Methods for making semiconductor device having improve contact structures including the operations of depositing a first dielectric material, depositing a barrier material over the first dielectric material, depositing a second dielectric material over the barrier material, etching a two-slope contact opening with an upper sidewall angle of the opening through the second dielectric material that is less than a lower sidewall angle of the opening through the first dielectric material, and filling the two-slope contact opening with a conductive material, the conductive material.