A method includes forming a first metal mesh over a carrier, forming a first dielectric layer over the first metal mesh, and forming a second metal mesh over the first dielectric layer. The first metal mesh and the second metal mesh are staggered. The method further includes forming a second dielectric layer over the second metal mesh, attaching a device die over the second dielectric layer, with the device die overlapping the first metal mesh and the second metal mesh, encapsulating the device die in an encapsulant, and forming redistribution lines over and electrically connecting to the device die.