Deconvolution of Atomic Force Measurements in Special Modes Methodology and Application

SFB 622

Deconvolution of Atomic Force Measurements in

Special Modes – Methodology and Application

Dipl.-Ing. T. Machleidt, PD Dr.-Ing. habil. K.-H. Franke, Dipl.-Ing. E. Sparrer

Computer Graphics Group / TU-Ilmenau

SFB 622 „Nanopositionier- und Nanomessmaschinen“

Teilprojekt C2 „Sensornahe Messdatenerfassung und Verarbeitung“

Dipl.-Ing. R. Nestler

Zentrum für Bild und Signalverarbeitung e.V.

Dipl. Wirtsch. Ing. M. Niebelschütz

FG Nanotechnologie / TU Ilmenau

SFB 622 „Nanopositionier- und Nanomessmaschinen“ Teilprojekt A8 „Multifunktionale Nanoanalytik“

SFB 622

Contents

¾ SFB 622

¾ Measurement System / Atomic Force Microscope ¾ Imaging Model of Kelvin Force Microscopy (KFM)

• Noise in KFM Data

• Analytical PSF Estimation ¾ Model Limitations

¾ Deconvolution Algorithm ¾ Deconvolution Results ¾ Conclusion & Outlook

SFB 622

SFB 622

Goal: Nanopositioning and Nanomeasuring Machine

Resolution: 0.05 nm Reproducibility: < 1 nm Positioning volume: 350 mm x 350 mm x 5 - 50 mm

Mesurement system: exchangable 2.5D, 3D

Role of supproject C2 Mirror Measure-ment X Measure-ment Z Metrological Frame _{Probes /}

Tools User-PC Server User-PC Server Primary 3D Features Interaction Probe / Object from the View of IP

Digital Signal Processor Data Compression

Measured Data Processing

SFB 622

Measurement System / Atomic Force

Microscope

Lateral Resolution:

AFM topography mode: approx. 2 nm

AFM special mode: approx. 50 – 100 nm

potential measurement (EFM, KFM),

magnetic force measurement (MFM), ...

Cantilever

Stage

Sample

Potential (KFM) measured by AFM

Deconvolution?

SFB 622

Measurement System / Atomic Force

Microscope

Deconvolution of AFM Measurement in Special Mode

Imaging process Deconvolution process

• PSF determination • Noise suppression Object

Disturbed

image Disturbedimage

Object estimation

PSF _Inversion

SFB 622

Kelvin Force Microscopy - KFM

Principle: Indirect determination of surface potential by means of an electrostatic force acting on the measuring system

2nd pass

Surface potential measurement

Φ

(

x y

)

U t dxdy y x C y x F y x ac t c =

∫∫

′ ⋅ Φ −Φ ⋅ ⋅ , ,ω( , ) ( , ) ( , ) sin(ω ) 1st pass Topography determination

SFB 622

Imaging Model of KFM

noise n(x,y)

?

actual surface potential measured surface potential + LSI system PSF

Φ(x,y) Φ_t(x,y) Φ_t,n(x,y)

?

¾ LSI system: linear shift-invariant system

with a point spread function (PSF) as the convolution kernel

SFB 622

Imaging Model of KFM – Noise Analysis

Amplitude distribution:

Histogram counting of noise amplitude

SFB 622

Imaging Model of KFM – Noise Analysis

Frequency distribution:

Fourier-transformed KFM image equally distributed Ö white noise

SFB 622

Imaging Model of KFM

noise n(x,y)

9

actual surface potential measured surface potential + LSI system PSF

Φ(x,y) Φ_t(x,y) Φ_t,n(x,y)

?

SFB 622

Imaging Model of KFM – LSI Analysis

Image interrelation at KFM

(

x y

)

U t dxdy y x C y x F y x ac t c =

∫∫

′ ⋅ Φ −Φ ⋅ ⋅ , ,ω( , ) ( , ) ( , ) sin(ω ) dj di y x y x C y y x x C y x _{i j} j i j i ij t ( , ) ) , ( ) , ( ) , ( , Φ ⋅ ′ − − ′ = Φ

∫∫

control unit ) , ( ) , ( , 0 ) , ( , x y for x y x y F_cω = Φ = Φ_t convolution kernel

SFB 622

Imaging Model of KFM – PSF Calculation

Transform KFM tip geometry to polar coordinates

r α

Fit a hyperbola to each angle α2 2

1

2 _{C z C z}

r = +

Calculate the electric field distribution at η=0 and ξ by means of heights C₁ and C₂

SFB 622

Imaging Model of KFM

noise n(x,y)

9

actual surface potential measured surface potential + LSI system PSF

Φ(x,y) Φ_t(x,y) Φ_t,n(x,y)

9

¾ Additive white Gaussian noise

SFB 622

Imaging Model of KFM – Model Limitations

Assumptions:

¾

Sample topography must be negligible

¾

Only the electrostatic force is acting on the detection

system

Solution:

¾

Measurement at sufficiently large

tip-to-sample distance

SFB 622

Imaging Model of KFM - Deconvolution

Inversion of the PSF with Wiener noise subpression

Filter adjustment by resolution boundary } { ˆ , 2 * , , n t n F L L L OTF OTF n t n t ⋅ Φ + ⋅ = Φ Φ Φ λ Wiener filter inverted OTF

(Optical Transfer Function = Fourier-transformed PSF)

SFB 622

Imaging Model of KFM - Deconvolution

SFB 622

Conclusion

¾

KFM measurement data have bad lateral resolution

¾

The imaging process can be described as an LSI model

¾

An analytical method was presented to determine the PSF

¾

Deconvolution was demonstrated using inversion of the

SFB 622

Outlook

¾

Using a measured

method to determine the PSF

Sample to determine the PSF (Developed by ZMN Ilmenau, SFB 622 TP A8)

¾Expansion of the deconvolution method (e.g. pixon method)

¾Forder practical analysis

Nanoscale stripe pattern for testing of lateral resolution and calibration of length scale

SFB 622

The 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