## 3 Results and Discussion  
A silicon nanowire (SiNW) structure was fabricated by the metal-catalyzed electroless chemical etching method. The length of the nanowire was controlled by controlling the etching time. Figure 1 shows the Scanning Electron Microscope (SEM) images of SiNW photoelectrode deposited with reduced graphene oxide (rGO), and energy-dispersive X-ray spectroscopy (EDS) shows the presence of each element on the photoelectrode. The elements of silicon, oxygen and carbon make up the constituents of rGO, which was deposited uniformly on the SiNW photoelectrode through the EDS image. Cross-sectional SEM images also showed uniform coating of rGO on the SiNW with average length of 22 um. To provide more insights into the photocathodic efficiency of the SiNW photoelectrode, the inherent current density was measured in the potential window ranging from 0.4 V to \(-\)0.7 V vs. RHE using a three-electrode cell. In our measurement setup, a 300 W Xe lamp was used with a light intensity of 100 mW/cm\({}^{2}\) and the light passed through an air mass 1.5 global filter, in 1 M of aqueous perchloric acid (HClO\({}_{4}\)) under acidic condition (pH = 0). In Figure 2, a voltammogram with a linear sweep under light illumination is presented, which shows the current density according to the specific applied potential. First, the reductive current density starts to increase from a specific point as the applied potential increased negatively. The current density saturates at a higher applied potential, which typically is described as limiting current density or saturation current density. The onset potential is better described as a potential at which a sharp increase in current density (\(-\)1 mA/cm\({}^{2}\)) is observed. The onset potential of SiNW electrode under illumination is 0.179 V vs. RHE, while bare planar silicon electrode only shows \(-\)0.106 V vs. RHE. (Figure 2 and Table 1). Saturation current density also increased when surface nanostructuring was implemented. The saturation current density of SiNW showed 38.2 mA/cm\({}^{2}\), which is approximately 1.2 times higher than that of bare planar Si (32.8 mA/cm\({}^{2}\)). To calculate the solar-to-hydrogen conversion efficiency (STH), the concept of applied bias photon-to-current efficiency (ABPE) was introduced, according to the following equation [22; 23]:  
\[\text{ABPE}=[\text{j}_{\text{ph}}\ (\text{mA/cm}^{2})\times(\text{V}_{ \text{redox}}-\text{V}_{\text{b}})\ (\text{V})/\text{P}_{\text{in}}(\text{mW/cm}^{2})]_{\text{AM1.5G}}\times 1 00(\%) \tag{1}\]  
Figure 1: **Surface characterization of rGO-SiNW sample. ** (**a**) Top view scanning electron microscope (SEM) image of reduced graphene oxide (rGO) on the silicon nanowire (SiNW) structure and corresponding Energy-dispersive X-ray Spectroscopy (EDS) elemental mapping describing the presence of Si, C, and O. (**b**) Cross-sectional SEM image of rGO on SiNW and corresponding EDS elemental mapping describing the presence of Si, C, and O.  
where \(\rm j_{ph}\) is the photocurrent density obtained under the applied potential \(\rm V_{b}\), \(\rm V_{redox}\) is the redox potential required for hydrogen production (0 V vs. RHE), \(\rm V_{bias}\) is the applied external bias potential that is typically necessary to achieve reasonable photocurrents, and \(\rm P_{light}\) is the intensity of the applied incident light under AM 1.5 G conditions (100 mW/cm\({}^{2}\)). Half STH can be defined as the STH in the 3-electrode cell system, which is also the maximized value of ABPE and can also be calculated using the following equation [23]:  
\[\rm Half\,STH=[\,|\,j_{sc}\,|\,(mA/cm^{2})\times(V_{oc})\,(V)\times FF/P_{in} \,(mW/cm^{2})]_{AM1.5G}\times 100(\%) \tag{2}\]  
where \(\rm j_{sc}\) is the current density at the reversible potential (the density at the 0 V vs. RHE), \(\rm V_{oc}\) is the potential at the zero-current density (the open circuit potential), and FF is the fill factor in the J-E curve in the 4-quadrant region.