A Two-Parameter Function for Nanoscale Indentation Measurement of Near Surface Properties

A two-parameter function for estimation of projected area in instrumented indentation measurement is obtained to account for indenter tip imperfection. Imperfection near indenter tip is modeled using a spherical function and combined with a linear function describing the edge boundary of the indenter. Through an analytical fusion technique, the spherical and linear functions are combined into a single function with two unknown geometric parameters of tip radius of curvature and edge slope. Data from indentation measurement of force and displacement, using a Berkovich tip and single crystal alumina and silica samples, are implemented in the proposed area function yielding estimated values of Young’s modulus. Results were compared with that obtained from Oliver and Pharr technique for deep as well as shallow indentation regimes. The estimates for Young’s modulus were found to agree quite favorably. More importantly, in contrast to the Oliver–Pharr technique, the use of the two-parameter function resulted in a significantly more accurate estimation of Young’s modulus for shallow indentation depth of $0–50nm$⁠. The error in estimation of Young’s modulus was found to be within 10% for indentation depths of $25–50nm$ and within 20% for indentation depths of $0–25nm$⁠.