Thickness dependence of nanofilm elastic modulus

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 epsilon(0) as epsilon(-2)(0). For Si nanofilms, the variation of dimensionless elastic modulus Psi=E/E-bulk with the dimensionless film thickness eta=h/h(b) can be represented in the following form: Psi=eta(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.