A method for an integrated circuit structure includes providing a semiconductor substrate; forming a metallization layer over the semiconductor substrate; forming a first dielectric layer between the semiconductor substrate and the metallization layer; forming a second dielectric layer between the semiconductor substrate and the metallization layer, wherein the second dielectric layer is over the first dielectric layer; and forming 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.