Thickness dependence of nanofilm elastic modulus

摘要

Young's modulus is a fundamental physical parameter that determines not only the mechanic but also the electronic properties of a solid thin film. In here, we show that the elastic modulus is not a constant as that of conventional treatment but varies with film thickness. Scaling behavior is found based on the theoretical analysis of the free energy of surface-to-volume ratio of the film and results of the elastic modulus measurement. It has been shown that there exists some film thickness h_b when the surface energy of the film comes into play. The h_b is inverse proportional to the bulk Young's modulus and depends strongly on the in-plain strain ε_0 as ε_0~(-2). For Si nanofilms, the variation of dimensionless elastic modulus ψ=E/E_(bulk) with the dimensionless film thickness η=h/h_b can be represented in the following form: ψ= η~(0.226). The present investigation illustrates the importance of the effect of dimensionality on the basic parameter of a thin film as well as providing important implications for electronic devices, in particular for the Si-based strained nanodevices.