Optics Communications 283 (2010) 2309–2317

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Optics Communications

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Measurement technique for characterizing odd aberration of lithographicprojection optics based on dipole illumination

Bo Peng a,b,*, Xiangzhao Wang a,b, Zicheng Qiu a,b, Qiongyan Yuan c

a Information Optics Laboratory, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, Chinab Graduate School of the Chinese Academy of Sciences, Beijing 100039, Chinac KLA-Tencor China, Shanghai 201203, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 15 August 2009Received in revised form 30 December 2009Accepted 10 January 2010

Keywords:LithographyOdd aberrationImage displacementDipole illumination

0030-4018/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.optcom.2010.01.021

* Corresponding author. Address: Information OInstitute of Optics and Fine Mechanics, Chinese Aca201800, China.

E-mail address: victor5956@gmail.com (B. Peng).

A dipole illumination based measurement technique for measuring odd aberration of lithographic projec-tion optics is proposed. In the present technique, odd aberration is extracted from the image displace-ments at multiple illumination settings. Theoretical analysis of the impact of illumination profile onthe measurement accuracy is presented. By use of dipole illumination, the image displacement variationrange that determines the measurement accuracy is enlarged. Using lithographic simulator PROLITH, themeasurement accuracies of odd aberration under conventional illumination and dipole illumination arecompared. The simulation results show that the measurement accuracy of odd aberration increases sig-nificantly when dipole illumination is used.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

Aberrations of projection optics are one of the most impor-tant problems lithographers have to deal with in the state-of-art lithography tools. Excess unwanted aberrations cause a dete-rioration of image quality as well as a significant reduction ofprocess latitude of lithographic process [1–3]. Of all the aberra-tions, odd aberration causes image displacement and linewidthasymmetry that influence the critical dimension uniformity(CDU) [4,5]. In practice, reliable production of advanced inte-grated circuits requires a constant monitoring and control ofodd aberration of projection optics. As the feature size printedwith lithography tools continues to shrink, the aberration toler-ance of lithographic projection optics becomes tighter, thereforeit is essential to develop a more accurate in situ measurementtechnique to predict and monitor odd aberration in the manufac-turing process.

Over the past few years, various in situ techniques for measur-ing aberrations in the projection optics have been proposed.Phase wheel method detects aberrations through inspection ofimages of printed resist patterns and fitting of the aberratedwavefront [6–8]. The approach is based on the inspection of

ll rights reserved.

ptics Laboratory, Shanghaidemy of Sciences, Shanghai

printed resist through focus, thus the exposure process is com-plex and time-consuming. Canon corporation made someimprovements to the PMI and integrated it into the exposure tool,they named this novel interferometer in situ Phase MeasurementInterferometer (iPMI) [9,10]. iPMI is capable to measure wave-front aberrations at a high accuracy. However, the cost increasesbecause the technique requires a modification of illuminator ofthe lithography tools. The extended Nijboer–Zernike (ENZ) ap-proach retrieves aberration based on the observation of the inten-sity point-spread function of the projection lenses [11,12]. WhenENZ approach is used as an in situ measurement method, expo-sure process is necessary and aberration is retrieved from thescanning electron microscope (SEM) image of the exposed resist.The measurement time is relatively long because a process of re-sist image evaluation usually takes several hours. The transmis-sion image sensor (TIS) at multiple illumination settings(TAMIS) is a sensor-based method developed by ASML [13,14].In this technique, binary marks are used as measurement marksfor aberration measurement. The image displacements of themarks at multiple illumination settings are measured by theTIS, which is built into the wafer stage. With the image displace-ments and focus shifts acquired from the TIS data, the Zernikecoefficients can be calculated accordingly. The even aberrations,such as spherical and astigmatism, are extracted from the focusshifts of the horizontal and vertical patterns on the marks. Theodd aberrations, such as coma, are extracted from the imagedisplacements of the patterns on the marks. Although TAMIS is

2310 B. Peng et al. / Optics Communications 283 (2010) 2309–2317

robust and fast because of its direct measurement of the aerialimage, its measurement sensitivity is restricted by the use of bin-ary marks and conventional illumination. Recently, several meth-ods using alternating phase shifting mask (Alt-PSM) marks as themeasurement marks to enhance the measurement accuracy wereproposed [5,15,16]. Then the optimization of Alt-PSM marks wasexplored to enhance the measurement accuracy further [18]. Butthe influence of the illumination profile on the measurementaccuracy is still not investigated.

