## 1 Introduction  
Power devices are used widely in trains, aircraft, and power plants that require high power control. Additionally, their usability has recently increased with the commercialization and popularization of electric vehicles [1, 2, 3, 4]. Until now, power devices have been dominated by Si-based devices such as IGBTs and MOSFETs [3, 4]. However, existing Si-based power devices are showing limitations due to several issues [3, 4, 5, 6]. Si cannot be free from the degradation of operational stability caused by hot electrons generated at high temperatures due to its low bandgap of 1.12 eV. Furthermore, limitations were encountereddue to the relatively small bandgap for high voltage operation and insufficient electron mobility for high current operation. There have been efforts to bypass these limitations through research on the structure and operation method of Si power devices. Although some minor improvements have been made, it is not easy to overcome the material's fundamental limitations. GaN/AlGaN High Electron Mobility Transistors (HEMTs) have been widely studied in recognition of their potential to overcome the fundamental limitations of Si with its larger bandgap and higher mobility [1; 2; 3; 4; 5; 6]. GaN is a material with a wide band gap of 3.4 eV and has a much higher temperature and higher voltage stability than Si. Additionally, it has high electron mobility due to the two-dimensional electron gas (2 DEG) formed at the interface between AlGaN and GaN, enabling high current operation. It has a high efficiency in high-frequency operation due to its high switching speed [1; 2; 3; 4; 5; 6]. It has already been commercialized as a high frequency RF device. GaN/AlGaN HEMTs are typically grown and manufactured on substrates such as sapphire, Si, GaN, and SiC [7; 8; 9; 10; 11; 12]. SiC boasts an excellent thermal conductivity of 300-490 W/mK and superior operating characteristics, but its high substrate price is a significant drawback [7; 10; 12; 13; 14]. Sapphire substrates have been extensively studied due to their use in GaN-based LED production, and the growth technology of GaN on sapphire is well established. However, sapphire's low thermal conductivity of \(\sim\)30 W/mK hampers its ability to dissipate the heat generated by self-heating in HEMTs, leading to poor performance [10; 11; 12]. This is a critical disadvantage for power devices operating at high voltages and currents. GaN substrates offer advantages such as being stress-free and having a low defect density, making them ideal for GaN epitaxial materials. However, their high cost, low productivity, and lower thermal conductivity (\(\sim\)220 W/mK) compared with SiC limit their widespread use [15; 16]. Despite its relatively low thermal conductivity (\(\sim\)130 W/mK) and poorer crystal quality than SiC substrates, Si has recently become the most widely used substrate for GaN/AlGaN HEMTs--particularly in power electronics--owing to its low cost and its higher thermal conductivity compared with sapphire [8; 9; 10; 12]. Nevertheless, several issues remain critical to the efficiency, lifetime, and reliability required for commercial power devices. Performance degradation, reduced lifetime, and sudden failure due to self-heating are still commonly reported [17; 18; 19; 20]. Therefore, research on minimizing the self-heating effect and improving heat dissipation in GaN/AlGaN HEMTs grown on Si substrates is essential for enhancing the performance, lifetime, and reliability of these devices. To study the self-heating effect and heat dissipation in power devices, it is very important to measure the distribution of heat generated in the device. The channel length of power devices is gradually decreasing to achieve performance improvements and the high integration of the device, and the current commercialized GaN/AlGaN HEMT power devices have a channel length of several tens of \(\upmu\)m. Due to the shortened channel length, a spatial resolution of less than 1 \(\upmu\)m is required to measure the heat distribution.