Frontiers in Accurate Mapping of Three-Dimensional Nano-Electromechanics

Atomic Force Microscopes (AFMs) have become a standard tool for high resolution surface mapping of a wide variety of nanoscale samples. The vast majority of existing AFMs make use of an optical beam detector (OBD) that measures the bending of the flexible cantilever beam. Despite its popularity, accurate and reproducible mechanical measurements using this detection approach remains extremely challenging. Specific barriers to widespread accurate AFM include (i) highly inconsistent sensitivity calibrations, (ii) measurement noise floors significantly higher than thermal motion of the cantilever probes and (iii) uncontrolled mixing of vertical and in-plane forces acting on the tip. Component mixing inevitably complicates attempts at accurate mechanical measurements and can lead to enormous, and often unacknowledged uncertainties. In this work, we build on earlier previous interferometric results to develop and demonstrate new workflows that allow the full three-dimensional nanoscale mechanical response of samples – limited by the fundamental thermal (Brownian) fluctuations of the cantilever with an accurate sensitivity calibrated by the wavelength of light. These workflows are based around a new quadrature phase differential interferometer (QPDI) that routinely achieves a detection noise down to ≈5 fm√Hz on standard commercial cantilevers. The QPDI measurement remains linear and accurate for large deflections (>1 μm) down to sub-picometer thermal fluctuations. This improved low noise floor and accurate calibration reveals details and features that have been hidden from view using conventional OBD measurements. We demonstrate new workflows for a variety of materials including functional ferroelectrics, including high frequency (5G) filter design and manufacturing, beyond Moore’s law computing materials such as HfO and HZO and 2D van der Waals materials including twisted graphene and hBN and soft polymeric samples. We demonstrate significantly improved accurate force quantification of in-plane and vertical forces that are typically mixed in an uncontrolled manner with with conventional PFM measurements.