In this paper, we propose a novel method for measuring oddaberration of lithographic projection optics. Conventional illumi-nation is replaced by dipole illumination to enlarge the image dis-placement variation range induced by odd aberration. Usinglithographic simulator PROLITH, the variation ranges of aberrationsensitivities that are the key factors related with measurementaccuracy are calculated. The measurement accuracy of odd aberra-tion is analyzed compared with the previous techniques operatedunder conventional illumination.

2. Theory

2.1. Optical lithography imaging model

The configuration of an optical lithography imaging system isshown in Fig. 1. To elucidate the essence of investigation, thedimensionless normalized variables bx, by, bf and bg [19] are used:

bxo ¼ �Mxo

k=NA; cyo ¼ �

Myo

k=NA;

bxi ¼xi

k=NA; byi ¼

yi

k=NA; ð1Þ

bf ¼ fNA=k

; bg ¼ gNA=k

;

where k is the wavelength of the monochromatic radiation and NAis the image-side numerical aperture of the projection optics. M isthe magnification factor of the projection optics. ðxo; yoÞ, ðxi; yiÞ,and ðf ; gÞ are the Cartesian coordinates of the object plane, imageplane and pupil plane respectively. The intensity distribution ofthe image plane is given by the Hopkins formula of partial coherentimaging:

Fig. 1. Representation of an optica

Iðbxi ; byi Þ ¼Z þ1

�1

Z Z ZTCCðbf 0; bg 0;bf 00; bg 00; rÞOðbf 0; bg 0ÞO�ðbf 00; bg 00Þ

� e�i2p

"ðbf 00�bf 00Þbxiþðbg 0�bg 00Þbyi

#dbf 0dbg 0dbf 00dbg 00; ð2Þ

where TCC is the transmission cross-coefficient:

TCCðbf 0; bg 0;bf 00; bg 00; rÞ ¼ Z þ1

�1

ZJ bf ; bg ;r� �

H bf þ bf 0; bg þ bg 0� �H�

� bf þ bf 00; bg þ bg 00� �dbf dbg : ð3Þ

Here O bf 0; bg 0� �is the diffraction spectrum of a mask. J bf ; bg ;r� �

de-

scribes the effective source intensity distribution under Kohler illu-mination. For conventional illumination, the effective source isdescribed as

Jðbf ; bg ;rÞ ¼ 1pr2 circ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffibf 2 þ bg2

qr

0@ 1A ¼ 1pr2 if

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffibf 2 þ bg2

q6 r;

0 otherwise;

(ð4Þ

where r is the partial coherence of conventional illumination. Fordipole illumination, the effective source is described as

Jðbf ; bg ;rÞ ¼ 12pr2

rcirc

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðbf � rÞ2 þ bg2

qrr

0@ 1A¼

12pr2

rif

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðbf � rÞ2 þ bg2

q6 rr ;

0 otherwise;

(ð5Þ

where rr is the radius sigma, and r is the center sigma of dipole illu-mination. Hðbf ; bgÞ is the objective pupil function and is given by theequation

Hðbf ; bgÞ ¼ e�i2p

k W

�bf ;bg�; where bf 2 þ bg2 < 1: ð6Þ

W bf ; bg� �is the wavefront aberration defined as the optical path dif-

ferences between actual wavefront and ideal spherical wavefront.To aid in the interpretation of optical tests, it is convenient to ex-press the wavefront aberration in terms of Zernike fringe polynomi-als [20]:

l lithography imaging system.

