A film deposition process for depositing an amorphous metal oxide film, for example, an amorphous tantalum oxide film and a film treatment process for improving film quality of the amorphous tantalum oxide film in the state in which an amorphous state of the amorphous metal oxide film is being maintained by a high-density plasma radiation treatment based upon ion and radical reactions and which contains at least oxygen at an ion current density higher than 5 mA/cm2 are carried out, whereby a low-temperature treatment in the whole process is made possible. In addition, since the amorphous metal oxide film, which is excellent in film quality, can be deposited, the amorphous metal oxide film can be made high in reliability and can be produced inexpensively. The amorphous tantalum oxide film which is excellent in film quality can be manufactured inexpensively by a low-temperature treatment. Also, when a capacitance element having an amorphous metal oxide film and a semiconductor device are manufactured, the amorphous metal oxide film which is excellent in film quality can be deposited by a low-temperature treatment and highly-reliable capacitance element and semiconductor device can be manufactured.