Scanning and Positioning System

In the AFM, the precise manipulation of the sample and its scanning is executed using piezoelectric devices that provide adequate displacement sensitivity (from few to tenths of nanometers per volts) and fast initial response times (~10 gs). The piezoelectricity is a phenomenon in which the electric charge is accumulated in certain materials in response to mechanical stress. This direct piezoelectric effect converts mechanical energy into the electrical one. The effect is reversible—the applied voltage causes a change in length (this is called inverse piezoelectric effect), thus electrical energy is converted into the mechanical one. Careful control of the voltage applied to piezoelectric material, provides small displacements of the material.

Early constructions of the scanning system were based on a tripod (separate transducers fixed in orthogonal directions) or a bimorph (two piezoelectric layers bonded to a thin metal shim sandwiched in the middle) arrangements. Most commonly, scanners have a form of a tube made of lead zirconate titanate (Fig. 3.6).

(a) Scheme of the piezoelectric scanner (tube) with outer

Figure 3.6 (a) Scheme of the piezoelectric scanner (tube) with outer

surface divided to four electrodes to which positive and negative voltages V are applied. (b) A photo of two typical piezo scanners.

The scanner (termed also a piezo scanner) has the outer surface segmented parallel to the tube axis into four electrodes (Fig. 3.6a). The tube interior wall serves as an internal electrode. A voltage applied to each electrode causes an appropriate bending depending on the magnitude and sign of the given voltage.

where DL is the change in length [m], L0 is the initial length of the piezoelectric tube [m], and dj is the piezoelectric coefficient of the material [m/V]. The extension or contraction in Z-direction is accomplished by applying positive or negative voltage to all four electrodes. This leads to changes in piezo scanner length L and radius R:


where V is the applied voltage, w is the wall thickness of the tube, and d31 and d33 are directional (tensor) coefficients characterizing the piezo material: d33 describes the strain parallel to the polarization vector of the ceramics (thickness) used when calculating the displacement of stack actuators; d31 is the strain orthogonal to the polarization vector (width) used for calculating tube and strip actuators.

After applying voltage to one of the outer electrodes, the tube bends in the direction perpendicular to the length axis. The magnitude of bending is proportional to the voltage difference between the common and the outer electrode. Thus, precise movement in the XY plane may be executed by applying voltage to two neighboring outer electrodes. Additionally, the scanning range may be enhanced (doubled) by applying voltages of opposite sign to the opposite electrodes. Maximum scan range S realized by a single quadrant under the applied voltage V may be calculated using the following formulae [4]:

The XY motion is not entirely orthogonal to Z-movement. Scanning is achieved by piezoelectric scanner bending, therefore, a scanner of the form of a tube scans the surface of a sphere rather than that of a plane [5]. The estimation for the Z deflection (referred as a distortion) from the XY plane is as follows:

The magnitude of the distortion is dependent on the piezoelectric tube length and the size of the scan area. For example, L = 1 cm and scanning range 5=1 gm, an error in the Z-direction is only 0.05 nm. Some of the currently available AFM systems do not use piezoelectric tube to move sample in XYZ directions, rather the XY movement is separated from the Z one by additional piezoelectric scanner that decouples Z motion from the X and Y scanning. This enables to eliminate a surface curvature for a wide variety of sample types and sizes, and it provides a flat, highly linear and orthogonal XY scan, with an accurate and precise angle measurement.

Depending on the sign of the applied voltage, both extension and contraction can be realized. The idea of how the tube moves in the AFM is presented in Fig. 3.7.

The idea of a scan realized in the AFM. Starting from zero position, the voltage is applied leading to tube bending along x-axis (fast scan direction (1)), followed by voltage

Figure 3.7 The idea of a scan realized in the AFM. Starting from zero position, the voltage is applied leading to tube bending along x-axis (fast scan direction (1)), followed by voltage

withdrawing, scanner is returning to zero position on the

same way (2). After coming back, the voltage is updated in у-axis (slow scan) direction (3). The voltage step is related to the scan resolution.

Beginning with the “start” position (maximum bending both in X and Y directions), the voltage of scanner electrodes responsible for tube bending along X-axis (called fast scan direction) is increased up to a maximum value. When voltage is removed, the tube returns to the “start” position along the same path. Next, voltage of electrodes responsible for the bending along Y-axis (slow scan direction) is updated, followed by the applying of voltage in fast scan direction, and so on.

The properties of an exemplary piezoscanner made of lead zirconate titanate are presented in Table 3.2.

Table 3.2 Properties of an exemplary piezoelectric scanner made of lead zirconate titanate (the piezoelectric scanner type EBL #2 from Stavely Sensors, USA)


Lead zirconate titanate



0.5 or 1 inch


0.25 inch

Wall thickness

0.02 inch


Piezoelectric coefficient d31

-173 x 10-12 m/V

Piezoelectric coefficient d33

380 x 10-12 m/V

Max. Voltage

300 V

Curie temperature



53 kHz

For piezoelectric scanner, described by properties presented in Table 3.2, in the case of the length of the 0.5 inch, the voltage sensitivity calculated from the manufacturer’s data is equal to 4.3 nm/V for Z approach and to 15.6 nm/V for XY scanning. For example, by applying the voltage of 100 V, one can achieve the extension DL = 0.43 gm and the full scan range 2S = 3.1 gm. High frequency constant ensures good mechanical properties, while high Curie temperature allows applications in the UHV environment, where baking of the whole system is required.

Piezoelectric scanners are far from ideal and suffer from many parasitic effects [6]. Main sources of distortion are nonlinear voltage response and hysteresis (Fig. 3.8). Hysteresis and scanner nonlinearity cause various artifacts in scanned images that can be easily observed in topography images of a calibration grating.

Nonlinear response introduces size errors, especially at higher voltages needed for large-scale scans (~1 gm), while in the case of small features in AFM imaging the assumption of linear behavior can be justified. This effect may be minimized when the function describing the response of the piezoelectric scanner is known. Then, the voltage value corrections may be applied online during the scan.

The hysteresis and non-linearity of piezoelectric scanner is observed when the piezoelectric scanner response

Figure 3.8 The hysteresis and non-linearity of piezoelectric scanner is observed when the piezoelectric scanner response (e.g., its displacement) induced by the applied voltage has nonlinear character. Actually, the imaged steps of a calibration grating (right image) are linear and parallel.

The influence of the piezoelectric scanner hysteresis and non-linearity is also observed in measurements carried out in the force spectroscopy mode.

The influence of the hysteresis and piezoelectric scanner nonlinearity in force curves recorded using AFM force spectroscopy mode on

Figure 3.9 The influence of the hysteresis and piezoelectric scanner nonlinearity in force curves recorded using AFM force spectroscopy mode on (a) a hard surface (a glass coverslip) and (b) on soft sample (a living cell). Reprinted with permission from [9].

The force curves recorded with a non-linearized scanner show distinct behavior depending on their mechanical properties. In case of stiff, non-deformable surfaces, when a non-linearized scanner is used, the approach part of the force curve does not

overlap with the retract one (Fig. 3.9a). After the correction, both curves should overlap. Different behavior can be observed for soft samples, as living cells. Here, the scanner nonlinearity may lead to totally wrong interpretation. In the upper plot of Fig. 3.9b, both parts of the force curve overlap, which suggests a pure elastic interaction of the AFM probe with a living cells. However, after the correction, true data shows the presence of an approach-retract hysteresis, resulting from viscoelastic character of the studied sample.

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