Apparatuses and methods to provide a fully self-aligned via are described. A first metallization layer comprises a set of first conductive lines extending along a first direction on a first insulating layer on a substrate, the set of first conductive lines recessed below a top portion of the first insulating layer. A capping layer is on the first insulating layer, and a second insulating layer is on the capping layer. A second metallization layer comprises a set of second conductive lines on the second insulating layer and on a third insulating layer above the first metallization layer. The set of second conductive lines extend along a second direction that crosses the first direction at an angle. At least one via is between the first metallization layer and the second metallization layer. The via is self-aligned along the second direction to one of the first conductive lines. The tapering angle of the via opening may be in a range of from about 60° to about 120°.