Vibrational dynamics of concentrated-mass cantilevers in atomic force acoustic microscopy: Presence of modes with selective enhancement of vertical or lateral tip motion

Concentrated-mass (CM) cantilevers previously proposed by the author have features significantly effective for atomic force acoustic microscopy (AFAM), in which sample stiffness can be detected at nano scale by a vibrating tip. CM cantilevers improve the sensitivity of the detection and simplify the dynamics then lead to success in evaluations of the elastic modulus. The present study proposed a new type of CM cantilevers based on analyses of the vibrational dynamics taking account of previously ignored factors including the lateral contact stiffness and the inertia moment of a particle attached as a CM. A rod-like particle was attached on a tip in the new type to enhance the inertia moment in addition to the translational inertia. The first two modes behaved like one-freedom models, namely translational (vertical) and rotational (lateral) motions of the attached mass and the tip. Experiments on a sapphire wafer verified that the vertical and lateral stiffness can be simultaneously evaluated without mutual interference