## 3 Results and Discussion
### I-V Curve  
The I-V curve was measured using a probe station to evaluate leakage current caused by the electrical stress. Although thermal resistance is commonly used as an indicator of packaging failure [20,21], this study employed the I-V curve to characterize internal electrical degradation. At 2.5 V and 2.8 V, the electrical characteristics of the package remained identical to those of the undamaged (fresh) package up to 1 h. In the previous heat generation measurements shown in Figures 4a-d and S3, only slight thermal accelerations were observed under these voltage conditions. It was interesting to note that the packages exhibited a maximum temperature difference of approximately 13 \({}^{\circ}\)C among the cooling environments. However, the measurement results demonstrated no significant differences in electrical behavior.  
On the other hand, distinct electrical behaviors were observed under 3.0 V and 3.1 V conditions, as shown in Figures 5a-d and S4. As previously anticipated, the greatest difference in electrical behavior occurred when 3.1 V was applied for 30 min in the air environment. Variations in the I-V curve exhibited a time-dependent trend in both the immersion and air cooling environments. Based on the regular operating voltage of 1.2 V, the package currents were compared under 3.0 V and 3.1 V conditions in both two environments. At 3.0 V, the current of the package stressed in the immersion cooling environment was 0.905 mA at 10 min, 1.105 mA at 30 min, and 1.127 mA at 60 min, while the current of the package in the air was 0.921 mA at 10 min, 1.558 mA at 30 min, and 1.705 mA at 60 min. At 3.1 V, the package stressed in the coolant showed a current of 1.033 mA at 10 min and 1.704 mA at 30 min, whereas that cooled in the air environment showed increases in current to 1.545 mA at 10 min and 3.282 mA at 30 min.  
These electrical behaviors were consistent with the thermal performance characterizations. Interestingly, no significant degradation of electrical performance was observed at relatively low voltage stress, whereas a nonlinear increase in leakage currents occurred at higher voltages, accompanied by accumulated heat within the package. This indicates that heat accumulation is a primary factor influencing package leakage current and suggests that immersion cooling is an effective method for maintaining device reliability under elevated voltage stress conditions.  
These time-dependent I-V characteristics indicate that electrical degradation accelerated notably beyond 3.0 V, as reflected in the increasing slope of the I-V curve. This nonlinearity suggests the onset of stress-induced leakage current mechanisms, which may stem from charge trapping and oxide weakening in the MOSFET structure. The substantial  
Figure 4: I-V characteristics under different environmental conditions and voltage: **(a)** 2.5 V applied over time in coolant, **(b)** 2.5 V applied over time in air, **(c)** 2.8 V applied over time in coolant, and **(d)** 2.8 V applied over time in air. Measurements were taken for fresh samples and after exposure to voltage stress conditions for 10 min, 30 min, and 1 h.  
current increase at 3.0 V, particularly in the air-cooled environment, implies that this voltage exceeds the safe operational margin and could act as a practical failure threshold for long-term reliability. These observations further support the need to define conservative voltage limits in package design, especially when operated under limited cooling conditions.