## 2 Materials and Methods  
### Theoretical Consideration: Photosensitivity of SiNW Photodetector  
The principle of solid-state optoelectronic devices basically relies on the Beer-Lambert law, which is shown in Equation (1):  
\[\mathbf{P}=\mathbf{1}-\mathbf{e}^{-\mathbf{\kappa}\mathbf{x}} \tag{1}\]  
where \(P\) is a percentage of the light absorbed, \(\alpha\) is an absorption coefficient, and \(\mathbf{x}\) is the path length of the light. According to this equation, most energy of incident light illuminating the bulk semiconductor is absorbed at the surface. When a uniform optical injection occurs on the p-type semiconductor, the conductivity at the surface increases as follows:  
\[\mathbf{\sigma}=\mathbf{\sigma_{0}}+\Delta\sigma=\mathbf{q}\left(\mathbf{\mu_{n}}\mathbf{u_{0}}+ \mathbf{\mu_{p}}\mathbf{p_{0}}\right)+\mathbf{q}\left(\mathbf{\mu_{n}}\Delta\mathbf{n}+\mathbf{\mu_{p }}\Delta\mathbf{p}\right) \tag{2}\]  
where \(\sigma_{0}\) is dark conductivity, \(\Delta\sigma\) is the difference between conductivity in the dark state and under illumination, \(\mathbf{q}\) is the electron charge, \(\mu\) is the carrier mobility, \(\mathbf{n_{0}}\) and \(\mathbf{p_{0}}\) are electron and hole concentrations in the dark state, and \(\Delta\mathbf{n}\) and \(\Delta\mathbf{p}\) are excess carrier concentrations. Therefore, the photocurrent is defined as the following equation:  
\[\mathbf{I_{ph}}=\mathbf{q}\Delta\mathbf{n}\mathbf{v_{d}}=\mathbf{q}\Delta\mathbf{n}\frac{\mathbf{L}}{\mathbf{ t_{n}}}=\left(\mathbf{q}\Delta\mathbf{L}\mathbf{g}\right)\frac{\mathbf{\tau_{n}}}{\mathbf{t_{n}}} \propto\frac{\mathbf{\tau_{n}}}{\mathbf{t_{n}}} \tag{3}\]  
Figure 2a illustrates a simplified model of the SiNW photodetector discussed in this paper to explain the operation. SiNW photodetectors have high photoconversion gain due to structural characteristics [19]. Surface states increase carrier recombination rates and affect devices with high surface-to-volume ratios like nanowires. When the device is in a dark environment and no light is absorbed by the nanowire, mobile carriers are trapped on the surface. The inside of the nanowire is, therefore, fully depleted. As shown in Figure 2b, when the nanowire is illuminated, electron-hole pairs are generated. The photons with energy greater than the bandgap of the silicon excite the carriers and create electrons in the conduction band. The remaining holes stay at the core of the nanowire, which contributes to photocurrent when the device is biased. Therefore, the lifetime and the transit time of the holes (majority carriers) contribute to the photocurrent, whereas minority carriers play dominantly in conventional photodetectors. Hence, similarly to Equation (3), the internal conductive gain of the SiNW (\(G_{NW}\)) can be expressed as a ratio of the hole lifetime (\(\tau_{p}\)) (\(G_{NW}=\tau_{p}/t_{p}\)) as derived in the previous research [26].  
Figure 1: Overview of the top-level block diagram for the proposed SiNW photodetector-integrated retinal stimulator.  
The photoconductive gain of the conventional bulk Si photoconductor depends on the recombination rate of minority carriers, \"\(\tau_{n}/t_{n}\)\". On the contrary, the gain of the SiNW can be expressed as the function of majority carriers, \"\(\tau_{p}/t_{p}\)\". The typical recombination rate, \"\(\tau_{n}\)\", for the photodetector is several nanoseconds, and the hole lifetime, \"\(\tau_{p}\)\", of the SiNW is several microseconds. Therefore, assuming the transit time is the same, the SiNW has a much greater gain than that of conventional photodetectors.