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Spin-transfer torque (STT) enables magnetization switching by passing a spin-polarized current through nanostructures such as spin-valves or magnetic tunnel junctions (MTJs). The required switching current depends on the pulse width which is related to the feature of switching modes. In this work the STT-induced switching processes for several nano-sized MTJs were studied with pulse widths ranging from 100 ms to 2 ns. We found that the intrinsic critical switching current depends on the junction area; and the crossover region of pulse width between two typical switching modes, i.e., thermal-activation and precession-amplification, is around 20 ns.