We experimentally demonstrate that the crystallization process of Ge-Sb-Te crystallites during the set operation in non-volatile phase change memory commences after threshold switching event. It is also shown that the nucleation and growth rates have opposite behaviors with the increase of set operation power: the incubation time in nucleation stage can be minimized at higher power, whereas the percolation time in growth stage is smaller at lower power. Based on these results, we introduce a two-step set pulse of high-power nucleation and low-power growth making the set write operation much faster than conventional simple rectangular or slow-quenched form.