A faceplate of a showerhead has a bottom side that faces a plasma generation region and a top side that faces a plenum into which a process gas is supplied during operation of a substrate processing system. The faceplate includes apertures formed through the bottom side and openings formed through the top side. Each of the apertures is formed to extend through a portion of an overall thickness of the faceplate to intersect with at least one of the openings to form a corresponding flow path for process gas through the faceplate. Each of the apertures has a cross-section that has a hollow cathode discharge suppression dimension in at least one direction. Each of the openings has a cross-section that has a smallest cross-sectional dimension that is greater than the hollow cathode discharge suppression dimension.