## 3 Results  
### Photovoltaic Configuration  
In PV mode, the PD operates as a two-terminal device: an electric current passing through the junction is measured. The typical device I-V characteristic in dark conditions is reported in Figure 2a as a blue line which establishes the rectifying properties of the NSH heterojunction. Lighting the junction with 100 mW/cm\({}^{2}\) white light (Figure 2a, red curve), a downshift of the curve in reverse polarization (V \(\leq\) 0) is shown due to the photocurrent generation. This downshift highlights the potentialities of this device for PD applications. A typical NSH PD external quantum efficiency (EQE) measurement is shown in the inset of Figure 2a. The high efficiency in the UV-VIS-NIR range indicates the goodness of the junction in charge generation and collection. Moreover, the shape of the EQE, mainly reflecting the typical Si p-n junction behavior, highlights that the main photogeneration process in this spectral region is due to photon absorption and electron (_e_)-hole (_h_) pair formation in the Si substrate [31]. Responsivity (\(\mathcal{R}\)), detectivity (\(\mathcal{D}\)), and noise equivalent power (\(\mathcal{NEP}\)) are important figures of merit to quantify the performances of a PD and to make a comparison among detectors. The former gives a measurement of the light/dark gain, the last two evaluate the smallest optical signal, competing with the noise, that can be revealed. They are defined by the following equations:  
\[\mathcal{R}=\frac{I_{SC}-I_{0}}{P_{opt}}\]  
\[\mathcal{D}=\sqrt{\frac{A}{2 eI_{0}}\mathcal{R}}\]  
\[\mathcal{NEP}=\frac{\sqrt{A\ \Delta f}}{\mathcal{D}}\]  
where \(I_{0}\) and \(I_{SC}\) are the diode inverse saturation current and the short circuit photocurrent, respectively, \(A\) is the area of the junction, \(e\) is the electron charge, and \(\Delta f\approx 0.35\ \tau_{r}\)[32] is the signal bandwidth, with \(\tau_{r}\) rise time of the detector. In particular, \(\mathcal{NEP}\) provides the smallest detectable signal independently on the active area of the PD, allowing a comparison among different PD technologies. Indeed, the signal bandwidth scales inversely with the PD active area. In order to quantify such parameters, we measured the device response under illumination with a number of calibrated LED in VIS range (\(\lambda\) = 460 nm), supplied by a 10 Hz variable frequency on-off voltage at different power in short circuit condition \(V\) = 0. Typical PD responses for increasing incident light power are reported in Figure 2b. Since the SWCNT film thickness determines its sheet resistance and transparency, we evaluated the PD performances as a function of the SWCNT film transparency, \(T\). We considered three different thicknesses characterized by a \(R_{S}\) value no greater than 1 k\(\Omega\) and \(T\) of 42%, 44%, and 63% at 550 nm. Figure 2c shows the responsivity and detectivity as a function of the optical power of the incident monochromatic LED light, \(P_{opt}\), for the three different PDs. The best \(\mathcal{R}\), \(\mathcal{D}\), and \(\mathcal{NEP}\) values are obtained for the most transparent SWCNT film (\(T\) = 63%) which shows \(\mathcal{R}\approx\)1.6 AW\({}^{-1}\), \(\mathcal{D}\approx 10^{14}\) Jones, and \(\mathcal{NEP}\approx 5\times 10^{-15}\) WHz\({}^{-1/2}\) at \(P_{opt}\) = 1 mW/cm\({}^{2}\), resulting as the best carbon-based detectors [18]. The higher the film transparency, the higher the \(\mathcal{R}\) and \(\mathcal{D}\) values and, correspondingly, the lower the \(\mathcal{NEP}\). In order to understand such a behavior of the PD performances with the SWCNT transparency and to handle the tools for PD design optimization, a deeper insight into the operation principle of these NSH-based PDs is necessary. When light impinges on the device active area, most of the incident photons pass through the CNT semi-transparent film, reaching the underlying region of n-doped Si  
Figure 2: (**a**) Current versus voltage characteristics acquired in dark conditions (dark) and under illumination (light).