Atomic force microscopy: Principles and systems viewpoint enabled methods

Atomic force microscopy and related principles have enabled nanoscale science and engineering, which have impacted basic and applied sciences in a fundamental way. The main focus of the chapter is to elucidate the important role that a systems and controls perspective has played in improving the resolution and bandwidth of the atomic force microscope (AFM) and in providing newer methods of imaging. After providing basic foundations of atomic force microscopy, a framework is developed for analysis, design, and evaluation of nanopositioning systems. Fundamental limitations on the control design are determined and the relative tradeoffs between the resolution, bandwidth, and robustness objectives are analyzed. System theoretic designs that achieve desired tradeoffs between resolution and bandwidth objectives are presented. A design from this framework that demonstrates sub-nanometer positioning resolution is illustrated, where it is also shown that tracking error can be made largely independent of scan speed. Using the systems framework, an optimal multi-input multi-output (MIMO) control design is developed for a multi-axis positioning system. This design compensates for the interaxial coupling between the dynamics allowing for stages with smaller masses thereby increasing bandwidth. It is shown that a systems approach to the main probe and its interaction with the sample facilitates a viewpoint of a linear system in a feedback interconnection with a static nonlinearity that has lead to considerable simplification of the analysis of dynamic mode operation. Based on this approach, a method of reconstruction of the tip-sample nonlinearity is presented. A new mode of AFM-based sample detection, the transient force atomic force microscopy method is developed that has led to two orders increase in sample detection rates. Real-time models also help in detection of probe-loss that plagues most high bandwidth AFM-based nanointerrogation methods. A method for real-time detection of probe-loss and its subsequent correction is highlighted in the chapter. The imaging of sample parameters based on a bank of models is subsequently presented. Finally, an ultra-high resolution minimally invasive sample interrogation method is presented.