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Production sequence of Si-spheres and interferometrical determination of the sphere volume




Influence of atomic force microscopy (AFM) tip on AFM measurements is crucial in two ways. Firstly, the tip-sample interaction determines the fundamental measurement properties of AFM instrument.Secondly, the tip geometry defines the resolution capability of AFM. From the morphological point of view, the profile measured by AFM is actually the dilated result of the real structure by the effective tip geometry, where the effective tip geometry takes both effects into account, the physical tip geometry and the tip sample interaction.
A new method and detailed algorithm for tip form characterization in a critical dimension AFM (CD-AFM) have been developed at PTB. Based on the classical morphological theoryseveral new design ideas and methods have been carefully developed and applied for achieving high accuracy. Firstly, the line width standard type IVPS100-PTB1, jointly developed by PTB and the company Team-Nanotec, has been applied as the tip characterizer. It has advantages, such as excellent geometry uniformity and well-known feature geometry which is ultimately calibrated to the lattice constant of crystal silicon. Secondly, the tip characterization is realized in a two-step approach to overcome the influence of the line width roughness (LWR) of the tip characterizer. In the first step, the effective tip width is determined as the difference between the apparent line width and the calibrated line width, which is the averaged value of a relatively large area (a typical size of a few µm). Owing to the averaging effects, the obtained tip width is relatively insensitive to the LWR. In the second step, the tip form is determined by applying the morphological operations with the tip width obtained in the first step as the pre-information. Thirdly, the morphological algorithm has been applied with the assistance of spline filtering, re-sampling and fine-fitting algorithms to account for the practical limits of measurements, such as measurement noise, limited pixel density and the averaging of the obtained point cloud.
A thorough experimental investigation has been performed to verify the performance of the developed method. Fig.1 depicts a reconstructed tip profile of a CDR120 tip, which was obtained in five repeated tip characterization processes. The result shows an excellent repeatability of below 0.1 nm. To investigate the possible influence of the non-uniformity of the tip characterizer and the tip wear in the measurement, Fig.2 shows a reconstructed tip profile of a CDR120 tip. The result is based on 20 characterization processes, obtained from two different tip characterizers (both with the type IVPS100-PTB) before and after a customer calibration. The result indicates a difference between obtained tip profiles of about 0.4 nm between the two different tip characterizers. However, the tip profile has a stability of better than 0.1 nm before and after a customer calibration, indicating very slight tip wear.

Reconstructed tip profile of a CD-AFM tip type CDR120, which was obtained in five successively repeated tip characterizations. The insert figures show the detailed view of the tip profile zoomed in the marked area. The result shows an excellent repeatability of below 0.1 nm.