In this review paper, traditional and novel demodulation methods applicable to amplitude-modulation atomic force microscopy are implemented on a widely used digital processing system. As a crucial bandwidth-limiting component in the z-axis feedback loop of an atomic force microscope, the purpose of the demodulator is to obtain estimates of amplitude and phase of the cantilever deflection signal in the presence of sensor noise or additional distinct frequency components. Specifically for modern multifrequency techniques, where higher harmonic and/or higher eigenmode contributions are present in the oscillation signal, the fidelity of the estimates obtained from some demodulation techniques is not guaranteed. To enable a rigorous comparison, the performance metrics tracking bandwidth, implementation complexity and sensitivity to other frequency components are experimentally evaluated for each method. Finally, the significance of an adequate demodulator bandwidth is highlighted during high-speed tapping-mode atomic force microscopy experiments in constant-height mode.
In dynamic mode atomic force microscopy (AFM), the imaging bandwidth is governed by the slowest component in the open-loop chain consisting of the vertical actuator, cantilever and demodulator. While the common demodulation method is to use a lock-in amplifier (LIA), its performance is ultimately bounded by the bandwidth of the post-mixing low-pass filters. This article proposes an amplitude and phase estimation method based on a strictly positive real Lyapunov design approach. The estimator is designed to be of low complexity while allowing for high bandwidth. Additionally, suitable gains for high performance are suggested such that no tuning is necessary. The Lyapunov estimator is experimentally implemented for amplitude demodulation and shown to surpass the LIA in terms of tracking bandwidth and noise performance. High-speed AFM images are presented to corroborate the results.
Abstract-We present new insights into the modeling of the microcantilever in dynamic mode atomic force microscopy and outline a novel high-bandwidth tip-sample force estimation technique for the development of high-bandwidth z-axis control. Fundamental to the proposed technique is the assumption that in tapping mode atomic force microscopy, the tip-sample force takes the form of an impulse train. Formulating the estimation problem as a Kalman filter, the tip-sample force is estimated directly; thus, potentially enabling high-bandwidth z-axis control by eliminating the dependence of the control technique on microcantilever dynamics and the amplitude demodulation technique. Application of this technique requires accurate knowledge of the models of the microcantilever; a novel identification method is proposed. Experimental data are used in an offline analysis for verification.
A fundamental challenge in dynamic mode atomic force microscopy (AFM) is the estimation of the cantilever oscillation amplitude from the deflection signal, which might be distorted by noise and/or high-frequency components. When the cantilever is excited at resonance, its deflection is typically obtained via narrow-band demodulation using a lock-in amplifier (LIA). However, the bandwidth of this measurement technique is ultimately bounded by the low-pass filter, which must be employed after demodulation to attenuate the component at twice the carrier frequency. Furthermore, to measure the amplitude of multiple frequency components, such as higher eigenmodes and/or higher harmonics in multifrequency AFM, multiple LIAs must be employed. In this paper, the authors propose the estimation of amplitude and phase using a linear time-varying Kalman filter that is easily extended to multiple frequencies. Experimental results are obtained using square-modulated sine waves and closed-loop AFM scans, verifying the performance of the proposed Kalman filter. IndexTerms-Amplitude estimation, atomic force microscopy (AFM), field-programmable gate array (FPGA) implementation, high bandwidth, Kalman filter, state estimation.
SummaryUsing standard microelectromechanical system (MEMS) processes to coat a microcantilever with a piezoelectric layer results in a versatile transducer with inherent self-sensing capabilities. For applications in multifrequency atomic force microscopy (MF-AFM), we illustrate that a single piezoelectric layer can be simultaneously used for multimode excitation and detection of the cantilever deflection. This is achieved by a charge sensor with a bandwidth of 10 MHz and dual feedthrough cancellation to recover the resonant modes that are heavily buried in feedthrough originating from the piezoelectric capacitance. The setup enables the omission of the commonly used piezoelectric stack actuator and optical beam deflection sensor, alleviating limitations due to distorted frequency responses and instrumentation cost, respectively. The proposed method benefits from a more than two orders of magnitude increase in deflection to strain sensitivity on the fifth eigenmode leading to a remarkable signal-to-noise ratio. Experimental results using bimodal AFM imaging on a two component polymer sample validate that the self-sensing scheme can therefore be used to provide both the feedback signal, for topography imaging on the fundamental mode, and phase imaging on the higher eigenmode.
This work proposes a novel self-sensing tapping-mode atomic force microscopy operation utilizing charge measurement. A microcantilever coated with a single piezoelectric layer is simultaneously used for actuation and deflection sensing. The cantilever can be batch fabricated with existing micro electro mechanical system processes. The setup enables the omission of the optical beam deflection technique which is commonly used to measure the cantilever oscillation amplitude. Due to the high amount of capacitive feedthrough in the measured charge signal, a feedforward control technique is employed to increase the dynamic range from less than 1 dB to approximately 35 dB. Experiments show that the conditioned charge signal achieves excellent signal-to-noise ratio and can therefore be used as a feedback signal for atomic force microscopy imaging.
QPlus sensors are non-contact atomic force microscope probes constructed from a quartz tuning fork and a tungsten wire with an electrochemically etched tip. These probes are self-sensing and offer an atomic-scale spatial resolution. Therefore, qPlus sensors are routinely used to visualize the chemical structure of adsorbed organic molecules via the so-called bond imaging technique. This is achieved by functionalizing the AFM tip with a single CO molecule and exciting the sensor at the first vertical cantilever resonance mode. Recent work using higher-order resonance modes has also resolved the chemical structure of single organic molecules. However, in these experiments, the image contrast can differ significantly from the conventional bond imaging contrast, which was suspected to be caused by unknown vibrations of the tip. This work investigates the source of these artefacts by using a combination of mechanical simulation and laser vibrometry to characterize a range of sensors with different tip wire geometries. The results show that increased tip mass and length cause increased torsional rotation of the tuning fork beam due to the off-center mounting of the tip wire, and increased flexural vibration of the tip. These undesirable motions cause lateral deflection of the probe tip as it approaches the sample, which is rationalized to be the cause of the different image contrast. The results also provide a guide for future probe development to reduce these issues.
An important issue in the emerging field of multifrequency atomic force microscopy (MF-AFM) is the accurate and fast demodulation of the cantilever-tip deflection signal. As this signal consists of multiple frequency components and noise processes, a lock-in amplifier is typically employed for its narrowband response. However, this demodulator suffers inherent bandwidth limitations as high-frequency mixing products must be filtered out and several must be operated in parallel. Many MF-AFM methods require amplitude and phase demodulation at multiple frequencies of interest, enabling both z-axis feedback and phase contrast imaging to be achieved. This article proposes a model-based multifrequency Lyapunov filter implemented on a field-programmable gate array (FPGA) for high-speed MF-AFM demodulation. System descriptions and simulations are verified by experimental results demonstrating high tracking bandwidths, strong off-mode rejection and minor sensitivity to cross-coupling effects. Additionally, a five-frequency system operating at 3.5 MHz is implemented for higher harmonic amplitude and phase imaging up to 1 MHz.
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