Effective thermal expansion behaviors of ultrathin low-dielectric polymer film for microelectronic applications

The thickness dependent effective thermal expansion properties for low-dielectric polycrystalline polymer film in the thickness range of 96 nm to 1154 nm are investigated. It is demonstrated that the coefficients of thermal expansion (CTE) are strongly thickness dependent. It is evident that the numerical range for the coefficients of thermal expansion is smaller for thinner samples and becomes increasingly larger for thicker samples with increasing temperature. The results show that the thickness-dependent CTEs depend on the film thickness as a result of the mobility at both film/surface and film/substrate, and a model for the film thickness-dependent CTE is also discussed. The thickness dependence of dCTE/dT is also investigated and is seen to be strongly thickness dependent for the ultrathin films. Ultrathin films have a very low dCTE/dT, which increases with thickness but eventually plateaus above a certain film thickness. The results are explained in terms of the confinement effect on a silicon substrate.