ...
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J. Phys. Chem. C 2007, 111, 10404-10411

Energy Levels and Optical Spectroscopy of Er3+ in Gd2O3 Nanocrystals Xueyuan Chen,*,†,‡ En Ma,† and Guokui Liu‡ State Key Laboratory of Structural Chemistry, National Engineering Research Center for Optoelectronic Crystalline Materials, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, China, Chemistry DiVision, Argonne National Laboratory, Argonne, Illinois 60439 ReceiVed: April 17, 2007; In Final Form: May 10, 2007

Based on the high-resolution excitation and emission spectra at 10 and 297 K, we have determined 107 crystal-field (CF) levels below 43 000 cm-1 of Er3+ at the C2 site of Gd2O3 nanocrystals. The levels were analyzed in terms of 16 free-ion and 14 CF parameters. The CF modeling of the experimental energy levels yielded physically reasonable Hamiltonian parameters with a final root-mean-square deviation of 12.5 cm-1. A modified Judd-Ofelt (JO) intensity analysis was proposed in evaluating the spectroscopic parameters such as JO parameters, radiative lifetime, and branching ratios for rare-earth ions doped in nanocrystals. Three JO parameters were obtained (Ω2,4,6 ) 4.96, 2.23, and 0.49, in units of 10-20 cm2). The effect of J-mixing was taken into account in the energy-level-fitting and in the J-J′ transition intensity calculation, which is observed to be responsible for the significant increase of the radiative transition rate of 4S3/2. Furthermore, the luminescence lifetimes of several excited multiplets of Er3+ were measured, and vibronic side bands and self-absorption were observed in the 10 K emission spectrum.

I. Introduction Rare-earth (RE) ions doped in inorganic nanophosphors are one of the most promising materials for a variety of applications in solid-state lasers, lighting and displays, and biolabels.1,2 Due to high luminescence efficiency and long lifetime, Eu3+:Gd2O3 nanophosphors have been used as fluorescent markers in a variety of immunosensing applications.3,4 Recently, anomalous thermalization phenomenon resulting from the restricted phonon relaxation has been observed in Eu3+:Gd2O3 nanotubes.5 The use of upconverting nanophosphors of Gd2O3 doped with Er3+ or Sm3+ as biolabels for immunoassays is stimulating even more interest, since they possess distinct advantages such as the absence of autofluorescence of biomolecules and no need for time-resolved detection compared to commonly used downconverting phosphors.6 Furthermore, since Gd3+ is a known contrast agent for magnetic resonance imaging (MRI), RE doped Gd2O3 nanophosphors may function as both fluorescence and MRI labels.6 Most of the previous work on Er3+:Gd2O3 nanophosphors was focused on the material synthesis, characterization, or upconversion mechanism.7-10 So far, no detailed spectroscopic study of Er3+:Gd2O3 crystals such as crystal-field analysis has ever been reported. In a preceding paper, we have investigated the excited-state dynamics of the 4S3/2 multiplet of Er3+ in Gd2O3 nanocrystals.11 It is evident that the optical behaviors of Er3+:Gd2O3 depend critically on its energy level structures. Given that Er3+:Gd2O3 crystals have versatile applications, a thorough understanding of the energy levels and optical spectroscopy of this crystal is of significant importance. In this paper, we report the optical spectra and electronic structures of Er3+ in Gd2O3 nanocrystals in detail. Crystal-field (CF) levels below 43 000 cm-1 of Er3+ at the C2 site of Gd2O3 * Corresponding author. Phone and fax: +86-591-8764-2575. E-mail: [email protected]. † Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences. ‡ Argonne National Laboratory.

are determined based on the high-resolution excitation and emission spectra at low temperature. Energy-level fitting yields a very small standard deviation (12.5 cm-1) from the experiments. By means of a modified Judd-Ofelt (JO) intensity calculation that we propose, spectroscopic parameters such as JO parameters and radiative lifetimes are determined. Different from the semiconductor host, the exciton Bohr radius of the Gd2O3 host is very small (less than a few angstroms).12 Thus, quantum size confinement in 40-50 nm Gd2O3 nanocrystals should not affect the localized electronic states of Er3+. As a result, the reported energy levels of Er3+:Gd2O3 nanocrystals are applicable to the bulk counterparts. II. Experimental Section The cubic Er3+:Gd2O3 (1 atom %) nanocrystals used in this study were prepared by a simple sol-gel method. A detailed description of the preparation and characterization of the sample has been reported by Guo et al.8 The nanocrystals have a broad size distribution with an average size of 40∼50 nm, and the nanoparticles tend to aggregate. The powder X-ray diffraction pattern can be exclusively indexed as cubic Gd2O3 phase (JCPDS #86-2477, space group Ia3h , cell parameter a ) 1.080 nm). Emission and excitation spectra and transient decays were recorded on an Edinburgh Instruments FLS920 spectrofluorimeter equipped with both continuous (450 W) xenon and pulsed xenon (microsecond) or hydrogen (nanosecond) lamps. For low temperature measurements, samples were mounted on a closed cycle cryostat (10-350 K, DE202, Advanced Research Systems). Laser spectroscopic experiments were performed at Argonne. The sample was mounted on an Optistat Bath Cryostat (Oxford Instruments, 2-350 K). A pulsed dye laser (Lambda Physik, Scanmate 2EC), which provides a pulse width of 5 ns, a repetition rate of 10 Hz and a tunable range from 480 to 550 nm, or a pulsed ultraviolet laser at 355 nm was used to pump the samples. The fluorescence was dispersed by a 1-m

