Hysteresis and Aging

Hysteresis

Because of differences in the material properties and dimensions of each piezoelectric element, ech scanner responds differently to an applied voltage. This response is conveniently measured in terms of sensitivity, a ratio of piezo movement to piezo voltage (i.e., how far the piezo extends or contracts per applied volt).

Sensitivity is not a linear relationship with respect to scan size. Because piezo scanners exhibit more sensitivity (i.e., more movement per volt) at the end of a scan line than at the beginning, the relationship of movement versus applied voltage is nonlinear. This causes the forward and reverse scan directions to behave differently and display hysteresis between the two scan directions.

The effect of nonlinearity and hysteresis can be seen from the curve above. As the piezo extends and retracts throughout its full range, it moves less per applied volt at the beginning of the extension than near the end. The same is true when the piezo is retracting—the piezo moves less per applied volt at the beginning of its extension than near the end.

Nonlinearity and hysteresis can cause feature distortion in SPM images if not properly corrected. Examples of these effects on AFM images are shown below on a 10 μm pitch calibration grating:

Figure 1: 100 mm x 100 mm scans in the forward (trace) and reverse (retrace) directions of a two-dimensional 10 mm pitch grating without linearity correction.

This nonlinear relationship is corrected one of two ways:

• In closed loop, the scanner's sensors detect the actual location of the scanner in X, Y, and Z at all times and continually correct for non-linearities during the scan.
• In open loop, a patented calibration routine (Bruker) determines the nonlinear voltage to apply in real time to produce a linear scan in X and Y in both trace and retrace directions:

Aging

The sensitivity of piezoelectric materials decreases exponentially with operation time. This causes most of the change in the sensitivity to occur at the beginning of a scanner's life, as shown in the graph below. Before Bruker scanners are shipped, they are run approximately 48 hours to get the scanner past the point where the sensitivity changes dramatically over short periods of time. As the scanner ages the sensitivity will change less with time, and eventually it will very seldom require recalibrating.

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