Energy Transfer Efficiency from ZnO-Nanocrystals to Eu3+ Ions Embedded in SiO2 Film for Emission at 614 nm

In this work, we study the energy transfer mechanism from ZnO nanocrystals (ZnO-nc) to Eu3+ ions by fabricating thin-film samples of ZnO-nc and Eu3+ ions embedded in a SiO2 matrix using the low-cost sol-gel technique. The time-resolved photoluminescence (TRPL) measurements from the samples were analyzed to understand the contribution of energy transfer from the various ZnO-nc emission centers to Eu3+ ions. The decay time obtained from the TRPL measurements was used to calculate the energy transfer efficiencies from the ZnO-nc emission centers, and these results were compared with the energy transfer efficiencies calculated from steady-state photoluminescence emission results. The results in this work show that high transfer efficiencies from the excitonic and Zn defect emission centers is mostly due to the energy transfer from ZnO-nc to Eu3+ ions which results in the radiative emission from the Eu3+ ions at 614 nm, while the energy transfer from the oxygen defect emissions is most probably due to the energy transfer from ZnO-nc to the new defects created due to the incorporation of the Eu3+ ions.


Introduction
The study of the excitation of rare-earth (RE) ions through energy transfers from semiconductor nanocrystals, especially from Zinc oxide nanocrystals (ZnO-nc) has attracted a lot of attention lately. The emission from the 3.37 eV wide bandgap of ZnO-nc has been shown to efficiently excite a wide variety of RE ions ranging from Ce 3+ to Yb 3+ ions [1][2][3][4][5][6][7][8]. Nonetheless, the mechanism of energy transfer from ZnO-nc to RE ions is not well understood. For instance, Huang et al. [8] report that the energy transfer from ZnO-nc to RE ions, specifically Eu 3+ ions, is mainly due to the defects in the ZnO-nc. However, reports by Luo et al. [5] show that the energy transfer from ZnO-nc could be due to a combination of the band edge emission from the ZnO-nc and the defects in the ZnO-nc. Furthermore, in most of these works, the study of the energy transfer from ZnO-nc is based on steady-state photoluminescence (PL) emission from the nanocrystals, while there have been fewer studies based on time-resolved photoluminescence (TRPL) measurements from the ZnO-nc [2,3]. Moreover, there have been almost no studies that aim to further the understanding of the de3cay dynamics of various ZnO-nc emission centers and their effect on the efficiency of the energy transfer mechanism from ZnO-nc to RE ions. This article is a direct continuation of our earlier work [9], in which the steady-state PL emission from ZnO-nc was studied to elucidate the contribution of seven ZnO-nc centered at 360, 378, 396, 417, 450, 500, and 575 nm [10], were identified as band-edge emissions from the smallest ZnO-nc, which possibly experiences some quantum confinement effect (QC) [11], excitonic emission (EE) [12,13], and five different defect state emissions, namely Zn defect (Zni to VZn) [14], oxygen interstitial defect (Oi) [15,16], and oxygen vacancy defects (Vo, VȮ, VӦӦ) [14,17,18], respectively. In this work, we study the contribution of energy transfer from various ZnO-nc emission centers to Eu 3+ ions based on TRPL measurements. We calculate the decay time from the TRPL measurements for various ZnO-nc emission centers and then calculate the efficiency of energy transfer from each of the ZnO-nc emission centers to the Eu 3+ ions. Furthermore, the transfer efficiency is also calculated from steady-state PL emission data for comparison. The results in this work show high transfer efficiencies from the EE (at 378 nm) and Zni to VZn (at 396 nm) emission centers, mostly due to the energy transfer from ZnO-nc to Eu 3+ ions which results in radiative emission from Eu 3+ ions at 614 nm, while the energy transfer from the oxygen defect emissions at 417, 450, 500, and 575 nm is most probably due to the energy transfer from ZnO-nc to the new defects created due to the incorporation of the Eu 3+ ions, as proposed in our previous work [9]. Understanding the energy transfer mechanism from ZnO-nc to Eu 3+ ions will help to further the understanding of the energy transfer process to RE ions and in the development of energy efficient RE ion-based light sources such as lasers, amplifiers, phosphors, etc. that can be excited by the sensitizing effect of semiconductor nanocrystals.

