Semiconductor device production method and semiconductor device

A semiconductor device production method comprising:

• forming an insulating film on a semiconductor substrate,
• forming a concave portion in the insulating film,
• forming a gate insulating film at bottom of the concave portion, the bottom being on the semiconductor substrate;
• forming a first gate electrode film over the gate insulating film, over an inner wall surface of the concave portion, and over a top face of the insulating film, the first gate electrode film being made of an electrically conductive material containing a first metal;
• after the forming a first gate electrode film, forming a covering film over the first gate electrode film, the covering film being made of a material having a second melting point higher than a first melting point of the electrically conductive material, the first gate electrode film on the inner wall surface of the concave portion being uncovered with the covering film;
• and
• after the forming a covering film, performing heat treatment to reflow the first gate electrode film.