A cantilever-based, ultrahigh-vacuum, low-temperature scanning probe instrument for multidimensional scanning force microscopy

• Hao Liu,
• Zuned Ahmed,
• Sasa Vranjkovic,
• Manfred Parschau,
• Andrada-Oana Mandru and
• Hans J. Hug

Beilstein J. Nanotechnol. 2022, 13, 1120–1140, doi:10.3762/bjnano.13.95

• islands on top (see section “Results and Discussion”). There is a third noise source, namely the oscillator noise given by Equation 3, which is, however, relevant only for low-quality factor conditions [59]. An experimental evaluation of the measured frequency shift noise revealed that it depends as on

Noise in NC-AFM measurements with significant tip–sample interaction

• Jannis Lübbe,
• Matthias Temmen,
• Philipp Rahe and
• Michael Reichling

Beilstein J. Nanotechnol. 2016, 7, 1885–1904, doi:10.3762/bjnano.7.181

• & Astronomy, The University of Nottingham, University Park, Nottingham NG7 2RD, UK 10.3762/bjnano.7.181 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; cantilever stiffness; closed loop; detection system noise; frequency shift noise; non-contact atomic force microscopy (NC-AFM); Q-factor; spectral analysis; thermal noise; tip–sample interaction; Introduction Non-contact atomic force microscopy (NC-AFM) [1][2] is an unmatched surface

• demodulator (mostly a phase-locked loop detector, PLL), cantilever properties and ultimately thermal noise [11]. The footing of our work are these precursor studies, and the rigorous system analysis introduced by Polesel-Maris et al. [12], showing that the frequency shift noise at close tip–sample distance is

Determining cantilever stiffness from thermal noise

• Jannis Lübbe,
• Matthias Temmen,
• Philipp Rahe,
• Angelika Kühnle and
• Michael Reichling

Beilstein J. Nanotechnol. 2013, 4, 227–233, doi:10.3762/bjnano.4.23

• which the PLL transfer function is known. The former condition requires the detection system noise floor to be so low that, at least over a significant fraction of the PLL demodulator bandwidth, the frequency shift noise spectral density (fm) of the detection system is negligible compared to the

• thermal frequency-shift noise spectral density (fm) [6]. Results and Discussion Stiffness from displacement thermal noise In a displacement noise measurement of a cantilever with a high Q-factor, the spectrum analyser measures the total displacement noise spectral density (f) for the nth cantilever

• output or loop filter Gfilter, the frequency shift noise spectral density at the PLL output can be represented as [6] This allows us to obtain the modal stiffness from a measurement of if all other parameters are known: Practically, the spectral analysis can be restricted to the frequency range of 10 Hz

Thermal noise limit for ultra-high vacuum noncontact atomic force microscopy

• Jannis Lübbe,
• Matthias Temmen,
• Sebastian Rode,
• Philipp Rahe,
• Angelika Kühnle and
• Michael Reichling

Beilstein J. Nanotechnol. 2013, 4, 32–44, doi:10.3762/bjnano.4.4

• ) consists of cantilever thermal noise, tip–surface-interaction noise and instrumental noise from the detection and signal processing systems. We investigate how the displacement-noise spectral density dz at the input of the frequency demodulator propagates to the frequency-shift-noise spectral density dΔf

• of 100 Hz to 1 kHz. As the noise is transformed by the demodulator in a similar way, we define and as the frequency-shift-noise spectral density and the frequency-shift-noise power spectral density, respectively, and discuss separate noise contributions and to the frequency-shift signal Δf, as

• used in the detection system. In contrast to thermal noise, which is a fixed quantity for a given cantilever and temperature, the detection-system noise floor can be reduced by technical improvements of the detection system [3][7][8]. Frequency-shift noise The frequency demodulator of the NC-AFM system