Results and Discussion
In this work, we studied the TRPL spectra of two types of thin-film samples; namely ZnO-nc in SiO2 (ZnO-nc:SiO2) and ZnO-nc in SiO2 co-doped with 12 mol % Eu 3+ ions (Eu 3+ :ZnO-nc:SiO2). The 12 mol % Eu 3+ :ZnO-nc:SiO2 sample was used in this study because the 12 mol % sample has the highest PL emission from the Eu 3+ ions at 614 nm due to energy transfer from ZnO-nc, in comparison with 4, 8, and 16 mol % Eu 3+ :ZnO-nc:SiO2 samples, which has been reported in our previous work [9]. The TRPL spectra were measured at each of the peak wavelengths of the seven ZnO-nc emission centers. The TRPL signals from the last three longest wavelengths of the seven signals, namely at 450, 500 and 575 nm, were weak compared to the other four emissions at 360, 378, 396 and 417 nm.
In our PL measurements [9], we also observed that the 450, 500 and 575 nm emissions have the lowest emission intensity. These weak emissions are possibly due to the larger number of phonons required as compared to the emissions at 360, 378, 396 and 417 nm, shown schematically in Figure 1 (the energy band diagram of ZnO-nc in SiO2 showing various transitions). The number of phonon emissions required by the 450, 500 and 575 nm emissions is estimated to be around three to nine times more than those required by the 417 nm emission process. The probability of multi-phonon emissions decreases with increasing the number of phonons required for the de-excitation process, leading to a lower number of excited state ZnO-nc electrons being involved in the emissions at 450, 500 and 575 nm, causing weak emissions at these wavelengths. The energy band diagram in Figure 1 also illustrates the energy transfer from various ZnO-nc emission centers to Eu 3+ ions in the SiO2 matrix, together with the various transitions corresponding to the emissions from ZnO nanocrystals and Eu 3+ ions. This figure is a modified version of the band diagram reported in our earlier work [9], where the bandwidth of the various ZnO-nc emission centers is represented using the colour gradients in the broad vertical energy bands. Here, we note that there is a possibility of back energy transfer from the excited Eu 3+ ions to the ZnO-nc, especially from the 5 D0 state of Eu 3+ to the VȮ defect center in the ZnO-nc with the cooperation of phonons. However, we do not consider the effect of the energy back transfer process on the PL and TRPL emissions of the ZnO-nc in this study.
) [14,17,18], respectively. In this work, we study the contribution of energy transfer from various ZnO-nc emission centers to Eu 3+ ions based on TRPL measurements. We calculate the decay time from the TRPL measurements for various ZnO-nc emission centers and then calculate the efficiency of energy transfer from each of the ZnO-nc emission centers to the Eu 3+ ions. Furthermore, the transfer efficiency is also calculated from steady-state PL emission data for comparison. The results in this work show high transfer efficiencies from the EE (at 378 nm) and Zn i to V Zn (at 396 nm) emission centers, mostly due to the energy transfer from ZnO-nc to Eu 3+ ions which results in radiative emission from Eu 3+ ions at 614 nm, while the energy transfer from the oxygen defect emissions at 417, 450, 500, and 575 nm is most probably due to the energy transfer from ZnO-nc to the new defects created due to the incorporation of the Eu 3+ ions, as proposed in our previous work [9]. Understanding the energy transfer mechanism from ZnO-nc to Eu 3+ ions will help to further the understanding of the energy transfer process to RE ions and in the development of energy efficient RE ion-based light sources such as lasers, amplifiers, phosphors, etc. that can be excited by the sensitizing effect of semiconductor nanocrystals.

Results and Discussion
In this work, we studied the TRPL spectra of two types of thin-film samples; namely ZnO-nc in SiO 2 (ZnO-nc:SiO 2 ) and ZnO-nc in SiO 2 co-doped with 12 mol % Eu 3+ ions (Eu 3+ :ZnO-nc:SiO 2 ). The 12 mol % Eu 3+ :ZnO-nc:SiO 2 sample was used in this study because the 12 mol % sample has the highest PL emission from the Eu 3+ ions at 614 nm due to energy transfer from ZnO-nc, in comparison with 4, 8, and 16 mol % Eu 3+ :ZnO-nc:SiO 2 samples, which has been reported in our previous work [9]. The TRPL spectra were measured at each of the peak wavelengths of the seven ZnO-nc emission centers. The TRPL signals from the last three longest wavelengths of the seven signals, namely at 450, 500 and 575 nm, were weak compared to the other four emissions at 360, 378, 396 and 417 nm.
