1. Introduction

In recent years, a lot of studies have been conducted to fabricate systems of semiconductor nanocrystals and rare-earth (RE) ions due to its potential for use as energy efficient solid state lighting devices. Semiconductor nanorcrystals like zinc oxide nanocrystals (ZnO-nc), cadmium selenide nanocrystals, tin oxide nanocrystals, etc. have been widely used to sensitise a wide variety of RE ions through the energy transfer process. Amongst the many semiconductor nanocrytsal, ZnO-nc has been particularly attractive due to its ability to excite a large number of RE ion dopants such as Ce³⁺, Yb³⁺, Tb³⁺, Er³⁺, Ho³⁺, Dy³⁺ and Eu³⁺ [1–9]. Furthermore, ZnO-nc doped with aluminum and gallium has also been studied extensively for plasmonic application [10–12].

The energy transfer from ZnO-nc to Eu³⁺ ion is of particular interest [8, 13–24] due to the sharp red emission at 614 nm from the Eu³⁺ ions which can be used to make energy efficient red light sources or as phosphors in displays. The broadband ultra-violet/visible emission from an optically excited ZnO-nc efficiently transfers energy to excite the Eu³⁺ ions, which subsequently de-excites radiatively to give a sharp red emission at 614 nm. In most of the studies on energy transfer from ZnO-nc to Eu³⁺ ions, the focus has been to understand the properties of such a system. For instance, Ntwaeaborwa et. al. [22] and Pessoni et. al. [20] report on the structural, optical and dielectric properties of ZnO-nc and Eu³⁺ system. While Najafi et. al. [18] report about the effects of fabrication conditions and the nature of the intrinsic defects on the energy transfer process. Even earlier works by our group has been focused on studying the contribution and mechanism of energy transfer from the various ZnO-nc emission centers to the Eu³⁺ ions based on the photoluminescence emission [23] and time-resolved photoluminescence emission [24] properties of ZnO-nc and Eu³⁺ ions. Interestingly, there has been no report on the nature of energy transfer from ZnO-nc to Eu³⁺ ions based on the interaction distance between ZnO-nc and Eu³⁺ ions, which is an important parameter that can greatly affect the energy transfer efficiency from the ZnO-nc to Eu³⁺ ions.

Hence in this work, we study the effect on energy transfer from the ZnO-nc to the Eu³⁺ ions by varying the interaction distance between the ZnO-nc and the Eu³⁺ ions. Two different types of thin film samples were studied to understand the effect of interaction distance between the ZnO-nc and the Eu³⁺ ions. In the first type, the ZnO-nc and Eu³⁺ ion are co-doped in the same SiO₂ matrix and in the second type, three layer thin film samples are fabricated with the ZnO-nc and Eu³⁺ ions doped in separate layers of SiO₂ which are separated by a buffer layer of SiO₂ matrix. The detail of the samples fabrication is described below in the method section. The average shortest interaction distance between the ZnO-nc and the Eu³⁺ ions and the average shortest interaction distance between two Eu³⁺ ions in these samples is then calculated by modeling and deriving the equation based on the ratio of Zn, Si and Eu³⁺ ions in the sample and using the density and molecular mass of ZnO and SiO₂. It is important to note that, the interaction distance between the ZnO-nc and the Eu³⁺ ions and the interaction distance between two Eu³⁺ ions are the average shortest distances between the two interaction species. However, in this paper we simply refer to them as the interaction distance between the ZnO-nc and the Eu³⁺ ions and the interaction distance between two Eu³⁺ ions, for convenience. The results from this work quantitatively show that at lager interaction distances between ZnO-nc and Eu³⁺ ions the energy transfer is mostly radiative energy transfer. However, as the interaction distance between the ZnO-nc and the Eu³⁺ ions decrease the energy transfer increases and takes place through both radiative and non-radiative process resulting in higher red emission at 614 nm from the Eu³⁺ ions. The results also show that the interaction distance between two Eu³⁺ ions is an important factor in the intensity of red emission from the Eu³⁺ ions at 614 nm. At shorter interaction distances between two Eu³⁺ ion the 614 nm emission from the Eu³⁺ ions is quenched due to migration of energy between adjacent Eu³⁺ ions. The knowledge gained from this work on the energy transfer process from ZnO-nc to Eu³⁺ ions based on the interaction distance between the ZnO-nc and the Eu³⁺ ions, will definitely help in advancement of energy efficient light sources based on the energy transfer process from semiconductor nanocrystal to rare-earth ions. These could be used to make lasers, phosphors, amplifiers, etc. which can be used for varied applications in numerous industries.

