## 3 Results and Discussion
### Capacitance-Voltage Characterization  
Capacitance-voltage measurements, in the dark and under light, were performed to obtain the built-in potential and the behavior of the spatial charge density. The capacitance of the p-n junction can be expressed for any diode as follows [42]:  
\[C=constant\cdot\left(1+\frac{V}{V_{bi}}\right)^{-\beta} \tag{9}\]  
Here, C represents the capacitance of the junction, V denotes the reverse bias, V\({}_{\rm bi}\) stands for the barrier potential, and \(\beta\) is a coefficient accounting for the dependency of C on the reverse bias V. For an ideal junction with an abrupt charge density step profile, \(\beta\) = 1/2. \(\beta\) can be determined from the slope of the linear fit of ln(C) vs. ln(V) in dark and light condition (see Figure 10). This procedure enables the determination of the spatial distribution of a space charge within the junction region. The values of \(\beta\) result in \(\frac{1}{2.94}\) and \(\frac{1}{3.06}\) in dark conditions and under light, respectively. Both values are very close to \(\frac{1}{3}\) and suggest a linear dependence of C\({}^{3}\) vs. V, which corresponds to a linear dependence of the space charge density within the space charge region, according to the C-V theory for a linearly graded junction reported in [43; 44].  
The relationship between depletion region capacitance and applied voltage is thus as follows:  
\[\frac{1}{C^{3}}=\frac{12(\text{V}_{bi}-V)}{q(\delta\rho)A^{3}(\epsilon_{0} \epsilon)^{2}} \tag{10}\]  
where \(V\) represents the applied voltage, \(V_{bi}\) is the built-in potential, q is the electron charge, (\(\delta\rho\)) indicates the impurity gradient expressed in cm\({}^{-4}\), \(A\) denotes the active area of the diode, \(\epsilon\) is the relative dielectric constant (assumed to be 15.1 [45; 46]), and \(\epsilon_{0}\) represents the vacuum dielectric constant. Equation (10) is indeed confirmed by the plot in Figure 11 that reports the plot of \(1/C^{3}\) vs. applied bias, and the linear fit in the negative bias region can be used to determine the built-in potential from the intercept with the V-axis. \(V_{bi}\) was found to be (0.53 \(\pm\) 0.05) V and (0.82 \(\pm\) 0.05) V under light and dark conditions, respectively [35; 36; 37]. The result reveals a higher built-in potential in dark conditions compared to that under light. This discrepancy contradicts classical theory, as these two values are expected to be equal and suggest the presence of an illumination-linked potential. Indeed, when we  
Figure 10: Plot of ln(C) (C unit: F) against ln(V + V\({}_{\rm bi}\)) (V + V\({}_{\rm bi}\) unit: V) under light and dark conditions. The linear fit of the experimental data is made in the reverse bias region for V \(>V_{bi}\).  
consider the height (0.3 V) of the barrier attributed to the hole-blocking heterojunction and add it to \(V_{bi}\) under illumination (0.53 V), we obtain a value very close to the \(V_{bi}\) (0.83 V) in the dark. This confirms that the first term on the left side of Equation (8) is significantly influenced by \(g\), the photocarrier generation rate, as corroborated by the presence of the crossover discussed above.