In our PL measurements [9], we also observed that the 450, 500 and 575 nm emissions have the lowest emission intensity. These weak emissions are possibly due to the larger number of phonons required as compared to the emissions at 360, 378, 396 and 417 nm, shown schematically in Figure 1 (the energy band diagram of ZnO-nc in SiO 2 showing various transitions). The number of phonon emissions required by the 450, 500 and 575 nm emissions is estimated to be around three to nine times more than those required by the 417 nm emission process. The probability of multi-phonon emissions decreases with increasing the number of phonons required for the de-excitation process, leading to a lower number of excited state ZnO-nc electrons being involved in the emissions at 450, 500 and 575 nm, causing weak emissions at these wavelengths. The energy band diagram in Figure 1 also illustrates the energy transfer from various ZnO-nc emission centers to Eu 3+ ions in the SiO 2 matrix, together with the various transitions corresponding to the emissions from ZnO nanocrystals and Eu 3+ ions. This figure is a modified version of the band diagram reported in our earlier work [9], where the bandwidth of the various ZnO-nc emission centers is represented using the colour gradients in the broad vertical energy bands. Here, we note that there is a possibility of back energy transfer from the excited Eu 3+ ions to the ZnO-nc, especially from the 5 D 0 state of Eu 3+ to the V Materials 2017, 10, 930 2 of 9 centered at 360, 378, 396, 417, 450, 500, and 575 nm [10], were identified as band-edge emissions from the smallest ZnO-nc, which possibly experiences some quantum confinement effect (QC) [11], excitonic emission (EE) [12,13], and five different defect state emissions, namely Zn defect (Zni to VZn) [14], oxygen interstitial defect (Oi) [15,16], and oxygen vacancy defects (Vo, VȮ, VӦӦ) [14,17,18] ions, as proposed in our previous work [9].
Understanding the energy transfer mechanism from ZnO-nc to Eu 3+ ions will help to further the understanding of the energy transfer process to RE ions and in the development of energy efficient defect center in the ZnO-nc with the cooperation of phonons. However, we do not consider the effect of the energy back transfer process on the PL and TRPL emissions of the ZnO-nc in this study.  Figure 2 shows the normalized TRPL spectra (the decay of the normalized PL emission intensity with respect to time) of ZnO-nc:SiO2 and Eu 3+ :ZnO-nc:SiO2 samples at 360, 378, 396 and 417 nm. We can clearly see that the PL intensity of the sample with the Eu 3+ ions decays faster than the sample without Eu 3+ ions at all emission wavelengths. The decay of the PL emission in the ZnO-nc:SiO2 sample is due to the radiative and non-radiative de-excitation processes in the ZnO-nc. However, the decay of the PL emission in the Eu 3+ :ZnO-nc:SiO2 sample has additional components that contribute to the decay rate, namely (i) the energy transfer from ZnO-nc to Eu 3+ ions which results in the radiative emission from Eu 3+ ions at 614 nm, and (ii) the energy transfer from ZnO-nc to the additional new defects created due to the incorporation of the Eu 3+ ions [9]. To study the contribution of the energy transfers from the ZnO-nc to the Eu 3+ ions and the defects created by the Eu 3+ ions, the intensities of the different TRPL spectra of the two samples are expressed using the stretched exponential decay fitting function [19] as follows:

Transfer Efficiency from Time-Resolved Photoluminescence Emission
where ( ) is the intensity of the TRPL measurement at time t, is the intensity of the TRPL measurement at = 0, is the decay time of the TRPL intensity, and β is the stretching exponential coefficient, which is a wavelength-dependent constant. The stretched exponential decay fitting function is the most widely used fitting function to represent the TRPL decay curves of ZnO-nc [19], and semiconductor nanocrystals in general [20][21][22][23], as they account for the complex nature of the decay curves which cannot be expressed using simple exponential decay functions. Using the stretch exponential decay fitting function, we obtained very good fitting curves for the TRPL spectra of the ZnO-nc. In the stretched exponential decay equation, β ranges from 0 to 1 and is a measure of interaction between identical ZnO-nc emission centers. This interaction, for instance, could be in the form of the migration of excitons between ZnO-nc or the migration of carriers between identical ZnOnc defect centers [22,23]. The value of β approaches 0 when the effect of interaction between two or more identical ZnO-nc emission centers is large, and β approaches 1 when the effect of interaction between the identical emission centers is negligible [22,23]. For the 360-nm band edge emission (QC) of the ZnO-nc, the value of β is 0.65 for the sample without Eu 3+ ions and 0.69 for the sample with Eu 3+ ions, as shown in Table 1. However, for the 378-nm excitonic emission (EE), 396-nm Zn defect (Zni to VZn) emission, and 417-nm oxygen interstitial defect (Oi) emission, the β values are around 0.61-0.62 for the samples with and without Eu 3+ ions. These results indicate that the 360-nm band edge emission (QC) experiences lesser interactions compared to the EE, Zni to VZn, and Oi emissions.  