Automated FM-AFM Feedback Tuning
Atomic Resolution Imaging Made Easy
- Fig. 1: Schematic of FM-AFM. The common implementation of FM-AFM feedback electronics is depicted. Reproduced with permission from Rev. Sci. Instrum. 86, 103703 (2015). Copyright 2015 AIP Publishing LLC.
- Fig. 2: Mica in 100 mM aqueous KCl solution imaged by FM-AFM using feedback parameters calculated by the presented algorithm. The image shows unfiltered raw data, which were only plane-fitted. Scale bar, 2 nm.
FM-AFM is an extremely powerful and versatile imaging technique capable of atomic resolution imaging in vacuum, air or liquid. However, obtaining such results in practice currently requires tedious and time consuming manual tuning of many feedback parameters by trial and error. We present a recently developed algorithm for automated tuning of FM-AFM feedback parameters. The algorithm optimizes the performance of FM-AFM and makes it significantly simpler to operate.
Recent advances in Frequency Modulation Atomic Force Microscopy (FM-AFM) have enabled high-resolution imaging of surfaces and molecules in liquid at room temperature. In this regime, hydration structure , ion ordering , and various biological molecules [3,4] have been resolved using FM-AFM at an unprecedented 3D atomic resolution. FM-AFM has therefore become an extremely promising tool for nanoscience. However, the application of these new capabilities is still not widespread.
Despite its great potential, the impact of FM-AFM is limited by not being very accessible to inexperienced users. To obtain high-resolution images, users must tune various imaging parameters for each sample and cantilever they use, an often difficult and frustrating process. In particular, tuning of feedback parameters is the most challenging aspect of FM-AFM operation.
FM-AFM utilizes a sharp tip oscillated by external excitation, three feedback loops and a piezo motor (fig. 1). The piezo motor is used to move the tip relatively to the sample in all three axes. As the tip is moved in parallel to the sample surface, its oscillation amplitude and resonance frequency are modulated by variations in tip-sample interaction and separation. The feedback loops control these variations to generate an image of the sample. The amplitude loop controls the cantilever excitation to maintain a constant oscillation amplitude. The frequency loop controls the excitation frequency to oscillate the cantilever at its resonance frequency. The piezo loop controls the tip-sample separation to maintain a constant resonance frequency. Thus, the tip tracks surfaces of equal resonance frequency as it scans the sample and the surface topography is obtained by recording the piezo extension as a function of tip position.
The three feedback loops are regulated by a large number of feedback parameters which are tuned by the AFM operator during scanning to obtain stability, high sensitivity, and low noise in the imaging process.
Most commonly, each loop is implemented with one proportional-integral (PI) controller which is regulated by two parameters, a proportional gain and a time constant. Additionally, the feedback loops share a lock-in amplifier which is regulated by a cutoff frequency and filtering order.
The amplitude loop is weakly coupled to the other loops and its two PI parameters are in practice relatively straightforward to tune independently. However, the remaining six frequency and piezo loop parameters are much more challenging to tune due to a strong coupling between them by nonlinear and generally unknown tip-sample interactions. A variation in tip-sample distance originating from the piezo loop causes a variation in tip-sample interaction. This causes a variation in resonance frequency and consequentially modifies the frequency loop error signal. In response, the frequency loop alters the cantilever excitation frequency, modifying the piezo loop error signal and consequentially the tip-sample distance. Due to this coupling, the six frequency and piezo loop feedback parameters must be optimized simultaneously in the presence of an unknown interaction, a challenging, high dimensional, and nonlinear optimization problem. Currently, optimization of FM-AFM parameters is generally performed manually by a tedious and time-consuming process of trial and error, and by relying on the experience of expert users. Although several methods have been devised for obtaining first-guess frequency and piezo loop parameters [5,6], these parameters still usually require a great deal of manual tuning for high performance applications of FM-AFM.
Automated Feedback Tuning
In a recent work , we have developed and implemented an algorithm for automated optimization of frequency and piezo loop parameters. Using a linear model of the coupled feedback loops, we have calculated the transfer function Gδz which relates the modulation of tip-sample distance due to scanning, δz, to the piezo extension signal ∆z: ∆z(s) = Gδz(s)δz(s). Gδz is a function of the feedback parameters and of the tip-sample interaction. By finding the feedback parameters that optimize the bandwidth and step response of Gδz we are able to optimize tracking of the sample surface and minimize noise. Our algorithm optimizes Gδz in two steps. In the first step, which is performed prior to scanning, the optimal feedback parameters are partially determined numerically. In the second step the tip-sample interaction is determined by analyzing noise in the system and the feedback parameters are fully optimized. The second step is performed rapidly during scanning, enabling real time optimization of feedback parameters and adaptation to varying tip-sample interaction.
Feedback parameters generated by the algorithm consistently deliver excellent performance, even in applications that require a high degree of feedback optimization such as atomic resolution imaging in liquid. Using these parameters, we have been able to enhance stability and reduce noise in our images as well as substantially improve image quality and reproducibility compared with manual optimization. The quality of parameters generated by our algorithm is demonstrated in a typical scan of Mica in 100 mM KCl solution shown in figure 2.
Integration of the proposed algorithm into AFM software enhances the capabilities of FM-AFM, makes it considerably easier to operate, and makes it far more accessible to inexperienced users. Aside from feedback parameter optimization, all significant aspects of FM-AFM operation can currently be performed programmatically. Therefore, our algorithm removes the only major hurdle preventing a fully automated high-resolution FM-AFM system.
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Technion – Israel Institute of Technology
Department of Physics