## 4 Discussion  
Under the indirect 330 nm excitation, which is associated to the SnO\({}_{2}\) band-gap, the \({}^{4}I_{13/2}\)\(\rightarrow\)\({}^{4}I_{15/2}\) emission spectrum exhibits Stark splitting and narrow peaks (see Figure 3). This aspect revealed two important points: (i) the location of Er\({}^{3+}\) in the crystalline environment, i.e., SnO\({}_{2}\) nanocrystals [13; 16; 18; 19], and (ii) the energy transfer from SnO\({}_{2}\) to the rare earth ions. The 1500 nm broad band emission acquired by directly exciting Er\({}^{3+}\) ions using the 514 nm emission of the Xenon lamp disclosed the location of Er\({}^{3+}\) in a disordered environment. Although the intensity-based analysis can suffer variations from the experimental factors, e.g. light sources, detectors, and refractive indices, the difference in the integrated intensity of Er\({}^{3+}\) emission band centered at 1500 nm in the case of the two excitation schemes was evident. The emission intensity was higher for the 330 nm excitation with respect to that recorded in the case of the 514 nm excitation. The more intense emission of Er\({}^{3+}\) upon excitation at 330 nm proved the efficient role of SnO\({}_{2}\) as a luminescence sensitizer for the rare earth ions. A similar effect was demonstrated in the case of silica-tin oxides waveguides activated by Eu\({}^{3+}\) ions [4] and Er\({}^{3+}\) ions [10].  
\({}^{4}I_{13/2}\rightarrow\)\({}^{4}I_{15/2}\) photoluminescence spectrum obtained upon direct excitation of the \({}^{2}H_{11/2}\) level of the Er\({}^{3+}\) ions is shown in Figure 4. The large emission bandwidth, together with less pronounced Stark splittings, are observed. This shows the presence of Er\({}^{3+}\) ions in an amorphous environment.  
The excitation spectra in Figure 5 clearly show that the dominant contribution to both 1553.5 nm and 1535.5 nm emission was due to energy transfer from the SnO\({}_{2}\) nanocrystals to the imbedded Er\({}^{3+}\) ions, i.e., the indirect excitation scheme. The weak bands observed at 489 nm, 520 nm, and 655 nm are due to direct excitation of Er\({}^{3+}\) electronic states. These results again confirm that SnO\({}_{2}\) were efficient sensitizers of Er\({}^{3+}\) luminescence.  
To assess some parameters that will be useful for the modelling of a possible laser, the lifetimes and the corresponding fractions of the ions in the \({}^{4}I_{13/2}\) metastable state were determined. The decay curve of Figure 6 is similar to the ones already observed in the (\(100-x\))SiO\({}_{2}\)\(\times\)TiO\({}_{2}\)-1 Er\({}_{2}\)O\({}_{3}\) glass-ceramic system in Reference [20]. The results listed in Table 2 show that about 75% of the Er\({}^{3+}\) ions in the \({}^{4}I_{13/2}\) state had an exponential decay of about 4.9 ms. Considering that the lifetime of the metastable state of Er\({}^{3+}\) in SnO\({}_{2}\) crystals is in the order of 6 ms [21], is reasonable to assume that the majority of the Er\({}^{3+}\) ions were imbedded in the SnO\({}_{2}\) crystals [22]. The short decay component of 0.5 ms could be assigned to the ion-ion interaction energy transfer or Er-OH centers. As recently discussed by [PERSON] et al. [17], the spectral response of the Er\({}^{3+}\) in SnO\({}_{2}\) is highly complex and more site-selective spectroscopic measurements are mandatory to accurately define the more suitable pumping schema for a solid-state laser based on the system presented here. It could be that, following the paper already mentioned, besides well-defined narrow band crystalline-like emission, corresponding to substitutional sites, broader band emission is also present, which suggests the presence of a wide variety of crystal fields at the Er\({}^{3+}\) sites of SnO\({}_{2}\)[17]. In any case, this could be useful for the laser system increasing the number of ions available for the population inversion.