2. Method

In this work, two different types of thin film samples were fabricated as mentioned in the introduction. The two types of samples are labelled as A type sample and B type sample, for easy reference. A schematic representation of A type sample and B type sample is shown in Fig. 1. The first type of samples namely A type sample, shown in Fig. 1(a), is a single layer of SiO₂ matrix co-doped with ZnO-nc and Eu³⁺ ions. This sample was fabricated using the low cost sol-gel process and then deposited on Si substrate by spin-coating. It was eventually densified into thin film samples by annealing using rapid thermal annealing process (RTP) at 450°C. Four different samples of this type with varying Eu³⁺ concentration ranging from 4 mol% to 16 mol% were fabricated. The four different A type samples are referred as A_x (where x refers to mole fraction of Eu³⁺ ions calculated using $x=\frac{moles of \left(E{u}^{3+}\right)}{moles of \left(E{u}^{3+}+Zn+Si\right)}$ and it ranges from 0.04 to 0.16). Table 1 shows a summary of the different A_x samples. We would like to point out that the four different A_x samples are exactly the same samples used in our previous work [23], where the effect of Eu³⁺ concentration on the energy transfer mechanism from ZnO-nc to Eu³⁺ ion was studied. A detailed report of the fabrication steps of the A_x samples has also been reported in the previous publication [23].

 

Fig. 1 Schematic diagram of the two types of samples from this study. a) A type Sample which is a single layer of SiO₂ matrix co-doped with ZnO-nc and Eu³⁺ ions b) B type Sample which is a three-layer thin film sample in which the ZnO-nc and Eu³⁺ ions are doped in separate layers of SiO₂ with a buffer layer of plane SiO₂ between them.

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Table 1. A summary showing the names of the four different A_x samples and the five different B_d samples.

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The second type of sample namely, B type sample is three-layer thin film samples which were prepared using a combination of sol-gel process with spin coating and RF sputtering deposition. The schematic representation of this three-layer thin film sample is shown in Fig. 1(b). The first layer of the sample is a thin film of SiO₂ matrix embedded with Eu³⁺ ions (Eu³⁺:SiO₂), which was prepared using the sol-gel process and deposited on the Si substrate by spin-coating. The sol for the SiO₂ matrix was prepared using tetraethyl orthosilicate (TEOS) as the precursor and the Eu³⁺ ions were introduced by mixing europium (III) nitrate pentahydrate salt in this sol. The TEOS sol was aged for 24 hours before deposition and then annealed at 900°C for 60 sec. in O₂ environment using RTP. The ratio of Eu³⁺:Si in this layer was maintained at 9:44 which is the same ratio of Eu³⁺:Si as in the A_0.12 sample. The A_0.12 sample was shown to have the optimum Eu³⁺ ions concentration for maximum photoluminescence emission (PL) at 614 nm which has been reported in detail in our earlier work [23]. Thus, due to this the ratio of Eu³⁺:Si was maintained at 9:44 in the B type samples. However, even though the ratio of Eu³⁺:Si is the same in both A_0.12 sample and B type samples, the actual number of Eu³⁺ ions in the two samples are different. The number of Eu³⁺ ions in A_0.12 sample is $4.12\times {10}^{21}$ per cm³, while the number of Eu³⁺ ions in B type samples is $5.43\times {10}^{21}$ per cm³. The reason for maintaining the same ratio of Eu³⁺:Si in both A_0.12 sample and B type samples as opposed to maintaining the actual number of Eu³⁺ ions in both the samples, is explained in the results and discussion section.

The second layer of the B type samples, a layer of SiO₂ matrix, was deposited on the first layer using radio-frequency (RF) magnetron sputtering of SiO₂ target. The RF magnetron sputtering was used for the second layer because it has a better control to deposit SiO₂ thin film of a few nanometer thicknesses as compared to the sol-gel process. The second layer which is a buffer layer of SiO₂, provides the space separation between the Eu³⁺ ions from the first layer and ZnO-nc from the third layer. The thickness of this layer can be controlled to a magnitude of 1 nm by adjusting the sputtering deposition time. Five different samples with varying thickness of the second layer ranging from 0 to 8 nm were fabricated to study the effect of interaction distance on the energy transfer process from the ZnO-nc to the Eu³⁺ ions. Similar to the first layer, the second layer was also annealed at 900°C for 60 sec. in O₂ environment using RTP. Finally, a third layer of ZnO-nc embedded in SiO₂ matrix (ZnO-nc:SiO₂) prepared again using the sol-gel process was deposited on the second layer by spin-coating a mixed sol of ZnO-nc and SiO₂. This layer was fabricated in exactly the same way samples of ZnO-nc in SiO₂ were prepared in our previous work, using sol-gel process by spin-coating the sample on Si substrate and then annealing the thin film sample at 450°C using RTP [23]. The ratio of Zn:Si in this layer was kept at 1:2, similar to the samples from our group’s earlier work [23]. A detailed report of the sol-gel fabrication steps of the Eu³⁺:SiO₂ layer and ZnO-nc:SiO₂ layer is also reported in our preceding work [23]. The five different three-layer thin film samples are referred as B_d (where d refers to the thickness, in nm, of the second layer which varies from 0 to 8 nm) samples in this work. The summary of the different B_d samples is also shown in Table 1.

