The invention provides a technique to manufacture a highly reliable semiconductor device and a display device at high yield. As an exposure mask, an exposure mask provided with a diffraction grating pattern or an auxiliary pattern formed of a semi-transmissive film with a light intensity reducing function is used. With such an exposure mask, various light exposures can be more accurately controlled, which enables a resist to be processed into a more accurate shape. Therefore, when such a mask layer is used, the conductive film and the insulating film can be processed in the same step into different shapes in accordance with desired performances. As a result, thin film transistors with different characteristics, wires in different sizes and shapes, and the like can be manufactured without increasing the number of steps.