Abstract
The frequency shift noise in non-contact atomic force microscopy (NC-AFM) imaging and spectroscopy consists of thermal noise and detection system noise with an additional contribution from amplitude noise if there are significant tip–sample interactions. The total noise power spectral density DΔf(fm) is, however, not just the sum of these noise contributions. Instead its magnitude and spectral characteristics are determined by the strongly non-linear tip–sample interaction, by the coupling between the amplitude and tip–sample distance control loops of the NC-AFM system as well as by the characteristics of the phase locked loop (PLL) detector used for frequency demodulation. Here, we measure DΔf(fm) for various NC-AFM parameter settings representing realistic measurement conditions and compare experimental data to simulations based on a model of the NC-AFM system that includes the tip–sample interaction. The good agreement between predicted and measured noise spectra confirms that the model covers the relevant noise contributions and interactions. Results yield a general understanding of noise generation and propagation in the NC-AFM and provide a quantitative prediction of noise for given experimental parameters. We derive strategies for noise-optimised imaging and spectroscopy and outline a full optimisation procedure for the instrumentation and control loops.
Highlights
Non-contact atomic force microscopy (NC-AFM) [1,2] is an unmatched surface science tool, especially when it comes to studying non-conducting surfaces [3,4], to map sub-molecular structures [5] or to measure forces [6] and force fields [7] with highest resolution
The frequency shift noise in non-contact atomic force microscopy (NC-AFM) imaging and spectroscopy consists of thermal noise and detection system noise with an additional contribution from amplitude noise if there are significant tip–sample interactions
Dictated by the cantilever response function Hc(f). This cantilever oscillation is measured as the cantilever displacement signal. Noise contributions in this signal are described in frequency space by the thermal noise displacement power spectral density and by the detection system noise power spectral density
Summary
Non-contact atomic force microscopy (NC-AFM) [1,2] is an unmatched surface science tool, especially when it comes to studying non-conducting surfaces [3,4], to map sub-molecular structures [5] or to measure forces [6] and force fields [7] with highest resolution. The frequency response Hfilter of the PLL system is used for describing the propagation of noise from the cantilever oscillation to the frequency shift signal at the output of the frequency demodulator This frequency response function strongly depends on the PLL filter settings [11] and will here be modelled for a typical experimental setup described in section “Noise propagation model”. For the numerical evaluation of signal vs time traces and noise spectra, the explicit frequency response functions and system parameters for our experimental setup are used; all frequency response functions are listed in the appendix and the implementation in MATLAB is available in Supporting Information File 1 This approach enables a numeric evaluation in absolute physical units and, allows the direct comparison between experiment and our model
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