## 4 Results and Discussion
As illustrated in Table 3, the efficiency is increased with the increase in the excess carrier concentration and reaches 20% for ECC equal to 5.0 \(\times\) 10\({}^{-15}\) cm\({}^{-3}\). However, the ECC value is strongly related to the effective lifetime of the carriers, where the maximum value of the effective lifetime is 3 ms, which is obtained at ECC = 1 \(\times\) 10\({}^{-15}\) cm\({}^{-3}\). The NP material plays a very important role, as illustrated in Equation (6), which consequently changes the \(J_{sc}\) and \(\mu\) values. Figure 7 shows the absorbed energy for different NP materials, namely Au, Ag, Al, and Cu. In the visible region, the absorptions of all NP materials are almost the same, very close to each other, and one cannot distinguish between them, so the main factor in determining the best material is the short-circuit current density and consequently the PCE. Gold NPs produce a high \(J_{sc}\) and PCE, while silver and copper have \(J_{sc}\) values equal to 37.6 and 37.4 mA/cm\({}^{2}\), respectively, as clearly given in Table 4. Aluminum NPs give a short-circuit current density of 33.1 mA/cm\({}^{2}\) and overall efficiency of 15.1%. The maximum obtained power conversion efficiency is 19.0% at short-circuit current density \(J_{sc}\) = 41.7 mA/cm\({}^{2}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Excess Carrier Concentration** & \multicolumn{1}{c}{**V\({}_{\mathbf{oc}}\) (V)**} & **FF** & **PCE (\%)** \\ \hline
**0.5** & 0.61 & 0.72 & 17.8 \\
**0.6** & 0.61 & 0.73 & 18.0 \\
**0.7** & 0.62 & 0.73 & 18.2 \\
**0.8** & 0.62 & 0.73 & 18.3 \\
**0.9** & 0.62 & 0.73 & 18.4 \\
**1.0** & 0.63 & 0.73 & 19.0 \\
**2.0** & 0.64 & 0.73 & 19.2 \\Plasmonic nanoparticle radius is also considered as one of the main factors that affect solar cell performance. Figure 8 shows the absorbed energy for different Au NP radii, namely 30, 40, 50, and 60 nm. Due to the oscillation of the absorbed power in the NIR region, no distinction between different radii can be considered, so the short-circuit current density is the main factor of choice. The maximum performance, \(J_{sc}\) of 41.6 mA/cm\({}^{2}\) and \(\mu\) of 19.0%, has been obtained at 50 nm Au NP radius, as introduced in Table 5. \begin{table}
\begin{tabular}{c c c} \hline
**NPs Material** & **J\({}_{\text{sc}}\) (mA/cm\({}^{2}\))** & **PCE (\%)** \\ \hline
**Gold, Au** & 41.7 & 19.0 \\
**Silver, Ag** & 37.6 & 17.1 \\
**Aluminum, Al** & 33.1 & 15.1 \\
**Cupper, Cu** & 37.4 & 17.0 \\ \hline \end{tabular}
\end{table} 
Table 4: Short-circuit current density and overall efficiency for different NP materials. Figure 8: Light absorption (%) as a function of wavelength for different NP radii. Figure 7: Absorbed energy as a function of wavelength for different NP materials. Figure 9 gives the density of the distributed Au NPs (%) for different radii; the maximum performance of the solar cell is obtained at an NP radius equal to 50 nm, as shown in Table 5.  
To calculate the Au NP density, the area of all distributed NPs in the unit cell is divided by the available area on the silicon substrate, without NWs. The period, \(P\), between each NW has a significant effect on the solar cell performance. So, the effect of changing the period from 350 to 600 nm on the short-circuit current density and power conversion efficiency is simulated and summarized in Table 6.  
The optimum performance is obtained at period \(P\) = 550 nm, which gives \(J_{\text{sc}}\) = 41.7 mA/cm\({}^{2}\) and \(PCE\) = 19.0%. The values of short-circuit current density and PCE decrease as the NW separation distance increases, larger than 500 nm, as the concept of multireflection of the incident light is decreased. Moreover, the height of the NWs also plays a very important role in solar cell performance.