In a process for fabricating a nonvolatile semiconductor memory of the tunneling type, when tunnel windows are formed in an oxide film on a semiconductor substrate, the oxide film is etched first by a dry etching process, then by a wet etching process. The dry etching process quickly removes most of the oxide material in the window areas, without enlarging the windows laterally, but stops short of the substrate, thereby avoiding damage to the substrate surface. The wet etching process takes the windows the rest of the way down to the semiconductor substrate surface. Since only a small amount of oxide needs to be wet-etched, lateral enlargement of the windows by the wet etching process can be tightly controlled, and small tunnel windows can be formed without the need for extravagantly sophisticated fabrication equipment.