Influence of data analysis and other factors on the short-term stability of vertical scanning-probe microscope calibration measurements

Abstract

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.