Fig. 2. Aerial images of a 600 nm pitch Alt-PSM mark under the illuminationsettings of (a) NA = 0.5, r = 0.3 and (b) NA = 0.8, r = 0.8. The threshold fordetermining the image displacement is 0.3.

B. Peng et al. / Optics Communications 283 (2010) 2309–2317 2311

Wðbf ; bgÞ ¼X1n¼1

ZnRnðbf ; bgÞ¼ Z1 þ Z2

bf þ Z3bg þ � � �þ Z7½3ðbf 2 þ bg2Þ � 2�bf þ Z8½3ðbf 2 þ bg2Þ � 2�bg þ � � �þ Z10ð4bf 3 � 3bf Þ þ Z11ð3bg � 4bg3Þ þ � � �þ Z14ð10ðbf 2 þ bg2Þ2 � 12ðbf 2 þ bg2Þ þ 3Þbfþ Z15ð10ðbf 2 þ bg2Þ2 � 12ðbf 2 þ bg2Þ þ 3Þbg þ � � � ;

ð7Þ

where Zn is the Zernike coefficient and Rnðbf ; bgÞ is the Zernike poly-nomial. Z7 and Z14 represent third-order x coma and fifth-order xcoma. Z8 and Z15 represent third-order y coma and fifth-order ycoma. Z10 is x three-foil, and Z11 is y three-foil.

2.2. Relationship between measurement accuracy and the illuminationprofile

In the present technique, Alt-PSM marks are used to measureodd aberration. The transmission function of an Alt-PSM markcan be expressed as

tðxoÞ ¼Xþ1

n¼�1dðxo � 2npÞ � rect

xo þ p=2w

� �� rect

xo � p=2w

� �� �;

n 2 Z; ð8Þ

where p is the pitch of the Alt-PSM mark, and w is the width of thephase region. The spectrum of the Alt-PSM mark is the Fouriertransformation of tðxoÞ

Oðf ; gÞ ¼ i �wp

XþN

n¼�N

d f � n2p

� �� sincðw � f Þ � sinðppf Þ � dðgÞ; n 2 Z;

ð9Þ

where f , g are the spatial frequencies of the object spectrum in the xand y direction, and sinc function is defined as sincðxÞ ¼ sinðpxÞ

px . N isthe highest order of diffraction light that can pass the exit pupil.Using the scaling relationship in Eq. (1), we can get the followingexpression:

Oðbf ; bgÞ ¼ i �wp

XþN

�N

d bf � nk2pNA

� �� sinc

wNAbfk

!

� sinppNAbf

k

!� dðbgÞ; n 2 Z; ð10Þ

where bf and bg are the normalized frequencies in the exit pupil. Thehighest order of diffraction light in the exit pupil is determined bychoosing the pitch and ratio of line/space of the Alt-PSM mark. Bysubstituting Eq. (2) with Eq. (10), the intensity distribution of theAlt-PSM mark image is obtained:

Iðbxi Þ ¼ C �XþN

m¼�N

XþN

n¼�N

sincmw2p

� �sin

m2

p� �

sincnw2p

� �sin

n2p

� �� TCCðmbf0 ; 0; nbf0 ;0;rÞe�i2pðm�nÞbf0bxi ; ð11Þ

where C is a constant factor, bf 0 ¼ k2pg�NA, and N is highest order of

diffraction light that is determined by the following equation:

N < ð1þ r0Þ=bf0 ; N 2 Z: ð12Þr0 is the partial coherence for conventional illumination and is theoutmost radius for other types of illumination.

