A package includes a device die, a molding material encircling the device die, wherein a top surface of the molding material is substantially level with a top surface of the device die, and a bottom dielectric layer over the device die and the molding material. A plurality of redistribution lines (RDLs) extends into the bottom dielectric layer and electrically coupling to the device die. A top polymer layer is over the bottom dielectric layer, with a trench ring penetrating through the top polymer layer. The trench ring is adjacent to edges of the package. The package further includes Under-Bump Metallurgies (UBMs) extending into the top polymer layer.