Acquisition of high-precision images for non-contact atomic force microscopy

The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of intermolecular forces with atomic-resolution characterization that can be employed in a broad spectrum of applications. The distance between cantilever tip and sample surface in non-contact AFM is a time-varying parameter even for a fixed sample height, and typically difficult to identify. A remedy to this problem is to directly identify the sample height in order to generate high-precision atomic-resolution images. For this, the microcantilever (which forms the basis for the operation of AFM) is modeled as a single mode approximation and the interaction between the sample and cantilever is derived from a van der Waals potential. Since in most practical applications only the microcantilever deflection is accessible, we will use merely this measurement to identify the sample height. In most non-contact AFMs, cantilevers with high-quality factors are employed essentially for acquiring high-resolution images. However, due to high-quality factor, the settling time is relatively large and the required time to achieve a periodic motion is long. As a result, identification methods based on amplitude and phase measurements cannot be efficiently utilized. The proposed method overcomes this shortfall by using a small fraction of the transient motion for parameter identification, so the scanning speed can be increased significantly. Furthermore, for acquiring atomic-scale images of atomically flat samples, the need for feedback loop to achieve setpoint amplitude is basically eliminated. On the other hand, for acquiring atomic-scale images of highly uneven samples, a simple PI controller is designed to track the desired constant sample height. Simulation results are provided to demonstrate the feasibility of the approach for both sample height identification and tracking the desired sample height.