When the aerial image is calculated by Eqs. (11) and (12), theimage displacement of a given mark can be determined from theaerial image contour at a threshold level of 0.3 as explained inmore details below. In the present technique, the Alt-PSM markwith the 1:2 line/space ratio is chosen. The selection of this

parameter is based on the principle that with the 1:2 line/space ra-tio, the ±3rd order diffraction beams of the Alt-PSM mark are elim-inated [18]. The image displacement increases as the pitchincreases until the ±5th order diffraction beams enter the exit pu-pil, therefore the sensitivity for measuring coma is enlarged com-pared with using the ordinary Alt-PSM mark with 1:1 line/spaceratio. However, the measurement accuracy is determined by thesensitivity variation range. Evaluating the measurement perfor-mance only by the sensitivity at a specific illumination setting isnot completely appropriate. Thus, the conclusion about the pitch’svalue is abandoned and reinvestigated later by more rigorous dis-cussion with regards to the practical multiple illumination settingsin the measurement process.

Besides the structure of the Alt-PSM mark, the effective sourcefunction of illumination also influences the image displacement. Inorder to investigate the image displacement of the Alt-PSM markdirectly from the formula, Eq. (11) is rewritten as

IðbxiÞ ¼ 2C �XþN

m¼�N

Xm�1

n¼�N

gðm; nÞ cos 2pðm� nÞbf0 bxi þ aðm;nÞh i

þ C �XþN

m¼�N

sinc2 mw2p

� �sin2 m

2p

� �� TCCðmbf0 ;0; mbf0 ;0; rÞ;

ð13Þ

Fig. 4. The illumination profiles of conventional, annular, quadrupole and dipoleillumination.

2312 B. Peng et al. / Optics Communications 283 (2010) 2309–2317

where gðm;nÞ ¼ sinc mw2p

� �sin m

2 p

sinc nw2p

� �sin n

2 p

Aðm; nÞ, A(m,n) is

the absolute value of TCCðmbf0 ;0; nbf0 ;0;rÞ, and aðm;nÞ is the argu-

ment of TCCðmbf0 ;0; nbf0 ;0;rÞ. When N = 1, the intensity distributionis the result of two-beam interference, and the Eq. (13) is reducedinto a summation of a cosine function and a constant. The imagedisplacement can be expressed as

Dbxi ¼að1;�1Þ

4pf0: ð14Þ

When N exceeds 1, the total intensity distribution is composedof a summation of a series of cosine functions and a constant. Theimage displacement varies when different thresholds are chosen, itis no longer possible to obtain the formula of image displacement.However, the image displacement under multiple-beam interfer-ence condition can be extracted from the aerial image contour.Fig. 2 shows the aerial image contour under two-beam interferenceand multiple-beam interference conditions, and shows how theimage displacement is determined.

Using Eqs. (11) and (12), the image distributions of the Alt-PSMmark under conventional illumination and dipole illumination arecalculated, and the image displacement variation ranges are ob-tained. In the calculation, NA varies from 0.5 to 0.8, and r (partialcoherence or center sigma) varies from 0.3 to 0.8. The maximumimage displacement and the minimum image displacement arefound out and the image displacement variation range of the Alt-PSM mark with certain pitch is calculated. As introduced in thenext section, the image displacement variation range is inverselyproportional to the measurement accuracy. Thus it is an appropri-ate criterion to evaluate the performance of the measurementtechnique. The pitch of the Alt-PSM mark is altered from 600 to1800 nm with a step of 120 nm to inspect the impact of two typesof illumination on the image displacement variation ranges underdifferent pitches. The results are shown in Fig. 3. As can be seenfrom the figure, the image displacement variation range underdipole illumination is larger than that under conventional illumi-nation in each calculated pitch, thus the image displacementvariation range of the Alt-PSM mark is enlarged when the dipoleillumination is used. The pitch with the maximum image

Fig. 3. Calculated image displacement variation ranges und

displacement variation range under dipole illumination is alsoobtained from the calculation results, which is 1080 nm.

With regards to all aberrations, only odd aberrations induceimage displacement. Ignoring the influence of higher order oddaberrations, the relationship between image displacement andZernike coefficients can be described by the following equation:

Dx ¼ S2Z2 þ S7Z7 þ S10Z10 þ S14Z14; ð15Þ

er dipole illumination and conventional illumination.

