## 5 Simulation Results and Discussion  
The first simulations were carried out by TLM-3D for the whole structure using the Maple language in order to evaluate the temperature at every node within the device, (see Figure 6). In 3D-TLM modelling process, matrices of temperature of incident and scattered pulses, transmission-line impedances, and thermal resistances need to be stored separately, and therefore the temperature at any node within the device can be evaluated as a function of time. For representation in _X-Y_ plan view, nodes are assigned to the position in _X_-axis and _Y_-axis. Spatial discretization \(\Delta x\) and \(\Delta y\) are selected to be 2 \(\upmu\)m and 12.5 \(\upmu\)m respectively for the whole HEMT structure device. The total input power dissipated in whole device is 12.5 W, then corresponding to a power density of 7 W/mm injected [22]. Due to the thinness of the conductive channel, the heat source can be typically treated as a set of surface heat fluxes applied to areas corresponding to the size (\(W_{\mathrm{g}}\times L_{\mathrm{g}}\)) at each gate finger. The heat source is due to the strong electric field located at the gate edge area near the AlGaN/GaN interface layer. A micro-channel heat-sink temperature was assumed to be 300 \({}^{\circ}\)K. Under same bias conditions, a comparison is made between the device channel temperatures simulation by TLM method and the micro-Raman Spectroscopy measurements. We observe a hot-area with maximum temperature which is equal approximately to 230.21 \({}^{\circ}\)C. However, a little difference temperature value as \(\Delta T\approx\) 5 \({}^{\circ}\)C, is observed between experience measurement and 3D-TLM simulations. In the most thermal modelling works, researchers are usually taking a half and/or a quarter views of devices structure due to of the device symmetry. However, in TLM simulations, we can take whole system to be simulated. This is among the advantage and efficiency of 3D-TLM method. Figure 5: Raman Spectroscopy Thermal profile of an 8 gate AlGaN/GaN HEMT measured [22]. The thermal profile simulated by TLM method in two dimensions (2-D) is shown in Figure 6a. As we observe a hot-area with maximum temperature equal approximately to 230.21 \({}^{\circ}\)C, located at the center of the device and which is assigned by the two gates 4 and 5. The peak temperature  
Figure 6: (**a**) 3D-TLM simulation view of the whole structure device; (**b**) \(X\)-\(Y\) plan view showing the hottest region gate 4 & gate 5; (**c**) simulated temperature distribution (gate finger width) in device center gate along finger for (8 \(\times\) 250) \(\upmu\)mAlGaN/GaN HEMT device; (**d**) \(Y\)-axis view; (**e**) Comparison between 3D-TLM simulation and experimental results. occurs in the multi-finger (8-gate) device center, and decreases towards the device edges. Since the temperature in the central source-drain portion is higher than in the source-drain portion located closer to the multi-finger device edges, thermal coupling is clearly apparent. Reasonable agreement relative to the maximum temperature between micro-Raman experiment and TLM-3D simulation is achieved. However, a little difference temperature value as \(\Delta T\approx\) 5 \({}^{\circ}\)C, is observed between experience measurement and 3D-TLM simulation by accepting an error less than 2.2% according to Figure 6e. Heat is generated in the conducting channel of the device near the GaN top surface layer, whereas experience Raman spectroscopy measures the average temperature of the GaN layer and consequently the peak channel temperature is underestimated. Moreover, heat transfer across interfaces inside the semiconductor devices, including the impact on material imperfections such as dislocations [42], are essential both for microwave and for power switching devices [43]. Figure 6. shows a three-dimensional view preceded by TLM simulation that represents a thermal distribution of a whole 8-gate AlGaN/GaN HEMT structure (L\({}_{\text{HEMT}}\)XW\({}_{\text{HEMT}}\)).