## 1 Introduction  
The GaN HEMTs (High Electron Mobility Transistor) application is currently growing due to its superior properties, such as high breakdown voltage and high cut-off frequency, which allow designing power switches devices and high efficiency power amplifiers for next generation wireless communication, satellite communication and radar systems [1]. The heterojunction AlGaN/GaN-based HEMTs have been recognized as the most promising devices for high-power applications at microwave and millimeter-wave frequency range. However, the ability of generating high RF-output power makes AlGaN/GaN HEMTs an attractive alternative solution compared to traditional GaAs and InP devices [2; 3; 4]. GaN takes advantage of the interesting material properties of the III-nitrides, such as wide bandgap (3.4 eV), high breakdown electric field (E \(\sim\)4.106 V/cm), thermal stability (up to 1250 K), excellent thermal conductivity (K\({}_{\text{GaN}}\)\(\sim\)1.3 W/cm\(\cdot\)K) and high electron mobility (1600 cm\({}^{2}\)/Vs) [3; 4]. In addition, the essential feature of nitride heterostructures is the formation of two-dimensional electron gas (2 DEG) with a high density (ns \(\sim\)10\({}^{13}\) cm\({}^{-2}\)) localized at AlGaN/GaN interface due to high (\(\sim\)10\({}^{5}\) V/cm) spontaneous and piezo-polarization fields that exist in such III-Nitride hetero-structures. AlGaN/GaN high electron mobility transistors grown on SiC substrate have recently been reported and have developed microwave applications with revealed power densities as high power dissipated exceeding 40 W/mm [5; 6; 7]. SiC have the best physical and electrical properties such as a thermal conductivity of (330-490 W/m\(\cdot\)K), high electron saturation velocity (2.7 \(\times\) 10\({}^{7}\) cm/s) and high breakdown electric field (up to 3 \(\times\) 10\({}^{6}\) V/cm). Its wide band-gap makes it a more suitable substrate to be used for very high temperature operations (up to 600 \({}^{\circ}\)C) than Silicon (200 \({}^{\circ}\)C). Its high thermal conductivity allows these high-power densities to be efficiently dissipated for realistic drain efficiencies to prevent the extreme channel temperatures that would occur due to self-heating with other substrates technologies [8; 9]. Moreover, TBR (thermal boundary resistance) at the GaN-substrate interface has an important role in self-heating effects. It is better to have low value, but also to have a realistic temperature-dependent thermal boundary resistance (TBR) between the GaN layer and SiC substrate [10]. TBR accounts for a large portion of the channel temperature, which may cause about a 100 K rise in the vertical temperature distribution of the device [11]. Furthermore, as any semiconductor component when GaN HEMTs operate at high power density negative factor appears; localized self-heating in the conducting channel with 2 DEG limits the output highest power density and decreases its reliability. The mobility reduces while increasing the temperature as (1/T)\({}^{2/3}\), resulting in DC and RF performance and creating small high temperature regions called hotspots which can significantly worsen the output characteristic of the HEMT [12]. The HPA (high power amplifiers) based on GaN reliabilities are directly dependent on the maximum operating channel temperature. Therefore, self-heating is a severe problem and is still a limiting factor for device reliability. As such, an accurate estimate for the channel temperature is needed [13; 14]. In addition to the self-heating effect which occurs in the single finger HEMT, a considered thermal-coupling effect among the neighboring fingers appears in multi-fingers transistors, therefore the thermal analysis becomes more accurate. Various thermal management solutions, for example, flip-chip bonding, two-phase spray cooling and mounting devices on to substrates, have been attempted.