Calibrating the Z-magnification of atomic force microscope below 10 nm by single-atom steps

• Step heights ranging from 0.3 nm to 10 nm were measured and analyzed.
• We present an image processing procedure for silicon (111) steps surface.
• The measurement uncertainty for step heights ranges from 4.7% to 5.9%.

This study identifies a procedure for the calibration of the Z-magnification of an atomic force microscope below 10 nm by single-atom steps and gives an uncertainty evaluation. A Si(111) surface with periodically arranged single-atom steps was used as a standard reference. The lattice constant of the Si(111) is 0.312 nm, which is traced to SI units through X-ray diffraction. The 33 layers of continuous stacked single-atom steps were scanned and step heights ranging from 0.3 nm to 10 nm were measured and analyzed. The influential factors of calibration for the Z-magnification of an atomic force microscope were identified to estimate the uncertainty according to ISO/IEC Guide 98-3:2008. The relative expanded uncertainties ranged from 4.7% to 5.9%.