The samples prepared in this work were studied by analysing the room-temperature photoluminescence (PL) emission spectra. A spectrofluorometer (SPEX Fluorolog-3 Model FL3-11) was used to excite the sample at 325 nm and the PL emission from the sample was measured at wavelengths ranging from 340 nm to 635 nm.

3. Theoretical calculation

The energy transfer from the ZnO-nc to Eu³⁺ ions depends significantly on the interaction distance between them and also the interaction distance between two Eu³⁺ ions. We calculate this interaction distance between the ZnO-nc and Eu³⁺ ions and the interaction distance between two Eu³⁺ ions using the ratio of Zn, Si and Eu³⁺ ions in the sample along with the density and molecular mass of ZnO and SiO₂. A detailed description of the modeling of the thin film samples and the calculation of interaction distance is reported in the following sub-sections.

3.1 A type sample

In this section, first the interaction distance between the ZnO-nc and the Eu³⁺ ions and then the interaction distance between two Eu³⁺ ions in A type sample is derived. As mentioned, A type sample is a single layer thin film sample with the Eu³⁺ ions and ZnO-nc co-doped in the same SiO₂ matrix which was prepared using the sol-gel process. In these samples, the ratio of Eu³⁺:Zn:Si and the size of the ZnO-nc are known values. The ratios of Eu³⁺:Zn:Si was calculated from the amount of Eu³⁺, Zn and Si precursors chemicals used which are controlled during the fabrication process. On the other hand, the size or the radius of the ZnO-nc was calculated from the TEM images of ZnO-nc in SiO₂ which was studied in detail and published in our group’s previous work on ZnO-nc in SiO₂ [25]. It is important note here that the shape of the ZnO-nc in the TEM images is not all spherical, nonetheless we can observe that they are nearly spherical. Thus, in order to analyze the interaction distances among the ZnO-nc and the Eu³⁺ ions presented in this work, the shape of ZnO-nc is assumed to be a regular geometric shape which is, in this work, taken as spherical. This spherical shape of ZnO-nc is further supported by studies by other groups where the ZnO-nc was fabricated using the sol-gel process with zinc acetate dihydrate (Zn(CH₃COO).2H₂O) as the precursor, similar to this work, and the shape of ZnO-nc is shown to be spherical [26–29]. Furthermore, the size of the ZnO-nc in these studies are in the range of 3 nm to 7 nm [27–29] which is very close to the nanocrystals from our group’s work which has a size of 4.83 nm [25]. Thus, using these known values we first calculate the number of ZnO-nc in one cm³ of the film and the number of Eu³⁺ in one cm³ of the film which are subsequently used to calculate the interaction distances.

We begin by calculating the volume of one ZnO nanocrystal, denoted by the symbol $V_{ZnO-nc}^A$(the superscript A indicates A type samples), using the radius of the nanocrystal with the following equation:

It is important to note here that the volume of the Eu³⁺ ions in the film is ignored in Eq. (3) as it is negligible. Now, with the total volume of ZnO and SiO₂, the total mass of these molecules in one cm³ of the film is obtained by multiplying the density of these materials with their respective volumes. For instance, the mass of ZnO molecules in one cm³ of the film, denoted by the symbol $m_{ZnO}^A$, is given by the formula:

In the above equations $M_{ZnO}$ and $M_{Si{O}_2}$ refer to the molecular weight of ZnO and SiO₂ respectively. Finally Eq. (6) and (7) are related to each other using the ratio of Zn:Si, denoted by the symbol $R_{Zn:Si}^A$, which is nothing but the ratio of $N_{ZnO}^A:N_{Si{O}_2}^A$. This is mathematically written as follows:

From Eq. (8) we can calculate $N_{ZnO-nc}^A$ which can be represented by rearranging Eq. (8) as follows:

All the values of the parameters on the right hand side of Eq. (9) are known constants, with $R_{Zn:Si}^A$ equal to 0.5 as determined during sample fabrication and $r_{ZnO-nc}^{}$ equal to 4.83 nm which was taken from the TEM images of ZnO-nc in SiO₂ annealed at 450°C published in our groups previous work on ZnO-nc in SiO₂ [25]. The values of $M_{ZnO}, {\rho }_{ZnO}, M_{Si{O}_2}$ and ${\rho }_{Si{O}_2}$ are material constants of ZnO and SiO₂ molecules which were also used to calculate the value of $N_{ZnO-nc}^A$.

