Elastic Modulus of Nanometer Silicon Membrane

In this article, a new method is presented to calculate the in-plane elastic modulus of nanometer silicon membrane. In comparing with the traditional model, it accounts for the discrete nature in the thickness direction of the silicon membrane. In this model, interatomic bonding forces are equivalent to spring forces. A method to obtain the spring constant k is also presented by using lattice dynamics theory. Investigating the obtained in-plane elastic modulus value, it is found that the value is highly dependent on the thickness of the membrane and approaches the bulk value as the thickness increases.