# Study of Self-Heating and High-Power Microwave Effects for Enhancement-Mode p-Gate GaN HEMT
## 3 Results and Discussion
### Thermal Characteristics
#### 3.2.2 HPM Effect  
HPM radiation is typically defined as comprising a frequency content between 300 MHz and 300 GHz, with a peak power of not less than 100 MW but often reaching the gigawatt level [37]. Large-scale military-grade electronic attack systems can generate peak electric fields of hundreds of kilovolts per meter to permanently destroy most unshielded electronic devices [38]. In the laboratory, HPM generation is performed by a pulse machine (PPM), which can generate voltages up to several thousand volts for 100 ns [39]. The peak power of the electromagnetic signal generated by the HPM source can reach hundreds of watts or even gigawatts, which can be coupled to the electrode ports of critical devices in the form of hundreds of volts. Compared with the irradiation method, the injection method can  
Figure 8: (**a**) Internal electric potential distribution of the device with self-heating effect; (**b**) electric field distribution near the hot spot. Figure 9: (**a**) Variation of electron mobility in the horizontal direction of the channel layer; (**b**) _Tmax_ curve with self-heating effect over time. better amplify the damage degree of HEMT and reduce the damage time threshold when HPM effect is investigated. In the numerical simulation, HPM does not act on the circuit port in the form of an electromagnetic field, but the equivalent voltage or current signal. Previously reported work concludes that the narrow-band HPM coupling voltage can be characterized by an unattenuated sinusoidal voltage signal [40]. In this work, a sine wave as the specific HPM signal with constant power (300 V, 5 GHz) is injected into the gate. Vds is biased as 1 V and defines the melting point of GaN (1973 K) as the burn-out threshold. It can be seen from Figure 10a that the maximum temperature (Tmax, red line) inside the device rises rapidly in the initial stage, and gradually slows down over time while the average temperature (Tave, blue line) is increased at a relatively stable rate. In a temperature rise period, the change of _Tmax_ is more obvious than _Tave_ as shown in Figure 10b. This can be understood as the accumulated thermal is averaged to the entire device, and the temperature rise is relatively slow. It can be seen from the _Tmax_ line in Figure 10a that the temperature rises steeply during the initial time period and then tends to stabilize. The specific waveform of \(T\) is similar to a sinusoidal signal with a rising trend that presents a step-like increase, and there is a slight hysteresis between the HPM signal and _Tmax_ waveform as shown in Figure 10b. On the one hand, because the accumulation of thermal energy takes a certain amount of time, the temperature change is continuous as the heat transfer takes time while the voltage does not. Another detailed explanation is that the dissipated power is related to the device temperature. The thermal accumulation leads to a larger temperature gradient between the device and the external environment which results in a greater dissipated power. Take the first temperature rise period as an example: at the moment the HPM signal is injected, the temperature rises with the accumulation of heat. The voltage amplitude corresponding to this initial temperature rise point is defined as the threshold value \(Vt\). The temperature keeps rising when the HPM signal reaches the peak of the first clock cycle (point A), indicating that the heat accumulation rate at this time is still greater than the heat dissipation rate. After the next \(1/4\) clock cycle, the HEMT device temperature reaches the first peak value (point B). At this moment, the dissipated power also reaches maximum because the temperature gradient between the device and the external reaches the maximum during this period. The two realize a dynamic balance, the rate at which the temperature rises \(\Delta T/\Delta t=0\). With additional time, the device temperature keeps dropping due to the net difference between the cumulative power of the heat and the external dissipation power.