Effective modulus of heterogeneous materials in thin film configurations

Thin film is one of the important geometric configurations in the microelectronic devices. The traditional theories for heterogeneous material are challenged for their application to the thin film configurations (the free-standing and substrate-attached thin films). In the present paper, a finite element analysis with a statistic procedure is proposed to estimate the effective properties of thin films. For the free-standing thin film, the effective stiffness decreases as film thickness decreases. Comparison is made between numerical simulations and analytical solutions derived from a plane stress self-consistent scheme. For the substrate-attached thin film, the effective stiffness is affected by the relative stiffness of the substrate to the film. The numerical simulation shows the effective stiffness of the substrate-attached thin film can vary between the equivalent value of the free-standing thin film and Voigt bound. The three-dimensional Hashin–Shtrikman bounds fail to gauge the effective stiffness of thin film.