## 2 Materials and Methods  
### 0.15 \(\mu\)m GaN HEMT _ISV Structure and Source via Effect_  
Due to high output power of several watts generated from a GaN HEMT device with a size of hundreds of micrometers, heat is inevitably generated from the device itself. The self-heating effect is a phenomenon in which device characteristics deteriorate due to temperature rise caused by power consumption in the device. In order to minimize this degradation, it is important to have a device layout that can dissipate heat well. An ISV structure in which heat is dissipated through multiple grounds by placing a backside ground via per source finger is widely used [26]. Figure 1 shows the ISV layout structure of a commercial GaN HEMT having a gate length of 0.15 \(\mu\)m and a gate width of 4 \(\times\) 50 \(\mu\)m. As shown in Figure 1b, the heat generated by the device is dissipated to the ground through the backside vias connected to each source. The size of the backside via used in this process is about 60 \(\times\) 90 um, and the height is about 100 um. Due to this source via structure, the conventional small-signal equivalent circuit also needs to be modified. In particular, parasitics related to the source via structure, which have not been considered in the past, may have a non-negligible effect at the frequencies of the millimeter-wave band above 30 GHz. In this work, the parasitic effect due to the coupling between drain and source feeding lines surrounding the source via structure is mainly investigated. Figure 2 shows an enlarged GaN HEMT layout around the source via structure and an equivalent circuit representing it. Parasitic components that are actually generated are more complex but are simplified for convenience. It is true that additional proof is needed to clarify the exact physical phenomenon of the proposed equivalent circuit, but the possible physical structure is inferred from the more accurate equivalent circuit found empirically. At high frequencies, parasitic inductance and via resistance and inductance may be generated for a long path among multiple paths generated, while signals are coupled and passed in various directions of the source via from the drain feeding line. As shown in Figure 2, these are modeled by C\({}_{\mathrm{d}\mathrm{s}\mathrm{l}}\), L\({}_{\mathrm{d}\mathrm{s}}\), R\({}_{\mathrm{s}}\)  
Figure 1: (**a**) Test pattern layout; (**b**) 3D view of 0.15 \(\times\) 4 \(\times\) 50 \(\mu\)m GaN HEMT _ISV_. and \(\rm L_{s}\). Some paths may be short and there may be coupling signals that drop directly to ground. This is modeled by \(\rm C_{ds2}\). More detailed verification of this will be carried out in a follow-up study. To confirm this, 2.5 dimensional electromagnetic (EM) simulation is performed on the drain-source layout of the GaN HEMT device using ADS momentum software. Figure 3a,b shows the EM layout and simulation results of the simplified one-port drain-source via structure. In particular, EM analysis is performed up to 120 GHz to confirm the inductance effect. The layout shown in Figure 3a is mostly composed of metal layers, so the resistance of the metal itself is very small. Since the GaN HEMT substrate has a semi-insulated structure similar to that of GaAs, the substrate loss is also small. Therefore, the EM simulation result shows almost no loss. The change in phase from \(-180^{\circ}\) to \(+180^{\circ}\) also occurs when a capacitive component changes to an inductive component. When looking at the Smith chart, the point going from the lower semicircle to the upper semicircle is the instantaneous transition point. From the simulation result shown on the Smith chart in Figure 3b, it can be confirmed that parasitic inductance exists in the coupling components between the drain and source feeding lines. Figure 4 shows the comparison of the S11 EM data obtained above with the simulation according to the equivalent circuit.