Dynamics of the Green and Red Upconversion Emissions in Yb³⁺-Er³⁺-Codoped Y₂O₃ Nanorods

Abstract

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 the synthesis. A microscopic nonradiative energy transfer model is used to approach the dynamics of the green, red, and infrared emissions. The excellent agreement between simulated and experimental decay suggests that the energy transfer mechanisms responsible of the visible emission depend on the solvent ratio.

1. Introduction

Synthesis and optical characterization of luminescent materials in their nanocrystalline form have led to their growing use in numerous military and medical applications, such as imaging, range finding, flash lidar, and remote sensing [1–4]. Yttrium Oxide (Y₂O₃) has been the material of choice for photonics applications, owing to its favorable physical properties and ease of synthesis in the nanometer regime [5–7]. In particular, nanometer-sized rare earth-doped Y₂O₃ has shown enhanced luminescence and quantum yields relative to its bulk counterparts [8]. Very recently, a great deal of research has focused on finding lanthanide-doped inorganic nanocrystalline materials that will undergo near infrared (NIR) to-visible upconversion [6, 9]. The Er³⁺ ion has a relatively low absorption cross-section for the transitions in the near-infrared (NIR) region around 1000 nm. On the other hand, the Yb³⁺ ion exhibits a larger absorption cross-section in this region, and thus, codoping with Yb³⁺ has proven to be a successful alternative for enhanced upconversion processes. In fact, there is a large spectral overlap between the ²F_5/2→²F_7/2 Yb³⁺ NIR emission and the ⁴I_11/2→⁴I_15/2 Er³⁺ absorption bands, which results in an efficient nonradiative energy transfer process, and in turn efficient upconversion emission. Some of the most important parameters on luminescent materials are the lifetime and quantum yield. Both parameters are related to nonradiative energy transfer processes among active ions within the host. There are several models that attempt to explain the lifetime and quantum yield dependence on nonradiative energy transfer rates. The pioneering works of Forster [10], continued later by Dexter [11] and Inokuti and Hirayama [12] allowed the estimation of the non radiative energy-transfer rates based on experimental fluorescence lifetime measurements [13]. With varying degrees of acceptance, all these models have been applied to a large variety of crystalline systems in spite of the fact that hose models consider that the luminescent centers are continuously distributed within the luminescent host. This certainly is not the case in a crystalline medium, where the ions are distributed in very specific positions within the crystal lattice. Further, the discreteness of the active ions distribution within the crystalline lattice might become increasingly important as we consider nanometer-sized luminescent materials. So, there is a need to revise those models and formulate alternative ones.

In this paper, we consider the discrete distribution of the active ions (Er³⁺ and Yb³⁺ ions) within the crystalline lattice to study the nonradiative energy transfer processes that lead to the visible upconverted emission in Y₂O₃ Er³⁺-Yb³⁺-codoped nanorods. Y₂O₃ nanorod samples were synthesized by hydrothermal method using two ethanol/water solvent ratios (SRs), 1 : 10 and 1 : 5. Experimental effective lifetimes, luminescent emissions, and nanorod sizes depend strongly on the SRs. A nonradiative energy transfer model is proposed to numerical simulate the dynamics of the excitation energy among the active ions as well as their emission fluorescence decays. By doing that we extend the understanding of the non radiative energy transfer process that affect the photoluminescent properties of Er³⁺ and Yb³⁺ ions in Y₂O₃ nanorods. These simulations results indicate that solvent concentration plays an important role on the upconversion luminescence processes, and therefore a change in the lifetime and quantum yield will be observed. It bears mentioning that our model is the only one at present that considers the discreet nature of the nanocrystals; in addition it also can consider more than one exited state (energy level) of the ions. All the above advantages are in contrast to the traditional models by Vasquez [13], Jerez et al. [14] and Parisi et al. [15], which do not consider the discreteness of the nanocrystals and are suitable only for systems of two levels ions.

