A process is provided with which amorphous silicon or polysilicon is deposited on a semiconductor substrate. Then, a low-temperature solid phase growth method is employed to selectively form amorphous silicon or polysilicon into single crystal silicon on only an exposed portion of the semiconductor substrate. A step for manufacturing an epitaxial silicon substrate exhibiting a high manufacturing yield, a low cost and high quality can be employed in a process for manufacturing a semiconductor device incorporating a shrinked MOS transistor. Specifically, a silicon oxide layer having a thickness which is not larger than the mono-molecular layer is formed on the silicon substrate. Then, an amorphous silicon layer is deposited on the silicon oxide layer in a low-temperature region to perform annealing in the low-temperature region. Thus, the amorphous silicon layer is changed into a single crystal owing to solid phase growth. Thus, a silicon epitaxial single crystal layer exhibiting high quality is formed on the silicon substrate. The present invention is suitable as a process for manufacturing a high-speed and high degree of integration of a semiconductor device having an elevated source/drain structure and a SALICIDE structure.