Abstract: An etching gas mixture containing CHF3, SF6 and a non-oxidizing gas such as Ar is used as an etching gas mixture for the anisotropic plasma-chemical dry-etching of a silicon nitride layer differentially or selectively relative to a silicon oxide layer. The gas mixture does not contain oxygen, chlorine, bromine, iodine or halides in addition to the above mentioned constituents, so that the process can be carried out in reactor systems equipped with oxidizable electrodes. By adjusting the gas flow rates or composition ratios of CHF3, SF6, and argon in the etching gas mixture, it is possible to adjust the resulting etching selectivity of silicon nitride relative to silicon oxide, and the particular edge slope angle of the etched edge of the remaining silicon nitride layer. A high etch rate for the silicon nitride is simultaneously achieved.