Next we calculate the average distance between two ZnO-nc from the total number of ZnO-nc in one cm³ of the film. For this, we first assume that the ZnO-nc are uniformly distributed in the SiO₂ matrix as shown in Fig. 2. Thus, with this assumption we can calculate the volume occupied by one ZnO-nc in one cm³ of the film, which is mathematically written as:

 

Fig. 2 Schematic diagram of ZnO-nc uniformly distributed in SiO₂ matrix.

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Volume occupied by one ZnO-nc in one cm³ of the film$=\frac{1}{N_{ZnO-nc}^A}$

Finally, assuming the volume occupied by one ZnO-nc in one cm³ of SiO₂ film is a prefect cube as shown in Fig. 2, the average distance between the centres of two ZnO-nc, denoted as $d_{ZnO-nc}^A$, corresponds to the length of the cube. $d_{ZnO-nc}^A$ was calculated by taking the cube root of Eq. (10), which is mathematically shown as follows:

An important assumption in this calculation is that, all the Zn atoms incorporated in the samples during the fabrication process combine to form ZnO-nc. This assumption represents an ideal case and we note that it is quite unlikely that all the Zn atoms in the sample combine to form ZnO-nc. However, for simplification in this work we have assumed that all the Zn atoms in the sample combine to form ZnO-nc.

Now, for the calculation of interaction distance between ZnO-nc and Eu³⁺ ions we also need to calculate the average distance between the centers of two Eu³⁺ ions. Hence, similar to the average distance between the centres of two ZnO-nc, we first calculate the number of Eu³⁺ ions in one cm³ of the film which is subsequently used to calculate the average distance between the centers of two Eu³⁺ ions.

The number of moles of Eu³⁺ ions in one cm³ of the film was calculated from the ratio of Eu³⁺:Si in the film and the number of moles of SiO₂ molecules in one cm³ of the film which was calculated using Eq. (7). This relation is mathematically shown in the following equation:

In the above Eq. (13), the parameters on the right hand side are known constants, with $R_{E{u}^{3+}:Si}^A$ determined during sample fabrication, $r_{ZnO-nc}^{}$ equal to 4.83 nm obtained from our groups previous work [25] and $N_{ZnO-nc}^A$ determined from Eq. (9). Thus these values along with $M_{Si{O}_2}$ and ${\rho }_{Si{O}_2}$, which are material constants of SiO₂ molecules, were used to calculate the value of $N_{E{u}^{3+}}^A$.

Now, to calculate the average distance between two Eu³⁺ ions from the total number of moles of Eu³⁺ ions in one cm³ of the film we again assume that the Eu³⁺ ions are distributed uniformly in the SiO₂ matrix similar to the ZnO-nc. It is important to note here that the Eu³⁺ ions are embedded in the volume occupied by SiO₂, which is $1-\left(N_{ZnO-nc}^A\times \frac{4}{3}\pi r_{ZnO-nc}^3\right)$, and not in the entire volume of the film which includes the volume occupied by the ZnO-nc along with SiO₂. Thus, with this assumption we can calculate the volume occupied by one Eu³⁺ ion in one cm³ of the film, which is mathematically written as:

Volume occupied by one Eu³⁺ ion in one cm³ of the film$=\frac{1-\left(N_{ZnO-nc}^A\times \frac{4}{3}\pi r_{ZnO-nc}^3\right)}{N_{E{u}^{3+}}^A\times N_A}$

Finally, the interaction distance between the ZnO-nc and Eu³⁺ ions in A type sample, denoted by the symbol $d_{E{u}^{3+}/ZnO-nc}^A$, can be calculated from the above derived interaction distances. $d_{E{u}^{3+}/ZnO-nc}^A$ depends on the radius of ZnO-nc and the average distance between Eu³⁺ ions which is illustrated in Fig. 1(a). $d_{E{u}^{3+}/ZnO-nc}^A$, is mathematically written as:

3.2 B type sample

Having calculated the interaction distance between ZnO-nc and Eu³⁺ ions and the interaction distance between two Eu³⁺ ions in A type sample, next we calculate these interaction distance values in B type sample. B type sample, unlike A type sample, is a three layer sample with the ZnO-nc and Eu³⁺ ions doped in separate layers of SiO₂ with a buffer layer of SiO₂ between them. However, the initial steps of calculation of interaction distances in B type sample are similar to A type sample. In fact the derivation of average distance between the centres of two ZnO-nc in B type sample, denoted by the symbol $d_{ZnO-nc}^B$ (the superscript B indicates B type samples), is the same as in A type sample and it can be derived using the exact same steps as shown in Eq. (1) to (11). The average distance between the centres of two ZnO-nc in B type sample, $d_{ZnO-nc}^B$ is mathematically written as:

