## 4 Results and Discussion
Ideally, an optimal down-conversion system would emit two photons for each absorbed photon, resulting in an effective quantum efficiency of 200%. The relationship between transfer efficiency and effective quantum efficiency is linear and can be expressed as follows:  
\[\eta_{\rm{EQE}}=\eta_{\rm{TB-r}}(1-\eta_{\rm{TB-Yb}})+2\eta_{\rm{TB-Yb}}\]  
Figure 6: Luminescence decay of the \(\,\rm{Tb^{3+}:{}^{5}D_{4}\to{}^{7}F_{5}}\,\) transition of the different G (**left** column) (**a,c**) and GC (**right** column) (**b,d**) samples at 543 nm emission under 370 nm excitation. Here, \(\eta_{\text{Tb}-\text{r}}\) represents the quantum efficiency for Tb\({}^{3+}\) ions and is assumed to be equal to 1. From the decay curves obtained in our previous works [22; 27] the energy transfer efficiency and effective quantum efficiency have been calculated. The resulting energy transfer efficiency and effective quantum efficiency for two samples glass and glass ceramic \(70\text{SiO}_{2}-30\text{H}\text{O}_{2}\) co-doped with 3% Tb\({}^{3+}\) and 12% Yb\({}^{3+}\) are listed in Table 1. These results demonstrate that the effective quantum efficiency values for GC samples are greater than the ones obtained in the G samples. This is attributed to the glass-ceramic matrix's low phonon energy (700 cm\({}^{-1}\)), which effectively minimizes non-radiative transitions and enhances luminescence, as indicated in our previous research [22]. In Figure 7, a schematic of a silicon solar cell (SC) coated with DC layer is shown, along with an explanation of how this material can downshift, or absorb and reemit, certain wavelengths of light in the solar spectrum to understand the mechanism behind the improvement in solar cell performance. In order to study the effect of the DC layer coating on the solar cell's performance, the DC layer was applied directly to the surface of textured silicon solar cells (area: 0.8 \(\times\) 2.5 cm\({}^{2}\)). The I-V and P-V characteristics of a solar cell with and without a DC layer under three different conditions, a bare solar cell, a solar cell covered with G films, and a solar cell covered with GC films, are shown in Figure 8. The electrical measurements (\(\text{I}_{\text{m}},\text{V}_{\text{m}},\text{I}_{\text{sc}},\text{V}_{\text{ oc}}\)) were obtained from these curves, and the efficiency of conversion (\(\eta\)), filling factor (FF), and enhancement of efficiency (\(\Delta\eta\)) were calculated based on these results as follows:  
\[\text{FF}=\frac{\text{I}_{\text{m}}\text{V}_{\text{m}}}{\text{V}_{\text{oc}} \text{I}_{\text{sc}}}\]  
\[\eta=\frac{\text{I}_{\text{m}}\text{V}_{\text{m}}}{\text{A}\times\text{I}}\]  
Figure 4:0  
where:  
A is the solar cell area; I is the incident irradiance; and \(\eta_{\text{bare}\text{sc}}\) is the bare solar cell efficiency. The short circuit current for the devices with G and GC down-conversion layers was improved to 49.7 mA and 50.3 mA, respectively, compared to 49.5 mA for the bare solar cell. The improvement in light absorption of the devices did not impact the Voc and FF values. The parameters of the devices are provided in Figure 4:1 The energy conversion efficiency of the devices with glass and glass-ceramic downconverter layer was 10.78 and 10.68, respectively, which represented increases of 5.26% and 4.19% compared to the efficiency of a bare solar cell. It is worth noting that the efficiency of the solar cell covered with glass is slightly higher than that of the solar cell covered with glass ceramic. This increase in efficiency may be due to the optical properties of the host matrix, as previously suggested by [PERSON] et al. [20]. The integration of a downconverter material appears to effectively enhance the photoresponse of silicon solar cells in the UV-blue wavelength range. This is achieved through the efficient downshifting of high-energy photons beyond 2.5 eV and enhancing the utilization of photons in the process.