Calculation of Pore Size Distributions in Low-k Films

Abstract

Porosimetry is a key technology for the characterization of porous low-k dielectric films. A critical appraisal of the models used for quantitative interpretation of vapor adsorption isotherms obtained by ellipsometric and x-ray reflectivity measurements shows that conventional macroscopic methods based on the Kelvin equation are inadequate on the nanoscale. We have developed an advanced molecular model of toluene adsorption in nanopores and the method for pore size distribution calculations based on this mode. The method has been verified against reference ordered porous silicas and applied to selected low-k films. Significant deviations of the Kelvin equation were found for pores < 4 nm. The new method provides a unified framework for reliable calculations of micro- and mesopore size distributions. The results are generally consistent with available data of small angle neutron scattering porosimetry.