## 4 Results and Discussion
Figure 1: Schematic diagram of the proposed structure. between four cases, so the short-circuit current density and consequently PCE is the used in such case to choose which structure has better performance. The resultant short-circuit current density and the power conversion efficiency for each structure are given in Table 2. The maximum \(J_{sc}\), 34.72 mA/cm\({}^{2}\), is obtained when the SiNWs coated with a graphene layer and Au NPs are distributed on the silicon substrate surface, which gives maximum overall efficiency, 15.8%, as shown in Table 2.  
The absorbed light is increased and the short-circuit current density and power conversion efficiency are consequently increased as the graphene layer is added, due to its \begin{table}
\begin{tabular}{c c c} \hline \hline
**Proposed Structure** & **J\({}_{sc}\) (mA/cm\({}^{2}\))** & **PCE (\%)** \\ \hline
**Traditional SiNWs** & 31.56 & 14.40 \\
**SiNWs coated with graphene layer** & 31.91 & 14.60 \\
**SiNWs with Au NPs** & 33.20 & 15.10 \\
**SiNWs with graphene layer and Au NPs** & 34.72 & 15.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Short-circuit current density and overall efficiency of the proposed four structures. Figure 2: (**a**) Absorption and (**b**) transmission of the four proposed structures: traditional SiNWs, SiNWs coated with a graphene layer, SiNWs with Au NPs distributed on the substrate, and SiNWs with graphene layer and Au NPs. high absorption properties. On the other hand, adding Au NPs increased the absorbed light according to Equations (5) and (6). To compare between the given two structures, SiNWs with Au NPs and with/without graphene layer, the absorption and transmission are illustrated in Figure 3a,b. To increase the efficiency of the solar cell, Au NPs are distributed on the top silicon surface directly, without using the graphene layer, and the graphene layer is used to coat the top surface of the SiNWs, as illustrated in Figure 4a,b. The obtained short-circuit current density is 41.7 mA/cm\({}^{2}\) and the overall solar cell efficiency is 19.0%. A 3D structure of the configuration using the graphene layer is shown in Figure 4a, and the side view of the structure is given in Figure 4b. The graphene layer, on the top of NWs, absorbs the incident light and retransmits it into the NWs, which behave as nanoantennas, while the plasmonic Au NPs absorb the light and transfer it to the silicon substrate. Figure 3: (**a**) Absorption and (**b**) transmission of the main two structures: SiNWs with Au NPs distributed on the substrate and SiNWs with graphene layer and Au NPs. Figure 5 shows the absorption, reflectance, and transmission of the incident light on the proposed SiNW solar cell illustrated in Figure 4.  
The reflected and transmitted optical power have been obtained from the simulation analysis by using frequency-domain field and power monitors. Then, the absorption could be calculated using the formula (\(A=1-T-R\)), where \(T\), \(R\), and \(A\) are the transmitted, reflected, and absorbed optical power. The absorption is enhanced in the NIR region, which leads to increases in the short-circuit current and power conversion efficiency. The excess carrier concentration (ECC) has a great effect on the solar cell performance as it determines the open-circuit voltage, \(FF\), and solar cell efficiency. Figure 6 shows the effect of excess carrier concentration on the PCE of the solar cell, which increased with the increase in the excess carrier concentration. Figure 4: (**a**) Graphene layer coats the top SiNWs surface; (**b**) Au NPs distributed on the top of the silicon substrate. Figure 5: Percentage of absorption, reflectance, and transmission of the SiNWs with a graphene layer on the top of NWs and Au NPs distributed on the silicon substrate. The open-circuit voltage, \(FF\), and PCE are illustrated in Table 3 for different excess carrier concentrations.