Investigating Atomic Details of the CaF2_2(111) Surface with a qPlus Sensor

The (111) surface of CaF$_2$ has been intensively studied with large-amplitude frequency-modulation atomic force microscopy and atomic contrast formation is now well understood. It has been shown that the apparent contrast patterns obtained with a polar tip strongly depend on the tip terminating ion and three sub-lattices of anions and cations can be imaged. Here, we study the details of atomic contrast formation on CaF$_2$(111) with small-amplitude force microscopy utilizing the qPlus sensor that has been shown to provide utmost resolution at high scanning stability. Step edges resulting from cleaving crystals in-situ in the ultra-high vacuum appear as very sharp structures and on flat terraces, the atomic corrugation is seen in high clarity even for large area scans. The atomic structure is also not lost when scanning across triple layer step edges. High resolution scans of small surface areas yield contrast features of anion- and cation sub-lattices with unprecedented resolution. These contrast patterns are related to previously reported theoretical results.Comment: 18 pages, 9 Figures, presented at 7th Int Conf Noncontact AFM Seattle, USA Sep 12-15 2004, accepted for publication in Nanotechnology, http://www.iop.or

Probing the shape of atoms in real space

The structure of single atoms in real space is investigated by scanning tunneling microscopy. Very high resolution is possible by a dramatic reduction of the tip-sample distance. The instabilities which are normally encountered when using small tip-sample distances are avoided by oscillating the tip of the scanning tunneling microscope vertically with respect to the sample. The surface atoms of Si(111)-(7 x 7) with their well-known electronic configuration are used to image individual samarium, cobalt, iron and silicon atoms. The resulting images resemble the charge density corresponding to 4f, 3d and 3p atomic orbitals.Comment: Submitted to Phys. Rev. B, 17 pages, 7 figure

Attempts to test an alternative electrodynamic theory of superconductors by low-temperature scanning tunneling and atomic force microscopy

We perform an experiment to test between two theories of the electrodynamics of superconductors: the standard London theory and an alternative proposed by J. E. Hirsch [Phys. Rev. B 69, 214515 (2004)]. The two alternatives give different predictions with respect to the screening of an electric field by a superconductor, and we try to detect this effect using atomic force microscopy on a niobium sample. We also perform the reverse experiment, where we demonstrate a superconductive tip mounted on a qPlus force sensor. Due to limited accuracy, we are able neither to prove nor to disprove Hirsch's hypothesis. Within our accuracy of 0.17 N/m, the superconductive transition does not alter the atomic-scale interaction between tip and sample.Comment: 7 pages, 5 figures. Minor amendment

Electron scattering in atomic force microscopy experiments

It has been shown that electron transitions, as measured in a scanning tunnelling microscope (STM), are related to chemical interactions in a tunnelling barrier. Here, we show that the shape and apparent height of subatomic features in an atomic force microscopy (AFM) experiment on Si(111) depend directly on the available electron states of the silicon surface and the silicon AFM tip. Simulations and experiments confirm that forces and currents show similar subatomic variations for tip-sample distances approaching the bulk bonding length.Comment: 5 pages and 4 figure

Localization of the phantom force induced by the tunneling current

The phantom force is an apparently repulsive force, which can dominate the atomic contrast of an AFM image when a tunneling current is present. We described this effect with a simple resistive model, in which the tunneling current causes a voltage drop at the sample area underneath the probe tip. Because tunneling is a highly local process, the areal current density is quite high, which leads to an appreciable local voltage drop that in turn changes the electrostatic attraction between tip and sample. However, Si(111)-7×7 has a metallic surface state and it might be proposed that electrons should instead propagate along the surface state, as through a thin metal film on a semiconducting surface, before propagating into the bulk. In this paper, we first measure the phantom force on a sample that displays a metallic surface state [here, Si(111)-7×7] using tips with various radii. If the metallic surface state would lead to a constant electrostatic potential on the surface, we would expect a direct dependence of the phantom force with tip radius. In a second set of experiments, we study H/Si(100), a surface that does not have a metallic surface state. We conclude that a metallic surface state does not suppress the phantom force, but that the local resistance Rs has a strong effect on the magnitude of the phantom force