Figure 2 shows the normalized TRPL spectra (the decay of the normalized PL emission intensity with respect to time) of ZnO-nc:SiO 2 and Eu 3+ :ZnO-nc:SiO 2 samples at 360, 378, 396 and 417 nm. We can clearly see that the PL intensity of the sample with the Eu 3+ ions decays faster than the sample without Eu 3+ ions at all emission wavelengths. The decay of the PL emission in the ZnO-nc:SiO 2 sample is due to the radiative and non-radiative de-excitation processes in the ZnO-nc. However, the decay of the PL emission in the Eu 3+ :ZnO-nc:SiO 2 sample has additional components that contribute to the decay rate, namely (i) the energy transfer from ZnO-nc to Eu 3+ ions which results in the radiative emission from Eu 3+ ions at 614 nm, and (ii) the energy transfer from ZnO-nc to the additional new defects created due to the incorporation of the Eu 3+ ions [9]. To study the contribution of the energy transfers from the ZnO-nc to the Eu 3+ ions and the defects created by the Eu 3+ ions, the intensities of the different TRPL spectra of the two samples are expressed using the stretched exponential decay fitting function [19] as follows:

Transfer Efficiency from Time-Resolved Photoluminescence Emission
where I(t) is the intensity of the TRPL measurement at time t, I o is the intensity of the TRPL measurement at t = 0, τ is the decay time of the TRPL intensity, and β is the stretching exponential coefficient, which is a wavelength-dependent constant. The stretched exponential decay fitting function is the most widely used fitting function to represent the TRPL decay curves of ZnO-nc [19], and semiconductor nanocrystals in general [20][21][22][23], as they account for the complex nature of the decay curves which cannot be expressed using simple exponential decay functions. Using the stretch exponential decay fitting function, we obtained very good fitting curves for the TRPL spectra of the ZnO-nc. In the stretched exponential decay equation, β ranges from 0 to 1 and is a measure of interaction between identical ZnO-nc emission centers. This interaction, for instance, could be in the form of the migration of excitons between ZnO-nc or the migration of carriers between identical ZnO-nc defect centers [22,23]. The value of β approaches 0 when the effect of interaction between two or more identical ZnO-nc emission centers is large, and β approaches 1 when the effect of interaction between the identical emission centers is negligible [22,23]. For the 360-nm band edge emission (QC) of the ZnO-nc, the value of β is 0.65 for the sample without Eu 3+ ions and 0.69 for the sample with Eu 3+ ions, as shown in Table 1. However, for the 378-nm excitonic emission (EE), 396-nm Zn defect (Zn i to V Zn ) emission, and 417-nm oxygen interstitial defect (O i ) emission, the β values are around 0.61-0.62 for the samples with and without Eu 3+ ions. These results indicate that the 360-nm band edge emission (QC) experiences lesser interactions compared to the EE, Zn i to V Zn , and O i emissions. The weaker interaction of the 360-nm band edge emission (QC) center could be due to the smaller size of the ZnO-nc, as this emission is attributed to the possible quantum confinement effect. Table 1 also show the decay time τ for different ZnO-nc emission centers of the ZnO-nc:SiO 2 and Eu 3+ :ZnO-nc:SiO 2 samples. The decay time τ is primarily the lifetime of the electrons in the excited state of the ZnO-nc emission center, and its values depend on the rates of the different de-excitation processes from the ZnO-nc emission centers. For instance, the decay time of any ZnO-nc emission center in the ZnO-nc:SiO 2 sample τ ZnO−nc:SiO 2 is given by: where R r is the rate of radiative emission and R nr is the rate of non-radiative emission from the ZnO-nc emission center. Similarly, the decay time of any ZnO-nc emission center in the Eu 3+ :ZnO-nc:SiO 2 sample τ Eu 3+ :ZnO−nc:SiO 2 is given by: The weaker interaction of the 360-nm band edge emission (QC) center could be due to the smaller size of the ZnO-nc, as this emission is attributed to the possible quantum confinement effect. Table 1 also