A self-similarity model for dielectric constant of porous ultra low-k dielectrics

Abstract

A self-similarity model applying the Sierpinski carpet approximation for the effective dielectric constant of nanoporous low-k dielectrics is proposed based on the statistically self-similar characteristics of pore size distributions in the medium and on the ‘mixture rule’ technique. The proposed model for the dielectric constant is expressed as a function of porosity (related to stage n of Sierpinski carpet) and the dielectric coefficient of components of the medium. The model predictions are compared with the existing experimental data and with other model predictions, and good agreement is obtained between the present model predictions and the experimental data. The proposed technique may have the potential of analysing other properties such as thermal conductivity and Young's modulus.