initial layer has been transferred.142 The orientation of the sample with respect to the compressing barriers also has an influence on the quality of the deposited film.143
Figure 2.20: Lines of motion of a monolayer during deposition of Langmuir films onto a substrate aligned either parallel or perpendicular to the direction of barrier motion. Inspired by a Figure in Langmuir-Blodgett Films.102 When the monolayer material is transferred to the sample, material has to be replen-ished from the surrounding air-water interface. A sample with surfaces parallel to the barriers is better supplied by the compressed film as the barriers push the film directly to the sample (Fig. 2.20). This effect increases with growing sample size.
is then used to measure and control the tip-sample distance via a feedback circuit. As an improvement to the STM technique, G. Binning, C. Quate and C. Gerber invented the atomic force microscope (AFM) in 1985 to overcome a basic drawback with STM -it can only image conducting or semiconducting surfaces. The AFM has the advantage of imaging almost any type of surface, including polymers, ceramics, composites, glass, and biological samples. The probe consists of a very sharp tip, which is ideally only of a few atoms in size. The tip is mounted to a flexible lever. This probe is guided along the surface of the sample, only a few nanometers above. Interactions of the probe with molecules or atoms of the sample of about1 nNare used for a feedback loop to control the distance between probe and sample.154
With the invention of scanning probe microscopy, the large gap between the macro-scopic world and single-atom sensitivity has been bridged in one step. Interactions between micro-fabricated probes and the sample allow imaging, analysis and manipu-lation155 on the atomic scale.156
2.5.1 Atomic Force Microscope
The basic concept of an AFM is the measurement of forces between a sharp tip and a sample surface. Most commonly, the tip is mounted to the end of a flexible lever (cantilever) which serves as a force sensor. Either the static deflection of the cantilever or the change in its dynamic properties due to interactions between tip and surface can be exploited.156 The sample is being moved relative to the cantilever in a rectan-gular way to create an areal scan of the sample. This is usually done by piezoelectric actuators.
To detect the small bending of the cantilever due to interacting forces, the most com-monly used procedure is the beam-deflection method (Fig. 2.21).157 Thereto, a laser beam is deflected from the rear side of the cantilever and is then monitored by a position-sensitive photodiode.158 Though most of the interactions cause a bending in its normal direction, a four-segment photodiode also allows to detect torsion of the cantilever. Sensitivity of this detection technique is mainly limited due to the thermal noise of the cantilever.159
Other methods can be used to detect the cantilevers bending, like optical interfer-ometry160 or piezoelectric detection.161 In the original AFM of Binning and Gerber, electron tunneling was used.162 There, a STM tip is placed above the cantilever to de-tect tunneling current from the cantilever to the STM tip, which varies in dependence of the cantilevers bending.
Figure 2.21: Schematic of the laser beam deflection method, used in an AFM. The cantilever deflection and torsion are measured using a four-quadrant photo diode, while the sample is scanned. The feedback system is shown by solid lines. The actual deflection signal of the photo diode is compared with the set point chosen by the user. The resulting error signal is fed into the controller, which moves the z-position of the scanner in order to minimize the deflection signal. Figure provided by N. Biere, Bielefeld University, Germany.
Detection of the cantilevers deflection is essential to control the z-position of the tip in relation to the sample. While the lateral motion of the cantilever is usually performed line-by-line, resulting in rectangular frames, the z-position is controlled by a closed-loop feedback system. In the simplest case, the difference between the actual bending of the cantilever and a preset setpoint is used to correct the tip-sample distance.