For the calculation of average distance between the centers of two Eu³⁺ ions, the derivation is slightly different from A type sample even though the final result is the same. For this calculation we first derive the number of moles of SiO₂ molecules in one cm³ of the first layer of B type sample, which is the Eu³⁺:SiO₂ layer. Then using the number of moles of SiO₂ molecules in one cm³ of the film along with the ratio of Eu³⁺:Si in the film, the number of moles of Eu³⁺ ions in one cm³ of the film is derived. This is similar to the derivation of number of moles of Eu³⁺ ions in A type sample and subsequently using number of moles of Eu³⁺ ions in one cm³ the average distance between the centers of two Eu³⁺ ions in Eu³⁺:SiO₂ layer of the B type sample is derived.

We begin the derivation of average distance between the centers of two Eu³⁺ ions in B type sample, from the volume of SiO₂ molecules in one cm³ of the Eu³⁺:SiO₂ film, denoted by the symbol $V_{Si{O}_2}^B$. $V_{Si{O}_2}^B$ is equal to 1 cm³ as the volume of Eu³⁺ ions in the film is ignored in the sample as it is negligible. Next, the total mass of these SiO₂ molecules in one cm³ of the film, denoted by the symbol $m_{Si{O}_2}^B$, is obtained by multiplying the density of SiO₂ with volume of SiO₂. $m_{Si{O}_2}^B$ is mathematically given by the formula:

The total number of moles of SiO₂ molecules in one cm³ of Eu³⁺:SiO₂ film is then calculated by dividing the mass of SiO₂ with its molecular weight. Mathematically it is written as:

Next step in the calculation of average distance between the centers of two Eu³⁺ ions is the derivation of the number of moles of Eu³⁺ ions in one cm³ of Eu³⁺:SiO₂ film. As mentioned above, it is calculated from the ratio of Eu³⁺:Si in the film and the number of moles of SiO₂ molecules in one cm³ of the film. This is mathematically shown in the following equation:

The number of moles of Eu³⁺ ions in one cm³ of Eu³⁺:SiO₂ film in the B type sample can be easily calculated by substituting in Eq. (21), the value of $R_{E{u}^{3+}:Si}^B$ determined from the sample fabrication and the values of $M_{Si{O}_2}$ and ${\rho }_{Si{O}_2}$, which are material constants of SiO₂ molecules.

Now, for the calculation of average distance between the centers of two Eu³⁺ ions from $N_{E{u}^{3+}}^B$, we assume that the Eu³⁺ ions are uniformly distributed in the SiO₂ matrix, which is similar to the assumption in A type sample, and this is illustrated in Fig. 3. With this assumption, the volume occupied by one Eu³⁺ ion in one cm³ of the film can be calculated using the following equation:

 

Fig. 3 Schematic diagram of Eu³⁺ ions uniformly distributed in SiO₂ matrix.

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Volume occupied by one Eu³⁺ ion in one cm³ of the film$=\frac{1}{N_{E{u}^{3+}}^B\times N_A}$

It is interesting to note here that the final results of Eq. (14) and Eq. (22), which show the volume occupied by one Eu³⁺ ion in one cm³ of the film in A type sample and B type sample, respectively, are exactly the same. The volume occupied by one Eu³⁺ ion in one cm³ of the film in both sample depend only on the ratio of Eu³⁺:Si in the respective samples.

Lastly, the average distance between the centres of two Eu³⁺ ions in B type sample, denoted by the symbol $d_{E{u}^{3+}}^B$, is calculated from the volume occupied by one Eu³⁺ ion in one cm³ of the film. For this, it is assumed that the volume occupied by one Eu³⁺ ion in one cm³ of the film is a prefect cube as shown in Fig. 3 and so the average distance between the centres of two Eu³⁺ ions corresponds to the length of the cube. This average distance between the centres of two Eu³⁺ ions, can be calculated as follows:

Finally, the interaction distance between the ZnO-nc and Eu³⁺ ions in B type sample which is denoted by the symbol $d_{E{u}^{3+}/ZnO-nc}^B$_{is calculated from the above derived interaction distance. The distance $d_{E{u}^{3+}/ZnO-nc}^B$ depends on the average distance between the centres of two Eu³⁺ ions, the average distance between the centres of two ZnO-nc and also on the thickness of the middle SiO2 buffer layer. $d_{E{u}^{3+}/ZnO-nc}^B$ is schematically shown in Fig. 1(b) and is mathematically written as:}

