DynamicsoftheGreenandRedUpconversionEmissionsin...

Hindawi Publishing CorporationJournal of NanomaterialsVolume 2010, Article ID 491982, 8 pagesdoi:10.1155/2010/491982

Research Article

Dynamics of the Green and Red Upconversion Emissions inYb3+-Er3+-Codoped Y2O3 Nanorods

O. Meza,1 L. A. Diaz-Torres,1 P. Salas,2 C. Angeles-Chavez,3 A. Martınez,4

J. Morales,4 and J. Oliva1

1 Grupo de Espectroscopia de Materiales Avanzados y Nanoestructurados (EMANA), Centro de Investigaciones en Optica, A. C.,A. P. 1-948, 37160 Leon, Mexico

2 Centro de Fısica Aplicada y Tecnologıa Avanzada, Universidad Nacional Autonoma de Mexico,A. P. 1-1010, 76000 Queretaro, QRO, Mexico

3 Programa de Ingenierıa Molecular, Instituto Mexicano del Petroleo, A. P. 14-805, 07730 Mexico, D.F., Mexico4 Universidad Autonoma Metropolitana—Azcapotzalco, DCBI-Ciencias Basicas, Area de Fısica Atomica Molecular Aplicada,Sn Pablo 180, 02200 Mexico, D.F., Mexico

Correspondence should be addressed to L. A. Diaz-Torres, [email protected]

Received 28 January 2010; Accepted 4 June 2010

Academic Editor: Kui Yu

Copyright © 2010 O. Meza et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Efficient green and red upconversion emission in Y2O3:Yb3+, Er3+ nanorods under 978 nm radiation excitation is achieved.Experimental effective lifetimes, luminescent emissions, and nanorod sizes depend strongly on the solvent ratios used during thesynthesis. A microscopic nonradiative energy transfer model is used to approach the dynamics of the green, red, and infraredemissions. The excellent agreement between simulated and experimental decay suggests that the energy transfer mechanismsresponsible of the visible emission depend on the solvent ratio.

1. Introduction

Synthesis and optical characterization of luminescent mate-rials in their nanocrystalline form have led to their growinguse in numerous military and medical applications, such asimaging, range finding, flash lidar, and remote sensing [1–4]. Yttrium Oxide (Y2O3) has been the material of choicefor photonics applications, owing to its favorable physicalproperties and ease of synthesis in the nanometer regime [5–7]. In particular, nanometer-sized rare earth-doped Y2O3 hasshown enhanced luminescence and quantum yields relativeto its bulk counterparts [8]. Very recently, a great deal ofresearch has focused on finding lanthanide-doped inorganicnanocrystalline materials that will undergo near infrared(NIR) to-visible upconversion [6, 9]. The Er3+ ion has a rel-atively low absorption cross-section for the transitions in thenear-infrared (NIR) region around 1000 nm. On the otherhand, the Yb3+ ion exhibits a larger absorption cross-sectionin this region, and thus, codoping with Yb3+ has provento be a successful alternative for enhanced upconversion

processes. In fact, there is a large spectral overlap between the2F5/2 → 2F7/2 Yb3+ NIR emission and the 4I11/2 → 4I15/2 Er3+

absorption bands, which results in an efficient nonradiativeenergy transfer process, and in turn efficient upconversionemission. Some of the most important parameters onluminescent materials are the lifetime and quantum yield.Both parameters are related to nonradiative energy transferprocesses among active ions within the host. There areseveral models that attempt to explain the lifetime andquantum yield dependence on nonradiative energy transferrates. The pioneering works of Forster [10], continued laterby Dexter [11] and Inokuti and Hirayama [12] allowed theestimation of the non radiative energy-transfer rates basedon experimental fluorescence lifetime measurements [13].With varying degrees of acceptance, all these models havebeen applied to a large variety of crystalline systems in spiteof the fact that hose models consider that the luminescentcenters are continuously distributed within the luminescenthost. This certainly is not the case in a crystalline medium,where the ions are distributed in very specific positions

2 Journal of Nanomaterials

within the crystal lattice. Further, the discreteness of theactive ions distribution within the crystalline lattice mightbecome increasingly important as we consider nanometer-sized luminescent materials. So, there is a need to revise thosemodels and formulate alternative ones.