show the decay time for different ZnO-nc emission centers of the ZnO-nc:SiO2 and Eu 3+ :ZnOnc:SiO2 samples. The decay time is primarily the lifetime of the electrons in the excited state of the ZnO-nc emission center, and its values depend on the rates of the different de-excitation processes from the ZnO-nc emission centers. For instance, the decay time of any ZnO-nc emission center in the ZnO-nc:SiO2 sample ( : ) is given by: where R r is the rate of radiative emission and R nr is the rate of non-radiative emission from the ZnOnc emission center. Similarly, the decay time of any ZnO-nc emission center in the Eu 3+ :ZnO-nc:SiO2 sample : : is given by: : : where R tr is the combined rate of energy transfer from ZnO-nc to Eu 3+ ions which results in the radiative emission from the Eu 3+ ions at 614 nm and energy transfer from ZnO-nc to the additional new defects created due to the incorporation of the Eu 3+ ions. As expected, the decay time for the sample with Eu 3+ ions ( : : ) is lower than the decay time for the sample without Eu 3+ ions ( : ) for all wavelengths, due to the additional energy transfer decay mechanisms in the Eu 3+ :ZnO-nc:SiO2 sample.
The E TRPL T transfer efficiency calculated for each of the four ZnO-nc emission centers is shown in Figure 3.
The transfer efficiency calculated for each of the four ZnO-nc emission centers is shown in Figure 3.

Transfer Efficiency from Steady-State Photoluminescence Emission
Furthermore, for comparison, the transfer efficiency of each of the seven ZnO-nc emission centers was also calculated from the steady-state PL intensity measurements of the two samples in this study, ZnO-nc:SiO2 and Eu 3+ :ZnO-nc:SiO2. Savchyn et al. [24] report a similar analysis calculating the transfer efficiency from the steady-state PL emission intensity for a silicon nanocrystals and Er 3+ ions system. Our results on the steady-state PL intensity for the samples without and with Eu 3+ ions have been reported in Reference [9], and we used those results to calculate the energy transfer efficiency, denoted by , in this report. The intensity of steady-state PL emission from the ZnO-

Transfer Efficiency from Steady-State Photoluminescence Emission
Furthermore, for comparison, the transfer efficiency of each of the seven ZnO-nc emission centers was also calculated from the steady-state PL intensity measurements of the two samples in this study, ZnO-nc:SiO 2 and Eu 3+ :ZnO-nc:SiO 2 . Savchyn et al. [24] report a similar analysis calculating the transfer efficiency from the steady-state PL emission intensity for a silicon nanocrystals and Er 3+ ions system. Our results on the steady-state PL intensity for the samples without and with Eu 3+ ions have been reported in Reference [9], and we used those results to calculate the energy transfer efficiency, denoted by E PL T , in this report. The intensity of steady-state PL emission from the ZnO-nc:SiO 2 I ZnO−nc:SiO 2 and Eu 3+ :ZnO-nc:SiO 2 I Eu 3+ :ZnO−nc:SiO 2 samples can be mathematically represented by Equations (5) and (6) [25] can be written as follows: where G is the total number of ZnO-nc generated to the excited state of an emission center per unit volume per unit time. The value of G depends on the intensity of the steady-state PL excitation source and the absorption cross-section of the ZnO-nc. Similarly, the rate equation of N Eu 3+ :ZnO−nc:SiO 2 [25] can be written as follows: Thus, from Equations (7) and (8), we can see that during the PL measurement, i.e., under a steady-state condition ∂N ∂t = 0 , N ZnO−nc:SiO 2 depends only on R r and R nr for the ZnO-nc:SiO 2 sample and N Eu 3+ :ZnO−nc:SiO 2 depends on R r , R nr , and R tr for the Eu 3+ :ZnO-nc:SiO 2 sample. Here, we have assumed that the addition of Eu 3+ ions into the SiO 2 matrix does not affect the generation process of ZnO-nc in the excited state of any given emission center, because the intensity of the steady-state PL excitation source and the absorption cross-section of ZnO-nc are constant values in the steady-state PL measurement of the two samples. This implies that the values of G are the same for the samples without and with Eu 3+ ions. Since the intensity of the PL emission is directly proportional to the number of ZnO-nc per unit volume in the excited state of an emission center, as shown in Equations (5) and (6), then using Equations (7) and (8) The energy transfer efficiency from the PL steady-state measurements E PL T can then be written as follows: The values of E PL T are shown in Figure 3, together with those of E TRPL T , for the various ZnO-nc emission centers. The figure also shows the error bar for each of the transfer efficiency values calculated using the two different methods.
