A 2D phase-field model was applied to simulate the phase-transition kinetics and the thermal field distribution during the lateral crystallization of a-Si induced by single pulse excimer laser. The higher tilt of solid/liquid interface increases the supercooling temperature in the melt due to the fast latent heat extraction at the solid/liquid interface. The lateral growth velocity is in average four times faster than the vertical one. When the lateral growth velocity exceeds the critical value of 19 m/s, amorphization of Si can be initiated because of unstable growth front. Therefore, thickness of Si film and the thermal properties of underlying layer play a crucial role not only in ultra-large grain fabrication but also in defect-free crystal growth.