4. Results and discussion

In this work, the PL emission from the four different A type samples and the five different B type samples, as tabulated in Table 1, were analysed to study the effect of interaction distance between ZnO-nc and Eu³⁺ ions on the energy transfer process from ZnO-nc to Eu³⁺ ions. The PL spectra were measured by exciting the samples using 325 nm excitation wavelengths and observing the samples emission using a photo detector. The PL emission spectra of the four different A_x samples have been reported and studied in detail in our group’s earlier work on ZnO-nc and Eu³⁺ ions [23]. In this work we extend the analysis of the PL emission from A_x samples, especially at 614 nm due to energy transfer from ZnO-nc to Eu³⁺ ions. We study the PL emission from the Eu³⁺ ions at 614 nm based on the interaction distance between ZnO-nc and Eu³⁺ ions and the interaction distance between two Eu³⁺ ions, which greatly affect the energy transfer from ZnO-nc to Eu³⁺ ions.

Figure 4 shows the 614 nm emission intensity from the four different A_x samples as a function of the Eu³⁺ ion concentration, which has been reported in our earlier work [23] along with the interaction distance between ZnO-nc and Eu³⁺ ions in these samples which has not been reported earlier. We see that the 614 nm emission intensity increases significantly in these single layer thin film samples with increasing Eu³⁺ ion concentration from 4 mol% to 12 mol%. This is due to the fact that the interaction distance between ZnO-nc and Eu³⁺ ions reduces with increasing Eu³⁺ ion concentration resulting in higher energy transfer from excited ZnO-nc to Eu³⁺ ions. Specifically, as the interaction distance between ZnO-nc and Eu³⁺ ions reduces the non-radiative energy transfer between donor (ZnO-nc in our case) and acceptor (Eu³⁺ in our case) species increases [30–32]. The radiative energy transfer process on the other hand is an interaction distance independent process, i.e. it is independent of the distance between ZnO-nc and Eu³⁺ ions.

 

Fig. 4 614 nm PL emission intensity from the four different A_x samples along with the interaction distance between ZnO-nc and Eu³⁺ ions in these samples.

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The interaction distance between ZnO-nc and Eu³⁺ ions in A_x samples, which is shown in Fig. 4, was calculated using Eq. (16). It is evident from the figure that as the interaction distance between ZnO-nc and Eu³⁺ ions reduces from 5.25 nm in A_0.04 sample to 5.11 nm in A_0.12 sample the red emission at 614 nm increases due to increased non-radiative energy transfer from ZnO-nc to Eu³⁺ ions in the sample. However, as the Eu³⁺ ion concentration is further increased to 16 mol%, the red emission at 614 nm does not increase even though the interaction distance between the ZnO-nc and Eu³⁺ ions reduces to 5.08 nm in A_0.16 sample. In fact the 614 nm PL emission in A_0.16 sample reduces and this is attributed to a competing process known as Eu³⁺ ion concentration quenching as reported in our earlier work [23]. Eu³⁺ ion concentration quenching is the non-radiative dissipation of energy from the Eu³⁺ ions through the quenching sites in the sample as a result of migration of energy between neighbouring Eu³⁺ ions [33]. This migration of energy between the Eu³⁺ ions increases with decreasing distance between the Eu³⁺ ions. In the four A type samples the interaction distance between two Eu³⁺ ions decreases as the Eu³⁺ ion concentration increases from 4 mol% to 16 mol%, which is shown in Fig. 5 along with the 614 nm PL emission intensity from these samples. The interaction distance between two Eu³⁺ ions in A type sample was calculated using Eq. (15). The interaction distance reduces from 0.84 nm in A_0.04 sample to 0.51 nm in A_0.16 sample and at distances less than 0.57 nm (which is the interaction distance between two Eu³⁺ ions in A_0.12 sample), the migration of energy between the adjacent Eu³⁺ ions start become stronger. This leads to the quenching of energy transferred from the ZnO-nc to the Eu³⁺ ions and thus reducing the PL emission at 614 nm. Thus, in conclusion 5.11 nm is optimum interaction distance between ZnO-nc and Eu³⁺ ions and 0.57 nm is the optimum interaction distance between adjacent Eu³⁺ ions to maximise the red emission at 614 nm from the Eu³⁺ ions in A type sample.

 

Fig. 5 614 nm PL emission intensity from the four different A_x samples along with the interaction distance between two Eu³⁺ ions in these samples.

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To further understand the effect of the interaction distance between ZnO-nc and Eu³⁺ ions on the energy transfer from ZnO-nc to Eu³⁺ ions and its subsequent effect on the 614 nm emission from the Eu³⁺ ions, the PL emission from the five different B type samples, namely B₀, B₂, B₄, B₆ and B₈ were analysed. Figure 6 shows the PL emission spectra of the five different B_d samples with a spacer distance of 0, 2, 4, 6 and 8 nm. We clearly observe a broadband emission from all the five samples ranging from 340 to 635 nm. This PL emission is very similar to the PL emission from the four A_x samples reported in our previous work [23].