We notice that the E PL T and E TRPL t 360, 378, 396, 417, 450, 500, and 575 nm [10], were identified as band-edge emissions from est ZnO-nc, which possibly experiences some quantum confinement effect (QC) [11], mission (EE) [12,13], and five different defect state emissions, namely Zn defect (Zni to VZn) en interstitial defect (Oi) [15,16], and oxygen vacancy defects (Vo, VȮ, VӦӦ) [14,17,18], ly. In this work, we study the contribution of energy transfer from various ZnO-nc emission Eu 3+ ions based on TRPL measurements. We calculate the decay time from the TRPL ents for various ZnO-nc emission centers and then calculate the efficiency of energy om each of the ZnO-nc emission centers to the Eu 3+ ions. Furthermore, the transfer is also calculated from steady-state PL emission data for comparison. The results in this high transfer efficiencies from the EE (at 378 nm) and Zni to VZn (at 396 nm) emission ostly due to the energy transfer from ZnO-nc to Eu 3+ ions which results in radiative rom Eu 3+ ions at 614 nm, while the energy transfer from the oxygen defect emissions at 417, defect emission at 575 nm. The transfer efficiencies obtained in this work are quite similar to the energy transfer efficiencies from silicon nanocrystals to Er 3+ ions reported by Savchyn et al. [24], calculated using similar methods. In our previous work [9], we calculated the spectral overlap integral of each of the seven ZnO-nc emissions with the Eu 3+ excitation spectrum to obtain a measure of the energy transfer from ZnO-nc to the Eu 3+ ions resulting in the emission at 614 nm. It has been found and reported in Reference [9] that the EE and Zn i to V Zn emission centers emitting at 378 and 396 nm have the highest contribution to the energy transfer from ZnO-nc to Eu 3+ ions, while the oxygen defect emissions of ZnO-nc such as O i , V o , V 2 of 9 were identified as band-edge emissions from me quantum confinement effect (QC) [11], state emissions, namely Zn defect (Zni to VZn) n vacancy defects (Vo, VȮ, VӦӦ) [14,17,18], nergy transfer from various ZnO-nc emission e calculate the decay time from the TRPL and then calculate the efficiency of energy to the Eu 3+ ions. Furthermore, the transfer sion data for comparison. The results in this 378 nm) and Zni to VZn (at 396 nm) emission -nc to Eu 3+ ions which results in radiative nsfer from the oxygen defect emissions at 417, rgy transfer from ZnO-nc to the new defects , as proposed in our previous work [9]. ZnO-nc to Eu 3+ ions will help to further the s and in the development of energy efficient , phosphors, etc. that can be excited by the types of thin-film samples; namely ZnO-nc in 12 mol % Eu 3+ ions (Eu 3+ :ZnO-nc:SiO2). The study because the 12 mol % sample has the energy transfer from ZnO-nc, in comparison h has been reported in our previous work [9]. wavelengths of the seven ZnO-nc emission velengths of the seven signals, namely at 450, emissions at 360, 378, 396 and 417 nm. t the 450, 500 and 575 nm emissions have the ossibly due to the larger number of phonons and 417 nm, shown schematically in Figure 1 various transitions). The number of phonon s is estimated to be around three to nine times ss. The probability of multi-phonon emissions ired for the de-excitation process, leading to a involved in the emissions at 450, 500 and 575 The energy band diagram in Figure 1 also ission centers to Eu 3+ ions in the SiO2 matrix, he emissions from ZnO nanocrystals and Eu 3+ gram reported in our earlier work [9], where s is represented using the colour gradients in re is a possibility of back energy transfer from 5 D0 state of Eu 3+ to the VȮ defect center in the do not consider the effect of the energy back nO-nc in this study.