2.5.2 Forces
Two relevant force regimes must be considered, when operating an AFM tip in close contact to a surface. Short-range forces between tip and sample from the overlap of electron wave functions, resulting from the Pauli exclusion principle, which is stating that two electrons cannot occupy the same quantum state within a quantum system simultaneously.163
Though this kind of forces are generally repulsive, they can be attractive, when the sum of electron waves reduces the total energy (Fig. 2.22). These situations are comparable to molecular bondings. Attractive forces of this kind are in the order of 0.5–1 nN per interacting atom.156
The decay length of such forces is of around 0.05 nm for metallic adhesion, and 2 nm for covalent bonding.164 Secondly, van der Waals interactions are long-range forces with dipole-dipole character. These dipoles arise from fluctuations, which generate further dipoles in their environment that are induced by the electric field of the first dipole generation.165 They are always present and attract even chemically inert noble gas atoms. Van der Waals forces in the vacuum are in the range of 2 nN for a tip of 30 nm in radius and a tip-sample distance of0.5 nm.166 The medium between tip and sample has a high influence on the van der Waals forces, as they are greatly reduced, if the dielectric constant and the refractive index of the medium is close to the value of the tip and sample. For most solid materials, this is the case when immersing tip and sample in water.156
Figure 2.22: A Lennard-Jones potential. The AFM will operate in the attractive or the repulsive mode, depending on the part of the curve the AFM tip is held. Inspired by a Figure in Merindol.167
Finally, electrostatic forces can appear between localized charges on insulating tips and samples. They are very likely to occur by cleavage preparation, which is a com-mon technique to get fresh samples of sheet-like arranged material such as graphite.
Measurement in aqueous solutions with high salt concentrations are a way to reduce electrostatic repulsion, due to the shielding of ions in the water.168
2.5.3 Imaging Modes
The desired topographic information can be generated by a multitude of different operational modes. These can mainly be divided into static and dynamic modes. In the simplest case of a static mode, the scanner of the microscope maintains a fixed height of the cantilever. That way, the deflection of the cantilever reflects the topography of the sample. The main advantage of this constant height mode is high scanning speed which is only limited by the inertia of the tip.169 As a drawback, samples must be sufficiently smooth. Inconstant force mode of operation the deflection of the cantilever is maintained by the feedback circuitry on the preset value. That way, the vertical displacement of the scanner reflects the topography of the sample. However, scanning speed is limited to the response time of the feedback system.170 Both modes are associated with the so calledcontact mode. The sample and the tip are in physical contact and repulsive forces from the Pauli exclusion principle are dominating. Because these forces are proportional to z−12, with z being the sample-tip distance, vertical resolution of contact mode is paramount and can reach values down to 0.01 nm,171 mainly limited by the thermal noise of the deflection detection system.172, 173
However, lateral resolution of AFM is largely limited by the geometry of the tip. With a tip radius of 2 nm, a lateral resolution of approximately 0.4 nm is achievable.172 Investigations of biological or fragile samples using the contact mode are possible, but require certain precautions due to the risk of damage.174, 175
In the dynamic mode, the cantilever is excited to oscillate using a piezo actuator, and the tip is made to strike the surface on each oscillation. The driving frequency is usually close to the resonance frequency of the cantilever, with an amplitude of 20 to 100 nm.176 Interactions of tip and sample are registered by changes of vibrational properties of the cantilever. These properties include the eigenfrequency, the oscillation amplitude and the phase between excitation and oscillation of the cantilever.156 A change of the resonance frequency can be measured directly in the so called frequency modulation mode (FM). The change of the resonance frequency leads to a change of the vibration amplitude and of the phase between excitation and oscillation, which can be measured in the amplitude modulation mode (AM).177 Due to intermittent contact with the sample during measurement, this method is calledtapping mode and was first demonstrated in 1993.178 Through the short-time contact of sample and tip, repulsive forces dominate the acting potential and enable high resolution (Fig. 2.22).179 Lateral forces are greatly reduced, compared to the contact mode, because drag across the surface is minimized.156 In comparison to contact mode, less damage is done to the
sample, due to the short duration of the applied force onto the sample. In fact, tapping mode is even suitable for visualizing supported lipid bilayers in liquid medium,180 or molecules that are weakly attached to a surface.181
The tapping mode generates several channels of data, that can be used to gain infor-mation about the sample. The most important channel is the topographic inforinfor-mation, which is generated from the feedback signal. There, the perturbation on the oscillation amplitude is detected. The height variation is adjusted with the feedback to maintain the setpoint at a constant value.
Another important data channel results from the phase of the cantilevers oscillation with respect of its driving oscillator. Surface rigidity and adhesion can affect the phase shift. Therefore, the phase image is sensitive to those properties, which are not visible in the height image. It allows chemical mapping of surfaces based on such material differences.182