A metrological atomic force microscope (M-AFM) was developed for the length measurements of nanometer range, through the modification of a commercial AFM. To eliminate nonlinearity and crosstalk of the PZT tube scanner of the commercial AFM, a two-axis flexure hinge scanner employing built-in capacitive sensors is used for X-Y motion instead of PZT tube scanner. Then two-dimensional displacement of the scanner is measured using two-axis heterodyne laser interferometer to ensure the meter-traceability. Through the measurements of several specimens, we could verify the elimination of nonlinearity and crosstalk. The uncertainty of length measurements was estimated according to the Guide to the Expression of Uncertainty in Measurement. Among several sources of uncertainty, the primary one is the drift of laser interferometer output, which occurs mainly from the variation of refractive index of air and the thermal stability. The Abbe error, which is proportional to the measured length, is another primary uncertainty source coming from the parasitic motion of the scanner. The expanded uncertainty (k ＝ 2) of length measurements using the M-AFM is √(4.26)²＋(2.84×10－⁴×L)² (㎚), where L is the measured length in ㎚. We also measured the pitch of one-dimensional grating and compared the results with those obtained by optical diffractometry. The relative difference between these results is less than 0.01 %.
