A force-matching method for quantitative hardness measurements by atomic force microscopy with diamond-tipped sapphire cantilevers.

We present a new method to improve the accuracy of force application and hardness measurements in hard surfaces by using low-force (<50 μN) nanoindentation technique with a cube-corner diamond tip mounted on an atomic force microscopy (AFM) sapphire cantilever. A force calibration procedure based on the force-matching method, which explicitly includes the tip geometry and the tip-substrate deformation during calibration, is proposed. A computer algorithm to automate this calibration procedure is also made available. The proposed methodology is verified experimentally by conducting AFM nanoindentations on fused quartz, Si(100) and a 100-nm-thick film of gold deposited on Si(100). Comparison of experimental results with finite element simulations and literature data yields excellent agreement. In particular, hardness measurements using AFM nanoindentation in fused quartz show a systematic error less than 2% when applying the force-matching method, as opposed to 37% with the standard protocol. Furthermore, the residual impressions left in the different substrates are examined in detail using non-contact AFM imaging with the same diamond probe. The uncertainty of method to measure the projected area of contact at maximum force due to elastic recovery effects is also discussed.