10.1021/jp072980g CCC: $37.00 © 2007 American Chemical Society Published on Web 06/26/2007

Er3+ in Gd2O3 Nanocrystals

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10405

Figure 2. Emission spectrum of Er3+ in Gd2O3 nanocrystals under the 275 nm excitation at 10 K. The inset shows the self-absorption due to the 2H11/2r4I15/2 transition, and the six downward peaks marked by star signs correspond well to the six CF levels of 2H11/2.

Figure 1. Schematic energy levels of Er3+ and Gd3+ ions in cubic Gd2O3 nanocrystals.

monochromator (SPEX 1704) and detected with a cooled RCA C31034 photomultiplier. The signals were recorded using a gated boxcar (SR250, Stanford Research Systems). The fluorescence decay measurements were performed using a digital storage oscilloscope (Tektronix TDS680C). All spectra were corrected for the intensities as well as the line positions. III. Emission and Excitation Spectra Er3+

Gd3+

The energy level diagrams of and ions as well as the energy transfer (ET) path between them are schematically plotted in Figure 1. Er3+ ions in cubic Gd2O3 occupy two types of sites, a low-symmetry site of C2 and a centrosymmetric site of S6. For Er3+ at the S6 site, the electric-diople (ED) transition is forbidden and thus absent in the fluorescence spectra. In this paper, we will focus on the energy levels and optical spectra of Er3+ at the C2 site. Theoretically, for the f11 configuration at low site symmetry, there are totally 41 SLJ multiplets and 182 CF levels due to the time-reversal (Kramers) degeneracy. Each level (or doublet) belongs to the crystal quantum numbers µ ) (1/2 of the irreducible representation of C2 point group. Figure 2 shows the 10 K emission spectrum of Er3+:Gd2O3 nanocrystals under the 275 nm excitation which corresponds to the 6I7/2 r 8S7/2 excitation of Gd3+. The down-converting emissions from the lowest CF levels of 2P3/2, 2H9/2, 4S3/2, and 4F 3+ are observed and assigned in Figure 2. 9/2 multiplets of Er Due to the defect luminescence in nanocrystals, those sharp f-f transition lines are superimposed on a weak broad band in the background. The strongest green emission band in Figure 2 arises from the 4S3/2 f 4I15/2 transition. The emissions from 2P3/2 to the lower multiplets (below 2H11/2) dominate the whole spectrum, which play a key role in the following assignment of the CF levels of the multiplets below 2H11/2. The emission lines from 2H9/2 are much weaker than those from the 2P3/2 or 4S3/2 states, whereas no emission from 4G11/2 can be observed due to the very fast nonradiative relaxation from 4G11/2 to 2H9/2. The 6P 8 3+ can also be seen in the 7/2 f S7/2 emission from Gd ultraviolet region. Interestingly, the self-absorption peaks which

Figure 3. Emission spectrum of Er3+ in Gd2O3 nanocrystals under the 519.6 nm excitation at 10 K. The inset shows the weak vibronic structures around the ZPLs. The phonon side bands are marked by star and circle signs (see the discussion in the text).

correspond to those hypersensitive transitions of 2H11/2 r 4I15/2 and 4G11/2 r 4I15/2 were observed around 520 and 380 nm, respectively. Note that both transitions from 4I15/2 to the 2H11/2 and 4G11/2 states have large rank-2 reduced matrix elements (RMEs) of the unit tensor, which could result in strong absorption as well as vibronic side bands.11 As enlarged in the inset of Figure 2, the self-absorption from the ground level to the six CF levels of 2H11/2 can be clearly identified, in good agreement with the excitation spectrum in the following. Er3+:Ln2O3 (Ln ) Y, Gd, and Lu) crystals are in general regarded as a weak electron-phonon coupling system. Tanner et al. observed weak phonon side bands in the 4S3/2 emission spectrum of Er3+:Y2O3 crystals.13 Recently, we reported much stronger phonon sidebands in the 5 K laser excitation spectrum for the 2H11/2 r 4I15/2 transition of Er3+ in Gd2O3 nanocrystals, which was ascribed to the M-process coupling with infraredactive lattice modes.11 It is expected that vibronic side bands should also appear in the emission spectrum of Er3+:Gd2O3. To investigate the vibronic structures in the emission, we focus on the strongest zero-phonon lines (ZPLs) at 563.7 nm (E1 f Z7, Z8), where E and Z stand for 4S3/2 and 4I15/2 multiplets respectively. As shown in Figure 2, the weak 2H9/2 f 4I13/2 emission coincidently locates at the low-energy side of the above ZPLs of our interest. To avoid the interference from the emission of 2H9/2 f 4I13/2, the excitation wavelength at 519.6 nm which corresponds to the hypersensitive transition of 2H11/2(6) r 4I15/2(1) was purposely chosen. Figure 3 shows the emission spectrum of Er3+:Gd2O3 nanocrystals under the 519.6 nm excitation at 10 K, showing high-resolution vibronic structures in the inset. No emission from 2H9/2 was observed. The green

