## 3 Results and Discussion
### Fast Transient Charging Effect with Pulse I-V  
To validate the presence of the fast transient charging effect in the two types of devices, we utilized the pulsed I-V measurement and single-pulse \(I_{D}\)-\(V_{G}\) techniques. These measurements were conducted using a semiconductor parameter analyzer in conjunction with the waveform generator module [27; 28; 29; 30; 31; 32]. During the pulsed I-V measurements, a single short pulse was applied to the gate and drain, and the resulting \(I_{D}\) was measured. When a signal is applied, the carriers of the channel are charged to the defect of the barrier. The migrated electrons cause rapid \(V_{t}\) and \(I_{D}\) degradation. This charge-trapping effect follows two steps. The first charging process at the shallow trap site near the InAlAs barrier's conduction band is expected to have a short charging time because the trap energy is very low, and the density of states is high in the channel's conduction band. Next, slow transient charging can be attributed to the capture of secondary electrons, which is induced from the charges trapped due to the fast charging process. These are called deep traps and are located deeper in the InAlAs conduction band than shallow traps. To effectively minimize the fast transient charge-trapping effect when applying the trapezoidal \(V_{G}\) pulse, rise (\(t_{r}\)) and fall (\(t_{f}\)) times of 50 ns were utilized, which were very short. If \(t_{r}\) and \(t_{f}\) are not minimized, charge trapping continuously occurs during the time the signal is applied, just like non-pulse signals. At this time, the current characteristics after the charge-trapping phenomenon has already occurred are checked. The fast transient charge-trapping effect is known to occur when a pulse shorter than 1 ms is applied [27]. Figure 3a,b display the results of single-pulse measurements for the two types of devices, presented in either the pulse-voltage or pulse-time domain. Indeed, charge trapping  
Figure 2: The characteristics with a gate length (\(L_{g}\)) of 50 nm are as follows: (**a**) \(I_{D}\) and \(I_{G}\) characteristics at \(V_{DS}\) = 0.05 V and 0.5 V. (**b**) \(g_{m}\) characteristics at \(V_{DS}\) = 0.05 V and 0.5 V. (**c**) RF performance at \(V_{DS}\) = 0.8 V, peak \(g_{m}\). had an impact on \(V_{t}\), as evidenced by the hysteresis observed in the \(I_{D}\)-\(V_{G}\) curve and the degradation in the drain current (\(I_{D}\)) over time in the \(I_{D}\)-time domains. Notably, these changes were more pronounced in MHEMT. The threshold voltage shift (\(\Delta V_{t}\)) was calculated using the equation [27]  
\[\Delta V_{t}=\frac{\Delta I_{D}\cdot(V_{G}-V_{t})}{I_{D}} \tag{1}\]  
The decrease in drain current (\(\Delta I_{D}\)) during the pulse width (PW) is calculated as the difference between the maximum \(I_{D}\) before the PW and the drain current during the PW. \(V_{G}\) represents the pulse amplitude. Equation (1) is applicable when the decrease in mobility because of the high vertical field of the channel is not large owing to the high gate bias. In Figure 3c, the fast transient charging effect was confirmed under various PW conditions (10, 50, 100, 150, 200 \(\upmu\)s) with \(t_{r}\) and \(t_{f}\) being maintained constant. The degradation of the drain current at different PW was attributed to the charge-trapping effect. Specifically, for PW = 200 \(\upmu\)s, the drain current degradation in LM-HEMTs and MHEMT was observed to be 14.21 \(\upmu\)A and 46.43 \(\upmu\)A, respectively. This suggests that MHEMT experienced a higher degradation in the drain current compared to LM-HEMTs under the same pulse-width conditions. Notably, the latter value is more than triple the former value. The higher degradation of the drain current in MHEMT compared to LM-HEMTs at the same pulse width suggests that channel carriers were more prone to getting trapped within the defective region of the device during the pulsed measurement.