Application of the equipartition theorem to the thermal excitation of quartz tuning forks

The deflection signal of a thermally excited force sensor of an atomic force microscope can be analyzed to gain important information about the detector noise and about the validity of the equipartion theorem of thermodynamics. Here, we measured the temperature dependence of the thermal amplitude of a tuning fork and compared it to the expected values based on the equipartition theorem. In doing so, we prove the validity of these assumptions in the temperature range from 140K to 300K. Furthermore, the application of the equipartition theorem to quartz tuning forks at liquid helium temperatures is discussed.Comment: 8 pages, 3 figures, published in Applied Physics Letter

Molecular Dynamics Simulations of Dynamic Force Microscopy: Applications to the Si(111)-7x7 Surface

Molecular dynamics simulations have been performed to understand true atomic resolution, which has been observed on the Si(111)-7$\times$7 surface by dynamic force microscopy in ultra high vacuum(UHV). Stable atomic-scale contrast is reproduced in simulations at constant mean height above a critical tip-sample separation when monitoring the interaction force between tip and sample. Missing or additional adatoms can be recognized in such scans, although they are less well resolved than native adatoms. The resonance frequency shift, as well as arbitrary scans, e.g. at constant force can be computed from a series of force-distance characteristics. By means of dynamic simulations we show how energy losses induced by interaction with an oscillating tip can be monitored and that they occur even in the non-contact range.Comment: 5 pages, 5 figures, accepted publication in Applied Surface Scienc

Searching atomic spin contrast on nickel oxide (001) by force microscopy

The (001) surface of NiO, an antiferromagnet at room temperature, was investigated under ultra-high vacuum conditions with frequency modulation atomic force microscopy (FM-AFM). The antiferromagnetic coupling between ions leads to a spin superstructure on (001) surfaces. Exchange interaction between the probe of a force microscope and the NiO (001) surface should allow to image spin superstructures in real space. The surface was imaged with three different probing tips: nonmagnetic W tips, ferromagnetic Co tips and antiferromagnetic NiO tips - and atomic resolution was achieved with all three of them in various distance regimes and in several channels. Evidence for spin contrast was obtained in experiments that utilize NiO tips and oscillation amplitudes in the \AA-regime, where optimal signal-to-noise ratio is expected. The spin contrast is weaker than expected and only visible in Fourier space images.Comment: 7 pages, 6 figures, submitted to Physical Review

A comparsion of force sensors for atomic force microscopy based on quartz tuning forks and length extensional resonators

The force sensor is key to the performance of atomic force microscopy (AFM). Nowadays, most AFMs use micro-machined force sensors made from silicon, but piezoelectric quartz sensors are applied at an increasing rate, mainly in vacuum. These self sensing force sensors allow a relatively easy upgrade of a scanning tunneling microscope to a combined scanning tunneling/atomic force microscope. Two fundamentally different types of quartz sensors have achieved atomic resolution: the 'needle sensor' that is based on a length extensional resonator and the 'qPlus sensor' that is based on a tuning fork. Here, we calculate and measure the noise characteristics of these sensors. We find four noise sources: deflection detector noise, thermal noise, oscillator noise and thermal drift noise. We calculate the effect of these noise sources as a factor of sensor stiffness, bandwidth and oscillation amplitude. We find that for self sensing quartz sensors, the deflection detector noise is independent of sensor stiffness, while the remaining three noise sources increase strongly with sensor stiffness. Deflection detector noise increases with bandwidth to the power of 1.5, while thermal noise and oscillator noise are proportional to the square root of the bandwidth. Thermal drift noise, however, is inversely proportional to bandwidth. The first three noise sources are inversely proportional to amplitude while thermal drift noise is independent of the amplitude. Thus, we show that the earlier finding that quoted optimal signal-to-noise ratio for oscillation amplitudes similar to the range of the forces is still correct when considering all four frequency noise contributions. Finally, we suggest how the signal-to-noise ratio of the sensors can be further improved and briefly discuss the challenges of mounting tips.Comment: 40 pages, 14 figure