The present invention provides a method for forming by plasma CVD a silicon nitride film that can be formed over heat-sensitive elements as well as an electroluminescent element and that has favorable barrier characteristics. Further, the present invention also provides a semiconductor device, a display device and a light-emitting display device formed by using the silicon nitride film. In the method for forming a silicon nitride film by plasma CVD, silane (SiH.sub.4), nitrogen (N.sub.2) and a rare gas are introduced into a deposition chamber in depositing, and the reaction pressure is within the range from 0.01 Torr to 0.1 Torr.