2. Experimental

The Y₂O₃:Yb³⁺, Er³⁺ nanorods, codoped with 1 mol% of Er₂O₃ and 2 mol% of Yb₂O₃, were synthesized by the hydrothermal precipitation method via cetyltrimethyl ammonium bromide (CTAB) complexation, for two different ethanol to water SRs, 1 : 5 and 1 : 10. All chemicals were reagent grade supplied by Aldrich, Inc. Samples were obtained using as precursors YCl₃6H₂O, Er(NO₃)₃5H₂O, YbCl₃6H₂O, and CTAB as cationic surfactant. In both cases, all components were mixed in the corresponding ethanol to water SR, at room temperature, under vigorous stirring. The precipitation was achieved by adding sodium hydroxide and the resulting solution was transferred into a sealed autoclave maintained at 100°C during 20 h. The precipitate was then washed with distilled water and dried in an oven at 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 equipment provided with a Cu tube with K_α radiation at 1.5405 Å, 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 electron microscope with accelerating voltage of 200 kV. The photoluminescence characterization was performed under 978 nm excitation forming a tunable OPO system (MOPO from Spectra Physics) pumped by the third harmonic of a 10 ns Nd:YAG pulsed laser. The fluorescence emission was analyzed with an Acton Pro 500i monochromator and two Hamamatsu photomultiplier tubes (R7400U-20 for VIS and for R3809U-68 for NIR) connected to an SR860 lock-in amplifier (Stanford Research). Fluorescence lifetimes were measured by connecting the photomultiplier to a 500 MHz Lecroy digital Oscilloscope. The system was controlled with a PC were emission spectra and decay trends where registered. All photoluminescence measurements were done at room temperature.

3. Model and Theory

The microscopic origin for nonradiative energy transfer processes can be visualized as an interaction between an excited ion, the donor D, and another not excited ion, the acceptor A, with an absorption transition resonant with the deexcitation of the first one [10, 11, 16]. In the case of Y₂O₃:Yb³⁺,Er³⁺ under pumping at 978 nm, Yb³⁺ ions can be visualized as donors and Er³⁺ ions as acceptors due to absorption cross-section differences between the Yb(²F_5/2) and Er(⁴I_11/2) energy levels [17]. The corresponding nonradiative energy transfer rate between 𝑖th Yb³⁺ ion and the 𝑗th Er³⁺ ion is given by [18] 𝑊(Yb^IS_FS→Er^IS_ES)_𝑖𝑗=𝐶(Yb^IS_FS→Er^IS_ES)(𝑅(Yb_𝑖,Er_𝑗))⁶, (1) where 𝑅(Yb_𝑖,Er_𝑗) is the distance between the 𝑖th Yb ion and the 𝑗th Er ion, 𝐶(Yb^IS_FS→Er^IS_ES) is the dipole-dipole microinteraction strength parameter [11, 19]. For simplicity we represent this process by 𝑊(Yb^IS_FS→Er^IS_ES)_𝑖𝑗. This notation indicates that the 𝑖th Yb³⁺ ion has a nonradiative relaxation from an initial state IS to a final state FS, and the freed energy excites the 𝑗th Er³⁺ ion from an initial state IS up to an excited state ES.

Under 978 nm pulsed excitation, the Er³⁺ ions are excited from the ground state ⁴I_15/2 to the excited state ⁴I_11/2, mainly by the phonon-assisted nonradiative energy transfer (ET) process Yb³⁺(²F_5/2,²F_7/2) → Er³⁺(⁴I_15/2, ⁴I_11/2). Then, the populated ⁴I_11/2 level is excited to the ⁴F_7/2 level mainly by phonon-assisted ET from excited Yb³⁺ ions [7]. The populated ⁴F_7/2 state rapidly relaxes to the two lower levels: ²H_11/2 and ⁴S_3/2, which produce green upconversion luminescence. So, in our model we consider this process as an overall Yb³⁺(²F_5/2,²F_7/2) → Er³⁺(⁴I_11/2, ²H_11/2+⁴S_3/2) non radiative ET process instead of the Yb³⁺(²F_5/2,²F_7/2) → Er³⁺(⁴I_11/2, ⁴F_7/2) ET followed by the nonradiative relaxation Er³⁺(⁴F_7/2) → Er³⁺(⁴I_11/2, ²H_11/2+⁴S_3/2). In addition, the populated Er³⁺(⁴I_11/2) state mostly relaxes to the long-living Er³⁺(⁴I_13/2) state. Electrons in the Er³⁺(⁴I_13/2) state may be promoted to the upper Er³⁺(⁴F_9/2) state by the ET process Yb³⁺(²F_5/2,²F_7/2) → Er³⁺(⁴I_13/2, ⁴F_9/2). The populated ⁴F_9/2 level mostly relaxes radiatively to the ground state ⁴I_15/2 level, which causes the Er red emissions. For simplicity in our model the Yb³⁺(²F_5/2,²F_7/2) → Er³⁺(⁴I_15/2, ⁴I_11/2), Yb³⁺(²F_5/2,²F_7/2)→Er³⁺(⁴I_13/2, ⁴F_9/2), and Yb³⁺(²F_5/2,²F_7/2) → Er³⁺(⁴I_11/2, ²H_11/2+⁴S_3/2) transition were denoted by 𝑊(Yb¹₀→Er⁰₂), 𝑊(Yb¹₀→Er¹₃), and 𝑊(Yb¹₀→Er²₄), respectively; see Figure 1.

