As it was previously stated, the aim of this work is to maximize the absorbance on the active layer of a conventional GaAs solar cell by taking advantage of light resonances of dielectric nanoparticles located on top of it. To optimize this arrangement, we previously made a search of the adequate geometrical properties; these are the height, diameter, and array period of the nanoparticles. Additionally, different potential dielectric materials have been also considered. After this recursive analysis and also comparing the results in terms of absorption and reflection with previous works , we observed that the geometrical properties providing the best results within the solar spectrum are a diameter (d) of 50 nm, a height (h) of 50 nm and a period w=250 nm. Regarding the material of the nanoparticles, the results are limited to two different dielectric materials: TiO2 and AlAs. Again, although we tested the results with several materials, these provided valuable results, for this reason hereinafter only those two dielectric materials are considered. In the last years, there can be found several ways to properly fabricate this kind of ordered arrays in an accurate way, so the geometrical properties are in accordance with the state of the art [35, 36, 37].
Figure 2 shows both the absorbance in the active layer (Figure 2a) and the total reflectance of the device (Figure 2b) as a function of the incident wavelength of a GaAs solar cell with different approaches and under a normal incidence. In particular, these figures show the cases of a conventional GaAs solar cell, a GaAs solar cell with an antireflection coating, a GaAs solar cell including plasmonic (Al) nanoparticles like in  and a GaAs solar cell with dielectric nanoparticles on top of it made of either TiO2 or AlAs as proposed in this work. The resonant behavior of these dielectric nanoparticles produces a strong confinement of light around them that is consequently reemitted to their bottom part, reducing the reflectance and increasing the amount of light going inside the photovoltaic device. The material and size of the nanoparticles as well as its arrangement allows us to select the bandwidth of these effects, matching them with the absorption window of the active material.
As it can be seen, all the considered cases provide an increase of the absorbance from 400 to 850 nm as well as a reduction of the total reflectance, maximizing the amount of light reaching inside the active layer and consequently increasing the amount of photogenerated electron-holes pairs. However, the results of each technique are quite diverse. For instance, the inclusion of an ARC improves the optical absorbance mainly at large wavelengths (600-850 nm), as it can be seen in Figure 2a. It also reduces the total reflectance in this spectral range, but its effects are remarkably worse at the lower end of the solar spectrum (Figure 2b). On the other hand, the inclusion of resonant nanoparticles at the top part of the solar device provides an overall increase of the absorbance and a reduction of the total reflectance compared to the conventional case. Nevertheless, we can still highlight remarkable differences between the metallic and dielectric cases.
Regarding the active absorbance, it can be seen that dielectric nanoparticles (TiO2 or AlAs) supporting Mie resonances [38, 39] provide a larger boost of the absorbance and in a wider spectral range than plasmonic nanostructures (Al). It is worth mentioning that the case of AlAs nanoparticles provides the best results in terms of absorbance, mainly due to the improvement, with a value up to a 40% higher than the conventional solar cell, in the absorbance in the blue part of the visible spectrum (400-500nm). In addition, the optical properties of these dielectric materials in the solar spectrum present a noticeable lower light absorption than that of metals (due to a lower imaginary part of its refractive index), strongly reducing the thermal effects produced in the case of Al nanoparticles. In the case of the total reflectance (Figure 2b), the effects of both metallic and dielectric nanostructures are similar: a general reduction of the reflectance compared to the conventional solar cell. Even so, again the effects of the dielectric particles are slightly better than those of the metallic ones, in particular in the UV range (< 400 nm) and at large wavelengths (> 600 nm).
While the maximum sensitivity of conventional solar cells is produced under a normal incidence, the addition of a textured or a nanostructured top surface may also increase the performance of the proposed device under non-normal incidence angles. In this sense, Fig. 3 shows a comparison of the spectral evolution of both the absorbance (left panel) and the reflectance (right panel) of a conventional solar cell, a solar cell including an antireflection coating and our proposed device including dielectric nanoparticles on the top surface under different angles of incidence. In particular, we consider an incidence of 20º, 40º and 60º as significant examples.
