Error estimation and enhanced stiffness sensitivity in contact resonance force microscopy with a multiple arbitrary frequency lock-in amplifier (MAFLIA)

In contact resonance force microscopy and related dynamic atomic force microscopy methods, an accurate description of the real-time cantilever dynamics is essential to the mapping of local material properties, such as viscoelasticity, piezo response, and chemical composition. Stiffness and damping variations of the tip-sample contact result in variations in the cantilever's resonance frequency and quality factor as it scans a sample of interest. When measuring characteristics of the resonance, generally, there is a tradeoff between full spectral coverage, best obtained by sweeping the amplitude versus frequency response in the time or frequency domain, and high-speed information, obtained by observing the cantilever response at one or two discrete frequencies, that may be required to track a resonance frequency that changes spatially. Here, we introduce a new option for performing contact resonance force microscopy with a low-cost multifrequency lock-in amplifier system with up to eight simultaneous independent excitation and detection frequencies. We demonstrate how the multifrequency approach can measure contact resonance frequency, quality factor, amplitude, and phase during imaging, with high precision and error estimation, without the need for frequency-tracking feedback. We show, using a wood composite sample, that this multifrequency approach can determine resonance frequency and quality factor, and associated uncertainty. This ability to estimate uncertainty of resonance parameters is not possible with 1 and 2 frequency methods. We further utilize the multifrequency lock-in to develop a novel means of increasing the stiffness range for highly sensitive nanomechanical sensing by dividing the eight lock-in frequencies to monitor two or four simultaneous eigenmodes, each of which is optimized for sensitivity in a particular stiffness regime. Overall, we show how multifrequency lock-in amplifiers with observation frequency chosen to coincide with an expected eigenmode's contact resonance can benefit the characterization of strongly heterogeneous samples, while maintaining fast measurement speed.