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TABLE 1: Energy Levels of Er3+ at the C2 Site of Gd2O3 Nanocrystals at 10 K multiplet 4

I15/2

4

I13/2

4

I11/2

4

I92

4

F9/2

4

S3/2

2

H11/2

4

F7/2

4

F5/2

4

F3/2

2

H9/2

a

energy (cm-1) exp fit 0 38 76 87 159 258 487 500 6513 6547 6593 6598 6690 6844 6870 10204 10225 10259 10279 10376 10394 12337 12448 12524 12588 12616 15138 15216 15297 15350 15450 18240 18326 19048 19055 19081 19196 19227 19250 20356 20453 20520 20587 22068 22095 22194 22426 22590 24385 24504

-1 36 80 88 163 264 481 500 6506 6542 6592 6596 6686 6840 6872 10194 10224 10258 10282 10384 10408 12336 12437 12539 12590 12625 15136 15224 15297 15350 15453 18234 18329 19061 19079 19097 19178 19214 19226 20354 20445 20520 20591 22075 22102 22190 22423 22589 24354 24486

∆Ea (cm-1) -1 -2 4 1 4 6 -6 0 -7 -5 -1 -2 -4 -4 2 -10 -1 -1 3 8 14 -1 -11 15 2 9 -2 8 -0 0 3 -6 3 13 24 16 -18 -13 -24 -2 -8 -0 4 7 7 -4 -3 -1 -31 -18

multiplet 2

H9/2

4

G11/2

2

K15/2 G9/2 2 G7/2 2

energy (cm-1) exp fit 24542 24574 24627 26113 26137 26228 26408 26437 26478 27201 27232 27275 27311 27323 27342 27464 27579 27653 27766 27903 27942 28003

2

P3/2

2

K13/2 2 P1/2 4 G5/2

4

G7/2

2

D5/2

28194 31317 31514 32519 32600 32731 32841 32863 32906 33075 33226 33331 33375 33798 33876 33957 34081 34574 34655 34732

4

G9/2

24548 24578 24628 26145 26166 26236 26388 26416 26463 27198 27226 27267 27299 27319 27340 27356 27485 27579 27654 27752 27884 27952 27977 28013 28133 28203 31321 31523 32526 32603 32733 32828 32846 32913 32993 33087 33210 33335 33370 33812 33884 33979 34069 34570 34650 34738 36269 36306 36426 36496 36527

∆Ea (cm-1) 6 4 1 32 29 8 -20 -21 -15 -3 -6 -8 -12 -4 -2

multiplet 4

D5/2

4

D7/2

energy (cm-1) exp fit 38181 38269 38292 38565 38810

2

I11/2 L17/2 2 H111/2 4 D3/2 2

21 0 1 -14 -19 10

40686 40735 40782 40806 40884 40947 40993 41085 41191

10 2

D3/2

9 4 9 7 3 2 -13 -17 7

2

I13/2 43189

4

D1/2 L15/2 2 H19/2 2

12 -16 4 -5 14 8 22 -12 -4 -5 6

2

D25/2

38167 38273 38300 38571 38808 38915 39180 40639 40690 40747 40779 40806 40886 40933 40994 41084 41193 41318 41450 41576 41766 41925 41991 42014 42576 42676 42970 43186 43192 43282 43406 43496 43743 46613 47049 47189 47291 47418 47507 47538 47630 47692 47737 47755 47798 48037 48187 48291 48555 48776

∆Ea (cm-1) -14 4 8 6 -2

4 12 -3 0 2 -14 1 -1 2

-3

The energy difference, ∆E ) Efit - Eexp.

and red emission bands correspond to the transitions from the lowest CF levels of 4S3/2 and 4F9/2 to the ground state. As shown in the inset of Figure 3, the side bands in the low-energy wing of the ZPLs marked by star signs is due to the emission of a photon plus the spontaneous emission of one phonon. This type of vibronic process is favored even at 10 K. It is difficult to assign those side bands marked by circle signs because they could originate from the vibronic coupling to other ZPLs terminating on the Z1 to Z6 levels with multiple combinations, similar to the case of Er3+:Y2O3.13 According to the infrared and Raman spectra of Gd2O3 crystals,9,14 the side bands at 112, 303, 367, and 470 cm-1 may arise from the coupling to both the infrared-active and Raman-active lattice modes, whereas that of 567 cm-1 is presumably ascribed to the coupling to the Raman mode at the maximum frequency. In general, vibronic coupling with infrared-active modes is typical of M process,