 

Fig. 6 PL emission spectra of five different B_d samples with a spacer distance of 0, 2, 4, 6 and 8 nm.

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The emission from 350 to 600 nm is attributed to the ZnO-nc, while the small peak at 614 nm is the signature emission of the Eu³⁺ ions. The broadband emission from the ZnO-nc is due seven different emission centers, which has been studied in detail in our previous publication [25]. The UV-blue emission of the ZnO is mainly due to band-edge [34], exciton [35, 36] and Zn defect emission centers [28] while the ZnO-nc emission above 400 nm wavelength is due to the oxygen defect centers in the nanocrystals [28, 37–40]. These emission centers when excited transfer energy to the Eu³⁺ ions through radiative and non-radiative processes which results in the red emission at 614 nm due to the ⁵D₀→⁷F₂ radiative de-excitation of the excited Eu³⁺ ions. The nature of the energy transfer mechanism and the contribution of energy transfer from the seven ZnO-nc emission centers has also been discussed in detail in our previous works [23, 24].

An important characteristic about the B type samples, which was also mentioned in the method section, is that the ratio of Eu³⁺:Si in the Eu³⁺:SiO₂ layer of the B_d samples was kept the same as the ratio of Eu³⁺:Si in the A_0.12 sample at 9:44. This was to ensure that the interaction distance between two Eu³⁺ ions in the B type sample was the same as that in A_0.12 sample which is 0.57 nm, the optimum interaction distance between two Eu³⁺ ions. The reason for maintaining the ratio of Eu³⁺:Si to control the interaction distance between two Eu³⁺ ions is understood from the formula for the interaction distance between two Eu³⁺ ions in A type sample and B type sample, given by Eq. (15) and Eq. (23) respectively. We can see that the interaction distance between two Eu³⁺ ions depend on the ratio of Eu³⁺:Si in the sample along with the density $\left({\rho }_{Si{O}_2}\right)$ and molecular weight $\left(M_{Si{O}_2}\right)$ of SiO₂. Since ${\rho }_{Si{O}_2}$ and $M_{Si{O}_2}$ are known material constants, the interaction distance between two Eu³⁺ ions depend only on the ratio of Eu³⁺:Si in the samples. Thus, by keeping the ratio of Eu³⁺:Si at 9:44 in the Eu³⁺:SiO₂ layer of B_d samples and in the A_0.12 sample, the interaction distance between two Eu³⁺ ions in these samples is maintained at 0.57 nm.

However, it is important to note here that while the ratio of Eu³⁺:Si is the same in both A_0.12 sample and B_d samples, the actual number of Eu³⁺ ions is not the same in both the samples, which has also been mentioned in the method section. The number of Eu³⁺ ions in A_0.12 sample is $4.12\times {10}^{21}$ per cm³, calculated using Eq. (13) while the number of Eu³⁺ ions in B_d samples $5.43\times {10}^{21}$ per cm³, calculated using Eq. (21). The lesser number of Eu³⁺ ions in A_0.12 sample is due to the fact that the Eu³⁺ ions are co-doped with ZnO-nc in the same SiO₂ matrix unlike the B_d samples in which the Eu³⁺ ions and ZnO-nc are doped in separate layers of the sample. The volume occupied by ZnO-nc in A_0.12 sample in the same SiO₂ matrix results in lesser number of Eu³⁺ ions in one cm³⁺ of the film (as shown in Eq. (13)) as compared to B type samples (as shown in Eq. (21)), even though the ratio of Eu³⁺:Si and subsequently the interaction distance between two Eu³⁺ ion is the sample in both the samples.

Higher Eu³⁺ ions in B_d samples as compared to A_0.12 sample means that the 614 nm emission from the Eu³⁺ ions in B_d samples is expected to be higher than that of the 614 nm emission from A_0.12 sample as B_d samples have more Eu³⁺ ions that can be excited. Interestingly, we notice that for the B_d samples the 614 nm emission is not strong and intense as that for the A_0.12 sample. Figure 7 shows a graphical representation of this comparison, where we can clearly see that the 614 nm emission from the A_0.12 sample is 10 times stronger than the 614 nm emission from the B type samples. This shows that the energy transfer from the ZnO-nc to the Eu³⁺ ions which results in the emission at 614 nm is much higher in A_0.12 sample as compared to B_d samples.

 

Fig. 7 614 nm PL emission intensity from the five different B_d samples along with the interaction distance between ZnO-nc and Eu³⁺ ions and the interaction distance between two Eu³⁺ ions in these samples. The graph also shows the 614 nm PL emission intensity from the A_0.04 and A_0.12 samples for comparison.

