SPIE conference, 3-8 march 2002, p 1 imec

Characterization of a projection lens usingthe extended Nijboer-Zernike approach

1) Philips Research

2) Delft University of Technology

3) IMEC

4) International Sematech

1

1

2

1Peter Dirksen, Joseph Braat, Peter De Bisschop,

Augustus Janssen, Casper Juffermans,Alvina Williams

3

4

SPIE conference, 3-8 march 2002, p 2 imec

Introduction to lens characterization

♦ Lens aberrations have an important contribution to CD variation and image misplacement

♦ Low k1-imaging requires tight aberration specifications.

♦ Focal plane deviation, astigmatism, coma and spherical aberration are all adjustable quantities.

♦ Aberrations may vary in time due machine drift.

SPIE conference, 3-8 march 2002, p 3 imec

♦ The new method is based of theobservation of the point spread function

♦ Resolves high and low order aberrations

♦ Illumination setting independent

♦ Wavelength independent

The new lens characterization method

Sensor, Resist

Lens

Simple binary mask, small hole

PSF

SPIE conference, 3-8 march 2002, p 4 imec

‘A slice from a point spread function’

The point spread function tells thewhole lens story

♦ Perfect lens: rotational symmetry, symmetry through focus

♦ Aberrations: symmetry is lost

SPIE conference, 3-8 march 2002, p 5 imec

♦ The experiment is straightforward.

♦ The problematic part is the interpretation and analysisof the measurement.

♦ This inverse problem, getting the Zernike’s, is solved by using a new analytical method: the extended Nijboer-Zernike approach

Interpretation of the experiment

SPIE conference, 3-8 march 2002, p 6 imec

Outline

♦ Introduction

♦ Extended Nijboer-Zernike approach

♦ Phase retrieval

♦ First experimental results

♦ Microscope

♦ Scanner

SPIE conference, 3-8 march 2002, p 7 imec

“Nijboer-Zernike theory of aberrations” (1942)

♦ Best focus, small aberrations

♦ Defocus included for a few loworder terms only

θα mr

rJirrJrU n

nmmn

n cos)(

2 )(

2 )( 1

,

11 ++�+≈

Airy pattern (1835)

SPIE conference, 3-8 march 2002, p 8 imec

��

�

=

++∞

=

−

+

−=

+≈

p

jljlm

ljl

lnm

nmm

nmnm

lrrJ

ififfrV

mCosViVfrU

0

2

1

1

100

)(v)2()exp(),(

),(22 ),( θα

♦ Good convergence for large defocus and radial values

♦ Good convergence for high order aberrations

♦ Nice symmetry and orthogonality properties

♦ The old theory is a special case of the new theory (f=0)

“Extended Nijboer-Zernike theory”A. Janssen, (2001)

New

SPIE conference, 3-8 march 2002, p 9 imec

0 5 10 15 20

0

0.2

0.4

Radial - axis

f = 0 f = πf = 2π

0 5 10 15 20

0

0.1

0.2

0.3

Radial - axis

Rea

l

Imag

inar

y♦ The complex amplitude as presented, is linear in αnm.

♦ The extension to large aberrations exist.

(r,f)V00pattern Airy focus- through:Example

SPIE conference, 3-8 march 2002, p 10 imec

0 2 4 6 8 10

0.02

0.04

0.06

0.08

0.1In

tens

ity

Radial axis

Extended Nijboer-ZernikeNumerical integration

Validation: example1/6 λ Spherical + 2π defocus

♦ More info: two publications in J.O.S.A. A., May 2002 issue

SPIE conference, 3-8 march 2002, p 11 imec

Outline

♦ Introduction

♦ Extended Nijboer-Zernike approach

♦ Phase retrieval

♦ First experimental results

♦ Microscope

♦ Scanner

SPIE conference, 3-8 march 2002, p 12 imec

Best focus

- focus

+ focus

Wavefront

Phase retrieval from intensity ?

SPIE conference, 3-8 march 2002, p 13 imec

)( functions Basic intensity Observed nmnm V�= α

Recipe for phase retrieval

♦ The Zernike coefficients are found on solving a linear system of equations.

Our approach to determine the lens aberrations is based onthe observation of the through-focus point spread function.

SPIE conference, 3-8 march 2002, p 14 imec

Validation phase retrieval

Position 0.0175 0.0175Focus -0.0187 -0.0187Astigmatism 0.0726 0.0726Coma -0.0588 -0.0588Spherical 0.2183 0.2183Three-point -0.0136 -0.0136Astigmatism 0.0114 0.0114Coma 0.1067 0.1067Spherical 0.0059 0.0059

Input: random aberrations Perfect retrieval

Intensity PSF

Low

ord

erH

igh

orde

r

♦ Details in the conference paper.

SPIE conference, 3-8 march 2002, p 15 imec

♦ MSM100, λ= 193 nm

♦ Load a reticle, observe aerial image on a CCD camera

Applications to a microscope

Ideal to observe the point spreadfunction of the objective lens

SPIE conference, 3-8 march 2002, p 16 imec

Through-focus aerial image of an isolated hole(λ=193 nm MSM-100)

The dominant term is high order coma

Retrieved Zernike coefficientsExperimental

Best focus- focus + focus

SPIE conference, 3-8 march 2002, p 17 imec

Applications to a scanner

FEM: combine contours into a through-focus aerial image

Single contour of the point spread function

SPIE conference, 3-8 march 2002, p 18 imec

The dominant terms are low order astigmatism and low orderthree-foil.

Retrieved Zernike coefficients

Through-focus aerial image of an isolated hole(ASML PAS 5500/950, λ=193 nm scanner)

Experimental

Best focus- focus + focus

SPIE conference, 3-8 march 2002, p 19 imec

Summary♦ The proof of principle of a new experimental method to

characterize a lens has been given.

♦ The method is based on the observation of the point spreadfunction.

♦ ‘Getting the Zernikes’ is solved analytically: the extended Nijboer-Zernike approach

Applications:

♦ Projection lenses 193, 157 and 13 nm

♦ Optical microscopes, such as reticle inspection tools

SPIE conference, 3-8 march 2002, p 20 imec

Acknowledgement

The authors wish to thank David van Steenwinckel, MichaelBenndorf and Johannes van der Wingerden from PhilipsReseach Leuven for their valuable input and experimentalsupport.