## 4 Conclusions  
Transparent oxides are widely used to work as top contacts in solar cells. However, the advantage of these materials in terms of their electrical and optical properties is coun  
Figure 4: Electric field (**a**) and magnetic field (**b**) maps for the TE and TM polarizations, respectively. These maps were calculated for short and long wavelengths (\(\lambda_{s}=600\) nm and \(\lambda_{l}=850\) nm), and for normal and oblique incidence conditions (\(\theta=0^{\circ}\) and \(\theta=60^{\circ}\)).  
Figure 5: Short-circuit current as a function of the angle of incidence for the nanostructured and planar solar cells. The red line with closed circles is for the perovskite cell and the green line with open circles is for the c-Si in the nanostructure cell. The black line with open stars is for the perovskite cell and the blue line with closed stars is for the c-Si in the planar cell.  
terweighted by some other issues: their availability is limited, they are rigid and not easily applicable to flexible designs, and the fabrication technique may involve processes that can compromise the performance of the device. To replace these materials and maintain the functionality of the system, we have presented a novel arrangement for tandem solar cells that include perovskites on c-Si. The ITO top contact layer is removed, and a gold layer is placed on top of a periodic 1D multilayer grating. This periodic structure contains the perovskite cell of the tandem arrangement, where the c-Si cell is placed under the grating.  
Our design optimizes the structure by maximizing the short-circuit current of the whole device when considering the solar spectral irradiance and its unpolarized character. To do this, we have used a computational electromagnetism package based on the finite element method that has been positively proved to describe the behavior of optoelectronic devices. The parameters used to optimize the system were: the width of the perovskite cell--which is directly related to the grating duty cycle--including the top metallic contact; and the thickness of the active layer of the perovskite cell. Using our simulations, we were able to balance the distribution of light between both cells and to generate an electrically matched tandem cell with a maximum short-circuit current. The calculated value of \(J_{\text{SC}}\) is 1.03 times the value of the reference planar tandem cell that uses an ITO top contact. Reaching this value ensures that the replacement of the ITO top electrode does not degrade the efficiency of the cell. The computational evaluation considers unpolarized solar irradiation by averaging the results from TE and TM incidences. We also analyzed the dependence of the device's performance with respect to the angle of incidence and we also observed a similar behavior of our device compared to the reference planar device with ITO contact.  
In summary, the approach presented in this paper shows advantages over the typical design in terms of the availability and cost of the materials, while providing a comparable performance.  
All the authors, [PERSON], O.E., A.C. and J.A., contributed equally to this paper. All authors have read and agreed to the published version of the manuscript.  
This work has been partially supported by the Spanish Ministry of Science, Innovation and Universities project NERA under grant RTI2018-101037-B-I00, and NANOROMS under grant PID2019-105918 GB-I00, by AEI/FEDER funds and by Comunidad de Madrid and FEDER Program SINFOTON2 CM under grant S2018/NMT-4326, and TELURO under grant RTC2019-007113-3.  
Not applicable.  
[PERSON] thanks the Ministry of Higher Education of Egypt (missions section) for their supporting grant. Authors thank [PERSON] for her critical reading and English grammar and style revision of the manuscript.  
The authors declare no conflict of interest.