The piezoelectric scanner

Modern AFMs use piezoelectric transducers to either raster-scan the imaging probe across the stationary sample, or the sample with respect to a stationary probe. Certain crystals exhibit a property known as the piezoelectric effect. When compressed or stretched, a piezoelectric crystal will build up alternate charges on opposite faces. 

Alternatively, if a potential difference is applied across opposite faces, the crystal will expand or contract. By using this property, a piezoelectric scanner can accurately control movement in the x-, y- and z-directions, with suh-nanometre resolution. The response time for the piezoscanner can become a limiting factor when observing fast real-time processes. 

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From Fig. 9.16, we obtain c/33 1.05 kN, a value consistent with the value listed in the catalog (1.27 kN). The value might be somewhat lower than the true value because the bonding of the tube ends is not perfectly rigid. If one end of the tube is free, or both ends are free, the deformation pattern varies significantly at the end(s). The net end effect is to reduce the value of the double piezoelectric response. Even if the end-bonding condition is unknown, an accurate measurement of the temperature or time variation of the piezoelectric constant can still be achieved. In other words, if the piezoelectric scanner is calibrated by a direct mechanical measurement or by the scale of images at one temperature, then its variation can be precisely determined by the electrical measurements based on double piezoelectric responses. 

Initially this technique was intended purely as a high-resolution imaging device, down to the sub-nanometre level (Alessandrini and Facci, 2005). However, it was soon adapted for measuring the interactive forces in a process known as force spectroscopy. In this process, the sample is moved towards the tip and then retracted, with the vertical displacement of the Piezoelectric scanner being recorded. This produces voltage data recorded by the photo detector as a function of the displacement of the Piezoelectric stage. A force curve can be produced from this which provides information about the interactions between the tip of the probe and the sample. This force data can be interpreted to... 

Figure 5.25 Image distortion caused by nonlinearity of the piezoelectric scanner (a) regular grid and (b) distorted image of grid. (Reproduced with permission from PC. Braga and D. Ricci (eds), Atomic Force Microscopy, Humana Press. 2004 Humana Press.)...

The simplest theory for the analysis of surface elasticity based on AFM force-distance curve measurement is Hertzian contact mechanics [Landau and Lifshitz, 1967], As shown schematically in Figure 3.1, a force-distance curve is a plot of the displacement, z, of the piezoelectric scanner normal to the specimen s surface as the horizontal axis and the cantilever deflection, A, as the vertical axis. Hertzian contact mechanics cannot treat adhesive force in principle. We need to make some effort to minimize the adhesive force in a practical experiment. Measurement in aqueous conditions is effective for polymeric materials with low water absorbability. A cantilever with a large spring constant also hides weak van der Waals forces. Figure 3.1a shows the... 

If the specimen surface is sufficiently rigid, the cantilever deflection. A, always coincides with the displacement, z — zo, of the piezoelectric scanner measured from a contact point (zo, 0) as depicted in the dashed line in Figure 3.1b. However, if the specimen surface undergoes elastic deformation as in the case of the solid line, we can estimate the sample deformation, 5, as follows ... 

An estimation of the magnitude of the capillary force can be done in the case of a conic tip with a half cone angle a. In the first approximation, assuming that the tip penetrates the LC film without changing its thickness, one can calculate the deflection Az of the cantilever as a function of the piezoelectric scanner movement Zg-. 

The piezoelectric scanners used in AFM have the same characteristics as those mentioned in the STM section. The sample can be mounted directly onto the scanner and rastered underneath the cantilever tip, or the cantilever can be mounted to a scanner tube and rastered over a sample fixed below it. The former case is advantageous in imaging larger samples and increases the speed of imaging. 

Fig. 2.34 Schematic picmre of an atomic force microscope. The sample of interest is placed on the piezoelectric scanner and a laser is reflected off the upper side of the cantilever and guided to a split photo detector. In this way, vertical and horizontal deflection signals can be measured. A well-defined colloidal particle can be glued to the tip of the cantilever as to measure the force between that particle and the surface...

In such experiments (with >10-min intervals between repeated measurements), it is important to take into account the drift of the piezoelectric scanner in order to ensure comparison of the obtained images and the adhesion-force maps. We solved this problem, being guided by characteristic details of images of the studied surface. For this purpose, we first obtained an AFM image of the surface with dimensions of 2000 x 2000 mn (Fig. 9.4a) and determined Ihe coordinates of the reference point (shown with an arrow) with an error no larger than 0.24 nm [27]. 

Constant-current feedback control Regulation of the piezoelectric scanner position based on the magnitude of the electron tunneling current in a scanning tunneling microscope. 

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