Quantitative elastic modulus measurement by magnetic force modulation microscopy

It is experimentally demonstrated that magnetic force modulation microscopy (MFMM) is a technique allowing quantitative elastic modulus measurements. A model of the cantilever-tip-sample interaction taking into account the la teral contact stiffness (i.e., the friction effects at the level of the tip -sample contact), the position of the magnetic force applied to the cantile ver with respect to the tip position, as well as the inclination of the can tilever arm with respect to the sample surface is presented. The model show s that MFMM is much less sensitive to lateral force than the other modulati on techniques and thus, in contrast to the latter, that the contrast of the stiffness images can be interpreted as a true elasticity contrast and not as a mixture of friction and elasticity. Thanks to the study of the normal contact stiffness versus normal load that allows the characterization of co ntact between tip and sample, it is possible to perform quantitative elasti c modulus measurements with a dynamic modulation method.