whereas coupling with Raman-active modes is typical of ∆ process.15,16 Currently the dominant mechanism that contributes to the above emission side bands remains unclear. Compared with the excitation side bands for the 2H11/2 r 4I15/2 transition,11 the emission side bands for the 4S3/2 f 4I15/2 transition are much weaker, due partly to the much smaller rank-2 RMEs of the unit tensor (Table 4) for M process.15 The Er3+ luminescence around 1540 nm, which corresponds to the wavelength for optical communication windows, was also investigated. Figure 4 shows the 4I13/2 f 4I15/2 emission at room temperature (RT) under the excitation to the 4G11/2 state. A very sharp and strong emission line was observed at 1536 nm corresponding to the transition from the lowest CF level of 4I13/2 to the ground level (Z1). The fluorescence decay of this line was measured, which fits well to a single-exponential function resulting in a lifetime of 5.54 ms.

Er3+ in Gd2O3 Nanocrystals

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10407

TABLE 2: Free-Ion and Crystal-Field Parameters (in cm-1) of Er3+ at the C2 Site of Gd2O3 Nanocrystalsa parameterb

C2 (Gd2O3)

C2 (Y2O3)c

Eavg F2 F4 F6 ξ R β γ T2 T3 T4 T6 T7 T8 M0 P2 B20 B22 B40 ReB42 ImB42 ReB44 ImB44 B60 ReB62 ImB62 ReB64 ImB64 ReB66 ImB66 rmsd

35367(16) 96617 (171) 68576(470) 50169(703) 2370(2) 17.65(0.25) -667.7(10) 2039(160) 60(37) 53(4) 37(5) -279(15) 165(22) 112(37) 4.46(0.29) 725(78) -174(29) -681(15) -1184(70) -1103(61) -385(83) 484(76) 915(46) 163(85) 297(53) -61(68) 142(66) 292(46) -43(48) 18(37) 12.5

96656 70798 52533 2383

TABLE 4: Measured and Calculated Absorption Line Strengths for Transitions from 4I15/2 of Er3+ in Gd2O3 Nanocrystalsa |〈ΦJ|U(k)|Φ′J′〉|2 λh (nm) Smea

multiplet 4

I13/2b 4 S3/2 2 H11/2 4 F7/2 4 F5/2 4 F3/2 2 H9/2 4 G11/2 2 G9/2+2K15/2+2G7/2 rms ∆S (10-20 2 c cm )

1548 551 528 493 456 449 411 383 365

Scal

k)2

1.059 1.059 0.0198 0.01902 3.723 4.550 0.7182 0.502 0.646 0.0032 0.121 0.114 0.0006 0.061 0.064 0.0001 0.302 0.185 0.0055 6.960 5.428 0.8584 1.530 0.980 0.0438 0.82

k)4

k)6

0.1175 0.0112 0.4170 0.1465 0.0015 0.0006 0.0224 0.4989 0.2718

1.4295 0.2087 0.1159 0.6206 0.2197 0.1271 0.2201 0.1160 0.3215

All Smea and Scal are in units of 10-20 cm2. b The line strength of 4 I15/2 f 4I13/2 derived from the measured radiative lifetime of 4I13/2, was used as a standard to determine the absolute values of Ω2,4,6 parameters thus scale the line strengths of other bands. c rms∆S ) [∑i)1N(Smea - Scal)2/(N - 3)]1/2. a

-150 -678 -1389 -1061 -239 712 852 252 271 -119 180 218 -24 42

a Values in parentheses are errors in the indicated parameters. b The Mj (j ) 0,2,4) and Pk (k ) 2,4,6) parameters were constrained at the following ratios: M2/M0 ) 0.56, M4/M0 ) 0.38; P4/P2 ) 0.75, P6/P2 ) 0.5. c FI parameters from ref 22; CF parameters from ref 21. For comparison, both original FI and CF parameters were converted according to the definitions or conventions used in this paper. d The rms deviation between the experimental and calculated energies was used as a figure of merit to describe the quality of a fit, with rms ) [∑(Eexp - Ecalc)2/(N - P)]1/2, where N ) 107, the number of levels fit, and P ) 30, the number of parameters freely varied.

Figure 4. Near-infrared emission spectrum for 4I13/2 f4I15/2 at 297 K under the 381.3 nm excitation to 4G11/2.

TABLE 3: CF Strengths of Er3+ Ions in Different Hosts host

symmetry

S (cm-1)

ref.

LaF3 LiYF4 LaCl3 YVO4 YAl3(BO3)4 LiNbO3 YAlO3 Y3Al5O12 Y2O3 Sr5(PO4)3F Gd2O3

C2V S4 D3h D2d D3 C3 Cs D2 C2 Cs C2

257 334 118 279 333 370 371 550 569 625 554

35 36 37 38 39 40 41 36 21 42 this work

Figure 5 shows the 10 K high-resolution excitation spectrum by monitoring the main emission at 563.7 nm. The most intense excitation peaks belong to the hypersensitive transitions to 2H11/2 and 4G11/2, consistent with the observation of self-absorption in Figure 3. Abundant CF levels of excited states above 4S3/2 were identified and assigned, spanning about 20 different SLJ multiplets. In addition to those sharp f-f transitions of Er3+, we can also identify f-f transitions (8S7/2 f 6P, 6I, and 6D) of Gd3+ as labeled in Figure 5. Similar to the spectrum of Eu3+: Gd2O3,5,17 the peak at 226 nm is due to the band-gap excitation of Gd2O3. Obviously, there exists energy transfer (ET) from

Figure 5. Excitation spectrum of Er3+ in Gd2O3 nanocrystals by monitoring the emission at 563.7 nm at 10 K. The peaks marked by star signs denote the vibronic side bands.

