The present invention is directed to a crystallization apparatus including an illumination system to illuminate a phase shift mask, which converts a light beam from the illumination system into a light beam that has a light intensity distribution of an inverse peak pattern having a minimum intensity in an area corresponding to a phase shift portion of the phase shift mask. A virtual image is created based on the single user-defined parameter and the original digital image. The control circuit may be configured to generate the first charge signal and the second charge signal in response to a first battery signal and a second battery signal. Thus, a semiconductor device including a driver circuit portion capable of high-speed operation and a pixel portion over one substrate can be manufactured.