Stan, G.
(2026),
Calibration method for the height and linearity of an AFM z-piezo transducer in the sub-nanometer to nanometer range using stepped surfaces, Measurement Science & Technology, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=961549 (Accessed October 9, 2026)
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Calibration method for the height and linearity of an AFM z-piezo transducer in the sub-nanometer to nanometer range using stepped surfaces
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Abstract
In this work, we present a method for height calibration of the z-piezo in an Atomic Force Microscope (AFM) using stepped surfaces with subnanometer staircases. The method analyzes common trace and retrace images obtained from AFM topography scans across straight terraces of these stepped surfaces. By combining these data from a single scan, we can determine both the quantitative height calibration and the linearity of the AFM z-piezo across a full range of heights. This eliminates the need to separately image artifacts of different heights. This approach is significant because it incorporates all measured step heights from a single scan, allowing calibration for any height difference between them. As a result, it serves as a multipoint calibration method that spans a height range from subnanometer levels to tens of nanometers. This contrasts with single-point methods, which typically calibrate against a single height derived from measurements of one or more artifacts. Our calibration method relies on straightforward metrics, including average measured step heights, standard errors from the mean, relative accuracy, and percentage uncertainty. The most sensitive metrics for detecting potential miscalibration and nonlinearity in the AFM z-piezo are the measured average residuals and relative accuracy. In contrast, the standard errors and percentage uncertainty primarily relate to the surface roughness of the stepped surface used in the calibration. We demonstrate the application of this calibration method on scans over a 6H-SiC(0001) surface, with calibrated heights ranging from a minimum step height of 0.756 nm to heights approaching 50 nanometers.Citation
Measurement Science & Technology
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Keywords
step height calibration, subnanometer, nanometer, stepped surfaces, atomic force microscopy
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Created August 19, 2026, Updated October 8, 2026