Algorithms for using silicon steps for scanning probe microscope evaluation

Abstract

Abstract The 2019 update to the Mise en Pratique for the metre adopted the lattice parameter of silicon as a secondary realisation of the metre for dimensional nanometrology. One route for this realisation is the use of amphitheatre like monoatomic steps of silicon. In response, in this paper we present new algorithms for one- and two-dimensional analysis of atomic force microscope images of these large area atomic terraces on the surface of silicon. These algorithms can be used to determine the spacing between the steps and identify errors in AFM scanning systems. Since the vertical separation of the steps is of the same order of magnitude as many errors associated with AFMs great care is needed in processing AFM measurements of the steps. However, using the algorithms presented in this paper, corrections may be made for AFM scanner bow and waviness as well as taking into account the edge effects on the silicon steps. Applicability of the data processing methods is demonstrated on data sets obtained from various instruments. Aspects of steps arrangement on surface and its impact on uncertainties are discussed as well.