1. A semiconductor device with a stacked array structure, comprising: two or more semiconductor layers vertically stacked and spaced apart from a substrate by a predetermined distance, the semiconductor layers running parallel to each other and to the substrate in a horizontal direction; a gate electrode vertically crossing all of the semiconductor layers with a gate insulator interposed between the gate electrode and each of the semiconductor layers; source/drain regions formed at both sides of the gate electrode in each of the semiconductor layers; and an interlayer insulator wrapping around the source/drain regions of each of the semiconductor layers or filling a space between the semiconductor layers.