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PROBLEM TO BE SOLVED : To obtain an epitaxial rare-earth oxide (001)/silicon (001) structure by epitaxially growing a rare earth oxide such as cerium oxide having (001) plane azimuth on a silicon substrate having (001) plane azimuth. SOLUTION : The surface of Si-substrate 1 of (001) plane azimuth is treated so as to convert the surface into a dimer structure by surface re-constitution of 2×1, 1×2, and then cubic or tetragonal rare-earth oxide, e.g. CeO2 film 2 is epitaxially grown in (001) plane azimuth on the Si-substrate 1 by a molecular beam epitaxy method or the like. During this growing, a raw material containing at least one rare earth element is supplied after starting of supplying an oxidizing gas onto the surface of Si-substrate 1. It is possible to thermally treat in vacuum after growing.