Linear Nanopositioning Systems for Scanning Probe Microscopy

Abstract

Scanning probe microscopes (SPM) are vital for visualizing and characterizing samples of interest to various fields with nanometer resolution, such as semiconductor fabrication, microbiology, and material engineering. The positioners of the SPM probe play a crucial role in achieving such a high resolution for the instrument over the desired range. Conventionally, a bare piezo actuator is used for positioning. However, it suffers from nonlinearity, thereby resulting in poor precision. Further, a trade-off exists between the range and speed of such a positioner. This work aims to develop linear nanopositioning systems for SPM to achieve large-range high-speed positioning. The first part of the thesis describes the positioning of the probe using integrated magnetic actuation and proposes a novel control strategy for regulating the tip-sample interaction force in contact mode operation. This positioning system comprises a magnetic particle attached to a probe which is actuated by magnetic fields generated by a current-carrying solenoid. The tip-sample interaction force is regulated by applying an equivalent magnetic force to the probe, which is equal in magnitude but opposite in direction to the measured interaction force. A quasi-static model is developed to determine the necessary current to the solenoid for regulating the force, whereas the dynamic model is developed to estimate the maximum achievable positioning speed. The analysis of these models led to two findings. First, the current through the solenoid must be proportional to the deformation of the probe to regulate the interaction force. Second, the eigenfrequency of the probe in contact with the stiff sample is significantly greater than a freely oscillating probe. Subsequently, experimental demonstrations show that the variation in the tip-sample force is reduced over an order of magnitude compared to when there is no force regulation. Finally, the proposed strategy employing magnetic positioning system is shown to be better than the conventional contact mode imaging that employs a piezo positioning system. In particular, they are shown to improve positioning accuracy by a factor of 9 and improve imaging speed by a factor of 100. The second part of the thesis investigates designing and optimizing a piezo-based positioner employing a single-stage bridge amplifier for achieving high bandwidth positioning. First, the design modifications to improve the bandwidth are proposed. Next, the quasi-static and dynamic models of the designs are developed, using which a closed-form expression relating the input to the output, amplification ratio and eigenfrequency of the positioner are obtained. Analysis revealed that applying the input, which results in compressive loading on the amplifier, is better than those with tensile loading as conventionally done, from the viewpoint of lower actuation force requirement and better linearity. Subsequently, an optimization methodology is developed to minimize the amplifier’s nonlinearity over a desired range. This optimization is used to develop an empirical relationship for the error and the optimal parameters of the amplifier in terms of amplification and range. These equations, along with the dynamic model, are used to optimize the bandwidth of the positioner to achieve desired range and linearity. An optimized amplifier is designed following the proposed guidelines, and its linearity has been shown to have improved over a factor of 10 compared to conventional bridge amplifiers. Finally, the bandwidth of the positioner has been shown to be over four times larger than that of a bare piezo actuator of a similar range. The third part of the thesis proposes the design optimization of the positioner employing two-stage amplification for large-range linear response, which addresses the low-range and small amplification ratio limitations of the single-stage bridge amplifier. Two designs for the amplifier are proposed. In the first design, the bridge amplifier mechanism is coupled with a lever amplifier. Next, the amplifier’s model is optimized and fabricated. Such an amplifier demonstrated a 23-fold improvement in linearity and a two-fold improvement in range compared to conventional bridge amplifiers of similar footprint. In the second design, two bridge amplifiers are cascaded. The quasi-static model is developed and used to develop the optimization methodology. Subsequently, an empirical relation between the error and the optimized parameters in terms of amplification ratio, amplifier’s length and range is developed. This is used to design an amplifier with an amplification of 30 and a range of 25% of its length. Such an optimized amplifier demonstrated over 500-fold improvement in linearity and eight-fold improvement in range compared to conventional bridge amplifiers of similar footprints. Lastly, the power-law relationship was discovered between the error and the range of the bridge amplifiers, with the exponent equal to the number of independent parameters available for tuning. The fourth part of the thesis showcases the applications of the developed positioning systems in Atomic Force Microscopy (AFM) to enhance its capabilities. First, the bandwidth and accuracy of the developed positioners are improved. The response speed of the magnetic-based positioning system improved by 10-fold using the model inversion technique. Further, a novel strategy is proposed to reduce the nonlinearity of the piezo actuator by actuating it over a fraction of its stroke and coupling it with an amplifier to compensate for the reduction in range. This strategy demonstrated a five-fold reduction in the nonlinearity of the positioner over the range of 18 µm using an amplifier of amplification of 28. The developed AFM, which combines both positioning systems, enabled the imaging of tall samples. Further, an AFM grating is imaged with speeds of 2.4 frames per second. This represents over 120-fold improvement in the imaging speed compared to conventional AFM. Lastly, simultaneous imaging and sample stiffness estimation is demonstrated, which is based on the magnetic actuation-based control strategy discussed in the first part of this thesis.