## 3 Results and Discussion
A normal T-shaped gate structure, without any extension, has a breakdown voltage of \(151\) V. The breakdown voltage relates directly to the FP length because of the extension of the gate edge point redistributing the peak electric field in the channel layer and a reduction of the electron punch-through effect. The propounded results also coincided with the experimental results presented by other groups [32; 33; 34; 35]. The maximum breakdown voltage of \(669\) V was achieved with the FP length of \(0.8\)\(\upmu\)m. A further increase in the FP length beyond \(0.8\)\(\upmu\)m decreased the breakdown voltage because of an utter increase in the high electric field-driven impact ionization process near the drain-side FP edge. The V\({}_{\text{th}}\) and I\({}_{\text{dss}}\) did not change with the drain-side FP extension. Figure 5: (a) Drain leakage current characteristics of AlGaN/GaN HEMT in a log scale and (b) breakdown voltage as a function of FP lengths. The drain-side FP structure significantly increased the breakdown voltage, but the RF characteristics of the device were deteriorated. Figure 6a shows the current gain characteristics of the device for fixed DC parameters at V\({}_{\text{ds}}\) = 12 V and V\({}_{\text{gs}}\) = \(-\) 2 V. The optimized 0.8 \(\upmu\)m FP structure showed the f\({}_{\text{T}}\) of 6.7 GHz, where the value of the normal T-shaped gate structure was 12.7 GHz. It was seen that the response characteristics were reduced to 52.8%. The unilateral gain of the device followed a similar trend, as shown in Figure 6b. The f\({}_{\text{max}}\) of the optimized FP structure and normal T-shaped gate structure were 25 and 37.6 GHz, respectively, which indicates 66.4% degradation. Equations (4) and (5) explain the small signal equivalent circuit [33; 34; 35; 36; 37],  
\[\text{f}_{\text{T}}= \text{g}_{\text{m}}/2\pi\left(\text{C}_{\text{gs}}+\text{C}_{\text {gd}}\right) \tag{4}\]  
\[\text{f}_{\text{max}}= \text{f}_{\text{T}}/2\left[\pi\text{f}_{\text{T}}\text{C}_{\text {gd}}\big{(}\text{R}_{\text{S}}\ +\text{R}_{\text{g}}+\text{R}_{\text{gs}}+2\pi\text{L}_{\text{s}}\big{)}+ \text{G}_{\text{ds}}\big{(}\text{R}_{\text{s}}+\text{R}_{\text{g}}+\text{R}_{ \text{gs}}+\pi\text{f}_{\text{T}}\text{L}_{\text{s}}\big{)}\right]^{1/2} \tag{5}\]  
where C\({}_{\text{gs}}\) and C\({}_{\text{gd}}\) dominate the decrease of f\({}_{\text{T}}\) and f\({}_{\text{max}}\). Parasitic capacitances need to be reduced for higher f\({}_{\text{T}}\). Source resistance, gate source resistance, and source inductance are designated as R\({}_{\text{s}}\), R\({}_{\text{gs}}\), and L\({}_{\text{s}}\), respectively. Gate resistance (R\({}_{\text{g}}\)) and output conductance (G\({}_{\text{ds}}\)) are other important components when considering the fabrication process [35]. Decreasing the denominator components would help to increase the f\({}_{\text{max}}\). The circuitry arrangement is shown in Figure 6c and contains parasitic resistances and capacitances. Considering the limited importance of the inductive components, they were not considered for device optimization. Figure 7a shows the schematic illustration of an optimized 0.8 \(\upmu\)m FP structure. There are certain limitations with drain-side FP structures because of their low RF characteristics. The breakdown voltage of the conventional T-shaped gate structure was not high enough, and the RF characteristics were dropped with the optimized FP structure. Hence, the IFP structure was adopted to minimize the capacitance increment, so that it could increase the RF response and minimize the breakdown voltage  
Figure 6: (a) Current gain; (b) unilateral gain of the optimized FP structure and normal T-shaped gate structure; (c) small signal equivalent circuit of the HEMT. degradation. The IFP structure was applied on the basis of the operation of an optimized FP structure. Figure 7b shows the schematic of an IFP structure, stretching from a 0.8 \(\upmu\)m optimized gate edge spot towards the gate direction.