Determination of Poisson's Ratio of Thin low-k Films using Bidirectional Thermal Expansion Measurement

Abstract

A recently developed bidirectional thermal expansion measurement (BTEM) method was applied to different types of low-k films to substantiate the reliability of the Poisson's ratio found with this technique and thereby to corroborate its practical utility. In this work, the Poisson's ratio was determined by obtaining the temperature gradient of the biaxial thermal stress from substrate curvature measurements, the temperature gradient of the whole thermal expansion strain along the film thickness from x-ray reflectivity (XRR) measurements, and reduced modulus of the film from nanoindentation measurements. For silicon oxide-based SiOC film having a thickness of 382.5 nm, the Poisson's ratio, Young's modulus and thermal extension coefficient (TEC) were determined to be ν f = 0.26, α f =21 ppm/K and E f =9,7 GPa. These data are close to the levels of metals and polymers rather than the levels of fused silicon oxide, which is characterized by ν f = 0.17 and E r = 69.6 GPa. The alkyl component in the silicon oxide-based framework is thought to act as an agent in reducing the modulus and elevating the Poisson's ratio in SiOC low-k materials. In the case of an organic polymer SiLK film with a thickness of 501.5 nm, the Poisson's ratio, Young's modulus and TEC were determined to be ν f = 0.39, α f =74 ppm/K and E r =3.1 GPa, which are in the typical range of ν = 0.34~0.47 with E =1.0~10 GPa for polymer materials. From the viewpoint of the relationship between the Poisson's ratio and Young's modulus as classified by different material types, the Poisson's ratios found for the silicon oxide-based SiOC and organic SiLK films are reasonable values, thereby confirming that BTEM is a reliable and effective method for evaluating the Poisson's ratio of thin films.

Poisson's ratio of BiFeO3 thin films: X‐ray reciprocal space mapping under variable uniaxial strain

“…Poisson's ratio of thin films can differ largely in bulk material due to preparation methods and microstructures, while for thin films, substrates and thus the effects of interfaces play a decisive role. Various methods have been established to obtain the Poisson's ratio of a thin film, such as optical deflection by measuring the curvature of the substrate or the thin film , acoustic microscopy by collecting the transverse and longitudinal acoustic speed , thermal expansion by surveying the dependence of the film stress on temperature and the reduced Young's modulus of the film by nanoindentation , mechanical deformation by using a strain gauge and theoretical calculation . Another method occasionally adopted is X‐ray diffraction.…”