Decoupling of Ion Diffusivity and Electromobility in Porous Dielectrics

Abstract

Porous back-end dielectric materials with porosity from 8% to 25%, sandwiched between Cu and W/Pt electrodes, have been investigated in terms of Cu diffusivity and mobility. In nonporous materials the diffusivity D and mobility m of charged particles such as an ion is related by the Einstein relation: μ=D q/kT. Here, we present evidence that in porous materials the diffusivity and mobility are decoupled on a global scale, even though the Einstein relation still holds locally. In porous materials, the voids lying in the path of the ion present an impenetrable barrier for ion migration. Voids can be only overcome by a detour around the obstacle by virtue of diffusion. We propose a modified relation between diffusivity and mobility in porous materials by μ=fp∙D q/kT where a porosity-tortuosity factor fp <1 is introduced. The factor fp depends on porosity and tortuosity of the porous material.