Stefan Hembacher

Calculation of the optimal imaging parameters for frequency modulation atomic force microscopy

True atomic resolution of conductors and insulators is now routinely obtained in vacuum by frequency modulation atomic force microscopy. So far, the imaging parameters (i.e., eigenfrequency, stiffness and oscillation amplitude of the cantilever, frequency shift) which result in optimal spatial resolution for a given cantilever and sample have been found empirically. Here, we calculate the optimal set of parameters from first principles as a function of the tip–sample system. The result shows that the either the acquisition rate or the signal-to-noise ratio could be increased by up to two orders of magnitude by using stiffer cantilevers and smaller amplitudes than are in use today.

Revealing the hidden atom in graphite by low-temperature atomic force microscopy.

Carbon, the backbone material of life on Earth, comes in three modifications: diamond, graphite, and fullerenes. Diamond develops tetrahedral sp3 bonds, forming a cubic crystal structure, whereas graphite and fullerenes are characterized by planar sp2 bonds. Polycrystalline graphite is the basis for many products of everyday life: pencils, lubricants, batteries, arc lamps, and brushes for electric motors. In crystalline form, highly oriented pyrolytic graphite is used as a diffracting element in monochromators for x-ray and neutron scattering and as a calibration standard for scanning tunneling microscopy (STM). The graphite surface is easily prepared as a clean atomically flat surface by cleavage. This feature is attractive and is used in many laboratories as the surface of choice for “seeing atoms.” Despite the proverbial ease of imaging graphite by STM with atomic resolution, every second atom in the hexagonal surface unit cell remains hidden, and STM images show only a single atom in the unit cell. Here we present measurements with a low-temperature atomic force microscope with pico-Newton force sensitivity that reveal the hidden surface atom.

Local Spectroscopy and Atomic Imaging of Tunneling Current, Forces, and Dissipation on Graphite

Theory predicts that the currents in scanning tunneling microscopy (STM) and the attractive forces measured in atomic force microscopy (AFM) are directly related. Atomic images obtained in an attractive AFM mode should therefore be redundant because they should be similar to STM. Here, we show that while the distance dependence of current and force is similar for graphite, constant-height AFM and STM images differ substantially depending on the distance and bias voltage. We perform spectroscopy of the tunneling current, the frequency shift, and the damping signal at high-symmetry lattice sites of the graphite (0001) surface. The dissipation signal is about twice as sensitive to distance as the frequency shift, explained by the Prandtl-Tomlinson model of atomic friction.

Stability considerations and implementation of cantilevers allowing dynamic force microscopy with optimal resolution: the qPlus sensor

In frequency modulation atomic force microscopy, the stiffness, quality factor and oscillation amplitude of the cantilever are important parameters. While the first atomic resolution results were obtained with amplitudes of a few hundred angstrom, it has subsequently been shown that smaller amplitudes should result in a better signal-to-noise ratio and an increased sensitivity to the short-range components of the tip–sample interaction. Stable oscillation at small amplitudes is possible if the product of stiffness and amplitude and the energy stored in the oscillating cantilever are large enough. For small amplitudes, stability can be achieved by using stiff cantilevers. Here, we discuss the physical requirements for small amplitude operation and present design criteria and technical details of the qPlus sensor, a self-sensing cantilever with large stiffness that allows small amplitude operation.

Imaging of atomic orbitals with the Atomic Force Microscope - experiments and simulations

Atomic force microscopy (AFM) is a mechanical profiling technique that allows to image surfaces with atomic resolution. Recent progress in reducing the noise of this technique has led to a resolution level where previously undetectable symmetries of the images of single atoms are observed. These symmetries are related to the nature of the interatomic forces. The Si(111)-(7 × 7) surface is studied by AFM with various tips and AFM images are simulated with chemical and electrostatic model forces. The calculation of images from the tip-sample forces is explained in detail and the implications of the imaging parameters are discussed. Because the structure of the Si(111)-(7 × 7) surface is known very well, the shape of the adatom images is used to determine the tip structure. The observability of atomic orbitals by AFM and scanning tunneling microscopy is discussed.

Evaluation of a force sensor based on a quartz tuning fork for operation at low temperatures and ultrahigh vacuum

The noise performance of the force sensor is crucial for optimizing the resolution in non-contact atomic force microscopy. Sensing forces in vacuum and low temperatures is even more demanding than at ambient conditions. Here we analyze the noise performance and the sensitivity of a force sensor based on a quartz tuning fork of which one of the prongs is fixed (qPlus sensor). The noise characteristic of the qPlus sensor, optical and piezoresistive detection schemes at room temperature are compared and the qPlus sensor is investigated at low temperatures. The frequency variation of quartz tuning forks as a function of temperature is experimentally determined for the temperature range from 4 to 300 K.