Figure 1 

Energy levels diagram of Y2O3 : Er3+, Yb3+ nanorods and the considered direct Yb3+ to Er3+ nonradiative energy transfer processes: (i) 𝑊(Yb10→Er02), (ii) 𝑊(Yb10→Er13), and (iii) 𝑊(Yb10→Er24).

By taking into account the above described ET processes one can write down ordinary differential equations that govern the excitation dynamics among all Yb³⁺ and Er³⁺ ions inside of an arbitrary Y₂O₃:Yb³⁺, Er³⁺ nanocrystal:𝑑𝑃¹_Yb𝑖1𝑑𝑡=−𝜏(Yb¹₀)𝑃¹_Yb𝑖−^𝑁Er_𝑚=1𝑊(Yb¹₀→Er⁰₂)_𝑖𝑚𝑃¹_Yb𝑖𝑃⁰_Er𝑚−^𝑁Er_𝑚=1𝑊(Yb¹₀→Er¹₃)_𝑖𝑚𝑃¹_Yb𝑖𝑃¹_Er𝑚−^𝑁Er_𝑚=1𝑊(Yb¹₀→Er²₄)_𝑖𝑚𝑃¹_Yb𝑖𝑃²_Er𝑚,𝑑𝑃¹_Er𝑗1𝑑𝑡=−𝜏(Er¹₀)𝑃¹_Er𝑗+1𝜏(Er²₁)𝑃²_Er𝑗,−^𝑁Yb_𝑚=1W(Yb¹₀→Er¹₃)_𝑚𝑗𝑃¹_Yb𝑚𝑃¹_Er𝑗𝑑𝑃²_Er𝑗1𝑑𝑡=−𝜏(Er²₀)𝑃²_Er𝑗−1𝜏(Er²₁)𝑃²_Er𝑗+1𝜏(Er³₂)𝑃³_Er𝑗+^𝑁Yb_𝑚=1𝑊(Yb¹₀→Er⁰₂)_𝑚𝑗𝑃¹_Yb𝑚𝑃⁰_Er𝑗−^𝑁Yb_𝑚=1𝑊(Yb¹₀→Er²₄)_𝑚𝑗𝑃¹_Yb𝑚P²_Er𝑗,𝑑𝑃³_Er𝑗1𝑑𝑡=−𝜏(Er³₀)𝑃³_Er𝑗−1𝜏(Er³₂)𝑃³_Er𝑗+1𝜏(Er⁴₃)𝑃⁴_Er𝑗+^𝑁Yb_𝑚=1𝑊(Yb¹₀→Er¹₃)_𝑚𝑗𝑃¹_Yb𝑚𝑃¹_Er𝑗,𝑑𝑃⁴_Er𝑗1𝑑𝑡=−𝜏(Er⁴₀)𝑃⁴_Er𝑗−1𝜏(Er⁴₃)𝑃⁴_Er𝑗+^𝑁Yb_𝑚=1𝑊(Yb¹₀→Er²₄)_𝑚𝑗𝑃¹_Yb𝑚𝑃²_Er𝑗, (2) where 𝑃¹_Yb𝑖 is the probability to finding the 𝑖th Yb³⁺ ion at its exited state ²F_5/2 at the time 𝑡.𝑃^𝑋_Er𝑖 is probability to finding the 𝑗th Er³⁺ ion at its X state (with X = 1,2,3,4, corresponding to the states ⁴I_13/2, ⁴I_15/2, ⁴I_11/2, ⁴F_9/2 and (²H_11/2+⁴S_3/2), resp.) at the time 𝑡. 𝜏(Yb¹₀) and 𝜏(Er^IS₀) are the free ion lifetimes for Yb³⁺ and Er³⁺, respectively, from the level IS to ground state, when no energy processes are present (see Table 1). And 1/𝜏(Er^IS_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). 𝑁_Yb and 𝑁_Er are the total number of active ions inside of the Y₂O₃:Yb³⁺, Er³⁺ nanocrystal.

