Three-dimensional measurement of atomic force microscope cantilever deformation to determine the three-dimensional applied force vector

The atomic force microscope (AFM) is the instrument of choice for measuring nano- to micro-Newton forces (10-9 to 10-6 Newtons). However, calibration is required for accurate measurements. AFM calibration has been studied for decades and remains a significant focus within the metrological community, in particular at international standards organizations. While progress has been made, there is still much to accomplish as current force calibration techniques yield relative uncertainties (+/-1 standard deviation/mean) of 10%-20%. For example, measuring a force of 500 nN would yield a result between 400-600 nN 68% of the time. The critical issue is the existing AFM metrology, which monitors deformation at a single (spatial) point on a structure that encounters a three-dimensional (3D) force and responds with a 3D deformation. This single-point calibration technique considers only to a limiting set of information, while additional information is available. Similarly, subsequent measurements by the AFM after calibration are restricted to the same limits. As a response, this project aims to improve AFM calibration and use by implementing a new metrological platform and analysis technique.;The new platform incorporates a scanning white light interferometer (SWLI) for 3D cantilever deformation measurements. The SWLI introduces two important changes over standard AFM metrology. First, it provides a multi-point measurement of the backside surface of the cantilever rather than a single-point measurement near the free end. Second, it is a direct displacement sensor which does not infer displacement from the measurement of another variable, such as the surface angle in the optical lever technique. In this study, the AFM is first described with a focus on its use as a force sensor. Then, the new platform design and construction, cantilever imaging tests, and the development of a new force model, which takes advantage of the 3D deflection data, are presented. The new force model addresses many of the challenges associated with traditional calibration strategies. Experimental validation is presented for the cases of "normal" force loading (i.e., perpendicular to the cantilever axis and resulting in bending deformation) and "torsional" loading.