## 2 Variation of Ambient Temperature
### Finite Element Method (FEM) models  
Thermal dissipation has a negative impact on the performance and lifetime of semiconductor devices and power converters. As shown in Figure 8, different colors constitute the thermal map and this simulation can be used to obtain the junction temperature (\(T_{j}\)) and case temperature (\(T_{c}\)), and the temperature at the chip and copper substrate layer is the highest.  
Therefore, thermal analysis modeling under different load conditions is essential, and it is necessary to seek the temperature calculation methods of power converters and the optimal distribution schemes of thermal distribution. As the size of a single traditional silicon-based device approaches its basic limit, a better understanding of the thermal distribution of adjacent devices under different operating conditions can help the system carry out reasonable thermal management, thus improving the performance of the converter system, and optimizing the overall structure of the converter [22]. The accuracy of the  
\begin{table}
\begin{tabular}{c c c c} \hline \(R/\Omega\) & \(8\) & \(6\) & \(5\) \\ \hline \(\Delta T_{c,M}/^{\circ}\)C & 5.83 & 11.23 & 14.02 \\ \(\Delta T_{c,D}/^{\circ}\)C & 16.44 & 23.01 & 25.02 \\ \hline \end{tabular}
\end{table}
Table 1: The temperature differences of case temperature under different load resistances.  
\begin{table}
\begin{tabular}{c c} \hline \(T_{c,M}\) [\({}^{\circ}\)C] & \(R_{ca,M}\) [\({}^{\circ}\)C/W] \\ \hline
25.75 & 69.32 \\
34.43 & 62.73 \\
53.27 & 61.76 \\
80.01 & 54.27 \\
146.85 & 45.15 \\ \hline \end{tabular}
\end{table}
Table 2: \(R_{ca}\) for the MOSFET.  
\begin{table}
\begin{tabular}{c c} \hline \(T_{c,D}\) [\({}^{\circ}\)C] & \(R_{ca,D}\) [\({}^{\circ}\)C/W] \\ \hline
50.66 & 60.39 \\
79.59 & 58.89 \\
105.85 & 54.35 \\
129.26 & 52.24 \\
149.19 & 49.60 \\ \hline \end{tabular}
\end{table}
Table 3: \(R_{ca}\) for the diode.  
thermal analysis model has a significant impact on the thermal management and reliability of devices and systems.  
For semiconductor devices and power converter systems, the commonly used thermal modeling methods mainly include the physical model calculation method, numerical calculation method, finite element method (FEM), thermal resistance network method, etc. [23; 24]. FEM can be used for the thermal calculation of devices or power converter systems, and the simulated structures can be simplified within the range of accuracy allowed. The FEM results can be used to analyze the temperature distribution directly by different colors, and the junction/case temperature can be extracted by adding virtual thermal probes to the corresponding components. Unlike the real probes or temperature sensors, the virtual probes are considered to have absolutely ideal thermal conductivity and insulation properties, which can be attached to the device surface or injected inside the devices, or anywhere in the air region [24; 25].  
However, it has difficulties when using FEM to establish thermal models for the semiconductor devices, because you should be familiar with the specific parameters of internal structures for power devices or modules. The FEM analysis needs 3D modeling of the devices or systems. Although the structures can be simplified, the structures of the devices and systems need to be better understood. In addition, in order to obtain a more accurate FEM analysis model, boundary conditions and the ambient domains are also essential [24; 26]. In this paper, the FEM method is used to analyze the convection thermal coupling of adjacent semiconductor devices considering different ambient domains in different cities.