## 1 Introduction  
Recently, many efforts in the energy field aim to develop sustainable and renewable energy sources [1]. Indeed, renewable energies can be considered as an inexhaustible, pollution-free and clean source of energy. One of these sources that may be used extensively in the generation of electricity utilizing photovoltaics is solar energy. In reality, the price of photovoltaic systems depends on both the difficulty of industrial production and the efficiency of the cells themselves [2]. The limited efficiency of the photovoltaic (PV) cells or panels is essentially due to the non-absorption of sunlight with energy below the bandgap as well as the thermalization effect due to the absorption of sun effect due to the absorption of sunlight with energy exceeding the semiconductor's band gap [3], which lead to a theoretical efficiency limit of approximately 30% for silicon based solar cells [4]. One of the keys to overcoming these losses and to obtain higher efficiency is by improving the spectral matching between the broad spectrum of the sun and the band gap of the semiconductor used in PV cells. In order to exploit the whole or maximum solar spectrum, two major solutions were envisaged [5]. The first solution uses multijunction solar cells [6] with several semiconductors having different band gaps which selectively absorb each part of the solar spectrum. The second solution is based on the modification of the solar spectrum to fit the gap of the cell by using down-conversion (DC) and up-conversion (UC) processes (Figure 1). Multi-junction cells can be considered as the most advanced approach since the conversion efficiency of these cells can reach more than 46% [7; 8]. Despite its numerous advantages, this approach has a few drawbacks related to the extremely high manufacturing costs [9], tracking problems caused by the sun tracking system [10; 11], optical device losses, and concentration problems [12]. Therefore, the use of down- and up-conversion layers offers several advantages, avoiding or reducing these drawbacks [13]. Indeed, the related materials are relatively cheap and can be simply combined with the cell without any radical modification of their architecture, in front for the DC system and in rear for the UC system. For instance, in the DC process, photons in the UV/VIS spectrum are converted into photons with energy appropriate for the solar cell's bandgap or 1.1 eV for silicon-based solar cells. Several methods have been used to implement the DC/UC solution, such as using quantum dots, nanocrystals, and rare-earth based optical layers. Of these, rare-earth ions have been found to be particularly effective for DC devices because of their diverse energy band structures. The down-conversion process results in a quantum efficiency that is higher than 100%, as theorized by [PERSON] et al. [14] and observed by other researchers using Pr\({}^{3+}\), Tm\({}^{3+}\), and Gd\({}^{3+}\) doped host matrices [15]. Recently, high quantum efficiencies approaching 200% have been achieved by [PERSON] et al. [16] on a LiGdF\({}_{4}\): Eu\({}^{3+}\)-Gd\({}^{3+}\) phosphor system, which has renewed interest in the development of efficient Quantum-cutting layers. Another system based on double co-doping Er\({}^{3+}\)-Gd\({}^{3+}\)-Tb\({}^{3+}\) has also been studied, but a system using Yb\({}^{3+}\) seems to be more promising because it only has one level available in excitation, the level \({}^{2}\)F\({}_{5/2}\). This level is well located for use in the silicon photovoltaic field because the relaxation \({}^{2}\)F\({}_{5/2}\rightarrow{}^{2}\)F\({}_{7/2}\) between the excited level and the fundamental level of Yb\({}^{3+}\) emits a photon with a wavelength of 980 nm which is located just at the silicon bandgap's edge. The Tb\({}^{3+}\) ion is employed as a sensitizer ion, with absorption in both the UV and blue regions at 488 nm via level \({}^{5}\)D\({}_{4}\) and cooperative transfer to Yb\({}^{3+}\) from level \({}^{5}\)D\({}_{4}\) (Figure 2).