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A carrier head that has a base assembly, a retaining ring assembly, a carrier ring, and a flexible membrane is described. The flexible membrane has a main portion and an outer annular portion, wherein a junction between the main portion and the outer annular portion comprises a peripheral edge hinge

A carrier head that has a base assembly, a retaining ring assembly, a carrier ring, and a flexible membrane is described. The flexible membrane has a main portion and an outer annular portion, wherein a junction between the main portion and the outer annular portion comprises a peripheral edge hinge and an annular recess above the hinge along the outer wall of the outer annular portion.

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1. A flexible membrane, comprising: a main portion with a lower surface to provide a substrate-mounting surface; andan outer annular portion extending substantially vertically from an outer edge of the main portion, wherein the outer annular portion comprises a lower edge connected to the main porti

1. A flexible membrane, comprising: a main portion with a lower surface to provide a substrate-mounting surface; andan outer annular portion extending substantially vertically from an outer edge of the main portion, wherein the outer annular portion comprises a lower edge connected to the main portion and an upper edge that is substantially laterally aligned with the lower edge, and wherein the outer annular portion comprises an outer surface that includes a substantially vertical surface that is substantially laterally aligned with the upper edge and the lower edge, a first annular recess that is recessed relative to the substantially vertical surface and is located between the substantially vertical surface and the lower edge, and a second annular recess that is recessed relative to the substantially vertical surface and is located between the substantially vertical surface and the upper edge. 2. The flexible membrane of claim 1, wherein the outer annular portion comprises an inner surface that includes a third annular recess located between the first annular recess and the lower edge. 3. The flexible membrane of claim 2, wherein the lower edge has rounded inner and outer surfaces. 4. The flexible membrane of claim 1, wherein the outer annular portion comprises an inner surface that includes an inwardly-protruding annular step. 5. The flexible membrane of claim 4, wherein the annular step is substantially vertically aligned with the second annular recess. 6. The flexible membrane of claim 4, wherein the annular step has non-horizontal upper and lower surfaces. 7. The flexible membrane of claim 1, wherein the second annular recess has a substantially uniform depth. 8. A flexible membrane, comprising: a main portion with a lower surface to provide a substrate-mounting surface;an outer annular portion extending substantially vertically from an outer edge of the main portion, wherein the outer annular portion comprises a lower edge connected to the main portion and an upper edge that is substantially laterally aligned with the lower edge, and wherein the outer annular portion comprises an outer surface that includes a first annular recess located between the upper edge and the lower edge and a second annular recess located between the first annular recess and the upper edge; andtwo annular flaps connected to the outer annular portion to divide a volume above the main portion into a plurality of chambers when the flexible membrane is secured to a carrier head. 9. The flexible membrane of claim 8, wherein the two annular flaps connected to the outer annular portion comprise a horizontal portion extending inwardly and a thick rim, the rim configured to be secured to a base assembly, the two annular flaps including an upper annular flap and a lower annular flap, and wherein the upper annular flap has a narrower horizontal portion than the lower annular flap. 10. The flexible membrane of claim 9, wherein the lower annular flap projects from a wedge-shaped portion of the outer annular portion. 11. A flexible membrane, comprising: a main portion with a lower surface to provide a substrate-mounting surface;an outer annular portion extending substantially vertically from an outer edge of the main portion, wherein the outer annular portion comprises a lower edge connected to the main portion and an upper edge that is substantially laterally aligned with the lower edge, and wherein the outer annular portion comprises an outer surface that includes a first annular recess located between the upper edge and the lower edge and a second annular recess located between the first annular recess and the upper edge; anda plurality of concentric annular flaps connected to the main portion to divide a volume above the main portion into a plurality of chambers when the flexible membrane is secured to a carrier head. 12. The flexible membrane of claim 11, wherein a first of the plurality of concentric annular flaps includes a laterally extending section and a vertically extending section connecting the laterally extending section of the first of the plurality of concentric flaps to the main portion and a second of the plurality of concentric annular flaps includes a laterally extending section and a diagonally extending section connecting the laterally extending section of the second of the plurality of concentric flaps to the main portion. 13. The flexible membrane of claim 12, wherein the first of the plurality of concentric annular flaps is an outermost flap. 14. The flexible membrane of claim 12, wherein the second of the plurality of concentric annular flaps is an innermost flap. 15. The flexible membrane of claim 12, wherein an innermost concentric annular flap of the plurality of concentric flaps comprises a horizontal portion extending outwardly, a thick rim along an outside edge of the horizontal portion, the thick rim configured to be secured to a base assembly, and an annular angled portion joined between the main portion and the horizontal portion, wherein the annular angled portion has a larger radius at its juncture with the main portion than at its juncture with the horizontal portion. 16. The flexible membrane of claim 12, wherein the second of the plurality of concentric annular flaps includes a notch at a juncture between the laterally extending section and the vertically extending lateral section. 17. The flexible membrane of claim 12, wherein at least one of the concentric annular flaps includes a notch at a juncture of the at least one of the concentric annular flaps with the main portion.