A structure and method for an insulator layer having carbon-graded layers above a substrate is disclosed, wherein the concentration of carbon increases in each successive carbon-graded layer above the substrate. The insulator comprises a low-k dielectric having a dielectric constant less than 3.3. The carbon-graded layer increases adhesion between the substrate and the insulator and between the insulator and the conductor layer. The structure may also include stabilization interfaces between the carbon-graded layers. More specifically, the carbon-graded layers include a first layer adjacent the substrate having a carbon content between about 5% and 20%, a second layer above the first layer having a carbon content between about 10% and 30%, and a third layer above the second layer having a carbon content between about 20% and 40%.