A nonvolatile, sophisticated semiconductor device with a small surface area and a simple structure capable of switching connections between three or more electrodes. In a semiconductor device at least one of the electrodes contains atoms such as copper or silver in the solid electrolyte capable of easily moving within the solid electrolyte, and those electrodes face each other and applying a voltage switches the voltage on and off by generating or annihilating the conductive path between the electrodes. Moreover applying a voltage to a separate third electrode can annihilate the conductive path formed between two electrodes without applying a voltage to the two electrode joined by the conductive path.