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The intrinsic mechanism of drain-lag and current collapse in GaN-based high-electron-mobility-transistors are studied by using two-dimensional transient simulations. The simulated drain-lag characteristics are in good agreement with the reported experimental data. Dynamic pictures of trapping of hot electron under drain-pulse voltages are discussed in detail. The trapped charges may accumulate at gate edge drain side, where the electric field significantly changes, causing a notable current collapse. Quantum-well HEMT structures have been proposed and demonstrated to obtain the optimized performance.