Mathematical Morphology Based Research On Blind Reconstruction Method Of AFM Probes

Atomic force microscope(AFM) plays a very important role in promoting the development of nanotechnology. However, for the measurements of linewidth, particle shape and surface roughness, the probe shape has a great influence on the results. In addition, for the measurements of the mechanical properties of materials, some important methods also require the accurate probe shape. Nowadays, there are many methods for the estimation of probe shape. Among these methods, the most promising one is the mathematical morphology based Blind Tip Reconstruction(BTR) method proposed by Villarrubia. The main advantage of this method is that it is able to determine the best upper bound of the probe shape without accurate calibration of the tip characterizer. However, there are only some fuzzy requirements of the suitable tip characterizer for BTR method. Based on the BTR algorithm, this paper provides a theoretical basis and practical verification for the selection of suitable tip characterizer to achieve accurate tip reconstruction. The main contents include the following:1. A review of the estimation of the tip shape is presented. Through the analysis of each method, this paper concentrates on the BTR algorithm proposed by Villarrubia.2. The detailed information about the derivation process, procedures design and parameters setting of BTR method are described. Based on the disadvantages of this method, the concept of the suitable tip characterizer is strengthened.3. Through the analysis of the SEM image of the actual probe shape, the conical structure of the probe shape is established. In order to balance the relationship between the lateral resolution and reconstructed time, a “2D interpolation” method is proposed. Based on the conical model, the suitable shape of tip characterizer is explored. And the results show that the curve structures are more suitable for BTR method than the plane structures. In addition, with suitable tip characterizer, BTR method can also be applied to accurate reconstruction of 3D shape of three pyramid probe.4. In order to quantitatively compare the accuracy of probe reconstructed by BTR method, a concept of BTR error is put forward. Firstly, based on BTR error, a series of simulation experiments about how the conical tip characterizer influences the conical probe are carried out. The simulation results show that, to reconstruct the probe accurately, the cone angle of the tip characterizer must be smaller than that of the tip. When it meets the above conditions, the BTR error is insensitive to the cone angle of the tip characterizer but increases linearly with the radius of curvature of tip characterizer. In particular, for sharp(20 nm radius) and blunt(80 nm radius) tips, the radius of curvature of the tip characterizer must be smaller than 5 nm. Secondly, a model to predict the associated BTR errors is established. The errors derived from the model are indeed in quantitative agreement with the simulation results.5. Some actual experiments for the calibration of the conical probe shape are done by using “Tipcheck” as a tip characterizer. Within the allowable error range, the results are in good agreement with the tip shape extracted from the SEM image.