1. A variable resistance device for a semiconductor memory, comprising: a first electrode made of a conductive material; a solid electrolyte having at least two regions with different thicknesses formed in a three-dimensional structure on an upper surface of the first electrode, wherein the thickness of each region of the solid electrolyte is measured from the upper surface of the first electrode to an upper surface of the region of the solid electrolyte, and wherein the first electrode is formed on the bottom of a through hole; and a second electrode made of a conductive material formed on an upper surface of the solid electrolyte to cover the regions with different thicknesses.