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A new method for employed electron-electron (e-e) and electron-ion (e-i) interactions in Monte Carlo particle based simulators is presented. By using a corrected Coulomb force in conjunction with a proper cutoff range, the "double" counting of the long range interaction is eliminated while reducing the simulation time for molecular dynamics by a factor of 1000. The proposed method naturally incorporated the multi-ion contributions, local distortions in the scattering potential due to the movement of the free charges, and carrier-density fluctuations. The doping dependence of the low-field mobility obtained from three-dimensional (3-D) resistor simulation closely follows experimental results, thus proving the correctness of the proposed approach.