## 2 Fatigue Characteristics of High-Power IGBT Model
### BAFT and the Analysis of BAFT Results  
The fatigue model reveals the relationship between the main factors affecting fatigue accumulation and the degree of fatigue. The load condition of the vehicle directly affects the fatigue of the switching device. The TC current output reflects the load level and this current flow completely through the switching device. Therefore, there is a one-to-one correspondence between the TC current output \begin{table}
\begin{tabular}{c c c} \hline \hline
**Load Condition** & \(\Delta T_{\rm j1}\) & \(\Delta T_{\rm j2}\) \\ \hline AW0 & 39.7 \({}^{\circ}\)C & 56.3 \({}^{\circ}\)C \\ AW2 & 52.6 \({}^{\circ}\)C & 72.1 \({}^{\circ}\)C \\ AW3 & 60.9 \({}^{\circ}\)C & 87.2 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(\Delta T_{\rm j}\) of Q\({}_{32}\) and D\({}_{32}\) under different load conditions. Figure 7: Junction Temperature Simulation of Q\({}_{32}\) and D\({}_{32}\) under AW0. and the fatigue level of the switching device, and there is a one-to-one correspondence between the device current and the fatigue level and between the device current and the device lifetime. The correspondence is shown in Equation (8). \[N_{\text{f}}=f(I_{\text{eq}}) \tag{8}\]  
\(N_{\text{f}}\) is the number of cycles the device can withstand before failure. We denote \(N_{\text{f}}\) as the lifetime of the device; \(I_{\text{eq}}\) is the equivalent current amplitude of the device. The acceleration effect of the FWD action means that the life of the device is shortened, as shown in Equation (9). \[N_{\text{f2}}=nN_{\text{f1}} \tag{9}\]  
In Equation (7), \(N_{\text{f2}}\) is the practical lifetime with FWD action, while \(N_{\text{f1}}\) is the lifetime of only considering IGBT action; \(n\) is a coefficient indicating an acceleration effect. However, \(n\) is difficult to obtain through experimental testing, so other ways need to be considered to express the aging acceleration effect of FWD on power modules. For better applicability, we present the Equation (8) in its current form, as shown in Equation (10). \[I_{\text{eq}}^{2}=i_{\text{G}}^{2}+\mu^{2}i_{\text{D}}^{2} \tag{10}\]  
In Equation (10), \(i_{\text{G}}\) is the current of the IGBT, \(i_{\text{D}}\) is the current of FWD and \(\mu\) is the acceleration factor. The fatigue of semiconductor devices is caused by the accumulation of thermal stress effects, so the current is in the form of RMS (Root-Mean-Square), and there is a square operation. In order to obtain \(\mu\), we propose a new AFT (BAFT) with bi-directional fatigue current. The BAFT test platform is shown in Figure 8.  
In Figure 8, the device functions are similar to those in the single-directional accelerated fatigue test platform of Figure 2, except that when G\({}_{2}\) and G\({}_{4}\) are turned on, \(I_{1}\) flows through the FWD portion inside the DUT. In BAFT, the number of cycles of IGBT and FWD is equal, so only half of the total number of actions is considered. For comparison, a bi-directional experiment was performed at \(I_{1}\) of 1500 A. Based on the data obtained from the bi-directional experiment, the cumulative failure rate curve of BAFT is shown together with the cumulative failure rate curve of SAFT at 1500 A in Figure 9. In Figure 9, the horizontal axis is the number of cycle times and the vertical axis is cumulative failure rate. It can be seen that the bi-directional experiment significantly accelerates the aging of the entire switching device. Figure 8: Schematic diagram of a bi-directional accelerated fatigue test.