Cantilever deflection

AFM Atomic force microscopy [9, 47, 99] Force measured by cantilever deflection as probe scans the surface Surface structure... 

Figure Bl.19.34. Cantilever deflection and corresponding frictional force in the v-direction as a fiinction of sample position as a mica sample is scaimed back and forth under a tungsten tip. (Taken from [124], figure 2.)...

Fig. 5. Block diagram of contact atomic force microscope system in which cantilever deflection monitored optically with position-sensitive photodiode...

For SFM, maintaining a constant separation between the tip and the sample means that the deflection of the cantilever must be measured accurately. The first SFM used an STM tip to tunnel to the back of the cantilever to measure its vertical deflection. However, this technique was sensitive to contaminants on the cantilever." Optical methods proved more reliable. The most common method for monitoring the defection is with an optical-lever or beam-bounce detection system. In this scheme, light from a laser diode is reflected from the back of the cantilever into a position-sensitive photodiode. A given cantilever deflection will then correspond to a specific position of the laser beam on the position-sensitive photodiode. Because the position-sensitive photodiode is very sensitive (about 0.1 A), the vertical resolution of SFM is sub-A. 

SPM force curves are acquired by moving the tip toward the sample and recording the cantilever deflection as a function of the so-called Z position. Cantilever deflection is directly proportional to the force exerted on the sample by the tip. If the spring constant (fc) of the cantilever is known, the force can be calculated. The Z position defines the distance from the sample to the piezo, to which the base of the cantilever is attached (Figure 9.13). By convention the closest point of approach by the piezo is designated as zero on the x-axis. Note that for some instruments the piezo is attached to the sample stage and thus moves the sample up toward the tip however, this does not change the analysis. 

Figure 9.14 shows a typical approach force curve along with schematic drawings of the relative positions of the SPM tip and the sample surface, as related to the force curve. At the start of the experiment, i.e., position A on the right-hand side of the figure, the tip is above the surface of the sample. As it approaches the surface the Z value decreases until at position B the tip contacts the surface. With further downward movement of the piezo the cantilever starts to be deflected by the force imposed on it by the surface. If the surface is much stiffer than the cantilever, we get a straight line with a slope of — 1, i.e., for every 1 nm of Z travel we get 1 nm of deflection (Une BC in Figure 9.14). If the surface has stiffness similar to that of the cantilever, the tip wUl penetrate the surface and we get a nonlinear curve with a decreased slope (line BD in Figure 9.14). The horizontal distance between the curve BD and the line BC is equal to the penetration at any given cantilever deflection or force. The piezo continues downward until a preset cantilever deflection is reached, the so-called trigger. The piezo is then retracted a predetermined distance, beyond the point at which the tip separates from the sample.

Force curve gives the relationship between the z-piezo displacement and the cantilever deflection as shown in Figure 21.10b. When a cantilever approaches to a stiff sample surface, cantilever deflection. A, is equal to the z-piezo displacement, z — Zo- The value of zo is defined as the position where the tip-sample contact is realized. On the other hand, z-piezo displacement becomes larger to achieve the preset trigger value (set point) of the cantilever deflection in the case of an elastic sample due to the deformation of the sample itself. In other words, we can obtain information about a sample deformation, 8, from the force-distance curve of the elastic surface by the following relationship ... 

FIGURE 6.8 Three force curves taken at locations of a gelatin film thickness of 150 nm (curve A), 410 nm (curve B), and 1.15 pm (curve C). At high forces, the force curves are steeper for small thicknesses because the cantilever deflection is influenced by the underlying stiff substrate at these small film thicknesses. For comparing the slopes more easily, the curves are shifted such that their points of contact coincide. Reprinted with permission from Domke and Radmacher (1998). 

The versatility of AFM is exemplified by the number of different operation modes, which have been employed with various degrees of success for the analysis of DNA molecules on surfaces. As mentioned before, AFM operates by measuring the attractive or repulsive forces between a tip and the specimen using a feedback system, with the cantilever deflection yielding the actual topography of the specimen. Different setups of the feedback and cantilever deflection result in different AFM operation modes, as summarised in Table 1. 

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. 

The tunneling current between two metal electrodes separated by a vacuum gap varies about one order of magnitude per A. Therefore, vacuum tunneling provides an extremely sensitive method for detecting minute displacements. The first AFM, demonstrated by Binnig, Quate, and Gerber (1986), utilized vacuum tunneling to detect the cantilever deflection. 

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

UFM detection is obtained by measuring the cantilever deflection as the ultrasound amplitude is modulated (Fig. 13.3). The ultrasonic excitation from a longitudinal wave transducer fixed to the bottom of the sample causes normal vibration of its surface. As the ultrasonic amplitude is increased, contact is eventually broken at the pull-off point (aI = hi), giving a discontinuity in the time-averaged displacement. We refer to this ultrasonic amplitude as the threshold amplitude, and the corresponding inflection in the displacement... 

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