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A method of producing a semiconductor device provided with an n-channel MISFET (Qn) which comprises : an Hf containing insulating film (5) which is a high permittivity gate insulating film containing hafnium, a rare earth element, and oxygen as main components; and a gate electrode (GE1) which is a metal gate electrode. The Hf containing insulating film (5) is formed by forming, from the bottom, a first Hf containing film containing hafnium and oxygen as main components, a rare-earth-containing film containing a rare earth element as a main component, and a second Hf containing film containing hafnium and oxygen as main components, then causing these to react.