Gd3+ to Er3+ and from the band gap of the host to Er3+. By utilizing the enhanced ET from Gd3+ to Er3+ in nanocrystals, the intrinsic fluorescence lifetimes of 4S3/2 at various temperatures were determined.11 The two peaks marked by star signs in Figure 5 correspond to the phonon side bands due to M process for the hypersensitive transitions from the ground state to the 2H11/2 and 4G11/2 states respectively, as already discussed in detail previously.11 IV. Crystal-Field Analysis So far, 107 CF levels have been located and assigned based on the low-temperature emission and excitation spectra obtained

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under the xenon or laser excitation, as shown in Table 1. The energy levels of 4G9/2 were not determined, because the excitation peaks in this region were masked by the much stronger 6I peaks of Gd3+ around 36 200 cm-1 as a consequence of co-incident overlap in the excitation spectrum. It is a general practice to perform the energy level fitting by parametrization of an effective operator Hamiltonian including free-ion (FI) and CF interactions. The commonly used effective operator Hamiltonian is

H ) HFI + HCF

(1)

where the FI Hamiltonian can be expressed as

Fkfk + ζ f ASO + RL(L + 1) + ∑ k)2,4,6 βG(R2) + γG(R7) + ∑ Titi + ∑ Mhmh + i)2,3,4,6,7,8 h)0,2,4 P fpf ∑ f)2,4,6

HFI ) Eavg +

(2)

There are up to 20 FI parameters in eq 2. The predominant terms in this Hamiltonian are the electrostatic and spin-orbit interactions represented by parameters Fk and ζf. The configuration interactions (R, β, γ), spin-spin and spin-other-orbit interactions (Mh), the two-body electrostatically correlated magnetic interactions (P f), and the three-particle configuration interactions (Ti) represent higher order interactions that are essential in order to accurately reproduce the energy level structure of f-element ions. The physical meanings of these FI parameters were described by Crosswhite and Carnall et al.18,19 Since there are enough (28 of a total of 41) SLJ multiplets of Er3+ being located and assigned, all FI parameters were allowed to vary freely in the least-squares fitting of the CF energy level structure except for the parameters of M2, M4, P4, and P6 which were constrained by the Hartree-Fock-determined ratios M2/M0 ) 0.56, M4/M0 ) 0.38; P4/P2 ) 0.75, and P6/P2 ) 0.5.18 The single-particle CF Hamiltonian is usually expressed in Wybourne’s notation in which the number of independent nonvanishing CF parameters is determined by site symmetry.20 For the C2 site of Er3+ ions, we have

HCF ) B02C02 + B22C22 + B04C04 + ReB24(C24 + C -24) + ImB24(C24 - C -24) + ReB44(C44 + C -44) + ImB44(C44 - C -24) + B06C06 + ReB26(C26 + C -26) + ImB26(C26 - C -26) + ReB46(C46 + C -46) + ImB46(C46 - C -46) + ReB66(C26 + C -26) + ImB66(C66 - C -66) (3) Due to the low site symmetry, all of the independent CF parameters except Bk0 are complex, each having real and imaginary parts denoted by Re Bkq and Im Bkq respectively. An axis rotation is introduced to make the imaginary part of B22 equal to zero, which reduces the total number of independent CF parameters from 15 to 14. Theoretically, the 4 f 11 configuration consists of 182 twofold degenerate CF levels. The energy-level-fitting was performed using the f-shell empirical programs of Prof. M. F. Reid, which enables a complete diagonalization without truncation of the 4 f 11 wave functions. The FI parameters of Er3+:LaF319 and the CF parameters of the Er3+:Y2O3 crystal21 listed in Table 1 were used as starting values. The effect of J-mixing is automatically

