Elasticity Analysis to Aid in Extracting Thin Film Elastic Moduli From Continuous Indentation Data

Abstract

This article provides elasticity solutions to the indentation of a bilayer by three-sided and four-sided indentors. These solutions aid characterization of thin film elastic moduli through continuous indentation techniques. The solutions are expressed in closed-form, and can be numerically evaluated on a small computer; additionally, graphs of some of the solutions are provided to aid in rapid data analysis. Simulations of unloading compliance, C, versus 1/A1/2 (A = projected area of indent) are compared with experimental data. The data are taken from measurements of single crystal Si, polycrystalline Al, and 1 μm Al deposited on Si. The elasticity analysis is used in the measurement of the elastic modulus of a sodium borosilicate glass, and the same glass but with a damaged surface layer introduced by suspension in an acid solution.