In this paper, we consider the discrete distribution ofthe active ions (Er3+ and Yb3+ ions) within the crystallinelattice to study the nonradiative energy transfer processesthat lead to the visible upconverted emission in Y2O3 Er3+-Yb3+-codoped nanorods. Y2O3 nanorod samples were syn-thesized by hydrothermal method using two ethanol/watersolvent ratios (SRs), 1 : 10 and 1 : 5. Experimental effectivelifetimes, luminescent emissions, and nanorod sizes dependstrongly on the SRs. A nonradiative energy transfer modelis proposed to numerical simulate the dynamics of theexcitation energy among the active ions as well as theiremission fluorescence decays. By doing that we extend theunderstanding of the non radiative energy transfer processthat affect the photoluminescent properties of Er3+ andYb3+ ions in Y2O3 nanorods. These simulations resultsindicate that solvent concentration plays an important roleon the upconversion luminescence processes, and therefore achange in the lifetime and quantum yield will be observed. Itbears mentioning that our model is the only one at presentthat considers the discreet nature of the nanocrystals; inaddition it also can consider more than one exited state(energy level) of the ions. All the above advantages are incontrast to the traditional models by Vasquez [13], Jerez etal. [14] and Parisi et al. [15], which do not consider thediscreteness of the nanocrystals and are suitable only forsystems of two levels ions.

2. Experimental

The Y2O3:Yb3+, Er3+ nanorods, codoped with 1 mol%of Er2O3 and 2 mol% of Yb2O3, were synthesized bythe hydrothermal precipitation method via cetyltrimethylammonium bromide (CTAB) complexation, for two dif-ferent ethanol to water SRs, 1 : 5 and 1 : 10. All chemicalswere reagent grade supplied by Aldrich, Inc. Samples wereobtained using as precursors YCl36H2O, Er(NO3)35H2O,YbCl36H2O, and CTAB as cationic surfactant. In both cases,all components were mixed in the corresponding ethanolto water SR, at room temperature, under vigorous stirring.The precipitation was achieved by adding sodium hydroxideand the resulting solution was transferred into a sealedautoclave maintained at 100◦C during 20 h. The precipitatewas then washed with distilled water and dried in an ovenat 100◦C for 15 h. Then it was annealed at 1000◦C for 3 h,with a heating rate of 31◦C/min. X-ray diffraction (XRD)patterns were obtained using SIEMENS D-5005 equipmentprovided with a Cu tube with Kα radiation at 1.5405 A,scanning in the 15–80◦ 2θ range with increments of 0.02◦

and a swept time of 2 s. Transmission electron microscopy(TEM) was performed in JEM-2200FS transmission elec-tron microscope with accelerating voltage of 200 kV. Thephotoluminescence characterization was performed under978 nm excitation forming a tunable OPO system (MOPOfrom Spectra Physics) pumped by the third harmonic of a

10 ns Nd:YAG pulsed laser. The fluorescence emission wasanalyzed with an Acton Pro 500i monochromator and twoHamamatsu photomultiplier tubes (R7400U-20 for VIS andfor R3809U-68 for NIR) connected to an SR860 lock-inamplifier (Stanford Research). Fluorescence lifetimes weremeasured by connecting the photomultiplier to a 500 MHzLecroy digital Oscilloscope. The system was controlled with aPC were emission spectra and decay trends where registered.All photoluminescence measurements were done at roomtemperature.

3. Model and Theory

The microscopic origin for nonradiative energy transfer pro-cesses can be visualized as an interaction between an excitedion, the donor D, and another not excited ion, the acceptor A,with an absorption transition resonant with the deexcitationof the first one [10, 11, 16]. In the case of Y2O3:Yb3+,Er3+

under pumping at 978 nm, Yb3+ ions can be visualizedas donors and Er3+ ions as acceptors due to absorptioncross-section differences between the Yb(2F5/2) and Er(4I11/2)energy levels [17]. The corresponding nonradiative energytransfer rate between ith Yb3+ ion and the jth Er3+ ion isgiven by [18]

W(

YbISFS −→ ErIS

ES

)i j=C(

YbISFS −→ ErIS

ES

)

(R(

Ybi, Er j))6 , (1)

where R(Ybi, Er j) is the distance between the ith Yb ionand the jth Er ion, C(YbIS

FS −→ ErISES) is the dipole-dipole

microinteraction strength parameter [11, 19]. For simplic-ity we represent this process by W(YbIS

FS −→ ErISES)i j . This

notation indicates that the ith Yb3+ ion has a nonradiativerelaxation from an initial state IS to a final state FS, and thefreed energy excites the jth Er3+ ion from an initial state ISup to an excited state ES.