taken into account in the program. Some strategies were employed to fulfill the fit repeatedly: first, we fit those multiplets whose CF levels were most reliably determined by freely varying both the FI parameters of Fk and ζf and the CF parameters. The other parameters were fixed at those values of Er3+:LaF3; second, finely tune the above fit by introducing other high-order FI parameters, or adding more CF levels of other multiplets such as those congested levels, or both; third, relocate or reassign those uncertain CF levels which resulted in anomalously large root-mean-square (rms) deviation of the fit, and simultaneously vary thirty parameters to fit all CF levels we observed. Finally, 107 levels of Er3+ in Gd2O3 were fitted to 30 freely varied parameters. The fitted energy levels below 49 000 cm-1 are compared with the experimental values in Table 1. Table 2 lists the final FI and CF parameters of the fit. The rms deviation of the fit is as small as 12.5 cm-1, which indicates a fairly good agreement between the observed and the calculated sets. It should be noted that the variation of two-body and threebody interaction parameters (R, β, γ, and Ti) significantly affects the fit of the CF levels of 4D5/2,7/2 and 4G11/2 multiplets. Similarly, Kisliuk et al. noticed a very large error for 4D5/2 in the fit of FI levels of Er3+:Y2O3 using only parameters of Fk and ζf.22 As compared in Table 2, the fitted FI parameters of Fk and ζf are close to those of Er3+:Y2O3,22 whereas most of the fitted CF parameters deviate slightly from those of Er3+: Y2O3,21 indicating a similar CF environment of Er3+ in either Gd2O3 or Y2O3. This has been confirmed by carefully comparing all of the observed CF levels of Er3+ in Gd2O3 and Y2O3. Compared to the case of Er3+:Y2O3,22 all multiplets below 30 000 cm-1 of Er3+:Gd2O3 except 4F3/2 are entirely blue-shifted within 0∼20 cm-1 and the CF splitting of each multiplet varies little. However, the 4F3/2 multiplet is found blue-shifted with an anomalously large value (100 cm-1) for unknown reason.22 The scalar CF strength (S) that reflects the overall CF interaction in the crystal is calculated to be 554 cm-1, according to Chang’s definition21

S)

(

)

Bkq|2 ∑ ∑ | 3 k)2,4,6 2k + 1 q 1

1

1/2

(4)

Table 3 compares the CF strengths of Er3+ ions in some common inorganic crystals, which were calculated based on the reported CF parameters in those hosts. The CF strength of Er3+: Gd2O3 crystal is very large among those reported in Table 3, a value close to that in Y2O3 but doubling that in YVO4 or LaF3, indicating a very strong CF experienced by Er3+ ions. The strong CF strength is in consistence with the low point-group symmetry of Er3+ sitting in the lattice of Gd2O3. Usually a higher pointgroup symmetry occupied by RE ions in the host results in a smaller CF strength. V. Judd-Ofelt Intensity Calculation To carry out the Judd-Ofelt (JO)23,24 intensity calculation, generally one has to quantitatively measure the RT absorption spectrum. However it is of technical difficulty to do so for RE ions diluted in nanocrystals. Recently, we observed a reciprocity relation between the excitation and emission spectra of Er3+: Gd2O3 nanocrystals,11 based on the fact that the excitation intensity was proportional to its absorption cross section for some transitions of interest. It turns out that the excitation spectrum reproduces well the corresponding absorption spectrum for the excitation to those multiplets that are followed by a very fast nonradiative relaxation to the monitored level (for example, excited to the 4F7/2,5/2,3/2 and 2H11/2 when monitoring the emission

Er3+ in Gd2O3 Nanocrystals

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10409

∑

Scal(J f J′) )

Ωt|〈ΦJ|U(t)|Φ′J′〉|2

(7)

t)2,4,6

The RMEs of the unit tensor |〈ΦJ|U(t)|Φ′J′〉|2 were calculated and listed in Table 433 using the JJINT program written by Prof. M. F. Reid which takes J-mixing into account. By a least-squares fitting of Scal to the measured line strengths Smea, the ratios of three JO intensity Ω2,4,6 parameters were obtained. Subsequently, the ED radiative transition rate of the 4I13/2 f 4I15/2 transition derived from the measured RT lifetime of 4I13/2, was used as a standard to determine the absolute values of Ω2,4,6 parameters according to Figure 6. Excitation spectrum of Er3+ in Gd2O3 nanocrystals by monitoring the emission at 563.7 nm at 297 K. Seven bands labeled in the figure are chosen for a modified JO intensity calculation.

AED(J f J′) ) n(n2 + 2)2

64π4e2 3h(2J + 1)λh

from the 4S3/2 for Er3+).11 As a matter of fact, this is equivalent to a special situation discussed by Partlow and Moos, in which the quantum efficiency ηAB from an excited multiplet (A) to its low-lying multiplet (B) is assumed to be 1.25 The above proportionality between the RT absorption and excitation spectra is utilized to perform the following modified JO calculation. In this modified JO analysis, the effect of J-mixing on the JO parameters (Ω2,4,6) and radiative transition rates is taken into account following the method proposed by Xia and Chen.26,27 Seven bands in the RT excitation spectrum (Figure 6), which correspond to the multiplets of 2H11/2, 4F7/2,4F5/2, 4F3/2, 2H9/2, 4G 2 2 2 11/2, and G9/2+ K15/2+ G7/2, are deliberately selected since they satisfy the aforementioned condition for the reciprocity relation. It should be noted that the nonradiative relaxation from the 2H9/2 multiplet is much faster at RT than at 10 K and no radiative transition from 2H9/2 is observed. The ratios of absorption line strengths from 4I15/2 to those multiplets were thus estimated according to the integrated excitation intensity (Γexc) for each band. The measured absorption line strengths Smea from the ground 4I15/2 multiplet (J ) 15/2) to the excited J′ manifold can be approximately obtained using the following expression:

