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We have performed Monte Carlo simulation of the terahertz (THz) quantum-cascade lasers (QCLs). We have studied the effect of electron-impurity and electron-electron scatterings on transport characteristics of THz QCL. It is shown that the electron-impurity scattering supplies an additional channel for the electrons to be injected into the next period of the QCL. It is as important as the electron-electron interaction.