Jannis Lübbe

Achieving high effective Q-factors in ultra-high vacuum dynamic force microscopy

The effective Q-factor of the cantilever is one of the most important figures-of-merit for a non-contact atomic force microscope (NC-AFM) operated in ultra-high vacuum (UHV). We provide a comprehensive discussion of all effects influencing the Q-factor and compare measured Q-factors to results from simulations based on the dimensions of the cantilevers. We introduce a methodology to investigate in detail how the effective Q-factor depends on the fixation technique of the cantilever. Fixation loss is identified as a most important contribution in addition to the hitherto discussed effects and we describe a strategy for avoiding fixation loss and obtaining high effective Q-factors in the force microscope. We demonstrate for room temperature operation, that an optimum fixation yields an effective Q-factor for the NC-AFM measurement in UHV that is equal to the intrinsic value of the cantilever.

Improvement of a dynamic scanning force microscope for highest resolution imaging in ultrahigh vacuum

We report on a modification of a commercial scanning force microscope (Omicron UHV AFM/STM) operated in noncontact mode (NC-AFM) at room temperature in ultrahigh vacuum yielding a decrease in the spectral noise density from 2757 to 272 fm/Hz. The major part of the noise reduction is achieved by an exchange of the originally installed light emitting diode by a laser diode placed outside the vacuum, where the light is coupled into the ultrahigh vacuum chamber via an optical fiber. The setup is further improved by the use of preamplifiers having a bandpass characteristics tailored to the cantilever resonance frequency. The enhanced signal to noise ratio is demonstrated by a comparison of atomic resolution images on CeO(2)(111) obtained before and after the modification.

Measurement and modelling of non-contact atomic force microscope cantilever properties from ultra-high vacuum to normal pressure conditions

The resonance frequency and Q-factor of cantilevers typically used for non-contact atomic force microscopy (NC-AFM) are measured as a function of the ambient pressure varied from 10−8 mbar to normal pressure. The Q-factor is found to be almost constant up to a pressure in the range of 10−2–10−1 mbar and then decreases by about three orders of magnitude when increasing the pressure further to normal pressure. The decrease in the resonance frequency measured over the same pressure range amounts to less than 1% where a significant change is observed in the range of 10–103 mbar. The pressure dependence of the effective Q-factor and resonance frequency is approximated by analytical models accounting for different processes in the molecular and viscous flow regimes. By introducing a heuristic approach for describing the pressure dependence in the transition regime, we are able to well approximate the cantilever properties over the entire pressure range.

Modification of a commercial atomic force microscopy for low-noise, high-resolution frequency-modulation imaging in liquid environment

A key issue for high-resolution frequency-modulation atomic force microscopy imaging in liquids is minimizing the frequency noise, which requires a detailed analysis of the corresponding noise contributions. In this paper, we present a detailed description for modifying a commercial atomic force microscope (Bruker MultiMode V with Nanoscope V controller), aiming at atomic-resolution frequency-modulation imaging in ambient and in liquid environment. Care was taken to maintain the AFMs original stability and ease of operation. The new system builds upon an optimized light source, a new photodiode and an entirely new amplifier. Moreover, we introduce a home-built liquid cell and sample holder as well as a temperature-stabilized isolation chamber dedicated to low-noise imaging in liquids. The success of these modifications is measured by the reduction in the deflection sensor noise density from initially 100 fm/√Hz to around 10 fm/√Hz after modification. The performance of our instrument is demonstrated by atomically resolved images of calcite taken under liquid conditions.

Precise determination of force microscopy cantilever stiffness from dimensions and eigenfrequencies

We demonstrate the non-destructive measurement of the stiffness of single-beam, monocrystalline silicon cantilevers with a trapezoidal cross-section and tips as used for atomic force microscopy from the knowledge of cantilever dimensions, eigenfrequencies and material parameters. This yields stiffness values with an uncertainty of ±25% as the result critically depends on the thickness of the cantilever that is experimentally difficult to determine. The uncertainty is reduced to ±7% when the measured fundamental eigenfrequency is included in the calculation and a tip mass correction is applied. The tip mass correction can be determined from the eigenfrequencies of the fundamental and first harmonic modes. Results are verified by tip destructive measurements of the stiffness with a precision instrument recording a force–bending curve yielding an uncertainty better than ±5%.

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

Summary The noise of the frequency-shift signal Δf in noncontact atomic force microscopy (NC-AFM) 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 d z at the input of the frequency demodulator propagates to the frequency-shift-noise spectral density d Δ f at the demodulator output in dependence of cantilever properties and settings of the signal processing electronics in the limit of a negligible tip–surface interaction and a measurement under ultrahigh-vacuum conditions. For a quantification of the noise figures, we calibrate the cantilever displacement signal and determine the transfer function of the signal-processing electronics. From the transfer function and the measured d z, we predict d Δ f for specific filter settings, a given level of detection-system noise spectral density d z ds and the cantilever-thermal-noise spectral density d z th. We find an excellent agreement between the calculated and measured values for d Δ f. Furthermore, we demonstrate that thermal noise in d Δ f, defining the ultimate limit in NC-AFM signal detection, can be kept low by a proper choice of the cantilever whereby its Q-factor should be given most attention. A system with a low-noise signal detection and a suitable cantilever, operated with appropriate filter and feedback-loop settings allows room temperature NC-AFM measurements at a low thermal-noise limit with a significant bandwidth.

Determining cantilever stiffness from thermal noise

Summary We critically discuss the extraction of intrinsic cantilever properties, namely eigenfrequency f n, quality factor Q n and specifically the stiffness k n of the nth cantilever oscillation mode from thermal noise by an analysis of the power spectral density of displacement fluctuations of the cantilever in contact with a thermal bath. The practical applicability of this approach is demonstrated for several cantilevers with eigenfrequencies ranging from 50 kHz to 2 MHz. As such an analysis requires a sophisticated spectral analysis, we introduce a new method to determine k n from a spectral analysis of the demodulated oscillation signal of the excited cantilever that can be performed in the frequency range of 10 Hz to 1 kHz regardless of the eigenfrequency of the cantilever. We demonstrate that the latter method is in particular useful for noncontact atomic force microscopy (NC-AFM) where the required simple instrumentation for spectral analysis is available in most experimental systems.

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

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 D Δ f(f m) 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 D Δ f(f m) 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.