Simulation of the dielectric constant of aerogels and estimation of their water content

Nanoporous silica aerogels are promising candidates for ultra-low-k dielect rics used in the metallization system of the 0.13 mum IC generation and bey ond. In this paper the relation between dielectric constant and microstruct ure is investigated. Application of an electrostatic field solver to severa l geometric models of microstructure shows that the effective dielectric co nstant is mainly determined by porosity, whereas the influence of geometric parameters such as pore shape, pore size, and pore-size distribution is co mparably weak. Evaluation of experimental data shows some measured values o f epsilon above the results of the simulation. The difference is due to con tamination of the internal surface area with hydroxyl radicals and water mo lecules depending on the manner of post-treatment of aerogel thin films. Th e effective concentration of water is estimated by comparison of experiment al data and simulation results. (C) 2001 Elsevier Science B.V. All rights r eserved.