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The electron velocity distribution is calculated for an idealized model of the high electron mobility transistor using a many‐particle Monte Carlo model and a self‐consistent two‐dimensional Poisson solver. Hot electron effects, nonstationary effects, and real space transfer are analyzed. The results show that significant velocity overshoot, 2.8×107 cm/s at 300 K and 3.7×107 cm/s at 77 K exists under the gate and that the velocity overshoot is limited by both k‐space transfer and real‐space transfer. The values of the overshoot velocities are much smaller than those obtained from the more conventional drift‐diffusion model.