Micromechanical contact stiffness devices and application for calibrating contact resonance atomic force microscopy

This paper reports the design, fabrication, and characterization of micromechanical devices that can present an engineered contact stiffness to an atomic force microscope (AFM) cantilever tip. These devices allow the contact stiffness between the AFM tip and a substrate to be easily and accurately measured, and can be used to calibrate the cantilever for subsequent mechanical property measurements. The contact stiffness devices are rigid copper disks of diameters 2-18 μm integrated onto a soft silicone substrate. Analytical modeling and finite element simulations predict the elastic response of the devices. Measurements of tip-sample interactions during quasi-static force measurements compare well with modeling simulation, confirming the expected elastic response of the devices, which are shown to have contact stiffness 32-156 N m^-1. To demonstrate one application, we use the disk sample to calibrate three resonant modes of a U-shaped AFM cantilever actuated via Lorentz force, at approximately 220, 450, and 1200 kHz. We then use the calibrated cantilever to determine the contact stiffness and elastic modulus of three polymer samples at these modes. The overall approach allows cantilever calibration without prior knowledge of the cantilever geometry or its resonance modes, and could be broadly applied to both static and dynamic measurements that require AFM calibration against a known contact stiffness.