a method of epitaxially growing semiconductor crystal by which a single crystal region which is superior in quality can be selectively formed at a high throughput without employing the lithography technique . a shield mask is formed on an upper face of an amorphous semiconductor layer formed on substrate , and excimer laser light is irradiated upon the amorphous semiconductor layer using the shield mask to produce , in the amorphous semiconductor layer , a core from which crystal is to be grown . after the shield mask is removed , low temperature solid phase annealing processing for the amorphous semiconductor layer is performed to grow crystal from the core to form a single crystal region in the amorphous semiconductor layer . alternatively , the silicon core is formed by irradiating an energy beam , which is capable of being converged into a thin beam and being used to directly draw a picture , at a predetermined position of the amorphous silicon film .