Abstract: A carrier head for a semiconductor wafer polishing apparatus includes a rigid plate which has a major surface with a plurality of open fluid channels. A flexible wafer carrier membrane has a perforated wafer contact section for contacting the semiconductor wafer, and a bellows extending around the wafer contact section. A retaining ring is secured to the rigid plate with a flange on the bellows sandwiched between the plate's major surface and the retaining ring, thereby defining a cavity between the wafer carrier membrane and the rigid plate. A fluid conduit is coupled to the rigid plate allowing a source of a vacuum and a source of pressurized fluid alternately to be connected to the cavity.