152. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622

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-IlmenauSFB 622 „Nanopositionier- und Nanomessmaschinen“

Teilprojekt C2: „Sensornahe Messdatenerfassung und Verarbeitung“

Contents:

MotivationMethods of estimating the tip radius• Tip characterization methods• Practical use• Application and results

Conclusion & outlook

252. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Motivation

Operating principle of an Atomic Force Microscope (AFM)

AFM tip

Cantilever

Stage

Sample

FC

Z

X

Display

-Z

-X

352. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Motivation

Operating principle of an Atomic Force Microscope (AFM)

AFM tip

Cantilever

Stage

Sample

FC

Z

X

Display

-Z

-X

452. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Motivation

Operating principle of an Atomic Force Microscope (AFM)

AFM tip

Cantilever

Stage

Sample

FC

Z

X

Display

-Z

-X

552. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Motivation

Results of measuring with the AFM technique

Titan sample: „Tipcheck“

652. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Motivation

Operating principle of an Atomic Force Microscope (AFM)

Cantilever

Stage

Sample

FC

Z

X

L=1,5 µm

R=20 nm

SEM image of an AFM tip

752. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Motivation

Information about the AFM tip are important for:

Analysis of the measured dataR[nm] dmin[nm]

5 2.050 6.3

Lateral resolutionEvaluation of structuresProcessing

“Deconvolution” of the measured data

Direct in AFM contact modeIndirect in AFM special mode to calculate the PSF

Study of tip wear processes

Optimized scan parameters for low tip wearReference table for tip wear classification

852. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Methods to Estimate the Tip Radius

Methods to reconstruct the 3D tip shape:Known tip characterizationBlind tip estimation

Reconstructed AFM tipRadius, apex angle, roughness

SPIP1: ”The radius is calculated from a sphere fit to the 5x5 center pixels of the tip.”

Z - 4 nmZ - 10 nm

Method to calculate the characterization area

Rtip = 20 nm (Zarea = 10 nm)

Characterization of the tip shape:

1Scanning Probe Image Processor

952. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Methods 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)

1052. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Methods to Estimate the Tip Radius

Correlation of the used apex area and the calculated tip radius

Result by Simulated Anealing

0

20

40

60

80

100

120

140

5 10 20 30 40 60 80 100

used apex area in nm

nm

Radius

RMS

Fit error plot by using standard non-linear fitting

(apex area 100 nm)

1152. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Methods to Estimate the Tip Radius

Software library1 for fitting and segmenting shaped element

),( kk xaFd rr=Perpendicular distance:

( ) ( )( ) Minimum ,,,2

1

)(1 →=∑

=

K

kk

kN xaFaaZ rr

KTarget function for fitting:

0,,01

=∂∂

=∂∂

NaZ

aZ

K

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!1www.zbs-ilmenau.de/software

1252. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Methods to Estimate the Tip Radius

Method

Shaped element

Fit all parame-ters

Fit with fixed parameters

Point of shaped element given

Fine segmenta-tion

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 part available available

Cone available available part available available

Torus available available not available available

3D Quad. Form available available ZBS Software library for fitting and segmenting shaped element

State of the development

1352. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Methods 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

Reconstructed AFM tip

apex point

W = 1

W = 0

1452. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Methods to Estimate The Tip Radius

Correlation of the used apex area and the calculated tip radius

Result by using new methods

0

20

40

60

80

100

120

140

5 10 20 30 40 60 80 100

used apex area in nm

nm

Radius (SA)

RMS (SA)

Radius (zbs w eighted)

RMS (zbs w eighted)

Radius (zbs f ix point)

RMS (zbs f ix point)

1552. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Methods to Estimate the Tip Radius

Fit error plot by using non-linear fit with apex as fix point (apex area 100 nm)

1652. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Methods 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 tipcharacterization

1752. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622Conclusion & 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

1852. Internationales Wissenschaftliches Kolloquium, TU Ilmenau

SFB 622The End

Thanks for your attention!

Acknowledgement

This work was supported by the German Science Foundation (DFG, SFB 622).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.