Under 978 nm pulsed excitation, the Er3+ ions areexcited from the ground state 4I15/2 to the excited state4I11/2, mainly by the phonon-assisted nonradiative energytransfer (ET) process Yb3+(2F5/2,2F7/2) → Er3+(4I15/2,4I11/2).Then, the populated 4I11/2 level is excited to the 4F7/2 levelmainly by phonon-assisted ET from excited Yb3+ ions [7].The populated 4F7/2 state rapidly relaxes to the two lowerlevels: 2H11/2 and 4S3/2, which produce green upconversionluminescence. So, in our model we consider this processas an overall Yb3+(2F5/2,2F7/2) → Er3+(4I11/2, 2H11/2+4S3/2)non radiative ET process instead of the Yb3+(2F5/2,2F7/2) →Er3+(4I11/2, 4F7/2) ET followed by the nonradiative relaxationEr3+(4F7/2) → Er3+(4I11/2, 2H11/2+4S3/2). In addition, thepopulated Er3+(4I11/2) state mostly relaxes to the long-livingEr3+(4I13/2) state. Electrons in the Er3+(4I13/2) state may bepromoted to the upper Er3+(4F9/2) state by the ET processYb3+(2F5/2,2F7/2) → Er3+(4I13/2,4F9/2). The populated 4F9/2

level mostly relaxes radiatively to the ground state 4I15/2

level, which causes the Er red emissions. For simplicityin our model the Yb3+(2F5/2,2F7/2) → Er3+(4I15/2, 4I11/2),Yb3+(2F5/2,2F7/2)→Er3+(4I13/2, 4F9/2), and Yb3+(2F5/2,2F7/2)→ Er3+(4I11/2, 2H11/2+4S3/2) transition were denoted by

Journal of Nanomaterials 3

W(Yb10 → Er0

2), W(Yb10 → Er1

3), and W(Yb10 → Er2

4),respectively; see Figure 1.

By taking into account the above described ET processesone can write down ordinary differential equations thatgovern the excitation dynamics among all Yb3+ and Er3+ ionsinside of an arbitrary Y2O3:Yb3+, Er3+ nanocrystal:

dP1Ybi

dt= − 1

τ(

Yb10

)P1Ybi −

NEr∑

m=1

W(

Yb10 −→ Er0

2

)imP1

YbiP0Erm

−NEr∑

m=1

W(

Yb10 −→ Er1

3

)imP1

YbiP1Erm

−NEr∑

m=1

W(

Yb10 −→ Er2

4

)imP1

YbiP2Erm ,

dP1Er j

dt= − 1

τ(Er1

0

)P1Er j +

1τ(Er2

1

)P2Er j ,

−NYb∑

m=1

W(

Yb10 −→ Er1

3

)mjP1

YbmP1Er j

dP2Er j

dt=− 1

τ(Er2

0

)P2Er j −

1τ(Er2

1

)P2Er j +

1

τ(

Er32

)P3Er j

+NYb∑

m=1

W(

Yb10 −→ Er0

2

)mjP1

YbmP0Er j

−NYb∑

m=1

W(

Yb10 −→ Er2

4

)mjP1

YbmP2Er j ,

dP3Er j

dt=− 1

τ(

Er30

)P3Er j −

1

τ(

Er32

)P3Er j +

1τ(Er4

3

)P4Er j

+NYb∑

m=1

W(

Yb10 −→ Er1

3

)mjP1

YbmP1Er j ,

dP4Er j

dt= − 1

τ(Er4

0

)P4Er j −

1τ(Er4

3

)P4Er j

+NYb∑

m=1

W(

Yb10 −→ Er2

4

)mjP1

YbmP2Er j ,

(2)

where P1Ybi is the probability to finding the ith Yb3+ ion at its

exited state 2F5/2 at the time t. PXEri is probability to findingthe jth Er3+ ion at its X state (with X = 1,2,3,4, correspondingto the states 4I13/2, 4I15/2, 4I11/2, 4F9/2 and (2H11/2+4S3/2),resp.) at the time t. τ(Yb1

0) and τ(ErIS0 ) are the free ion

lifetimes for Yb3+ and Er3+, respectively, from the level ISto ground state, when no energy processes are present (seeTable 1). And 1/τ(ErIS

ES) are the relaxation rates of the Er3+

ions from its upper state IS to the next lower state FS = IS−1,for IS = 4,3,2 (see Table 1). NYb and NEr are the total numberof active ions inside of the Y2O3:Yb3+, Er3+ nanocrystal.

