The main drawback of STM is the need of a conductive sample. This was circumvented soon after the development of the STM, with the invention of the atomic force microscope (AFM) by Binnig, Quate and Gerber [41] in 1985. Nowadays the AFM is by far the most commonly used of the scanning probes microscopes (SPM). It is a highly versatile SPM, with the advantage of imaging almost any type of surface, including polymers, ceramics, composites, glass, and biological samples [42].
The backbone of the AFM working principle is the sensing of the interaction forces between a sharp tip and a sample. A constant force is maintained between the probe and sample with the help of a feedback control unit, while the tip is raster–scanned across the surface. Different kind of forces can be measured with AFM such as, mechanical contact, Van der Waals, capillary, chemical bonding, electrostatic, magnetic, Casimir, etc. [43].
Fig. 2.6:Potential energy diagram of the interaction force between tip and sample vs separation distance.
In the AFM, the force is not measured directly. The tip is mounted at the end of a cantilever, which acts as a spring. Depending on the nature of the interaction and the separation distance, the tip is repelled by or attracted to the surface (Fig. 2.6), leading to a deflection of the cantilever.
Several detection schemes have been developed for measuring the amplitude of deflection. The preferred detection method is based on a position–sensitive array of photodiodes that records the angle of reflection of a laser beam focused on the top of the cantilever (Fig. 2.7).
During scanning, changes in the deflection of the cantilever are produced due to the surface topography. As a consequence, the reflection plane for the laser beam changes and thus its position on the photodiode. The change in the signal between the segments of the photodiode is a sensitive measure for the deflection of the cantilever.
By measuring the deflection of the cantilever, and knowing its stiffnessk, in a first approxi-mation, the force can be obtained using Hook’s law as
F =−kz (2.17)
2.3. ATOMIC FORCE MICROSCOPY 25 whereFis the force andzis the distance which the cantilever is bent.
A topographic image of the sample is obtained by plotting the deflection of the cantilever versus its position on the sample. Nowadays, micro–fabricated cantilevers (Silicon Nitride or single crystal Silicon) with spring constants of less than 0.1 N/m and resonance frequencies of more than 100 kHz are commercially available, allowing measurement at forces typically in the range from 1 nN (in liquids) to 100 nN (in air).
Measuring the force with the cantilever in the AFM can be achieved in a static and a dynamic mode. In the first mode, the deflection of the cantilever is directly measured. In the second mode, the cantilever is vibrated and changes in the vibration properties are recorded.
Fig. 2.7:Working principle of an AFM with an optical detection array of photodiodes. The contact mode image corresponds to Polyethylene crystals on mica [44]. The image size is 1µm x 1µm. The tapping mode image corresponds to Graphite [45]. Image size 2 nm x 2nm.
In the static mode, the tip is usually maintained at a constant force by adjusting the distance between tip and sample, while scanning. Since the typical surface–tip interactions are often less than one nano–newton, the tip is softly touching the surface; for this reason this mode is often called „contact “ mode.
In the „non–contact“ mode the tip is oscillated above the surface by a piezoelectric oscil-lator, close to its resonance frequency. The cantilever position is kept in the attractive regime (Van der Waals forces), meaning that the tip is quite close to the sample, but not touching it.
When the vibrating cantilever comes close to the surface (≈50–100 Å), the oscillation ampli-tude, phase and resonance frequency are modified by tip–sample interaction forces, in response to force gradients from the sample. In this way changes in the oscillation properties in respect to the external reference oscillation, provide information about the sample’s characteristics.
26 CHAPTER 2. EXPERIMENTAL METHODS The „dynamic contact mode “ (also called intermittent contact or „tapping mode “) was de-veloped in order to achieve higher resolution under ambient conditions. In the „tapping mode
“, the cantilever is oscillated in such a way, that it comes in contact with the sample within each cycle. To avoid dragging the tip across the surface, enough restoring force is provided by the cantilever spring to detach it from the sample. As the oscillating cantilever begins to intermit-tently contact the surface, the oscillation is necessarily reduced due to energy losses caused by the tip contacting the surface. Variations in the measured oscillation amplitude and phase are also indicators, in this case, of the tip–sample interaction.
In contrast to STM, AFM images can be directly interpreted as surface topography infor-mation both on the large and atomic scale. In the ideal situation, in which the tip is a dimen-sionless point and the piezos are perfectly linear, the image faithfully reproduces the surface topography. Thus, in a first order approximation, the influence of electronic inhomogeneities on the image features can be neglected. This property makes the AFM an effective tool for determining surface roughness or for the measurement of width, height and depth of individual nanostructures. Recently, with the use of lock–in techniques at low temperatures [46], high resolution images of the Ge(105)-1x2 surface formed on the Si(105) substrate have been achie-ved. „Non–contact“ AFM image shown in Fig. 2.8c reveals all dangling bonds on the surface, independently of any electronic contribution. For comparison, two STM images taken at nega-tive (Fig. 2.8a) and posinega-tive (Fig. 2.8b) bias voltage are also shown. The strong dependance on the bias voltage is evident for the STM images. The rebonded–step (RS) model of this surface is superimposed on the right image. Furthermore, chemical identification of individual surface atoms by means of AFM under dynamical mode has been possible at room temperature, with the use of a force normalization calibration method [47] (Fig. 2.8d).
Fig. 2.8:On the left: High resolution images of Ge/ Si(105) taken with a) a STM at negative bias voltage, b) a STM at positive bias voltage and c) a non–contact AFM at low temperature [46]. On the right:
chemical composition of Pb and Sn on Si(111). The color assignment of the atoms was given, among other measurements, through the maximum attractive total force obtained in the experiments [47].
In this work, all the AFM images were taken in tapping mode at room temperature. A
2.4. MOLECULAR BEAM EPITAXY 27