Atomic force microscopy (AFM) has become an extremely useful tool in materials science applications. In addition to imaging surfaces with nanometre resolution, the AFM can also be used to determine surface roughness [1], probe local changes in friction [2], measure surface forces [1,3], and assess changes in local elasticity over a sample surface. Recently much attention has been focused on the interpretation of AFM. force curves for characterizing tip-sample interactions [1,3-7]. Through appropriate analysis of force curves, a wealth of information can be obtained regarding the mechanical, chemical, and adhesive properties of the surface. To date, most studies using force mode AFM [3-6] have concentrated on the attractive and transition regions of the force curve. Very little effort has been dedicated to the examination of the contact portion (or so-called repulsive region) of the force curve. This region contains valuable information regarding the nanoseale mechanical response of the sample [7], In this paper, a technique is developed that (1) relates the elastic modulus of the sample to the sample response measured using AFM force curves; and (2) illuminates the importance of the relative stiffnesses of the cantilever probe and the sample to the determination of elastic modulus.
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