Optical beam deflection

After the microfabricated cantilever was introduced (Albrecht and Quate, 1988), the optical beam deflection method was successfully applied in the repulsive-force mode, and atomic resolution on insulators as well as conductors has been achieved (Manne et ah, 1990 Meyer and Amer, 1990). A schematic diagram of the optical beam deflection AFM is shown in Fig. 15.8. An 

AFM image of the classical ionic crystal, NaCl, obtained under ultra-high-vacuum conditions, is shown in Fig. 15.8. 

In the following, we discuss the detection limit of the optical beam deflection method. First, the relation between the variation of tip height Az and the deflection angle 0 at the end of the cantilever with length I is, according to Eq. (F.24), 

The dimension of the mirror 2w, which is the front end of the cantilever, should be a fraction of its length /. It imposes a diffraction limit on the spot size D of the laser beam at the detector, which is at a distance L from the mirror  

The shot noise is the major source of uncertainty. The shot noise over a bandwidth Afis, according to Eq. (11.6), 

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Meyer G and Amer N M 1990 Simultaneous measurement of lateral and normal forces with an optical-beam-deflection atomic force microscope Appl. Phys. Lett. 57 2089... 

Mayer, G. and Amer, N. M., Simultaneous Measurement of Lateral and Normal Forces with an Optical-Beam-Deflection Atomic Force Microscope, AppZ. Phys. Lett., Vol. 57, 1990, pp. 2089-2091. 

FIG. 8 Schematic of an atomic force microscope with optical beam deflection detection showing a typical angle of 10° between lever and sample. 

An important consideration for the direct physical measurement of adhesion via pull-off measurements is the influence of the precise direction of the applied force. In AFM the cantilever does not usually lie parallel to the surface, due to the risk that another part of the cantilever chip or chip holder will make contact with the surface before the tip. Another problem relates to the fact that the spot size in the optical beam deflection method is usually larger than the width of the lever. This can result in an interference effect between the reflection from the sample and the reflection from the cantilever. This is reduced if the cantilever and sample are not parallel. Most commercial AFM systems use an angle in the range of 10°-15° between the sample and the cantilever. Depending on this angle and the extent to which the cantilever is bent away from its equilibrium position, there can be a significant fraction of unintentional lateral forces applied to the contact. 

Cantilevers are usually microfabricated from silicon by using conventional pho-tomasking and etching techniques. Typical dimensions of a cantilever are 100 pm in length, 20 pm in width, and 1 pm in thickness. Silicon and silicon nitride cantilevers and cantilever arrays that utilize optical beam deflection for signal transduction are commercially available. Piezoresistive cantilever arrays are also commercially available. Piezoresistive cantilevers are 120 pm in length, 1 pm in thickness, and 40 pm in width. 

There exists a number of readout techniques based on optical beam deflection, variation in capacitance, piezoresistance, and piezoelectricity. Piezoelectricity is... 

Fifth, when optical beam deflection is used to measure cantilever deflection, the sensitivity is inversely proportional to the length of the cantilever (see the following). If the length of the cantilever is on the order of 100 p,m, the length of the "optical lever" can be as short as 1 cm for subangstrom resolution with an inexpensive position-sensitive detector. 

Many different methods have been developed for detecting the minute deflection of the cantilever (Sarid, 1991). In this. section, we present several important ones, including vacuum tunneling (Binnig, Quate, and Gerber, 1986), mechanical resonance (Diirig, Gimzewski, and Pohl 1986), optical interferometry (Martin et al., 1988 Erlandson et al., 1988), and optical beam deflection (Meyer and Amer, 1988). 

Fig. 15.7. Detection of cantilever deflection by optical beam deflection. A light...

Fig. 15.9. Noise characteristics of the AFM. The optical beam deflection method is applied. (Reproduced from Meyer and Amer, 1990, with permission.)...

With the advances in AFM, especially the optical beam deflection method in the repulsive-force regime, the AFM study of solid surfaces under an electrolyte becomes practical. Atomic resolution with AFM at a liquid-solid interface has been routinely achieved (Manne et al., 1990, 1991). A typical fluid cell for the AFM study of electrochemistry is shown in Fig. 15.10. The top of the cell is made of glass to allow light to go in and out. 

Deflection detection methods 317—323 detection limit 322 mechanical resonance 318 optical beam deflection 321 optical interferometry 319 vacuum tunneling 317 Density of states 23... 

Operational amplifiers 252, 379—381 current amplifiers, for 380 high-voltage applications, for 381 in current amplifiers 252 typical circuits 380 Optical beam deflection 321... 

Fig. 5. a Schematic representation of the SFM set-up using the optical beam deflection method, b When the tip interacts with the sample surface, the cantilever exhibits deflection perpendicular to the surface as well as torsion parallel to the surface plane. The normal force Fn and the lateral force FL corresponds to the force components which cause the deflection and torsion, respectively. Both responses are monitored simultaneously by the laser beam which is focused on the back side of the cantilever and reflected into a four-quadrant position sensitive detector (PSD)... 

There exist a number of readout techniques based on optical beam deflection, variation in capacitance, piezoresistance, and piezoelectricity. Piezoelectricity is more suited for a detection method based on resonance frequency than the method based on cantilever bending. The capacitive method is not suitable for liquid-based applications. The piezoresistive readout has many advantages, and it is ideally suited for handheld devices. 

The piezoresistive readout technique has several advantages over commonly used optical beam deflection methods. For example, optical beam deflection probes the bending of the free end of the cantilever. It is assumed that the bending is uniform along the length of the cantilever. The piezoresistive method, however, measures the integrated bending of the cantilever. Piezoresistive cantilevers can be encapsulated in silicon nitride... 

Optical beam deflection probe beam deflection... 

Fig. 1.1 (a) Schematic diagram of contact mode AFM and SEM images of (b) V-shaped AFM cantilevers and (c) tip. The basic elements of transducer (piezo positioner), cantilever and tip assembly, and ultrasensitive force detection system (optical beam deflection/photodiode detector) are common for most AFM techniques, while details may differ (reproduced with permission from [4])... 

X.-Z. Wu, H. Shindoh, M. Yamada, E. Kobayashi, T. Hobo, Development of a novel detector for flow-injection analysis based on optical beam deflection induced by reaction heat, Anal. Sci. 10 (1994) 203. 

There are several techniques suitable for the cantilever response read-out as the optical beam deflection, piezoresistivity, piezoelectricity, interferometry and capacitance, among the most important. However, the majority of the biochemical applications carried out with the cantilever-based sensor are based in the optical beam deflection method, because of its high sensitivity and its simplicity. 

The stress change can be determined directly fixim the optical-beam deflection signal. The stress change is given by Stoney s equation ... 

FIGURE 21-26 Side view of an optical beam deflection detector. Typically, deflections of 0.1 nm or less can be detected as the lip scans the sample surface. 

The term photothermal deflection is used as an equivalent to probe beam deflection the term optical beam deflection has been used only infrequently. 

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