## 3 Results and Discussion
### Crossover Effect in the J-V Characteristic
Two cases can be distinguished:  
* In the case where the doping density within the CdS + (Cd,Zn)S layer is quite low, in the order of 10\({}^{13}\) cm\({}^{-3}\), the electric field primarily drops in the n-type region and thep-type region will be only slightly depleted. In this region, there will be a relatively small accumulation of photogenerated positive charges. Therefore, a higher potential will be required to reach the crossover voltage, which is typically greater than \(\mathrm{V_{bi,c}}\). * In contrast, when the n-type region of the junction is more heavily doped than the p-type region, the latter experiences greater depletion. This results in a more pronounced bending of the energy bands in this region. Consequently, there is an increased accumulation of positive charges in this area, leading to a crossover point that is lower than \(\mathrm{V_{bi,c}}\). To understand which of the two situations we are in, we need to assess how much \(\mathrm{V_{bi,c}}\) depends on the series resistances of the device. Considering the series resistance values of our solar cell (\(\mathrm{R_{S}}\approx 3.6\ \Omega\cdot\mathrm{cm^{2}}\)), the relative voltage drop (\(\mathrm{J\cdot R_{S}}\)) across the materials is not significant, especially when the current density is very low, i.e., the voltage is close to \(\mathrm{V_{oc}}\) and/or the crossover point \(\mathrm{V_{x}}\). Therefore, \(\mathrm{V_{bi,c}}\) is approximately equal to \(\mathrm{V_{bi}}\). In summary, the condition where \(\mathrm{V_{x}}<\mathrm{V_{bi}}\) arises because of the higher doping level in \(\mathrm{Sb_{2}Se_{3}}\) compared to (Cd,Zn)S. It is now necessary to address the question of how \(\mathrm{V_{x}}\) is influenced by light (generation). The variation of \(V_{x}\) and \(V_{oc}\) as a function of the wavelength of the incident light has been illustrated in Figure 9a. Measurements were conducted using bandpass filters centered at wavelengths of 650 nm, 750 nm, 850 nm, and 950 nm. The \(V_{x}\) and \(V_{oc}\) values were then extracted from the standardized JV curves normalized for an equal number of absorbed photons. The graph (Figure 9a) indicates that \(\mathrm{V_{x}}\) is always slightly higher than \(\mathrm{V_{oc}}\), aligning with the definition of \(\mathrm{V_{x}}\). However, the difference between \(\mathrm{V_{x}}\) and \(\mathrm{V_{oc}}\) seems to widen as the wavelength decreases (Figure 9b). Considering the penetration depth of the light into the \(\mathrm{Sb_{2}Se_{3}}\) layer, carriers generated by a longer wavelength must cover a greater distance to reach the electrodes (Figure 8b), amplifying the impact of recombination effects. This phenomenon results in a diminished photovoltage. The graph in Figure 9a shows a non-uniform dependency of \(\mathrm{V_{x}}\) on light generation. The accumulation of photogenerated charges at the junction varies with the wavelength of the absorbed light. Holes generated by short-wavelength light are near the junction, allowing for more effective accumulation compared to holes generated farther away by long-wavelength light. Explaining this analytically is challenging, but the observed trend as a function of absorbed light aligns with what is depicted in Figure 9a,b. Figure 9: **(a)** Measurements of \(\mathrm{V_{x}}\) and \(\mathrm{V_{oc}}\) were conducted at different wavelengths, with all potential values standardized to an equal number of absorbed photons. The varied wavelengths were selected using passband filters centered at 650 nm, 750 nm, 850 nm, and 950 nm. **(b)**\(\Delta\mathrm{V}=\mathrm{V_{x}}-\mathrm{V_{oc}}\) as a function of the absorbed light wavelength. Additionally, the slight increase in V\({}_{\rm x}\) values compared to V\({}_{\rm oc}\) supports the accuracy of the V\({}_{\rm oc}\leq\) V\({}_{\rm x}\leq\) V\({}_{\rm bi}\) relationship.