The processes include: a layer superposition step in which the step of sputtering or vapor-depositing a mixture layer including a first pore-forming metal and a catalyst metal on a substrate and the step of forming an interlayer of a second pore-forming metal or a fibrous-carbon interlayer are alternately conducted repeatedly two or more times to thereby form a multilayer structure containing mixture layers and interlayers; and a pore formation step in which after the layer superposition step, the multilayer structure is subjected to a pore formation treatment.