Contact stiffness of layered materials for ultrasonic atomic force microscopy

A method to calculate the contact stiffness between a layered material and an ultrasonic atomic force microscope (UAFM) tip is proposed. The radiation impedance method is used to determine the ratio of the applied force to the average displacement within the contact area. This information is used in an iterative algorithm based on Hertzian theory to obtain the contact stiffness. The algorithm converges into a couple of iterations and does not suffer from numerical convergence difficulties as does finite element analysis (FEA). In the ultrasonic frequency range, comparisons with Hertzian theory and FEA show the validity of the results in a quasistatic case. Definitions of the minimum detectable layer thickness and the penetration depth of the UAFM are given and evaluated for several thin film-substrate pairs. These results also show the potential of the method for modeling defects and power loss due to radiation in layered materials. (C) 2000 American Institute of Physics. [S0021-8979(00)01110-5].