## 1 Introduction
In addition, according to the results of several simulation studies, a very localized hotspot of 1-2 \(\upmu\)m size, which is significantly higher in temperature than the surrounding area around the gate electrode in HEMTs, can be formed, and this can cause device failure [21; 22; 23; 24; 25; 26; 27]. Also, to find hotspots, a spatial resolution of less than 1 \(\upmu\)m is also required. The methods for measuring the heat generated from devices include infrared (IR) thermography, thermal reflectance measurement, gate resistance thermometry, and Raman measurement. Gate resistance thermometry provides an indirect estimation of temperature through variations in electrical characteristics. However, it suffers from several limitations, such as inaccurate absolute temperature measurements and the inability to resolve spatial temperature distributions. IR thermography is a method for measuring the temperature distribution using an infrared image of several tens of \(\upmu\)m by utilizing the temperature-dependent characteristics of the wavelength and intensity of blackbody radiation generated from a material [28; 29; 30; 31; 32]. This method has the advantage of being fast because it images the temperature of a large area using a photodetector pixel array, but since it uses a wavelength of several tens of \(\upmu\)m, it has a spatial resolution limit of 15 to 20 \(\upmu\)m mainly due to the diffraction limit [33; 34]. Therefore, it is not suitable for measuring the submicron heat distribution of an HEMT. Additionally, there are limitations in measuring the temperature of GaN because GaN is transparent to IR wavelengths [34]. Thermal reflectance measurements use the characteristic that reflectance changes with temperature [35; 36]. However, since the change in reflectance due to temperature is very small (\(\sim\)10\({}^{-4}\)), it can only be measured through heat modulation, repeated measurements, and signal amplification using a lock-in amplifier [35; 36; 37; 38]. This measurement method faces challenges in accurately determining absolute temperature because reflectance can be influenced by various physical factors such as electric fields, strain, and others, necessitating a rigorous calibration process [39; 40]. Additionally, only metals can have a valid heat reflection coefficient, so measurements can only be made on electrodes. The temperature measurement method using Raman spectroscopy is a method that measures temperature by changing the Raman spectrum according to temperature [41; 42; 43; 44; 45]. Since Raman spectroscopy usually uses a visible light laser, it basically has a spatial resolution of less than 1 \(\upmu\)m. There are three representative methods: measuring the energy shift in a specific Raman peak, measuring the FWHM, and using the intensity ratio of the Stokes signal and the anti-Stokes signal [41; 42; 43; 44; 45; 46; 47; 48]. The methods for measuring the energy shift and FWHM of the Raman peak use peak characteristics that change according to temperature, and they require a high spectral resolution. In order to achieve a high spectral resolution with Raman measurements, a grating with a high number of grooves must be used, which inevitably reduces the intensity of the Raman signal and therefore, increases the measurement time. In addition, peak energy and FWHM do not depend only on temperature, but on other factors such as electric field, strain, and composition fluctuation. On the other hand, the method using the ratio of the intensity of the Stokes signal and the anti-Stokes signal uses the principle that the probability of anti-Stokes scattering is affected by temperature [42; 43; 46; 47; 48]. The Stokes signal only serves as a reference for measuring the intensity of the anti-Stokes signal. The intensity of the anti-Stokes signal depends only on temperature since it is directly proportional to the number of phonons, and therefore, it is a method of measuring temperature more directly than the previous methods.