The hysteresis of the scanning elements in STM are known to cause geometrically distorted images. By analyzing the traces and retraces of the tip, the hysteresis can be quantified and a general model describing the hysteresis can be constructed. That the use of the inverse model can eliminate the hysteresis distortion in STM images is demonstrated. The method does not require any specific ordering of the image. Another method that can be used only on images of surfaces with ordered patterns is also presented. It is an iterative technique where the highest peak in the Fourier domain is maximized by tuning the hysteresis model.

We report a study of a fundamental limit to the accuracy of vertical measurements made using scanning-probe microscopes (SPM): the short-term stability of a vertical calibration using a waffle-pattern artifact. To test the instrumental component of this stability, we acquired three data series, at different humidity levels. We compare the variations in waffle-pattern depth in these three data series with the differences in depth estimates using several different analysis methods. The three methods tested are: a histogram method, the scanning-probe image processor, and the polynomial step-function fit. To clarify the importance of the analysis method, a discussion of the different leveling, averaging, and depth-estimation aspects of the various methods is presented. To understand the true repeatability limit of SPM calibration, it is necessary to treat imaging artifacts such as tilt, nonlinearities, and image bow carefully. We find that, when such care is taken, the dependence of the average waffle-cell depth on algorithm is around 0.1%. This is less than the standard deviation of the step-height estimates of around 0.5%, which may be attributed to short-term instrumental variations in vertical SPM calibration. This is a far better stability than the 5%–10% variations observed under long-term aging of the piezo scanner. However, the histogram algorithm, which does not correct image bow, gives an average waffle-cell depth estimate which is nearly 1% higher than the others, indicating that careful image analysis is necessary if the measurement accuracy is to be comparable to the short-term stability of the piezo scanner.

Because scanning probe microscopes produce three-dimensional data of almost any solid they have a strong potential as metrological tools. Results are presented from the first international intercomparison between four national metrology laboratories. On three-dimensional calibration standards the mean deviations between instruments were typically Ͻ2% in the x direction, Ͻ5% in the y direction, and Ͻ10% in the z direction. Eight samples were circulated for roughness measurements and 19 roughness parameters were calculated for each image. In the range where the scanning probe microscope measurements overlapped with classical techniques ͑profilometers͒ the agreement was good. Also a gauge block of hardened steel ͑Ϸ900 HV͒ with an array of Vickers indentations having diagonal lengths ranging from 3 to 60 m was circulated and measured.