Table 1 

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

Y₂O₃ is a cubic perovskite with spatial group symmetry Ia3 (206) [21, 22]. Using the coordinate data from Crystallographic tables for the spatial group Ia3(206) [23] a kth nanocrystal sample is numerically generated. Then the Yb³⁺ and Er³⁺ dopant ions are placed into the potential 24d and 8b crystal sites with a random uniform distribution by using the Monte Carlo method. With this random uniform placement Er³⁺ and Yb³⁺ ions each have a particular distribution of neighboring Er³⁺ and Yb³⁺ codopants within the particular kth generated nanocrystal. Thus, based on actual interionic distances and by assuming a dipole-dipole microinteraction strength parameter we compute all the non radiative transfer rates 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 the only free parameters are the 𝐶(Yb^IS_FS→ER^IS_ES) parameters. ith Yb³⁺ and jth Er³⁺ ions each have its own decay rate proportional to its own 𝑃¹_Yb𝑖𝑃¹_Yb𝑖 and 𝑃^𝑋_Er𝑗𝑃^𝑋_Er𝑖 probability of being exited at time t. Thus, the total fluorescence emission transient from the kth generated crystal will be the average over the individual emissions overall active ions within the kth nanocrystal, and the macroscopic emission will be proportional to the average over a large number of k numerically generated crystal samples, that is, 𝜑_Yb(𝑡)=⟨⟨𝑃¹_Ybi⟩_av.over𝑖⟩_av.over𝑘,𝜑^X_Er(𝑡)=⟨⟨𝑃¹_Erj⟩_av.over𝑗⟩_av.over𝑘. (3)

4. Results and Discussion

The XRD patterns of the Y₂O₃:Yb³⁺, Er³⁺ nanocrystalline powders prepared with 1 : 5 and 1 : 10 ethanol/water ratios (SR) are shown in Figure 2. Both samples exhibit almost identical patterns and the main characteristic diffraction peaks can be indexed as a pure cubic phase (space group Ia3 (206)) with cell parameter of 10.6056 Å 10.5818 Å for the water to ethanol SR 1 : 10 and 1 : 5, respectively. These values are in agreement with the standard value of 10.6 Å for the bulk cubic Y₂O₃ reported in card number JCPDS 41-1105 [22]. Figure 2 helps to show the dependency between the solvent radio and interionic distance, which alone affects the nonradiative ET processes for a same dopant concentration. Both samples present single nanorod morphology as can be observed in the TEM micrographics in Figure 3. For the 1 : 10 SR sample the nanorods are 745.6 nm lengths and 55.2 nm diameter in average, whereas for 1 : 5 SR the nanorods are 1464.8 nm length and 75.4 nm diameter. Taking into account the dopant concentration, size, shape, and ions distribution of the nanocrystals, we simulate a great number of nanorods. We estimated the mean Yb³⁺-Er³⁺ distance (R_YbEr) for each water to ethanol SR. These R_YbEare (7.661 ± 0.020) Å and (7.820 ± 0.0482) Å, at the 95.0% confidence level, for 1 : 5 and 1 : 10 SRs, respectively. Thus, form (1) and considering that in both samples the energy transfer processes among Yb³⁺-Er³⁺ pairs are the same, that is, the same dipole-dipole microinteraction strength parameter for each ET process, in general the nonradiative ET processes are expected to be 13% stronger in the 1 : 5 solvent ratio sample than for the 1 : 10 SR sample.

Figure 2 

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

(a)

(b)

Figure 3 

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

The absorption spectra of the Y₂O₃:Yb³⁺,Er³⁺ nanorods for the two studied SRs are shown in Figure 4. The absorption peaks for Er³⁺ and the corresponding transitions from the ground states are 1536 nm (⁴I_13/2), 965 nm (⁴I_11/2) overlapped with the broad absorption band of Yb³⁺ (²F_5/2), 800 nm (⁴I_9/2), 654 nm (⁴F_9/2), 539 nm (⁴S_3/2), 522 nm (²H_11/2). The new observable feature is a broad peak centered at 1382 nm indicating the presence of residual H₂O that could be keeping occluded within the Y₂O₃ nanorods. The ratio of the Er³⁺ (⁴I_13/2) band to the 1385 nm H₂O band is 3.28 and 1.21 for the 1 : 10 and 1 : 5 SRs, respectively, That is in agreement with the fact that the higher content of occluded H₂O is found in the sample obtained with a lower SR (1 : 5).