From an overall view of the results, it can be seen that the approach using AlAs nanoparticles provides the best results at any non-normal incidence in terms of both absorbance in the active layer and total reflectance. In the case of the absorbance (Figs. 3a, 3c and 3e), it can be observed that the use of these NPs in the top layer provides a smoother spectral response than the ARC case, as will be explained, and similar to that of a conventional solar cell. Moreover, this absorbance is larger than that of the conventional one at any wavelength in the range between 400 nm and 850nm. This enhancement is maintained for all the explored angles in the 500-800nm range. The improvement only decays in the 400-550 nm range at high angles. The maximum increase is estimated to be around a 44% compared to the conventional solar cell and a 33% to the case including an ARC at 440nm and under a normal incidence. The maximum enhancement is shifted at larger wavelengths at high angular incidence. In this sense, under an incidence of 60º the maximum increase is estimated to be around 80% (630 nm) compared to the conventional cell and an 82% (600 nm) compared to the case including an ARC. This effect allows a better performance of the solar cell during a larger number of hours in real installations without using solar tracker systems. Indeed, it is directly related with the total reflectance response in those wavelength intervals (Figures 3b, 3d and 3f), which spectral evolution shows that the minimum reflectance in the case of the solar cell with NPs is in the range between 600 and 700 nm. Again, the reflectance is much smaller within the solar spectrum than that of the other considered cases. In particular, this is clearly observed at incident angles of 20º and 40º (Figures 3b and 3d). The case of 60º (Figure 3f) is much complex because of the interferences produced in the multilayer ARC. Additionally, the differences between this minimum and the reflectance at other wavelengths are more prominent as the incident angle increases. It is also important to highlight the reflectance peaks appearing at ultraviolet wavelengths for the NPs case. These peaks become more prominent and wider as the incident angle increases, producing a lower absorbance of this approach in the spectral range (400-500 nm). However, these values are still better than those of a conventional solar cell.
In contrast to this response, the inclusion of ARC is mainly focused on its influence for normal incidence. The extra layers produce remarkable interferential effects, in both the absorbance and the total reflectance, which are more pronounced as the incident angle increases. This produces a response full of peaks -especially in the lower wavelengths- with mean values lower than the case of the solar cell with nanoparticles. Meanwhile, the behavior of the nanostructured solar cell is quite acceptable, keeping its effect on the improvement of absorbance quite well within the solar spectrum.
In order to examine the origin of these effects with detail, Fig. 4 shows the spatial distribution of the electric-field (left) and the magnetic-field (right) intensity inside the different solar devices we are comparing. While Figs. 4a and 4b corresponds to the conventional solar cell, Figs. 4c and 4d consider a GaAs solar cell with an ARC and Figs. 4e and 4f show the results of the GaAs solar cell with AlAs nanoparticles. All the figures are obtained at an incident wavelength of 620 nm (the one for remarkable differences in Fig. 3) and under four different incidence angles, which are labeled on the bottom part of the figure. These figures consider an air layer on the top part and a unit cell of the solar device. To clarify each structure a scheme of each one is included. It is clearly observed how the ARC (Figs. 4c and 4d) produces a larger concentration of light in the device than in the conventional case (Figs. 4a and 4b). This is more relevant in the layers that are above the active one, producing a certain reduction of the reflectance and an increase of the light reaching the active material. In contrast, the use of nanostructures on top of the device (Figs. 4e and 4f) provides a larger light confinement and also a more efficient guiding of light towards the active layer. In fact, it can be clearly observed that both the electric and the magnetic field are enhanced in this material compared to the previous cases. This phenomenon is mainly due to resonant effects of the nanoparticles with the incident field. The resonant nanoparticles efficiently confined the electromagnetic field and scatter it again towards the bottom part (the active region). Moreover, these effects are remarkably insensitive to the incidence angle, providing better results than the other two considered cases. This shows up that this solution is a promising way to improve the optical performance of solar cells.
Finally, Fig. 5 shows the simulated short-circuit current density (JSC) as a function of the incidence angle. As before and with the aim of comparing, this figure includes a conventional GaAs solar cell, the solar cell with an ARC and the solar cell with nanoparticles on top of it considering two cases: plasmonic Al nanoparticles, and the proposed dielectric AlAs nanoparticles. Again, it can be seen that although ARC improves the electric performance of a standard solar cell, the use of nanostructures on the top layer provides a better performance in a large angular range (JSC is larger than 10 mA/cm2 up to 80º instead of 70º in the ARC case). In this case, while metallic Al NPs, previously proposed in the literature , slightly improve the JSC of an ARC solution, the proposed AlAs NPs significantly rises the current density in the angular range from 0º to 70º, producing a much better response of the solar cell than the other considered cases, avoiding also the thermal effects of the plasmonic nanoparticles.