A stepped-sine curve-fit algorithm for finding cantilever resonance shifts in AFM
| Autor: | Zhixin Kang, Keith A. Brown, Verda Saygin, Sean B. Andersson |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
Cantilever business.industry Bode plot Fast Fourier transform Resonance 02 engineering and technology 010402 general chemistry 021001 nanoscience & nanotechnology 01 natural sciences Noise (electronics) Transfer function 0104 chemical sciences Signal-to-noise ratio Sine wave Optics 0210 nano-technology business |
| Zdroj: | ACC |
| DOI: | 10.23919/acc.2019.8814403 |
| Popis: | Atomic force microscopes (AFMs) are used not only to image with nanometer-scale resolution, but also to nanofabricate structures on a surface using methods such as dip-pen nanolithography (DPN). DPN involves using the tip of the AFM to deposit a small amount of material on the surface. Typically, this process is done in open loop, leading to large variations in the amount of material transferred. One of the first steps to closing this loop is to be able to accurately and rapidly measure the amount of deposition. This can be done by measuring the change in the resonance frequency of the cantilever before and after a write as that shift is directly related to the change in mass on the cantilever. Currently, this is done using a thermal-based system identification, a technique which uses the natural Brownian excitation of the cantilever as a white noise excitation combined with a fast Fourier transform to extract a Bode plot. However, thermal-based techniques do not have a good signal to noise ratio at typical cantilever resonance frequencies and thus do not provide the needed resolution in the DPN application. Here we develop a scheme that iteratively uses a stepped-sine approach. At each step of the iteration, three frequencies close to the approximate location of the resonance are injected and used to fit a model of the magnitude of the transfer function. The identified peak is used to select three new frequencies in a smaller range in a binary search to reduce the uncertainty of the measured resonance peak location. The scheme is demonstrated through simulation and shown to produce an accuracy of better than 0.5 Hz on a cantilever with a 14 $\mathbf{kHz}$ resonance in a physically realistic noise scenario. |
| Databáze: | OpenAIRE |
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