## 3 Results
In Equation (2), \(A\) is the area of the diode, \(A^{*}\) is the effective Richardson constant (32 A/cm\({}^{2}\) k\({}^{2}\) for p-Si [28]), and \(\varPhi_{b}\) is barrier height. The following equation is used to calculate \(n\):  
\[n=\frac{q}{kT}\frac{d\varomega}{d(lnI)} \tag{3}\]  
At \(V\) around 0 V, \(I_{0}\) is obtained from the intercept of the semilogarithmic \(I\)-\(V\) characteristics of the plot shown in Figure 4b. The value of \(I_{0}\) calculated from the ln(\(I\))-\(V\) curve is 0.07 nA, whereas the value of \(\varPhi_{b}\) is extracted from the y-intercept of the ln(\(I\))-\(V\) characteristics in the forward region. It is calculated from the following equation:  
\[\varPhi_{b}=\frac{KT}{q}ln\left(\frac{AA^{*}T^{2}}{I_{0}}\right) \tag{4}\]  
Using Equation (4), \(\varPhi_{b}\) is found to be 0.89 eV, which is a key parameter to determine the behavior of the depletion region in the heterojunction device. In p-type semiconductors such as PFB, \(\varPhi_{b}\) manifests itself as the energy difference between the Fermi level and the maximum valence band that controls the flow of holes across the interface of the device [29]. The ln(\(I\))-\(V\) characteristics are used to find the value of \(n\) for the Ag/PFB/p-Si heterojunction. The \(n\) normally describes dependence of the diode current on applied voltage and compares the quality of the fabricated device with that of the ideal one. For an ideal rectifying device (diode) the value of \(n\) is \"one\"; however, in practice, \(n\) always exceed unity [30] due to the possible formation of oxide layer on Si surface, which acts as insulating layer and results in increasing \(R_{s}\) at the interface of PFB/p-Si [31]. From the ln(\(I\))-\(V\) curve, along with Equation (3), \(n\) is calculated to be 3.23. Recently, it was widely reported that the value of \(n\) varies from 2 to 11 for organic-semiconductor-based rectifying devices [32; 33; 34; 35; 36]. In the present case, the higher value of \(n\) = 3.23 can be ascribed to \(R_{s}\) and the nonuniform surface profile of PFB thin film, which can be observed from the SEM and AFM images. Still, this value is small and closer to one when compared to the reported values for \(n\) in the case of other organic semiconductors. Hence, PFB/p-Si heterojunction can find its potential applications in electronic and optoelectronic devices. Besides the significance of \(R_{s}\), the performance and stability of the device also depend on shunt resistance (\(R_{sh}\)). Ideally, zero value of \(R_{s}\) allows maximum flow of charge in the device, while significantly high (infinite) values of \(R_{sh}\) cause minimum leakage current. A graph is plotted between the junction resistance \(R_{j}=dV/dl\) vs. V, as shown in Figure 4c, to calculate the values of \(R_{sh}\) and \(R_{s}\) for the Ag/PFB/p-Si heterojunction device. The flat portion of \(I\)-\(V\) characteristics provides the value of \(R_{s}\), while \(R_{sh}\) is obtained from the highest peak value in the graph. The extracted values of \(R_{sh}\) and \(R_{s}\) from the graph are 32 G\(\Omega\) and 171 M\(\Omega\), respectively. The deviation of the Ag/PFB/p-Si device from ideal behavior is due to the \(R_{s}\) = 171 M\(\Omega\) across the heterojunction of PFB/p-Si. [PERSON]'s function is an alternate technique to determine and/or cross-verify the values obtained for \(\varPhi_{b}\) and \(R_{s}\)[37]. [PERSON]'s function is expressed by Equation (5):  
\[F(V)=\frac{V}{\gamma}-\frac{kT}{q}ln\left(\frac{I}{AA^{*}T^{2}}\right) \tag{5}\]  
\[\varPhi_{b}=F(V_{0})+\frac{V_{0}}{\gamma}-\frac{kT}{q} \tag{6}\]  
\[R_{s}=\frac{kT(\gamma^{n})}{ql_{0}} \tag{7}\]  
The \(F(V_{0})\) denotes minimum value of \(F(V)\), \(I_{0}\) represents current at \(V=V_{0}\), and \(\gamma\) shows an integer whose value is always greater than \"\(n\)\". The \(F(V)\) vs. \(V\) plot is shown in Figure 4d for the Ag/PFB/p-Si device. Using Equations (5)-(7) along with Figure 4d, the values of \(R_{s}\) and \(\varPhi_{b}\) are extracted to be 173 M\(\Omega\) and 0.93 eV, respectively.