Computer simulated dense-random packing models as approach to the structure of porous low-k dielectrics

Nanoporous low-k dielectrics are simulated by means of the model of randomly packed hard spheres. The spheres and the space between them represent the pores and the solid material of the insulator, respectively. The generalisation of the model for arbitrary continuous distributions offers the opportunity to optimise the structures with respect to low k values. A local maximum of 70% porosity is obtained for a power-law pore size distribution with exponent −3.3. The elastic constants of the models are calculated for the isotropic case in the composite sphere assemblage approach. Results for the effective dielectric constant, the Young's modulus and the bulk and shear modulus are presented for the range of porosity up to 70%.