Piezoelectric elements in scanners are used to position the probe tip relative to the sample surface at the nanometer scale with great accuracy. However, the behaviour of the piezoelectric elements does not always meet the theoretical ideal, that is, a linear increase in movement along with an increase/ decrease in applied voltage. The movement of these piezoelectric devices is subject to deviations from the ideal including non-linearity, hysteresis and creep.
Scanner sensitivity is the movement (nm/ μm) per voltage (V).
Because of differences in the material properties and dimensions of each piezoelectric element, each scanner responds slightly differently to an applied voltage.
Nonlinearity means that the sensitivity of the scanner is not a linear function of the (amount of) applied voltage. Typically, sensitivity is greater at larger applied voltages than at near zero applied volts.
Nonlinearity of the x - y plane displays as surface features appearing stretched or contracted at the top of the image, and then appearing to correct nearer to the middle and bottom of the image. Some linear features may appear curved. This artefact will typically not reduce when the same region is scanned multiple times. Although obvious in images of linear structures like calibation grids, this artefact may go unnoticed in images of samples lacking evenly spaced features.
Figure 14. Image of a calibration grid showing non-linearity in the x - y plane.
Hysteresis occurs in piezoelectric elements in the scanners when the response traces a different path depending on the direction of a voltage change. The magnitude of the effect depends on many variables including the starting voltage, the size of the voltage change, the rate of voltage change, and the scan angle.
In AFM, rastering across the sample surface (driven by voltage changes to the piezoelectric elements) means the scanner will move non-uniformly in the x - y plane if hysteresis is present. This non-uniformity has several effects, including differences in scanner sensitivity at the beginning and end of a scan. If the scanner moves further than it should vertically, in the z plane, tall features will appear to have a very "sharp" edge in the image.
Hysteresis typically occurs when changing the scan size or the centre offset of the image, and typically only affects the first 10 - 20 lines of an image. Hysteresis can be reduced or eliminated by re-starting the scan, and/or scanning more slowly.
Figure 15. The dashed line represents an ideal linear relationship between applied voltage and the movement (extension) of the piezoelectric elements in a scanner. The red lines represent the actual nonlinear relationship that usually exists in piezo-scanners. This non-ideal relationship leads to the scanner artifacts of nonlinearity where scanner sensitivity depends on the size of the voltage, and hysteresis where scanner sensitivity depends on the direction of voltage change.
Creep describes the continued motion of the scanner after a rapid change in voltage, for example, when moving the scanning position. The piezo scanner does not respond all at once; it moves the majority of the distance quickly (< 1ms), then the last part of the movement is slower. The slow movement is called creep. If large voltage changes occur during scanning, then the slower movement causes a distortion of the image. Creep may result in surface features appearing smaller or longer in one direction than they actually are. Creep accounts for the initial lateral distortion apparent after zooming or moving to a new scan area, and which settles out after several scan lines have been traced.
Figure 16. The continued slow movement of the piezoelectric scanner after a rapid change in applied voltage results in creep. Creep is measured as the ratio of the slow dimensional change to the fast dimensional change.
To correct for scanner artefacts, some AFM machines employ a sensor to detect actual movement of the scanner and compensation adjustments are made to the scanner drive signal in real time; this is called a 'closed loop' AFM.