## 1 Introduction  
The commissioning of mechatronic systems has been accompanied by the appearance of failures and breakdowns that develop over time. These failures are not yet well mastered. Therefore, to identify these failures is necessary in order to ensure the systems reliability [1, 2]. The transistor is one of the important components in these systems. This element played a great role in the revolution of the design and development of such systems. For the most developed systems like airborne systems, we find that the origin of most of their failures is their high-power amplifiers (HPA), a large percentage of these failures are caused by high electron mobility transistors (HEMT) [3, 4]. The high electron mobility transistor (HEMT), based on aluminum gallium nitride/gallium nitride (AlGaN/GaN), is an important electronic component thanks to its structure and materials. Gallium nitride GaN is characterized by high mobility, very high electrical breakdown field and high thermal conductivity [5, 6]. Thanks to these characteristics, these components have been used in different high-temperature and high-frequency applications [7, 8], such as airborne systems, telecommunication and electronic warfare [9, 10]. HEMT has also been used in several systems such as high-power amplifiers, satellites and radars [11]. The failures in HEMT technology are strongly related to its operating temperature exceeding the critical values because of the component self-heating. The operating temperature is an important factor, it can influence the HEMT reliability because most of its characteristics, such as electron mobility, saturation rate [12], thermal conductivity and others, are temperature-dependent [13, 14]. All these characteristics degrade and decrease with the rise of temperature due to the self-heating phenomenon [3, 15]. The phenomenon of self-heating can give rise to different degradations such as gate burial, damage to the connection chip-package [8], electron mobility degradation and current reduction [16]. More authors have realized electrothermal or thermal modeling in order to determine the thermal behavior of the HEMT as a function of its electrical parameters, and they apply a voltage between the transistor terminals and observe the temperature variation [17; 18]. However, this method is very complex because we need to integrate several electrical and thermal equations and parameters, which makes the modeling difficult and the finite element model becomes very expensive in terms of necessary parameters and calculation time. In this paper, we propose another simple method of modeling that is based on the injection of the power dissipated at the active area instead of applying the voltage or current at the terminals of the component [19]. In the rest of this work, we will detail this method and the results obtained. In addition, we have developed an approach to estimating the reliability of the HEMT technology using the approximation methods SORM and FORM. These methods allow us to evaluate the reliability index and the failure probability of our system. We have developed a coupling between two models: a finite element model using Comsol multiphysics and the reliability model coded with Matlab software. This coupling allows us to evaluate the reliability index and the probability of failures in our component. In a first step, we will present a description of the HEMT technology and its structure, in order to have a clear idea about its topology as well as the thermal properties of its material. Then, we will develop a finite element model with Comsol multiphysics software in its thermal part, which will allow us to manipulate the different parameters: geometry, thermal properties and loads, and so forth. Afterwards, we will study the influence of some parameters, such as the power dissipation and the reference temperature, on the operating temperature of the HEMT. In the other section, the FORM and SORM methods used to estimate the reliability index and the failure probability will be presented.