Subsurface contrast due to friction in heterodyne force microscopy.

The nondestructive imaging of subsurface structures on the nanometer scale has been a long-standing desire in both science and industry. A few impressive images were published so far that demonstrate the general feasibility by combining ultrasound with an atomic force microscope. From different excitation schemes, heterodyne force microscopy seems to be the most promising candidate delivering the highest contrast and resolution. However, the physical contrast mechanism is unknown, thereby preventing any quantitative analysis of samples. Here we show that friction at material boundaries within the sample is responsible for the contrast formation. This result is obtained by performing a full quantitative analysis, in which we compare our experimentally observed contrasts with simulations and calculations. Surprisingly, we can rule out all other generally believed responsible mechanisms, like Rayleigh scattering, sample (visco)elasticity, damping of the ultrasonic tip motion, and ultrasound attenuation. Our analytical description paves the way for quantitative subsurface-AFM imaging.

Subsurface-AFM: sensitivity to the heterodyne signal.

Applying heterodyne force microscopy (HFM), it has been impressively demonstrated that it is possible to obtain subsurface information: 20 nm large gold nanoparticles that were buried 500 nm deep have been imaged. It is the heterodyne signal that contains the subsurface information. We elucidate, both theoretically and experimentally, the sensitivity to the heterodyne signal as a function of the tip-sample distance. This is crucial information for experiments as the distance, and therefore the sensitivity, is tunable. We show that the amplitude of the heterodyne signal has a local maximum in the attractive part of the tip-sample interaction, before it surprisingly reaches an even higher plateau, when the tip-sample interaction is repulsive. This can only be explained by a non-decreasing amplitude of the ultrasonic motion of the tip, although it is in full contact with the surface. We confirm this counterintuitive tip behavior experimentally even on a hard surface like silicon.

Subsurface atomic force microscopy: towards a quantitative understanding.

Recent experiments in the field of subsurface atomic force microscopy have demonstrated that it is possible to nondestructively image micro- and even nanoparticles that are embedded significantly deep within the bulk of a sample. In order to get insights into the contrast formation mechanism, we performed a finite element analysis and an analytical study, in which we calculated the amplitude and phase variation on the surface of an ultrasound wave that has traveled through the sample. Our calculations were performed as closely as possible to the situation in the experiments to enable a (future) comparison based on our predictions. We show that Rayleigh scattering of acoustic waves accounts for the measured contrast and we verify the characteristic Rayleigh dependences. The numerical results show that the contrast is independent of the depth at which a particle is buried, whereas the analytical study reveals a 1/depth dependence. In addition, we find a large deviation in the width of the particle in the contrast at the surface when applying the numerical or the analytical calculation respectively. These results indicate the importance of both the reflections of sound waves at the sample interfaces and bulk damping, as both are treated differently in our two models.

Fast and reliable pre-approach for scanning probe microscopes based on tip-sample capacitance.

Within the last three decades Scanning Probe Microscopy has been developed to a powerful tool for measuring surfaces and their properties on an atomic scale such that users can be found nowadays not only in academia but also in industry. This development is still pushed further by researchers, who continuously exploit new possibilities of this technique, as well as companies that focus mainly on the usability. However, although imaging has become significantly easier, the time required for a safe approach (without unwanted tip-sample contact) can be very time consuming, especially if the microscope is not equipped or suited for the observation of the tip-sample distance with an additional optical microscope. Here we show that the measurement of the absolute tip-sample capacitance provides an ideal solution for a fast and reliable pre-approach. The absolute tip-sample capacitance shows a generic behavior as a function of the distance, even though we measured it on several completely different setups. Insight into this behavior is gained via an analytical and computational analysis, from which two additional advantages arise: the capacitance measurement can be applied for observing, analyzing, and fine-tuning of the approach motor, as well as for the determination of the (effective) tip radius. The latter provides important information about the sharpness of the measured tip and can be used not only to characterize new (freshly etched) tips but also for the determination of the degradation after a tip-sample contact/crash.

Resonance frequencies of AFM cantilevers in contact with a surface.

To make the forces in an Atomic Force Microscope that operates in a dynamic mode with one or multiple vibrations applied to the cantilever, quantitative, one needs to relate a change in resonance frequency of the cantilever to a specific tip-sample interaction. Due to the time dependence of the force between the tip and sample caused by the vibrations, this task is not only difficult, but in fact only possible to solve for certain limiting cases, if one follows common theoretical approaches with a Taylor expansion around the deflection point. Here, we present an analytical method for calculating the resonance frequencies of the cantilever that is valid for any tip-sample interaction. Instead of linearizing the tip-sample interaction locally, we calculate an averaged, weighted linearization taking into account all positions of the tip while vibrating. Our method bridges, therefore, the difficult gap between a free oscillating cantilever and a cantilever that is pushed infinitely hard into contact with a surface, which describes a clamped-pinned boundary condition. For a correct description of the cantilever dynamics, we take into account both the tip mass and the tip moment of inertia. Applying our model, we show that it is possible to calculate the modal response of a cantilever as a function of the tip-sample interaction strength. Based on these modal vibration characteristics, we show that the higher resonance frequencies of a cantilever are completely insensitive to the strength of the tip-sample interaction.

Beating beats mixing in heterodyne detection schemes.

Heterodyne detection schemes are widely used to detect and analyse high-frequency signals, which are unmeasurable with conventional techniques. It is the general conception that the heterodyne signal is generated only by mixing and that beating can be fully neglected, as it is a linear effect that, therefore, cannot produce a heterodyne signal. Deriving a general analytical theory, we show, in contrast, that both beating and mixing are crucial to explain the heterodyne signal generation. Beating even dominates the heterodyne signal, if the nonlinearity of the mixing element (mixer) is of higher order than quadratic. The specific characteristic of the mixer determines its sensitivity for beating. We confirm our results with both a full numerical simulation and an experiment using heterodyne force microscopy, which represents a model system with a highly non-quadratic mixer. As quadratic mixers are the exception, many results of previously reported heterodyne measurements may need to be reconsidered.

