Grad Seminar: Open-loop Transient Atomic Force Microscopy

Abstract

The Atomic Force Microscope (AFM) is an instrument for measuring, in fact “seeing”, phenomena at nanoscale (10−9m) and all the way down to the atomic scale (<10−10m). It was borne out of a need to observe physical reality below the resolution of optical microscopes. Invented in 1986 by Binnig, it has aided scientists, researchers, and engineers spanning many scientific and industrial domains. The typical sensing apparatus of the AFM is a very sharp tip (a few atoms wide) attached to the free-end of a fixed-free micro-beam. The tip is brought close to the desired specimen to initiate localized force interactions between the top-most atoms of the specimen and the bottom-most atoms of the tip. The tip-sample coupled system introduces a relative shift in the deflection of the microcantilever, this shift is interpreted as the magnitude of the interaction force and used for topographical mapping as well as mechanical/electrical/thermal characterization of a single point on the specimen. By recording the cantilever deflections while laterally scanning the sample, an area is “imaged”. 

According to resonant sensing theory, the sensitivity of the deflection of an oscillating cantilever beam driven at its resonant frequency is increased by a factor proportional to its quality factor (Q). As such, it is very common for an AFM cantilever to be driven at (or near) its first resonant mode in order to increase the Signal-to-Noise ratio (SNR). Whilst away from the sample, the steady-state response is perfectly harmonic with a force-response phase difference of 90 degrees: the very definition of resonance. However, near the sample, the response becomes anharmonic, nonlinearly modulated by the tip-sample interactions. This anharmonic response needs to be demodulated to quantify the interaction forces. The deviation from the harmonic response is only instantly described if the instantaneous frequency and amplitude are known. Alas, this is not possible. System design engineers are confronted with the ultimate compromise, namely, the Heisenberg uncertainty principle. More specifically, the energy spread of any time-frequency transformed signal forms a rectangle in the time-frequency plane, this "Heisenberg resolution box" has a minimum surface area of 1/2 that ultimately limits the attainable time-frequency resolution.

This thesis proposes a framework for a holistic approach to an open-loop bottom-up AFM system design. Design decisions and compromises are discussed and analyzed based on the desired requirements such as the SNR, the minimum acceptable noise floor, the demodulation scheme, and the maximum/minimum response times. An electrothermally driven and piezo-resistively sensed single-chip AFM (sc-AFM) is used for testing and verification. System Identification is carried out in the frequency domain to characterize the noise and establish the best linear approximation (BLA) transfer function of the AFM cantilever. For imaging, the AFM cantilever is continuously driven by an excitation signal while the cantilever deflection signal is sampled and filtered digitally. The Short-Time-Fourier-Transform (STFT) and the Wavelet Transform time-frequency characteristics are compared and contrasted. An analysis window is selected to adequately capture both transient and steady-state responses of the cantilever deflection signal. Moreover, a complete digital processing pipeline is proposed and implemented using the STFT for nonlinear time-varying spectral signal processing. Finally, imaging results based on amplitude-modulation AFM (AM-AFM) are demonstrated.

Presenter

Seyed-Mahdi Olfat 

Attending this seminar will count towards the graduate student seminar attendance milestone!