Y2O3 is a cubic perovskite with spatial group symmetryIa3 (206) [21, 22]. Using the coordinate data from Crystal-lographic tables for the spatial group Ia3(206) [23] a kthnanocrystal sample is numerically generated. Then the Yb3+

and Er3+ dopant ions are placed into the potential 24d and 8bcrystal sites with a random uniform distribution by using theMonte Carlo method. With this random uniform placementEr3+ and Yb3+ ions each have a particular distribution ofneighboring Er3+ and Yb3+ codopants within the particularkth generated nanocrystal. Thus, based on actual interionicdistances and by assuming a dipole-dipole microinteractionstrength parameter we compute all the non radiative transferrates among ion pairs for the considered transfer processes(see Figure 1). After that, we are in the position to solve (2)by a fourth-order Runge-Kutta Method [24]. Notice that theonly free parameters are the C(YbIS

FS → ERISES) parameters.

ith Yb3+ and jth Er3+ ions each have its own decay rateproportional to its own P1

YbiP1Ybi and PXEr j P

XEri probability of

being exited at time t. Thus, the total fluorescence emissiontransient from the kth generated crystal will be the averageover the individual emissions overall active ions withinthe kth nanocrystal, and the macroscopic emission willbe proportional to the average over a large number of knumerically generated crystal samples, that is,

ϕYb(t) =⟨⟨P1

Ybi

⟩av.overi

⟩av.overk

,

ϕXEr(t) =

⟨⟨P1

Erj

⟩av.over j

av.overk.

(3)

4. Results and Discussion

The XRD patterns of the Y2O3:Yb3+, Er3+ nanocrystallinepowders prepared with 1 : 5 and 1 : 10 ethanol/water ratios(SR) are shown in Figure 2. Both samples exhibit almostidentical patterns and the main characteristic diffractionpeaks can be indexed as a pure cubic phase (space groupIa3 (206)) with cell parameter of 10.6056 A 10.5818 A for thewater to ethanol SR 1 : 10 and 1 : 5, respectively. These valuesare in agreement with the standard value of 10.6 A for thebulk cubic Y2O3 reported in card number JCPDS 41-1105[22]. Figure 2 helps to show the dependency between thesolvent radio and interionic distance, which alone affects thenonradiative ET processes for a same dopant concentration.Both samples present single nanorod morphology as can beobserved in the TEM micrographics in Figure 3. For the 1 : 10SR sample the nanorods are 745.6 nm lengths and 55.2 nmdiameter in average, whereas for 1 : 5 SR the nanorods are1464.8 nm length and 75.4 nm diameter. Taking into accountthe dopant concentration, size, shape, and ions distributionof the nanocrystals, we simulate a great number of nanorods.We estimated the mean Yb3+-Er3+ distance (RYbEr) for eachwater to ethanol SR. These RYbE are (7.661 ± 0.020) A and(7.820 ± 0.0482) A, at the 95.0% confidence level, for 1 : 5and 1 : 10 SRs, respectively. Thus, form (1) and consideringthat in both samples the energy transfer processes amongYb3+-Er3+ pairs are the same, that is, the same dipole-dipolemicrointeraction strength parameter for each ET process, ingeneral the nonradiative ET processes are expected to be 13%


0

556

0n

m

680

nm

1533

nm

1040

nm

10

15

20

En

ergy

(103

cm−1

)

4I15/2

4I13/2

4I11/2

4I9/2

4F9/2

4S3/2

11H11/2

4F7/2

0 02F7/2

2F5/21

Er3+ Yb3+

(i)(i.ii,iii)

1

2

(ii)

(iii)

3

4

Figure 1: Energy levels diagram of Y2O3 : Er3+, Yb3+ nanorods and the considered direct Yb3+ to Er3+ nonradiative energy transfer processes:(i) W(Yb1

0 → Er02), (ii) W(Yb1

0 → Er13), and (iii) W(Yb1

0 → Er24).