, and V 2 of 9 [10], were identified as band-edge emissions from s some quantum confinement effect (QC) [11], efect state emissions, namely Zn defect (Zni to VZn) xygen vacancy defects (Vo, VȮ, VӦӦ) [14,17,18], n of energy transfer from various ZnO-nc emission ts. We calculate the decay time from the TRPL ters and then calculate the efficiency of energy ters to the Eu 3+ ions. Furthermore, the transfer emission data for comparison. The results in this (at 378 nm) and Zni to VZn (at 396 nm) emission ZnO-nc to Eu 3+ ions which results in radiative transfer from the oxygen defect emissions at 417, energy transfer from ZnO-nc to the new defects ions, as proposed in our previous work [9]. om ZnO-nc to Eu 3+ ions will help to further the E ions and in the development of energy efficient fiers, phosphors, etc. that can be excited by the wo types of thin-film samples; namely ZnO-nc in with 12 mol % Eu 3+ ions (Eu 3+ :ZnO-nc:SiO2). The his study because the 12 mol % sample has the ue to energy transfer from ZnO-nc, in comparison which has been reported in our previous work [9]. peak wavelengths of the seven ZnO-nc emission t wavelengths of the seven signals, namely at 450, four emissions at 360, 378, 396 and 417 nm. that the 450, 500 and 575 nm emissions have the re possibly due to the larger number of phonons 396 and 417 nm, shown schematically in Figure 1 ing various transitions). The number of phonon sions is estimated to be around three to nine times rocess. The probability of multi-phonon emissions equired for the de-excitation process, leading to a ing involved in the emissions at 450, 500 and 575 hs. The energy band diagram in Figure 1 also c emission centers to Eu 3+ ions in the SiO2 matrix, to the emissions from ZnO nanocrystals and Eu 3+ diagram reported in our earlier work [9], where nters is represented using the colour gradients in t there is a possibility of back energy transfer from the 5 D0 state of Eu 3+ to the VȮ defect center in the r, we do not consider the effect of the energy back he ZnO-nc in this study.
, which are centered at 417, 450, 500, and 575 nm, respectively, have low energy transfer contributions to the Eu 3+ ions. Thus, combining the results of spectral overlap integrals from our previous work [9] with the transfer efficiencies results of this work, we can deduce that the high transfer efficiencies E PL T and E TRPL T of EE and Zn i to V Zn emission centers are mostly due to the energy transfer from ZnO-nc to Eu 3+ ions, which results in the radiative emission from the Eu 3+ ions at 614 nm. We also observe that for the oxygen defect emissions of ZnO-nc such as O i , V o , and V 2 of 9 entified as band-edge emissions from ntum confinement effect (QC) [11], issions, namely Zn defect (Zni to VZn) ncy defects (Vo, VȮ, VӦӦ) [14,17,18], ransfer from various ZnO-nc emission ulate the decay time from the TRPL en calculate the efficiency of energy Eu 3+ ions. Furthermore, the transfer ta for comparison. The results in this and Zni to VZn (at 396 nm) emission Eu 3+ ions which results in radiative m the oxygen defect emissions at 417, sfer from ZnO-nc to the new defects oposed in our previous work [9]. to Eu 3+ ions will help to further the n the development of energy efficient hors, etc. that can be excited by the thin-film samples; namely ZnO-nc in l % Eu 3+ ions (Eu 3+ :ZnO-nc:SiO2). The ecause the 12 mol % sample has the transfer from ZnO-nc, in comparison een reported in our previous work [9]. engths of the seven ZnO-nc emission ths of the seven signals, namely at 450, ons at 360, 378, 396 and 417 nm. 0, 500 and 575 nm emissions have the due to the larger number of phonons nm, shown schematically in Figure 1 s transitions). The number of phonon mated to be around three to nine times robability of multi-phonon emissions the de-excitation process, leading to a d in the emissions at 450, 500 and 575 ergy band diagram in Figure 1 also enters to Eu 3+ ions in the SiO2 matrix, sions from ZnO nanocrystals and Eu 3+ ported in our earlier work [9], where esented using the colour gradients in ossibility of back energy transfer from e of Eu 3+ to the VȮ defect center in the consider the effect of the energy back in this study.
