Variable resistive element, method for producing the same, and nonvolatile semiconductor memory device including the variable resistive element

A variable resistive element comprising

• a first metal oxide film which is an oxide film of a first metal and sandwiched between a first electrode and a second electrode, wherein
• through a forming process, a resistance state between the first and second electrodes of the variable resistive element is changed from an initial high resistance state before the forming process to a variable resistance state,
• the resistance state in the variable resistance state is changed between two or more different resistance states by applying an electric stress between the first electrode and the second electrode of the variable resistive element in the variable resistance state, and one resistance state after the change is used for storing information,
• a control layer containing oxygen is inserted between the first electrode and the first metal oxide film, and formed of a second metal capable of extracting oxygen from the first metal oxide film to prevent oxygen from being thermally diffused from the first metal oxide film to the first electrode,
• the second metal included in the control layer is different from the first metal, or same as the first metal,
• when the second metal is same as the first metal, a concentration distribution is provided in such a manner that an oxygen concentration of the control layer and the first metal oxide film becomes lower from the first metal oxide film toward the control layer across a boundary between the first metal oxide film and the control layer,
• oxide formation free energy of at least one element included in the control layer except for oxygen is lower than oxide formation free energy of an element included in the first electrode, and
• both work functions of the second metal and the first electrode are 4.5 eV or less.