Figure 4 

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

Figure 5 shows the VIS spectra of Y₂O₃ under 978 nm excitation for both samples. The green emissions were observed in the range of 510–580 nm, corresponding to the (²H_11/2, ⁴S_3/2)→⁴I_15/2 Er³⁺ transitions, while the red emissions were observed between 640 and 690 nm, corresponding to the ⁴F_9/2 →⁴I_15/2 Er³⁺ transitions. We can see that the sample with 1 : 10 SR has in general lower emission intensity for all observed visible emissions than the sample with a 1 : 5 SR, that in principle could be due to quenching of the population of the Er³⁺ (⁴I_13/2) and Yb³⁺(⁴F_5/2) excited levels by the residual H₂O responsible of the 1382 nm band observed in the absorption spectra. Figure 6 shows both experimental and simulated fluorescence decays for the Yb³⁺ and Er³⁺ ions for their visible and infrared emissions. The effective lifetime is obtained from the experimental fluorescence decay using the expression [25]:𝜏_𝑒=∫^∞₀𝐼(𝑡)𝑑𝑡,𝐼(𝑡=0) (4) where I(t) is the respective fluorescence decay. The quantum yield can be calculated from the ratio of effective lifetime (𝜏_𝑒) and free ion lifetime (𝜏) [25]. The computed effective life times and quantum efficiencies are reported in Table 2. It is observed that in general, the effective lifetimes for the 1 : 5 SR sample are slower than the ones for the 1 : 10 SR sample. That fact suggests that the 1 : 10 SR sample might be subjected to more quenching processes than the 1 : 5 SR sample. The NIR effective lifetimes are most affected to the quenching processes by the increase of solvent for the Yb³⁺ as well Er³⁺ ions. This is because the Yb³⁺(²F_5/2), Er³⁺(⁴I_13/2), and Er³⁺(⁴I_11/2) energy levels are more sensible to H₂O residuals. As a result, the visible emission will be lessened by an SR increase because the Yb³⁺(²F_5/2), Er³⁺(⁴I_13/2) and Er³⁺(⁴I_11/2) energy levels help to populate the VIS energy levels via upconversion process. The Visible emission quantum efficiency is reported in Table 2. This shows a slight decrease with an SR increase nevertheless the emission intensity is strongly dependent the SR change.

Table 2 

Experimental and simulated lifetimes, quantum efficiencies, and microinteraction parameters.

Figure 5 

Room temperature visible upconversion spectra of Y2O3:Er3+, Yb3+ nanorods under excitation at 980 nm.

(a)

(b)

(c)

(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.

