## 3 Results and Discussion
### Extraction of Schottky Parameters
#### 3.3.2 Method 2: d\(V\)/d(\(ln\)) vs. \(J\) and H(\(J\)) vs. \(J\)  
Since there is a limitation of method 1 to calculate the \(Rs\), method 2 was used in this study to determine the \(Rs\). The Schottky diode parameters were extracted from I-V characteristics, as studied by [PERSON] [28]. In this method, the resistance \(R_{\rm s}\) is modeled with a series combination of a diode and a resistor. Due to this, the voltage, \(V_{d}\) across the diode can be expressed as the total voltage drop across the diode and resistor. Therefore, the \(V\) in Equation (2) is replaced with \(V_{d}\). With \(V_{d}=V-R_{\rm s}I\), and \(Vd>3 kT\)/\(q\). Equation (2) can then be written as  
\[I = I_{g}exp\Bigg{[}\frac{q(V-R_{\rm s}I)}{nkT}\Bigg{]}. \tag{6}\]  
Rewriting Equation (6) in terms of current density, \(J\), where \(J\) is the current divided by the junction area. \[V = R_{\rm s}AJ\ +\ n\varrho_{\rm B}+\ \Bigg{(}\frac{n}{\beta}\Bigg{)}ln\Bigg{(} \frac{J}{A^{\star}T^{2}}\Bigg{)} \tag{7}\]  
in which \(\beta\) in this Equation (7) equals to \(q\)/\(kT\). Taking differentiation from Equation (7) with respect to \(J\) and rearranging the terms, Equation (8) is derived as follows:  
\[\frac{dV}{d(ln(J))} = R_{\rm s}AJ\ +\ \frac{n}{\beta}. \tag{8}\]  
Another function H(\(J\)) was plotted to calculate \(\varrho_{B}\). Value of H(\(J\)) is derived from the equation below:  
\[H(J) = V\ -\ \Bigg{(}\frac{n}{\beta}\Bigg{)}\ ln\Bigg{(}\frac{J}{A^{\star }T^{2}}\Bigg{)}. \tag{9}\]  
From Equation (7), we can deduce H(\(J\)) as the following:  
\[H(J) = R_{\rm s}AJ\ +\ n\varrho_{\rm B}. \tag{10}\]  
The plot of d\(V\)/d(\(ln\)) vs. \(J\) in Figure 7a gave a straight line with \(R_{\rm s}A\) as the slope and \(n\)/\(\beta\) as the y-axis intercept. Plot of H(\(J\)) vs. \(J\) in Figure 7b derived from Equation (10) also gave a straight line in which the y-axis intercept is equal to \(n\varrho_{\rm B}\) and \(R_{\rm s}A\) is the slope. The \(n\) value is calculated from Equation (8) to allow the determination of \(\varrho_{\rm B}\) from the y-axis intercept value. Table 1 summarizes the Schottky parameters derived from Methods 1 and 2 for GNW-TMBS and TiSi\({}_{2}\)-TMBS diodes. The use of standard \(ln(I)\) vs. \(V\) (Method 1) has its limitation in determining the voltage range to use for the calculation of the Schottky barrier height and ideality factor. Even though the condition of \(V\geq 3 kT\)/\(q\) is satisfied, the I-V curve obtained from the linear region is showing a bowing effect making it difficult to choose a suitable voltage to interpret the Schottky parameters. Several researchers [29; 31; 32; 33] also addressed the same behavior in their papers. It is well-known that the electrical characteristic of a Schottky diode is strongly influenced by ideality factor, series resistance, and leakage current [34; 35]. The conventional 1-V curve is suitable for a diode with low series resistance, \(Rs\), in which the \(R_{\rm s}\) can be neglected at low forward bias [35]. However, with high series resistance diode, the inconsideration of \(R_{\rm s}\) will lead to underestimation of \(\varrho_{\rm B}\)[36]. [PERSON]'s method takes into account the influence of series resistance and allows a better estimation of \(n\) and \(\varrho_{B}\). However, this method is only applicable at \(V>3 kT\)/\(q\)[29]. Here, the discussion of the Schottky parameters will be based on Method 2. From the calculation, \(\varrho_{\rm B}\) of the GNW-TMBS diode has higher values by 0.11 eV at 298 K compared to the TiSi\({}_{2}\)-TMBS diode. The same trend is also observed for other temperature settings. High \(\varrho_{B}\) for the GNW-TMBS diode is contributed by a high voltage drop at forward bias as observed in this experiment. The series resistance, \(Rs\), for the GNW is 10 times higher compared to TiSi\({}_{2}\) which couldbe potentially due to high contact resistance between metal to GNW layer, given that all the other processes involved are similar except incorporation of different barrier layer [37; 38].