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The reason for this huge difference in PL emission at 614 nm is again due to the interaction distance between ZnO-nc and Eu³⁺ ions in the two different types of samples, which is an important factor in the energy transfer process. At short distances the energy transfer from ZnO-nc and Eu³⁺ ion take place through both radiative and non-radiative process, which is the case in A type samples. However, as the distance between ZnO-nc and Eu³⁺ ions increases the contribution due non-radiative energy transfer process decreases significantly and beyond a certain distance the energy transfer between ZnO-nc and Eu³⁺ ions will take place only through the radiative process, which is the case in B type samples.

Figure 7 also shows the interaction distance between ZnO-nc and Eu³⁺ ions in B_d samples, which was calculated using Eq. (24), along with the 614 nm emission intensity from these samples. We clearly notice from this figure that even for the 0 nm SiO₂ spacer B₀ sample, the interaction distance between ZnO-nc and Eu³⁺ ions is 6.53 nm which is much higher than the interaction distance between ZnO-nc and Eu³⁺ ions in any of the A type samples. The interaction distance between ZnO-nc and Eu³⁺ ions A_x samples is 5.25 nm or lower. Thus, the shorter interaction distance between ZnO-nc and Eu³⁺ ions in A type samples mean that there is higher non-radiative energy transfer between ZnO-nc and Eu³⁺ ions in this sample compared to the B type samples. This results in the higher red emission at 614 nm from the Eu³⁺ ions in the A type samples.

Moreover, we also notice that the 614 nm red emission values from the five B_d samples is fairly similar even though the interaction distance between ZnO-nc and Eu³⁺ ions in these sample vary greatly from 6.53 nm to 14.53 nm as shown in Fig. 7. In these samples the energy transfer contribution from ZnO-nc to the Eu³⁺ ions is not affected by the interaction distance between the ZnO-nc and the Eu³⁺ ions, which indicates that the energy transfer through non-radiative process in negligible. The energy transfer from ZnO-nc to Eu³⁺ ions in these samples is predominately through radiative process, which is independent of the interaction distance between the ZnO-nc and Eu³⁺ ions, resulting in almost uniform 614 nm emission from the Eu³⁺ ions. Hence, we can conclude that at distance greater than 6.53 nm between ZnO-nc and Eu³⁺ ions, the energy transfer from ZnO-nc to Eu³⁺ ions is mostly through radiative energy transfer process.

5. Conclusion

In conclusion, we studied the effect of the interaction distance between the ZnO-nc and the Eu³⁺ ions and the interaction distance between two Eu³⁺ ions on the energy transfer processes from the ZnO-nc to the Eu³⁺ ions. For this study two different types of samples were fabricated, namely a single layer of ZnO-nc and Eu³⁺ ion are co-doped in the same SiO₂ matrix (A_x samples) and a three layer thin film sample with the ZnO-nc and Eu³⁺ ions doped in separate layers of SiO₂ separated by a buffer layer of SiO₂ matrix (B_d samples). The model to calculate the interaction distance between the ZnO-nc and the Eu³⁺ ions and the interaction distance between two Eu³⁺ ions in these samples have been discussed in detail and the equation to calculate these interaction distances was derived based on the ratio of Zn, Si and Eu³⁺ ions in the sample along with the density and molecular mass of ZnO and SiO₂. It is clearly shown that the energy transfer from ZnO-nc to Eu³⁺ ions is higher in A type samples compared to the B type samples as the interaction distance between the ZnO-nc and Eu³⁺ ions is shorter in A type samples. Furthermore, as the interaction distance between ZnO-nc and Eu³⁺ ions is reduced in A type samples, the energy transfer from the ZnO-nc to Eu³⁺ ions increases resulting in higher red emission at 614 nm due to the ⁵D₀→⁷F₂ radiative de-excitation of the excited Eu³⁺ ions. The A_0.12 sample which has 5.11 nm interaction distance between the ZnO-nc and Eu³⁺ ions has the maximum red emission at 614 nm due efficient energy transfer from ZnO-nc to Eu³⁺. At higher concentrations of Eu³⁺ ions even though the interaction distance the between ZnO-nc and Eu³⁺ ions decreases, the red emission does not increase due to Eu³⁺ ion concentration quenching effect which occurs as the interaction distance between the Eu³⁺ ions become shorter than 0.57 nm in the sample resulting in migration of energy between the Eu³⁺ ions which is non-radiatively dissipated. It is also shown that the energy transfer in the B type samples, which have a 6.53 nm or higher interaction distance between the ZnO-nc and Eu³⁺ ions, is mostly due to radiative energy transfer. The results from this work are important and it can be used in the development of energy efficient rare-earth ion light sources which makes use of the energy transfer process from semiconductor nanocrystal sensitizers.