A semiconductor device production method includes: 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; covering an inner wall surface of the concave portion and a top face of the insulating film with a first gate electrode film that is made of an electrically conductive material containing a first metal; covering the first gate electrode film with a covering film of a material having a second melting point higher than a first melting point of the electrically conductive material, leaving part of the side face of the concave portion uncovered; and performing heat treatment following the covering film formation to allow the first gate electrode film to reflow.