Application of Non-Linear Equalization for Characterizing AFM Tip Shape

Application of Non-Linear Equalization for Characterizing AFM Tip Shape Dipl.-Ing. T. Machleidt, PD Dr.-Ing. habil. K.-H. Franke, D. Kapusi, T. Langner Computer Graphics Group / TU-Ilmenau Nanopositionier- und Nanomessmaschinen Teilprojekt C2: Sensornahe Messdatenerfassung und Verarbeitung Contents: Motivation Methods of estimating the tip radius Tip characterization methods Practical use Application and results Conclusion & outlook 52. Internationales Wissenschaftliches Kolloquium, TU Ilmenau 1

Motivation Operating principle of an Atomic Force Microscope (AFM) Display Cantilever -Z -X FC AFM tip Sample Z X Stage 52. Internationales Wissenschaftliches Kolloquium, TU Ilmenau 2

3 Motivation Operating principle of an Atomic Force Microscope (AFM) Display -Z Cantilever -X AFM tip F C Z Sample X Stage

4 Motivation Operating principle of an Atomic Force Microscope (AFM) Display -Z Cantilever -X Z AFM tip F C Sample X Stage

5 Motivation Results of measuring with the AFM technique Titan sample: Tipcheck

6 Motivation Operating principle of an Atomic Force Microscope (AFM) R=20 nm L=1,5 µm Cantilever SEM image of an AFM tip F C Z Sample X Stage

7 Motivation Information about the AFM tip are important for: Analysis of the measured data Lateral resolution Evaluation of structures Processing Deconvolution of the measured data R[nm] d min [nm] 5 2.0 50 6.3 Direct in AFM contact mode Indirect in AFM special mode to calculate the PSF Study of tip wear processes Optimized scan parameters for low tip wear Reference table for tip wear classification

Methods to Estimate the Tip Radius Methods to reconstruct the 3D tip shape: Known tip characterization Blind tip estimation Characterization of the tip shape: Radius, apex angle, roughness Reconstructed AFM tip Z - 4 nm Z - 10 nm Method to calculate the characterization area SPIP 1 : The radius is calculated from a sphere fit to the 5x5 center pixels of the tip. R tip = 20 nm (Z area = 10 nm) 1 Scanning Probe Image Processor 52. Internationales Wissenschaftliches Kolloquium, TU Ilmenau 8

9 Methods to Estimate the Tip Radius 3D tip characterization using non-linear equalization 3D primitive: Pyramid, pyramid stump, tetrahedron, tetrahedron stump, sphere,... Optimization error: Z distance, orthogonal distance Optimization method: Simulated annealing method (uphill-downhill optimization) RMS (line) Annealing temperatur (doted) IDL software to characterize AFM tip (TU Ilmenau)

10 Methods to Estimate the Tip Radius Correlation of the used apex area and the calculated tip radius Result by Simulated Anealing 140 120 100 nm 80 60 40 20 Radius RMS 0 5 10 20 30 40 60 80 100 used apex area in nm Fit error plot by using standard non-linear fitting (apex area 100 nm)

Methods to Estimate the Tip Radius Software library 1 for fitting and segmenting shaped element Perpendicular distance: Target function for fitting: Z d k r r = F( a, xk ) ( k ) ( a, K, a ) F ( a, x ) K = 2 r r ( ) Minimum 1 N k k = 1 Z a 1 = 0, Z, To solve this non-linear problem either a Gauss-Newton algorithm or a Levenberg-Marquard algorithm can be used. Advantages: Weighted element fitting; constraints possible! K a N 1 www.zbs-ilmenau.de/software 52. Internationales Wissenschaftliches Kolloquium, TU Ilmenau 11 = 0

12 Methods to Estimate the Tip Radius State of the development Method Shaped element Fit all parameters Fit with fixed parameters Point of shaped element given Fine segmentation 2D Line available available available available Circle available available available available Ellipse available available not available available 2D Quad. Form available available Plane available available available available 3D Line available available available available Sphere available available available available Cylinder available available Cone available available part available part available available available Torus available available not available available 3D Quad. Form available available ZBS Software library for fitting and segmenting shaped element

13 Methods to Estimate the Tip Radius Usage of the ZBS library in IDL (tip characterization module) 1. Non-linear fit with exponential weighting by using the distance to the apex 2. Non-linear fit with a static point (tip apex) on the fitting element apex point W = 1 W = 0 Reconstructed AFM tip

14 Methods to Estimate The Tip Radius Correlation of the used apex area and the calculated tip radius Result by using new methods 140 nm 120 100 80 60 40 20 Radius (SA) RMS (SA) Radius (zbs w eighted) RMS (zbs w eighted) Radius (zbs fix point) RMS (zbs fix point) 0 5 10 20 30 40 60 80 100 used apex area in nm

15 Methods to Estimate the Tip Radius Fit error plot by using non-linear fit with apex as fix point (apex area 100 nm)

16 Methods to Estimate the Tip Radius Methods integrated in Scanning Probe Image Processor, SPIP New tip Worn out tip (0.5 m Si) Dialog box for tip characterization

17 Conclusion & Outlook Information about the AFM tip are important Stability of charcterized tip shape is insufficient ZBS library is useful for fitting geometric primitives under externel constraints Methods are included in IDL and SPIP Outlook: Expansion to other geometric primitives, rougness analysis, publication

18 The End Thanks for your attention! Acknowledgement This work was supported by the German Science Foundation (DFG, ). The authors wish to thank all those colleagues at the Technische Universität Ilmenau and the ZBS Ilmenau e. V., who have contributed to these developments.