Abstract
We have developed a wideband phase-locked loop (PLL) circuit with real-time phase correction for high-speed and accurate force measurements by frequency modulation atomic force microscopy (FM-AFM) in liquid. A high-speed operation of FM-AFM requires the use of a high frequency cantilever which, however, increases frequency-dependent phase delay caused by the signal delay within the cantilever excitation loop. Such phase delay leads to an error in the force measurements by FM-AFM especially with a low Q factor. Here, we present a method to compensate this phase delay in real time. Combined with a wideband PLL using a subtraction-based phase comparator, the method allows to perform an accurate and high-speed force measurement by FM-AFM. We demonstrate the improved performance by applying the developed PLL to three-dimensional force measurements at a mica/water interface.
Highlights
Frequency modulation atomic force microscopy (FMAFM)[1] has widely been used for atomic-scale studies on various materials in vacuum.[2, 3] In addition, recent advances in FM-AFM instrumentation[4] has enabled its operation in liquid with true atomic resolution,[5] which has stimulated subsequent studies on biological systems by FM-AFM.[6,7,8,9,10] biological systems have much larger fluctuations, corrugations, and inhomogeneity than those of the typical samples that have been studied by FM-AFM in vacuum
Molecular-scale imaging of relatively simple biological systems have been realized even with a present FM-AFM system,[6,7,8,9,10] a large part of the biological systems and phenomena have remained inaccessible by FM-AFM due to the insufficient operation speed
We have presented a design for a high-speed digital phase-locked loop (PLL) with a subtraction-based phase comparator (S-PLL).[14]
Summary
Frequency modulation atomic force microscopy (FMAFM)[1] has widely been used for atomic-scale studies on various materials in vacuum.[2, 3] In addition, recent advances in FM-AFM instrumentation[4] has enabled its operation in liquid with true atomic resolution,[5] which has stimulated subsequent studies on biological systems by FM-AFM.[6,7,8,9,10] biological systems have much larger fluctuations, corrugations, and inhomogeneity than those of the typical samples that have been studied by FM-AFM in vacuum. The improvement of the operation speed in FM-AFM requires to enhance the resonance frequency or the bandwidth of each component constituting the tip-sample distance feedback loop. It has become common to use a phase-locked loop (PLL) circuit for producing a cantilever excitation signal as well as for the detection of the frequency shift ( f ) of the cantilever oscillation in FM-AFM.[13] In the previous study, we have presented a design for a high-speed digital PLL with a subtraction-based phase comparator (S-PLL).[14] The developed S-PLL has a detection bandwidth of 100 kHz, which is much higher than that of a commonly used digital PLL with a multiplication-based phase comparator (M-PLL). We have developed a digital S-PLL with a real-time phase correction circuit for an accurate cantilever excitation and a high-speed f detection. (b) Simplified model of a cantilever excitation circuit used in FM-AFM
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