To establish the nature of the interaction between Yb³⁺ and Er³⁺ ions in Y₂O₃ we analyzed the experimental data using the Monte Carlo model (MC) described by (2). In such equations only the direct Yb³⁺ to Er³⁺ energy transfer processes 𝑊(Yb¹₀→Er⁰₂),𝑊(Yb¹₀→Er¹₃), and 𝑊(Yb¹₀→Er²₄) are considered and represent the cascading upconversion mechanism driven by nonradiative energy transfer processes. Note that the energy back transfer process (Er³⁺ to Yb³⁺) is not considered since the measured lifetimes (see Table 2) for the ²F_5/2 excited state of Yb³⁺ are short compared to the 0.8 ms values reported in bulk and ceramics [26]. Those short lifetimes suggest that the strong depopulation of the ²F_5/2 Yb³⁺ state is taking place and it might be due to strong direct Yb³⁺ and Er³⁺ energy transfer processes, which are stronger to any other processes that might induce repopulation of such state as is the case of the back transfer process. We considered dipole-dipole interaction to drive the energy transfers from Yb³⁺ to Er³⁺ ions, see (1). In order to use (1) we need to know the interionic distances between Yb³⁺ to Er³⁺ ions. We placed 𝑁_Yb ions of Yb³⁺ and 𝑁_Er ions of Er³⁺ with a uniform random distribution in k numerically generated nanorods, and using the crystallographic data for the Y₂O₃ synthesized nanorods. Then, by solving (2) and (3), we computed fluorescence simulations for the green ((²H_11/2, ⁴S_3/2)→⁴I_15/2), red (⁴F_9/2 →⁴I_15/2), and NIR (⁴I_13/2→⁴I_15/2) Er³⁺ emissions as well as the NIR (⁴F_5/2→⁴F_7/2) Yb³⁺ emission, see Figure 6. The simulations shown in Figure 6 provide good representations of the experimental fluorescence decays of the ⁴I_13/2, ⁴F_9/2 and ⁴S_3/2 states of the Er³⁺ and the ⁴F_7/2 state of Yb³⁺ in the nanorod samples. The free parameters used to compute these fluorescence decay simulations are the dipole-dipole microinteraction parameters reported in Table 2. Notice that the 𝐶(Yb¹₀→Er⁰₂) value for 1∶10 SR is greater than that for 1 : 5. Such higher 𝐶(Yb¹₀→Er⁰₂) value leads to the faster depopulation of the ²F_5/2(Yb³⁺) state in the 1 : 10 SR sample than for the 1 : 5 sample; see Table 2 and Figure 6(d). All other emission decays, both experimental and simulated, have almost the same decay trend. The main difference, among corresponding fluorescence decays is smaller intensity for the 1 : 10 SR sample. This agrees with the fact that the 𝐶(Yb¹₀→Er¹₃) and 𝐶(Yb¹₀→Er²₄) parameters are almost the same for both samples; so the second and third Yb³⁺ to Er³⁺ energy transfers have the similar probabilities for both SRs. The biggest differences between experimental and model simulations correspond to the decay curves for the green emissions from the (²H_11/2, ⁴S_3/2)→⁴I_15/2 Er³⁺ transition; see Figure 6(a). There, the simulated rise times are shorter than the experimental ones; this suggest the existence of additional depopulation channels of the ²H_11/2-⁴S_3/2 energy levels, such as Er³⁺ to Yb³⁺ energy back transfer processes, which have not been considered in our model. That also might be the reason why the experimental decays are under the simulated ones at intermediate times. In regard of the red emissions (⁴F_9/2→⁴I_15/2 Er³⁺ transition) there is an excellent agreement between the experimental and simulated decay trends, in particular the rise times are very well predicted by the simulations. Notice the offset at 𝑡=0 between experimental and simulation curves for the NIR Yb³⁺ fluorescence decays (Figure 6(d)), such discrepancies for short times suggest that our model is not taking in to account additional channels of deexcitation, such as exchange interactions among dopant ion pairs or fast transfer processes to first neighbor radiation traps such as OH radicals at the nanorod surfaces. Nevertheless, with the most simple approach taken of considering only the main three Yb³⁺ to Er³⁺ direct energy transfer processes, 𝑊(Yb¹₀→Er⁰₂),𝑊(Yb¹₀→Er¹₃), and 𝑊(Yb¹₀→Er²₄), we have very good agreements between experimental results and its corresponding simulations. And we can conclude that the most important interaction is the first energy transfer process 𝑊(Yb¹₀→Er⁰₂), that can be quantified by its microinteraction parameter 𝐶(Yb¹₀→Er⁰₂). Also the microinteraction parameters depend on the size and morphology, which on time depends on the water to ethanol SR. Our simulations mesh with existing literature; this confirms the validity of our results. It should be noted, however, that our model is the only one that explains qualitatively the types of energy process as well as its magnitude, taking into account the dopant concentration, more than one exited state (energy levels), ions distribution, size, and shape of the nanocrystals.

5. Conclusions

In summary, we have measured the fluorescence lifetime of the ⁴I_13/2, ⁴F_9/2, and ²H_11/2, ⁴S_3/2 states of Er³⁺, and the ⁴F_5/2 state of Yb³⁺ in Y₂O₃:Yb³⁺, Er³⁺ nanorods for two different SRs, 1 : 5 and 1 : 10. The effective lifetime, luminescent emissions, and nanorod sizes depend strongly on the SRs. The sample with 1 : 10 SR has lower effective lifetime and emission intensity than the sample with a 1 : 5 SR. The sample with 1 : 5 is bigger in size that 1 : 10 SR sample and both samples exhibit same cubic phase.

A novel method was proposed and implemented in order to explain the dynamics of the green and red upconversion emissions in Yb³⁺-Er³⁺-codoped Y₂O₃ Nanorods, taking into account the dopant concentration, more than one exited state (energy levels), ions distribution, size, and shape of the nanocrystals. A three-step nonradiative energy transfer model is proposed to explain the observed fluorescence decays characterized by dipole-dipole interactions. The corresponding microinteraction parameters are reported as well as quantum efficiency and effective lifetime for the visible emissions. Numerical simulations of fluorescence decays agree with experimental results. These results indicate that solvent concentration plays an important role on the upconversion luminescence processes, and therefore a change in the lifetime and quantum yield is observed.