Manufacturable extremal low-dielectric, high-stiffness porous materials

The drive toward increased semiconductor device densities and improved performance has set in motion the search for low-dielectric-constant materials. While introducing porosity in silica holds promise for reducing the dielectric constant, it remains elusive how to accomplish this without seriously degrading the thermomechanical performance. This article demonstrates a contemporary protocol for materials by design. Applying rigorous cross-property relations, we identify the extremal porous material structure that possesses the desired reduction in the dielectric constant while providing the highest possible stiffness for any given level of porosity. This structural design is crucial to the integration of porous low-dielectric materials into microelectronics and should serve as a guide to future synthetic efforts. Using recently developed self-assembly techniques, we also demonstrate that structures approaching the optimal one can be fabricated. Importantly, our procedure can be applied to general material design problems.