Method for etching film and plasma processing apparatus

A method for etching a film, comprising:

• supplying a precursor gas to a substrate provided with the film and including a side wall surface and a bottom surface defining an opening, thereby forming a precursor layer on the substrate;
• and
• etching the film with a chemical species from plasma formed from a processing gas so as to increase a depth of the opening, and simultaneous with the etching, forming a protective region from the precursor layer by reacting the precursor layer with the chemical species or another chemical species from the plasma,
• wherein a plurality of cycles each including the supplying the precursor gas and the etching the film is executed, and
• a temperature of the substrate during execution of the etching the film included in at least one cycle of the plurality of cycles and a temperature of the substrate during execution of the etching the film included in at least one other cycle of the plurality of cycles are set to be different from each other.