## 1 Introduction
However, it is difficult to use an optical system, for example, a long-pass filter to block elastically scattered light, to measure the Stokes and anti-Stokes signals simultaneously. A Raman measurement system that can measure a relatively wide spectral range simultaneously is required. Fortunately, this method does not require an ultra-high spectral resolution because the effect of the peak shift due to temperature is relatively small. Since the anti-Stokes scattering is about eight times smaller than the already-small Stokes Raman signal at room temperature, it takes a long time to map a whole area. The long measuring time is a very big disadvantage for mapping. For example, if it takes about 1 s to measure the anti-Stokes signal of GaN using a commercial spectrometer, it takes about 11 h to map a 100 \(\times\) 100 \(\upmu\)m\({}^{2}\) area at 0.5 \(\upmu\)m spatial resolution. This long measurement time can cause changes in the device characteristics during the measurement time, and this makes the method impractical, and significantly reduces the reliability of measurements as well. Raman measurements typically employ lasers with photon energies lower than the bandgap of the material. When performing Raman spectroscopy on GaN in Si-based HEMTs, signals from both the GaN/AlGaN channel and the Si substrate can be simultaneously detected, as the GaN layer is transparent to the excitation source. Since each signal contains temperature information specific to its respective material, the temperatures of the channel and the substrate can be measured independently. However, when the GaN layer is thick, the channel temperature may be underestimated, as the measurement reflects a volumetric average over the entire GaN layer. However, the advantage of being able to measure the temperature of the channel and the substrate simultaneously is obvious, which is difficult to achieve with IR thermography or thermal reflectance measurements. Of course, this advantage is only valid for devices with a transparent top layer, and measurements cannot be performed when the top layer is obscured by opaque materials such as electrodes. In this study, we simultaneously measured the submicron temperature distributions of the substrate and channel in GaN on Si-based GaN/AlGaN HEMTs during operation by measuring the temperature using the intensity ratio of the Stokes and anti-Stokes signals. To overcome the long measurement time, we constructed a highly sensitive spectral measurement system at the expense of slightly sacrificing the spectral resolution (to the extent that GaN and Si can be distinguished), and as a result, we achieved a speed of about 50 ms to obtain sufficient anti-Stokes signals of GaN, which is 20 times faster than the conventional method. Therefore, it took only about 35 min to map a 100 \(\times\) 100 \(\upmu\)m\({}^{2}\) area at 0.5 \(\upmu\)m intervals. This method can be applied not only to GaN on Si-based power devices but also to GaN/AlGaN HEMTs fabricated on other substrates. It is expected that it can be applied to other semiconductor devices such as SiC-based power devices through optimization, and it presents an effective and novel method to measure the submicron resolution temperature distribution of the device.