Smea(J f J′) )

9n C Γ λh (n2 + 2)2 exc

(5)

where C is a proportional constant, λh is the mean wavelength of the absorption band, and n is the refractive index of cubic Gd2O3 obeying the Sellmeier equation28

n(λ,unit:µm) ) x(- 0.0075356/λ2 + 0.364402)-1 + 1 (6) Note the difference between eq 5 and the commonly used expression for Smea.29-31 A relative value of Smea instead of an absolute one is determined by eq 5. TEM and SEM images showed that the nanocrystals tend to form the nanoaggregates in the micron range by self-assembling.11 Therefore, we use the index of refraction of bulk Gd2O3 in eq 5, instead of an effective index of refraction that takes into account the filling factor occupied by nanocrystals.32 To validate this, we compared the measured fluorescence lifetime of 4I13/2 when the sample was immersed in various solvents (such as air, C2H5OH, CS2 and C6H5Cl) and no significant lifetime change was observed. According to JO theory, the absorption line strength for an ED transition can also be expressed in terms of Ω2,4,6 parameters by31

AMD(J f J′) ) τr-1 )

3

9

Ωt|〈ΦJ|U(t)|Φ′J′〉|2 ∑ t)2,4,6

(8)

64π4e2n3 ep 2 |〈ΦJ|L + 2S|Φ′J′〉|2 3 2mc 3h(2J + 1)λh (9)

( )

[AED(J f J′) + AMD(J f J′)] ∑ J′

(10)

where τr is the radiative lifetime of the excited multiplet (J); |〈ΦJ|L + 2S|Φ′J′〉|2, the RME for the magnetic-dipole (MD) transition from J to J′, was calculated using the same JJINT program;33 we assume that the quantum efficiency of 4I13/2 approaches 1. It is reasonable since there is a large energy gap between 4I13/2 and 4I152 (∼6500 cm-1) which requires at least 11 phonons to bridge it. Note that the MD contribution from Er3+ at the C2 site was subtracted from the total radiative rate of the 4I13/2 f 4I15/2 transition in the calculation. The MD contribution from Er3+ at the S6 site is neglected due to the following facts: (1) the lifetime of 4I13/2 was measured under the selective excitation to 4G11/2 of Er3+ at the C2 site; and (2) the ratio of S6 and C2 sites occupied by Er3+ is approximately 1:3. As a result, the three JO intensity Ω2,4,6 parameters were obtained (Ω2,4,6 ) 4.96, 2.23, and 0.49, in units of 10-20 cm2). For comparison, we performed the above fit for the case without J-mixing, which resulted in similar values (Ω2,4,6 ) 4.38, 2.38, and 0.50). It turns out that J-mixing only slightly affects the determined JO parameters. In comparison with the JO parameters (Ω2,4,6 ) 4.93, 1.11, and 0.47) for Er3+:Y2O3,27 the parameters of Ω2 and Ω6 vary a little whereas Ω4 is doubled for Er3+:Gd2O3. The final values of the measured and calculated line strengths are compared in Table 4. As shown in Table 4, the rms deviation of the fitting is 8.2 × 10-21 cm2, which indicates that the fitting results basically agree with the experiments. Once the JO intensity parameters are determined, the ED and MD radiative transition rates A(JfJ′) in the crystal, corresponding to transitions from the excited multiplet to the lower multiplets, can be respectively calculated by eqs 8-10. The calculated ED, MD, and total radiative transition rates of the Er3+ excited multiplets for the cases of J-mixing and without J-mixing are compared in Table 5. The branching ratios for the J-J′ emission is βJfJ′ ) A(JfJ′)/∑J′A(JfJ′). The fluorescence lifetimes of several multiplets were experimentally determined and listed in Table 5 for comparison. As shown in Table 5, the effect of J-mixing significantly affects the calculated ED radiative transition rate and thus the radiative lifetime of the 4S 3/2 multiplet. That is, the total ED radiative transition rate of 4S -1 if J-mixing is taken 3/2 is increased from 1419 to 2336 s

10410 J. Phys. Chem. C, Vol. 111, No. 28, 2007

Chen et al.

TABLE 5: Calculated Radiative Transition Rates for the Emissions from the Excited Multiplet to Its Lower Multiplets at RT no J-mixing multiplet 4I 13/2 4 I11/2 4I 9/2 4 F9/2 4S 3/2 2

H11/2 4F 7/2 4 F5/2 4F 3/2 2 H9/2 4 G11/2 2P 3/2

J-mixing

Aed (s-1)

Amd (s-1)

radiative lifetime (µs)

Aed (s-1)

Amd (s-1)

radiative lifetime (µs)

108 169 452 3074 1419 14507 6113 3920 3010 4757 54550 9583

72 16 2.3 17 0 139 45 1 11 154 124 126

5543 5391 2202 324 705 68 162 255 331 204 18 103

106 176 428 2913 2336 15258 5900 3758 3102 5092 57697 9582

74 19 7 40 12 170 71 16 16 165 199 181

5543 5140 2297 339 426 65 167 265 321 190 17 102

TABLE 6: Calculated Branching Ratios (β) and Radiative Transition Rates (A) for the Emissions from 2P3/2 to the Lower Multiplets at RT

observed lifetime (µs) 5543(297K) 121(10K) 165(10K) 74(297K)

2.64(10K) 78(10K) 32(297K)

calculated radiative lifetime of 2P3/2 of Er3+:Gd2O3 is approximately 102 µs, somewhat larger than that of Er3+:Y2O3 (62 µs).34

β (%) multiplet

λh(nm)

obs.a

cal.