Table 1: Free ion lifetimes of Yb3+ and Er3+ are reported in [20].

τ(Yb10) τ(Er1

0) τ(Er20) τ(Er3

0) τ(Er40) τ(Er2

1) τ(Er32) τ(Er4

3)

Time (μs) 670 6030 6810 644 698 11.061 39.15 387.60

Inte

nsi

ty

10 20 30 40 50 60 70 80

2θ (deg)

1 : 101 : 5

Figure 2: XRD patterns of Y2O3:Er3+, Yb3+ nanorods.

stronger in the 1 : 5 solvent ratio sample than for the 1 : 10 SRsample.

The absorption spectra of the Y2O3:Yb3+,Er3+ nanorodsfor the two studied SRs are shown in Figure 4. Theabsorption peaks for Er3+ and the corresponding transitionsfrom the ground states are 1536 nm (4I13/2), 965 nm (4I11/2)overlapped with the broad absorption band of Yb3+ (2F5/2),800 nm (4I9/2), 654 nm (4F9/2), 539 nm (4S3/2), 522 nm

(2H11/2). The new observable feature is a broad peak centeredat 1382 nm indicating the presence of residual H2O thatcould be keeping occluded within the Y2O3 nanorods. Theratio of the Er3+ (4I13/2) band to the 1385 nm H2O band is3.28 and 1.21 for the 1 : 10 and 1 : 5 SRs, respectively, Thatis in agreement with the fact that the higher content ofoccluded H2O is found in the sample obtained with a lowerSR (1 : 5).

Figure 5 shows the VIS spectra of Y2O3 under 978 nmexcitation for both samples. The green emissions wereobserved in the range of 510–580 nm, corresponding to the(2H11/2, 4S3/2)→ 4I15/2 Er3+ transitions, while the red emis-sions were observed between 640 and 690 nm, correspondingto the 4F9/2 → 4I15/2 Er3+ transitions. We can see that thesample with 1 : 10 SR has in general lower emission intensityfor all observed visible emissions than the sample with a1 : 5 SR, that in principle could be due to quenching ofthe population of the Er3+ (4I13/2) and Yb3+(4F5/2) excitedlevels by the residual H2O responsible of the 1382 nmband observed in the absorption spectra. Figure 6 showsboth experimental and simulated fluorescence decays for theYb3+ and Er3+ ions for their visible and infrared emissions.The effective lifetime is obtained from the experimentalfluorescence decay using the expression [25]:

τe =∫∞

0 I(t)dtI(t = 0)

, (4)

where I(t) is the respective fluorescence decay. The quantumyield can be calculated from the ratio of effective lifetime(τe) and free ion lifetime (τ) [25]. The computed effec-tive life times and quantum efficiencies are reported in


Table 2: Experimental and simulated lifetimes, quantum efficiencies, and microinteraction parameters.

Solvent Ratio [water : ethanol]1 : 10 1 : 5

Experimental Simulation Experimental Simulation

Effective lifetimes [μs ]

τe(Er10) 6046.2 6002.9 6818.2 6779.5

τe(Er30) 269.4 284.8 290.5 316.1

τe(Er40) 248.4 283.0 250.3 298.4

τe(Yb10) 344.9 352.1 416.9 291.3

Visible emission quantum efficiencyQ(Er3

0) 0.4183 0.4422 0.4511 0.4908

Q(Er40) 0.3559 0.4080 0.3586 0.4275

Dipole-dipoleMicro interactionParameters [cm6/s]C(Yb1

0 → Er02) 2.4719 × 10−34 6.4800 × 10−35

C(Yb10 → Er1

3) 1.6340 × 10−34 1.6340 × 10−34

C(Yb10 → Er2

4) 1.0475 × 10−34 1.0475 × 10−34

1 μm

(a)

1 μm

(b)

Figure 3: TEM image of Y2O3:Er3+, Yb3+ nanorods for thewater/ethanol solvent radios: (a) 1 : 10 and (b) 1 : 5.

Abs

orpt

ion

(a.u

.)

