A device includes a Micro-Electro-Mechanical System (MEMS) wafer having a MEMS device therein. The MEMS device includes a movable element, and first openings in the MEMS wafer. The movable element is disposed in the first openings. A carrier wafer is bonded to the MEMS wafer. The carrier wafer includes a second opening connected to the first openings, wherein the second opening includes an entry portion extending from a surface of the carrier wafer into the carrier wafer, and an inner portion wider than the entry portion, wherein the inner portion is deeper in the carrier wafer than the entry portion.