Frequency stability in AFM

Atomic force microscopy (AFM) is a versatile surface-sensitive technique. One of the main challenges is to expand these capabilities to also image the subsurface structure of the sample, for example by using ultrasound. Existing ultrasound methodologies often indicate the phase of the cantilever vibration as the most sensitive subsurface channel. Even if such techniques can be developed to their full potential, it remains a question how accurate and fast these methods can become. To get an idea on the possibilities, we measured the frequency stability, which is similar to the phase stability, of a cantilever in a home-built AFM. We started by making the optical detection system and tested it by measuring the thermomechanical peak of the cantilever. Then the piezo inside the cantilever holder was fixed to drive the cantilever. In AFM the resonance frequency changes due to the tip-sample interaction. However no resonator is perfect, and the resonance frequency will vary even when...Show moreAtomic force microscopy (AFM) is a versatile surface-sensitive technique. One of the main challenges is to expand these capabilities to also image the subsurface structure of the sample, for example by using ultrasound. Existing ultrasound methodologies often indicate the phase of the cantilever vibration as the most sensitive subsurface channel. Even if such techniques can be developed to their full potential, it remains a question how accurate and fast these methods can become. To get an idea on the possibilities, we measured the frequency stability, which is similar to the phase stability, of a cantilever in a home-built AFM. We started by making the optical detection system and tested it by measuring the thermomechanical peak of the cantilever. Then the piezo inside the cantilever holder was fixed to drive the cantilever. In AFM the resonance frequency changes due to the tip-sample interaction. However no resonator is perfect, and the resonance frequency will vary even when there is no sample at all. To characterize the smallest tip-sample interactions that can be measured, one needs to characterize the frequency stability of the cantilever without a sample. To do this we have tracked the resonance frequency using a phase-locked loop. The cantilever was driven at its resonance frequency for 2 hours. The stability of its resonance frequency was analysed using the Allan deviation. We saw that for time intervals up to 30 seconds the Allan deviation had a downwards slope of −1 2 which corresponds to white frequency modulation. The short time interval Allan deviation was lower in measurements using a PLL bandwidth of 1000Hz. From the data became clear that using a PLL bandwidth of 1000Hz instead of 100Hz, the resonance frequency was flatter in time but had spikes. The lower PLL bandwidths we used were not able to resolve these spikes, that are probably caused by the unshielded cables used in the setup. Earlier we already saw spikes in the individual photodiode signals caused by these unshielded cables. For intervals longer than 30 seconds this slope for the Allan deviation was +1 (corresponds to drift in resonance frequency). This can be attributed to environmental changes, for instance temperature fluctuations, that change the resonance frequency of the cantilever. The minimum Allan deviation was aroundd 10−6. This is 11mHz RMS deviation for the 11kHz cantilever. This is equivalent to a 0.18mdeg phase noise, which is already less than the phase-contrast caused by a 50nm gold particle buried 200nm in a soft polymer at 1MHz. The minimum Allan deviation we measured is still 3 orders of magnitude above values found in the literature for resonators with a comparable mass. Shielding cables might improve this.Show less

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Frequency stability in AFM