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A simulation model and the dynamics of the forced modulation-doped heterostructure, which operates in the state far from thermodynamic equilibrium, are discussed. The numerical simulations clearly reveal that the system under an appropriate bias including DC and AC voltages exhibits expected complex dynamical behaviors. The amplitude and frequency of the externally applied microwave field are taken as the control parameters in the system. Because many nonlinear dynamical systems may have more than one possible time-asympotic final state depending on the different initial conditions, the basins of attractions of both ordinary attractor and chaotic attractor are also studied respecively. Finally, as a possible application a method based on pulse driving to control chaos in semiconductor is proposed.