Images and force measurements taken by an atomic‐force microscope (AFM) depend greatly on the properties of the spring and tip used to probe the sample’s surface. In this article, we describe a simple, nondestructive procedure for measuring the force constant, resonant frequency, and quality factor of an AFM cantilever spring and the effective radius of curvature of an AFM tip. Our procedure uses the AFM itself and does not require additional equipment.

Calibration of atomic‐force microscope tips

1. Introduction 2. Theoretical foundations 3. Propagation and focusing of optical fields 4. Spatial resolution and position accuracy 5. Nanoscale optical microscopy 6. Near-field optical probes 7. Probe-sample distance control 8. Light emission and optical interaction in nanoscale environments 9. Quantum emitters 10. Dipole emission near planar interfaces 11. Photonic crystals and resonators 12. Surface plasmons 13. Forces in confined fields 14. Fluctuation-induced phenomena 15. Theoretical methods in nano-optics Appendices Index.

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Principles of nano-optics

http://experimentationlab.berkeley.edu/sites/default/files/AFMImages/butt_AFM.pdf

Force measurements with the atomic force microscope: Technique, interpretation and applications

Molecular self-assembly presents a `bottom-up' approach to the fabrication of objects specified with nanometre precision. DNA
 molecular structures and intermolecular interactions are particularly
 amenable to the design and synthesis of complex molecular objects. We
 report the design and observation of two-dimensional crystalline forms
 of DNA that self-assemble from synthetic DNA double-crossover
 molecules. Intermolecular interactions between the structural units are
 programmed by the design of `sticky ends' that associate according to
 Watson-Crick complementarity, enabling us to create specific periodic
 patterns on the nanometre scale. The patterned crystals have been
 visualized by atomic force microscopy.

https://issg.cs.duke.edu/courses/spring04/cps296.4/papers/WLWS98.pdf

Design and self-assembly of two-dimensional DNA crystals

A method to determine the spring constant of a rectangular atomic force microscope cantilever is proposed that relies solely on the measurement of the resonant frequency and quality factor of the cantilever in fluid (typically air), and knowledge of its plan view dimensions. This method gives very good accuracy and improves upon the previous formulation by Sader et al. [Rev. Sci. Instrum. 66, 3789 (1995)] which, unlike the present method, requires knowledge of both the cantilever density and thickness.

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Calibration of rectangular atomic force microscope cantilevers

Phase imaging and stiffness in tapping-mode atomic force microscopy

Tapping mode atomic force microscopy in liquids gives a substantial improvement in imaging quality and stability over standard contact mode. In tapping mode the probe‐sample separation is modulated as the probe scans over the sample. This modulation causes the probe to tap on the surface only at the extreme of each modulation cycle and therefore minimizes frictional forces that are present when the probe is constantly in contact with the surface. This imaging mode increases resolution and reduces sample damage on soft samples. For our initial experiments we used a tapping frequency of 17 kHz to image deoxyribonucleic acid plasmids on mica in water. When we imaged the same sample region with the same cantilever, the plasmids appeared 18 nm wide in contact mode and 5 nm in tapping mode.

Tapping mode atomic force microscopy in liquids

A method is presented to measure the energy dissipated by the tip–sample interaction in tapping-mode atomic force microscopy (AFM). The results show that if the amplitude of the cantilever is held constant, the sine of the phase angle of the driven vibration is then proportional to changes in the tip–sample energy dissipation. This means that images of the cantilever phase in tapping-mode AFM are closely related to maps of dissipation. The maximum dissipation observed for a 4 N/m cantilever with an initial amplitude of 25 nm tapping on a hard substrate at 74 kHz is about 0.3 pW.

Energy dissipation in tapping-mode atomic force microscopy

We present the first atomic‐resolution image of a surface obtained with an optical implementation of the atomic‐force microscope (AFM). The native oxide on silicon was imaged with atomic resolution, and ≊5‐nm resolution images of aluminum, mechanically ground iron, and corroded stainless steel were obtained. The relative merits of an optical implementation of the AFM as opposed to a tunneling implementation are discussed.

An atomic-resolution atomic-force microscope implemented using an optical lever

We have designed and tested a family of silicon nitride cantilevers ranging in length from 23 to 203 μm. For each, we measured the frequency spectrum of thermal motion in air and water. Spring constants derived from thermal motion data agreed fairly well with the added mass method; these and the resonant frequencies showed the expected increase with decreasing cantilever length. The effective cantilever density (calculated from the resonant frequencies) was 5.0 g/cm3, substantially affected by the mass of the reflective gold coating. In water, resonant frequencies were 2 to 5 times lower and damping was 9 to 24 times higher than in air. Thermal motion at the resonant frequency, a measure of noise in tapping mode atomic force microscopy, decreased about two orders of magnitude from the longest to the shortest cantilever. The advantages of the high resonant frequency and low noise of a short (30 μm) cantilever were demonstrated in tapping mode imaging of a protein sample in buffer. Low‐noise images were tak...

V. Elings

Papers

Phase imaging and stiffness in tapping-mode atomic force microscopy

Tapping mode atomic force microscopy in liquids

Energy dissipation in tapping-mode atomic force microscopy

An atomic-resolution atomic-force microscope implemented using an optical lever

Short cantilevers for atomic force microscopy