Correction of surface roughness measurements in SPM imaging

Abstract

In STM and AFM, when rough surfaces are concerned, image formation is essentially governed by the nonlinear geometrical interaction between the specimen surface and the tip surface. The shape and finite size of the tip are responsible for imperfections in images. Consequently the measured roughnesses are not exact. They are always smaller than the true roughness value because the surface is imperfectly probed. We propose a method to predict the true roughness value from the experimental image obtained. For this purpose a large variety of different 3D surfaces which mimic the experimental ones are computed and classified with respect to the shape and density of grains composing the surface. Then, by using the mathematical morphology dilation operation which describes the image formation in SPM, the corresponding dilated images are computed for different tip geometries. For each category of surfaces and given tip shapes the correction factors between the true r.m.s. roughness values and the experimental ones are obtained. This allows us to predict the true roughness value. Scanning probe microscopy (SPM) (mainly scanning tunneling microscopy (STM) and atomic force microscopy (AFM)), have provided the unique possibility of 3D investigation of surface topography and access to material properties on the nanometer scale. These instruments are now currently used as precision dimensional metrology tools for the study and manufacturing control process of technologically important surfaces, such as semiconductor nanolithography devices, Si patterned wafers, magnetic thin films, optical data storage media and numerous others [1–8]. The number of nano-roughness measurements using SPM is increasing, since roughness parameters have profound practical consequences in many fields of engineering and pure science (nano-tribology, semiconductor devices, biomechanics, electrochemical or sputtering deposition etc.). A number of workers have used directly acquired images and SPM imaging processing software developed by the manufacturers ∗ Corresponding author to draw some quantitative conclusions about roughness parameters. Unfortunately, the surface is not perfectly probed by the tip, since it is not infinitely sharp. Its shape and finite size are responsible for the imperfections of images and thus for roughness measurement errors. These errors are particularly important in the case of highly corrugated surfaces. In this case, the surface features can be comparable in size to the tip and the image is strongly distorted. These distortions are well known, having been analyzed by several authors [9– 15], but very little work has been done to date to correct the roughness measurements. It has been shown recently that SPM image formation and restoration can be described by two mathematical morphology operations (dilation and erosion, respectively [16–20]) or by the concept of an envelope function [21]. Erosion is the dual operation of dilation, not its inverse function. Consequently, the image cannot be perfectly restored. The topography of the surface can only be corrected in the zones probed (“seen”) by the tip. Therefore the correction is partial and depends on the tip size that defines the amount of lost information. In this paper we propose a method, based on appropriate simulations and on mathematical morphology, of predicting the true r.m.s. roughness value from the experimental image if the tip shape is known. For this purpose, we have computed and classified, with respect to the shape and density of grains composing the surface, a large variety of different 3D surfaces which mimic the real ones. For each category of surfaces and a given tip, the correction factor between the true r.m.s. roughness value and the experimental one is obtained. 1 Tip influence on roughness measurements In SPM, the image is formed by recording the height of the tip apex when the tip is scanned across the surface. Unfortunately, the proximal point, i.e. the point of the tip surface which interacts with the specimen surface and, therefore, gives the useful signal, is not necessarily located at the tip apex, is not unique, and does not remain the same during the tip motion [8, 17]. This situation is the main reason why image formation has been qualified as a non-linear process.