, the values of the transfer efficiencies E PL T and E TRPL T are similar to those of EE and Zn i to V Zn emission centers, even though the spectral overlap integral values of oxygen defect emissions are low. This implies that the energy transfer from these oxygen defect emission centers is mostly due to the energy transfer from ZnO-nc to the additional new defects created due to the incorporation of the Eu 3+ ions [9], which was proposed in our earlier work [9]. The formation of Eu 3+ ion-induced defect centers is a very important result that needs to be considered when fabricating light-emitting devices which use the energy transfer process from ZnO-nc to excite RE ions. This result, together with the knowledge and understanding of ZnO-nc emission centers which contribute to the energy transfer process from ZnO-nc to Eu 3+ ions resulting in a strong emission at 614 nm, can help in fabricating future, energy-efficient red light-emitting devices.

Materials and Methods
The samples in this study were fabricated using the low-cost sol-gel process and made into thin films of approximately 300 nm by spin-coating on a Si substrate. The sol-gel process is essentially a three-step process where, in the first step of chemical mixing the precursor, the solvent and the catalyst were added together to create the sols. Separate sols were prepared for fabricating the SiO 2 matrix and the ZnO-nc. The SiO 2 sol was prepared with tetraethyl orthosilicate (TEOS) as the precursor dissolved in ethanol along with de-ionized water, while the ZnO-nc sol was prepared with zinc acetate dihydrate as the precursor and diethylamine as the catalyst dissolved in ethanol. In the second step, the sols were aged for 24 h, after which Europium(III) nitrate pentahydrate was added to the SiO 2 matrix sol to incorporate the Eu 3+ ions. The two sols were then mixed to create samples with Zn:Si in a 1:2 ratio and spin-coated on a (100) Si substrate. Finally, the samples were soft baked for 5 m at 100 • C and subsequently annealed at 450 • C in an O 2 environment for 60 s using the Rapid Thermal Annealing (RTP) process. The steps of fabrication are exactly same as those reported in our previous publications [9,10], and the exact same samples used in our previous study of the steady-state PL emission from ZnO-nc and Eu 3+ ions were also used for this work [9]. The formation of ZnO-nc embedded in an SiO 2 matrix using this sol-gel recipe has been studied in detail in our group's earlier publication [10], wherein the TEM images of the samples were analyzed to confirm the formation of ZnO-nc.
The TRPL spectra was obtained by exciting the sample using a femtosecond amplified-pulsed laser, which was tuned to 325 nm using an optical parameter amplifier and detected using a streak camera (OptoScope SC-10, Optronis, Kehl, Baden-Württemberg, Germany) [26]. The pulse-width and the repetition rate of the excitation pulse were 100 fs and 1 KHz, respectively. The PL measurements were obtained by exciting the samples at 325 nm using a spectrofluorometer (SPEX Fluorolog-3 Model FL3-11, Horiba, Edison, NJ, USA).

Conclusions
In this work we measured the TRPL spectra of ZnO-nc:SiO 2 and Eu 3+ :ZnO-nc:SiO 2 samples to study the contribution of energy transfer to the Eu 3+ ions from the various emission centers of ZnO-nc. The TRPL spectra of the two samples were analyzed by calculating the decay time and the stretching exponential coefficient values of the different ZnO-nc emissions centers at 360, 378, 396 and 417 nm using the stretched exponential decay function. The decay time showed that samples with Eu 3+ ions experience faster decay because of the additional components, namely the energy transfer from ZnO-nc to the Eu 3+ ions, which results in the radiative emission from the Eu 3+ ions at 614 nm, and the energy transfer to the additional new defects created due to the incorporation of the Eu 3+ ions, contributing to the decay rate. Furthermore, the transfer efficiencies of the ZnO-nc emissions calculated from the decay time are consistent with the transfer efficiencies calculated using the PL emission intensity data. These results show that the high transfer efficiencies of EE and Zn i to V Zn emission centers emitting at 378 and 396 nm is mostly due to the energy transfer from ZnO-nc to Eu 3+ ions, resulting in an emission at 614 nm, while the energy transfer from the oxygen defect emissions at 417, 450, 500 and 575 nm is most probably due to the energy transfer from ZnO-nc to the defects created due to the incorporation of the Eu 3+ ions in the Eu 3+ :ZnO-nc:SiO 2 samples, as proposed in our previous work. Moreover, the stretching exponential coefficient values, which are a measure of interaction between two or more identical ZnO-nc emission centers, show that the 360-nm band edge emission (QC) experiences lesser interactions compared to the EE, Zn i to V Zn , and O i emissions centered at 378, 396, and 417 nm, respectively. These are important results which will help in the fabrication of future efficient light sources based on the energy transfer process from semiconductor nanocrystals.