A subsurface add-on for standard atomic force microscopes.

The application of ultrasound in an Atomic Force Microscope (AFM) gives access to subsurface information. However, no commercially AFM exists that is equipped with this technique. The main problems are the electronic crosstalk in the AFM setup and the insufficiently strong excitation of the cantilever at ultrasonic (MHz) frequencies. In this paper, we describe the development of an add-on that provides a solution to these problems by using a special piezo element with a lowest resonance frequency of 2.5 MHz and by separating the electronic connection for this high frequency piezo element from all other connections. In this sense, we support researches with the possibility to perform subsurface measurements with their existing AFMs and hopefully pave also the way for the development of a commercial AFM that is capable of imaging subsurface features with nanometer resolution.

Improving the accuracy of walking piezo motors.

Many application areas require ultraprecise, stiff, and compact actuator systems with a high positioning resolution in combination with a large range as well as a high holding and pushing force. One promising solution to meet these conflicting requirements is a walking piezo motor that works with two pairs of piezo elements such that the movement is taken over by one pair, once the other pair reaches its maximum travel distance. A resolution in the pm-range can be achieved, if operating the motor within the travel range of one piezo pair. However, applying the typical walking drive signals, we measure jumps in the displacement up to 2.4 µm, when the movement is given over from one piezo pair to the other. We analyze the reason for these large jumps and propose improved drive signals. The implementation of our new drive signals reduces the jumps to less than 42 nm and makes the motor ideally suitable to operate as a coarse approach motor in an ultra-high vacuum scanning tunneling microscope. The rigidity of the motor is reflected in its high pushing force of 6.4 N.

Cantilever dynamics in Heterodyne Force Microscopy.

Experiments in Heterodyne Force Microscopy (HFM) show the possibility to image deeply buried nanoparticles below a surface. However, the contrast mechanism and the motion of the cantilever, which detects the subsurface signal, are not yet understood. We present a numerical study of the cantilever motion in different HFM modes using realistic tip-sample interactions. The results provide information on the sensitivity to the heterodyne signal. The parameters in our calculations are chosen as closely as possible to the situation in real experiments to enable (future) comparisons based on our predictions. In HFM both the tip and the sample are excited at slightly different ultrasonic frequencies such that a difference frequency is generated that can contain subsurface information. We calculate the amplitude and phase of the difference frequency generated by the motion of the cantilever. The amplitude shows a local maximum in the attractive Van-der-Waals regime and an even higher plateau in the repulsive regime. The phase shifts 180° or 90°, depending on the mode of operation. Finally, we observe oscillations in both the amplitude and the phase of the difference frequency, which are caused by a shift of the resonance frequency of the cantilever and an involved transient behavior.

Design of a high-speed electrochemical scanning tunneling microscope.

In this paper, we present a bottom-up approach to designing and constructing a high-speed electrochemical scanning tunneling microscope (EC-STM). Using finite element analysis (FEA) calculations of the frequency response of the whole mechanical loop of the STM, we analyzed several geometries to find the most stable one that could facilitate fast scanning. To test the FEA results, we conducted measurements of the vibration amplitudes using a prototype STM setup. Based on the FEA analysis and the measurement results, we identified the potentially most disturbing vibration modes that could impair fast scanning. By modifying the design of some parts of the EC-STM, we reduced the amplitudes as well as increased the resonance frequencies of these modes. Additionally, we designed and constructed an electrochemical flow-cell that allows STM imaging in a flowing electrolyte, and built a bi-potentiostat to achieve electrochemical potential control during the measurements. Finally, we present STM images acquired during high-speed imaging in air as well as in an electrochemical environment using our newly-developed EC-STM.

In situ real-time observation of thin film deposition: roughening, zeno effect, grain boundary crossing barrier, and steering.

We report on the first atomic-scale real-time in situ investigation of the growth of a polycrystalline gold film during its deposition performed with a scanning tunneling microscope. Continuously scanning while depositing the film enables the direct observation of atomic processes. The grain boundaries play a crucial role in the evolving film structure, as they initiate mound formation, thereby significantly increasing the film roughness. A possible additional roughness increase comes from atom steering, which also can delay the film closure in the early stages during film growth.

How asymmetric islands become symmetric.

Scanning tunneling microscopy reveals that sputtering of the Au(110) surface results in the formation of vacancy islands with a broken mirror symmetry. These islands exhibit two types of steps on opposite sides: a lower energy (111) step and a higher energy (331) step. We analyze the thermal fluctuations and especially the kink distribution of such vacancy islands. Despite the broken symmetry, which they adopt internally, these islands show a symmetric average outer contour. Their coarsening proceeds via a variety of pathways, often leading to new, symmetric structures, with exclusively (111) steps. The lowest energy vacancy configuration is a bound pair of two vacancy lines or islands.

Grains, growth, and grooving.

We report the in situ investigation of grain growth and grain boundary migration, performed with a variable-temperature scanning tunneling microscope (STM) on a polycrystalline gold film. Atomic step resolution allowed us to identify the individual grains and, thus, also the grain boundaries. Our special, thermal-drift-compensated STM design made it possible to follow the same sample area over large temperature intervals. In this way, we have directly observed grain boundary migration and grain growth. In a first quantitative analysis we correlate the observed, unexpected changes in surface roughness with the evolution of the grain and grain boundary configuration.