4S 3/2−2

H11/2

4F 9/2

4I 9/2 4

I 11/

2(E

r)+

2F 5/2

(Yb)

H2O

4I 1

3/2

400 600 800 1000 1200 1400 1600

Wavelength (nm)

1 : 101 : 5

Figure 4: Absorption spectra of Y2O3:Er3+, Yb3+ nanorods.

Inte

nsi

ty

500

2H

11/2

,4S 3/2−→

4I 1

5/2

4F 9/2−→

4I 1

5/2

550 600 650 700

Wavelength (nm)

1 : 101 : 5

Figure 5: Room temperature visible upconversion spectra ofY2O3:Er3+, Yb3+ nanorods under excitation at 980 nm.

6 Journal of NanomaterialsIn

ten

sity

(a.u

.)

0

1E−4

1E−3

0.012H11/2−4S3/2

0.0002 0.0004 0.0006 0.0008 0.001 0.0012

Time (s)

1 : 5 experimental1 : 10 experimental1 : 5 model1 : 10 model

(a)In

ten

sity

(a.u

.)

0

1E−4

1E−3

0.014F9/2

0.0002 0.0004 0.0006 0.0008 0.001 0.0012

Time (s)


(b)

Inte

nsi

ty(a

.u.)

0

1E−5

1E−4

1E−3 4I13/2

0.01 0.02 0.03

Time (s)


(c)

Inte

nsi

ty(a

.u.)

0

0.01

0.1

1

2F5/2

0.0005 0.001 0.0015

Time (s)


(d)

Figure 6: Experimental and simulated fluorescence decays of the (a) green ((2H11/2, 4S3/2) → 4I15/2), (b) red (4F9/2 → 4I15/2), and (c) NIR(4I13/2 → 4I15/2) Er3+ emissions, and (d) NIR (4F5/2 → 4F7/2) Yb3+ emission.

Table 2. It is observed that in general, the effective lifetimesfor the 1 : 5 SR sample are slower than the ones for the1 : 10 SR sample. That fact suggests that the 1 : 10 SR samplemight be subjected to more quenching processes than the1 : 5 SR sample. The NIR effective lifetimes are most affectedto the quenching processes by the increase of solvent forthe Yb3+ as well Er3+ ions. This is because the Yb3+(2F5/2),Er3+(4I13/2), and Er3+(4I11/2) energy levels are more sensibleto H2O residuals. As a result, the visible emission willbe lessened by an SR increase because the Yb3+(2F5/2),Er3+(4I13/2) and Er3+(4I11/2) energy levels help to populate

the VIS energy levels via upconversion process. The Visibleemission quantum efficiency is reported in Table 2. Thisshows a slight decrease with an SR increase nevertheless theemission intensity is strongly dependent the SR change.

To establish the nature of the interaction between Yb3+

and Er3+ ions in Y2O3 we analyzed the experimental datausing the Monte Carlo model (MC) described by (2).In such equations only the direct Yb3+ to Er3+ energytransfer processes W(Yb1

0 → Er02), W(Yb1

0 → Er13),

and W(Yb10 → Er2

4) are considered and represent thecascading upconversion mechanism driven by nonradiative


energy transfer processes. Note that the energy back transferprocess (Er3+ to Yb3+) is not considered since the measuredlifetimes (see Table 2) for the 2F5/2 excited state of Yb3+

are short compared to the 0.8 ms values reported in bulkand ceramics [26]. Those short lifetimes suggest that thestrong depopulation of the 2F5/2 Yb3+ state is taking placeand it might be due to strong direct Yb3+ and Er3+ energytransfer processes, which are stronger to any other processesthat might induce repopulation of such state as is the caseof the back transfer process. We considered dipole-dipoleinteraction to drive the energy transfers from Yb3+ to Er3+

ions, see (1). In order to use (1) we need to know theinterionic distances between Yb3+ to Er3+ ions. We placedNYb ions of Yb3+ andNEr ions of Er3+ with a uniform randomdistribution in k numerically generated nanorods, and usingthe crystallographic data for the Y2O3 synthesized nanorods.Then, by solving (2) and (3), we computed fluorescencesimulations for the green ((2H11/2, 4S3/2)→ 4I15/2), red(4F9/2 → 4I15/2), and NIR (4I13/2 → 4I15/2) Er3+ emissionsas well as the NIR (4F5/2 → 4F7/2) Yb3+ emission, seeFigure 6. The simulations shown in Figure 6 provide goodrepresentations of the experimental fluorescence decays ofthe 4I13/2, 4F9/2 and 4S3/2 states of the Er3+ and the 4F7/2

state of Yb3+ in the nanorod samples. The free parametersused to compute these fluorescence decay simulations arethe dipole-dipole microinteraction parameters reported inTable 2. Notice that the C(Yb1

