An integrated circuit structure includes a semiconductor substrate; a metallization layer over the semiconductor substrate; a first dielectric layer between the semiconductor substrate and the metallization layer; a second dielectric layer between the semiconductor substrate and the metallization layer, wherein the second dielectric layer is over the first dielectric layer; and a contact plug with an upper portion substantially in the second dielectric layer and a lower portion substantially in the first dielectric layer. The contact plug is electrically connected to a metal line in the metallization layer. The contact plug is discontinuous at an interface between the upper portion and the lower portion.