Vertical metrology using scanning-probe microscopes: Imaging distortions and measurement repeatability

Abstract

We report a study of the repeatability as limited by instrumental imaging distortions in scanning-probe microscope (SPM) measurements of the heights of nominal 44 and 88 nm steps in calibration artifacts. By imaging the same series of locations on different days, we are able to distinguish sample variations from variations originating in the imaging process. In particular, the value and repeatability of the measured step heights are found to depend upon the algorithm used to infer the step height from the SPM image. The three general approaches tested are: a manual single-point method, which represents the most commonly used practice in the SPM community; a histogram-based method, which is available in commercially available SPM image-analysis software; and the polynomial step-function fit (PSFF), which explicitly removes image bow and sample tilt. Factors related to variations in the sample measured such as image size and location on the sample cause up to 10% variations in the step-height measurements. Methods of statistical analysis of variance are used to separate sample variations from instrumental and algorithmic variations. Once image bow and sample tilt have been corrected properly using PSFF, SPM instrument-related variations are under 1%. Without PSFF, the step height exhibits a systematic dependence upon sample tilt and image bow which distorts the measured step height. In our study, these distortions occur at a level of up to 2% of the step height. However, these step-height distortions can be far more extreme in some cases. We show an example of a step-height measurement in which the image bow is so extreme that the step can barely be identified without first correcting the image bow. We also show that, for small images of a rough sample, tip wear can contribute a significant systematic error in the step height measurement, of up to 1% per image in this case, which can lead to large cumulative errors if the tip is not changed often enough. Thus, understanding SPM image distortions and their effect on step-height measurement repeatability is crucial to SPM metrology.