This paper presents a mathematically defined characterization of random porous media including random self-similarity and surface fractality. The initial two-phase structure is transformed into a three-phase system by introducing the internal surface layer as the third phase. Effective medium theories are utilized to calculate macroscopic dielectric and elastic properties. The dependence of both the static dielectric constant and Young's modulus on geometrical parameters is analyzed for different combinations of bulk and interface properties. It is shown that the modification of the properties of the internal surface layer is a promising way to improve the effective constants of the materials. The obtained analytical expressions are also used to determine confined regions in the space of structural parameters where pre-specified property combinations are realized. The results are discussed in terms of possible applications of nanometer-scale porous interlayer dielectrics with an ultralow dielectric constant and sufficient mechanical stiffness for future semiconducting devices.
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