0 → Er02) value for 1 : 10 SR

is greater than that for 1 : 5. Such higher C(Yb10 → Er0

2) valueleads to the faster depopulation of the 2F5/2(Yb3+) state inthe 1 : 10 SR sample than for the 1 : 5 sample; see Table 2 andFigure 6(d). All other emission decays, both experimentaland simulated, have almost the same decay trend. Themain difference, among corresponding fluorescence decays issmaller intensity for the 1 : 10 SR sample. This agrees with thefact that the C(Yb1

0 → Er13) and C(Yb1

0 → Er24) parameters

are almost the same for both samples; so the second and thirdYb3+ to Er3+ energy transfers have the similar probabilitiesfor both SRs. The biggest differences between experimentaland model simulations correspond to the decay curves forthe green emissions from the (2H11/2, 4S3/2)→ 4I15/2 Er3+

transition; see Figure 6(a). There, the simulated rise timesare shorter than the experimental ones; this suggest theexistence of additional depopulation channels of the 2H11/2-4S3/2 energy levels, such as Er3+ to Yb3+ energy back transferprocesses, which have not been considered in our model.That also might be the reason why the experimental decaysare under the simulated ones at intermediate times. Inregard of the red emissions (4F9/2 → 4I15/2 Er3+ transition)there is an excellent agreement between the experimentaland simulated decay trends, in particular the rise times arevery well predicted by the simulations. Notice the offsetat t = 0 between experimental and simulation curvesfor the NIR Yb3+ fluorescence decays (Figure 6(d)), suchdiscrepancies for short times suggest that our model is nottaking in to account additional channels of deexcitation,such as exchange interactions among dopant ion pairs orfast transfer processes to first neighbor radiation traps suchas OH radicals at the nanorod surfaces. Nevertheless, withthe most simple approach taken of considering only the

main three Yb3+ to Er3+ direct energy transfer processes,W(Yb1

0 → Er02),W(Yb1

0 → Er13), and W(Yb1

0 → Er24), we

have very good agreements between experimental results andits corresponding simulations. And we can conclude that themost important interaction is the first energy transfer processW(Yb1

0 → Er02), that can be quantified by its microinterac-

tion parameter C(Yb10 → Er0

2). Also the microinteractionparameters depend on the size and morphology, which ontime depends on the water to ethanol SR. Our simulationsmesh with existing literature; this confirms the validity ofour results. It should be noted, however, that our model isthe only one that explains qualitatively the types of energyprocess as well as its magnitude, taking into account thedopant concentration, more than one exited state (energylevels), ions distribution, size, and shape of the nanocrystals.

5. Conclusions

In summary, we have measured the fluorescence lifetimeof the 4I13/2, 4F9/2, and 2H11/2, 4S3/2 states of Er3+, andthe 4F5/2 state of Yb3+ in Y2O3:Yb3+, Er3+ nanorods fortwo different SRs, 1 : 5 and 1 : 10. The effective lifetime,luminescent emissions, and nanorod sizes depend stronglyon the SRs. The sample with 1 : 10 SR has lower effectivelifetime and emission intensity than the sample with a 1 : 5SR. The sample with 1 : 5 is bigger in size that 1 : 10 SR sampleand both samples exhibit same cubic phase.

A novel method was proposed and implemented in orderto explain the dynamics of the green and red upconversionemissions in Yb3+-Er3+-codoped Y2O3 Nanorods, taking intoaccount the dopant concentration, more than one exitedstate (energy levels), ions distribution, size, and shape ofthe nanocrystals. A three-step nonradiative energy transfermodel is proposed to explain the observed fluorescencedecays characterized by dipole-dipole interactions. Thecorresponding microinteraction parameters are reported aswell as quantum efficiency and effective lifetime for thevisible emissions. Numerical simulations of fluorescencedecays agree with experimental results. These results indicatethat solvent concentration plays an important role onthe upconversion luminescence processes, and therefore achange in the lifetime and quantum yield is observed.

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