A (s-1)

4I 15/2 4I 13/2 4I 11/2 4I 9/2 4F 9/2 4S 3/2

320 404 473 528 619 764 812 912 1075 1116 1452 1952

8.3 24.0 27.2 13.5 8.4 15.9 2.8

5.3 18.1 36.0 10.8 6.7 11.9 2.2 2.3 2.7 1.4 2.5 0.13

514 1768 3516 1050 650 1165 216 224 259 133 244 13

2H

11/2 4F 7/2 4F 5/2 4F 3/2 2H 9/2

4G

11/2

a

According to Figure 2; it is assumed that the branching ratios remain unchanged at RT.

into account. Since 4S3/2 and 2H11/2 are thermally coupled with a small energy separation of 710 cm-1, the J-mixing coefficient from 2H11/2 into 4S3/2 was estimated to reach about 2.7% according to the expression proposed by Xia and Chen.26,27 Therefore the ED transition from 4S3/2 is greatly enhanced as a result of the intensity borrowing from 2H11/2. Specifically, for the dominant green emission (4S3/2f4I15/2) that borrows the intensity from the hypersensitive transition of 2H11/2f4I15/2, the ED radiative transition rate was nearly doubled with an increase from 942 to 1863 s-1. In contrast, J-mixing has little impact on the other multiplets listed in Table 5. Based on the calculated radiative lifetimes of 4S3/2 and 2H11/2 (426 µs and 65 µs respectively), the temperature-dependent lifetime behavior of 4S 11 3/2 has been well addressed in the previous work. Due to the fact that the 2P3/2 multiplet plays an important role in the energy transfer from Gd3+ to Er3+ in Gd2O3, we calculated the branching ratios and radiative transition rates for the RT emissions from 2P3/2 to its lower multiplets (Table 6). Table 6 shows the overall agreement between the calculated and the measured branching ratios for the 2P3/2 emissions based on the three JO parameters we have determined. The calculated results show the dominant transitions to 4I11/2, 4I13/2, and 4S3/2, in accordance with the observed spectrum. This further confirms the validity of the modified JO intensity calculation based on the excitation spectrum. The 2P3/2 lifetime of Er3+:Gd2O3 is experimentally determined to be 78 µs at 10 K and 32 µs at 297 K, very different from that of Er3+:Y2O3 reported by Weber et al. (3.7 ms at RT).34 As shown in Tables 5 and 6, the

VI. Conclusions We have systematically investigated the optical spectra and electronic structures of Er3+ in Gd2O3 nanocrystals. A vast majority of CF levels below 43 000 cm-1 of Er3+ at the C2 site of Gd2O3 have been experimentally determined for the first time. Phonon side bands and the self-absorption with fine structures from the ground level to the hypersensitive multiplets were observed in the emission spectra of Er3+:Gd2O3 nanocrystals. By means of the parametrization of an effective operator Hamiltonian including 30 freely varied FI and CF parameters, energy-level fitting yields a very small standard deviation (12.5 cm-1) from the experiments. The set of CF levels we offer is essential to a reliable analysis of optical behaviors of Er3+ in Gd2O3, for instance, upconversion mechanism and energy transfer etc. Furthermore, a method based on the proportional relation between the excitation and absorption spectra to calculate the JO parameters has been proposed, which proves very useful in the spectroscopic evaluation of RE ions in nanosystems or bulk powders. Some important spectroscopic parameters such as JO parameters, radiative lifetime, and fluorescence branching ratios based on this method have been reported. It is found that J-mixing has considerable impact on the calculated radiative lifetime of 4S3/2. Since Er3+:Gd2O3 nanocrystals have promising applications in the fields of optoelectronics and biolabels, current achievements on the optical spectroscopy of Er3+:Gd2O3 may provide a general guide to understanding the RE luminescence mechanism and to designing functional nanomaterials. Acknowledgment. This work is supported by the One Hundred Talents Program from the Chinese Academy of Sciences, the National Natural Science Foundation of China (No. 10504032), the Startup Foundation from the State Ministry of Personnel of China, and the Talent Youth Foundation of Fujian Province of China (No. 2006F3137). Work at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, under Contract DE-AC0206CH11357. We are grateful to Prof. Min Yin for providing us the nanocrystals and to Prof. M.F. Reid for the use of f-shell empirical programs. References and Notes (1) Gordon, W. O.; Carter, J. A.; Tissue, B. M. J. Lumin. 2004, 108, 339.

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