It is an object to provide a semiconductor device the data writing of which can be performed except in manufacturing and the counterfeiting of which by rewriting can be prevented. Furthermore, it is another object of the invention to provide a semiconductor device constituted by an organic memory having a simple structure at low cost. A memory cell is constituted by connecting a transistor in parallel or series to an organic element having an organic compound layer, and each memory cell is connected in series or parallel to constitute a NAND memory or a NOR memory. The organic element can change its electrical property irreversibly by application of a current or a voltage, irradiation of light, or the like.