To provide a process for producing thin-film insulating layers with which desired characteristics are obtainable without degrading their insulation performance even if the film thickness decreases.

Dry gaseous N2 is supplied into a chamber in the state that a substrate is held mounted in this chamber (ST1 to 3). The gas in the chamber is discharged in compliance with this supply and, therefore, the presence ratio of the dry N2 increases as time passes. As a result, the moisture sticking to the inside walls of the chamber is evaporated and is discharged outside the chamber. Next, the vacuum degree is lowered down to the degree necessary for sputtering (ST4) and, thereafter, the substrate is preheated to remove the moisture sticking to the substrate surface (ST5). Since the vacuum degree is lowered by this heating, the vacuum evacuation is executed again and, thereafter, the insulating film is formed on the substrate surface by sputtering (ST6, 7). Since there is no moisture to retard the initial growth on the substrate surface, the film grows uniformly and the specified film thickness is obtd. The desired resistance value is obtd. as well.