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In Monte Carlo simulation of high electron mobility transistors (HEMTs), how to position the source and drain contacts will significantly affect the drain current. Unlike many Monte Carlo (MC) simulations of HEMTs in the past, in this work, the source and drain contacts are placed on the top of the caps as in the real device instead of on the side adjacent to the channel. In addition, to taking the quantum effects into consideration, the effective potential approach of quantum correction has been incorporated into our MC simulator. We have found that the simulated drain current is substantially increased compared to that of using the classical potential.