B. Peng et al. / Optics Communications 283 (2010) 2309–2317 2313

where Si represents sensitivity of an aberration. When the relativeimage displacement is measured, the impact of distortion can beeliminated [17]. The equation is revised as

Dx ¼ S7Z7 þ S10Z10 þ S14Z14: ð16Þ

When the mark is illuminated by dipole illumination, the image dis-placement caused by odd aberration depends on center sigma of theillumination source and NA of the projection optics. In considerationof NA and center sigma r, the relationship between image displace-ment and odd aberration is expressed as

DxðNA;rÞ ¼ S7ðNA;rÞZ7 þ S10ðNA;rÞZ10 þ S14ðNA;rÞZ14: ð17Þ

The sensitivity Si can be calculated by the following equation:

SiðNA;rÞ ¼ @DxðNA;rÞ@Zi

: ð18Þ

Fig. 5. Image displacement variation ranges of simulation results under the four typicalillumination.

A

Fig. 6. The sketch of the redesi

For each NA and r setting, a linear equation is obtained. With multi-ple NA and r settings, a series of equations can be expressed as

DxðNA1;r1ÞDxðNA2;r2Þ

..

.

..

.

2666664

3777775 ¼@DxðNA1 ;r1Þ

@Z7

@DxðNA1 ;r1Þ@Z10

@DxðNA1 ;r1Þ@Z14

@DxðNA2 ;r2Þ@Z7

@DxðNA2 ;r2Þ@Z10

@DxðNA2 ;r2Þ@Z14

..

.

..

.

26666664

37777775Z7

Z10

Z14

264375: ð19Þ

Eq. (19) is over determined and can be solved by the least squaremethod. When the samplings with multiple illumination settingsare finished, Zernike coefficients Z7, Z8, Z10, Z11, Z14 and Z15 can bedetermined. When variation range of the data used in least squarefit procedure is larger, the measurement accuracy of the aberrationwill be higher.

illuminations in comparison with calculation results under dipole and conventional

B

gned measurement marks.

Fig. 7. Image displacement contours of redesigned Alt-PSM mark measured under conventional illumination and dipole illumination. (a) Z7, conventional illumination. (b) Z7,dipole illumination. (c) Z10, conventional illumination. (d) Z10, dipole illumination. (e) Z14, conventional illumination. (f) Z14, dipole illumination.

Table 1Simulation results of aberration sensitivities and measurement accuracies.

Zernikecoefficient

Illuminationtype

Maximumsensitivity

Minimumsensitivity

Measurementaccuracy(nm)

Z7 Conventionalillumination

1.81 0.69 0.89

Dipole illumination 1.79 �0.33 0.47Z10 Conventional

illumination�0.04 �0.22 5.55

Dipole illumination �0.13 �0.79 1.51Z14 Conventional

illumination0.21 �2.08 0.44

Dipole illumination 1.19 �1.95 0.32

2314 B. Peng et al. / Optics Communications 283 (2010) 2309–2317

3. Simulation

3.1. Comparison of measurement results under typical illuminations

In order to test the validity of the theoretical analysis, imagedisplacements under the four typical illuminations are simulatedusing lithographic simulator PROLITH. The illumination profilesof the four typical illuminations are shown in Fig. 4. The wave-length used in the simulation is 193 nm. Of 0:05k third-order xcoma aberration is assumed. The input aberration is defined at0.93 NA. The variation range of NA is 0.5–0.8. The variation rangeof r (partial coherence or center sigma) is 0.3–0.8. The sigma ra-dius of dipole and quadrupole illuminations is 0.2, and the widthsigma of annular illumination is 0.4. The line/space ratio is keptconstant as 1:2 in the simulation. The pitch of the Alt-PSM markis altered from 600 to 1800 nm, and the simulation step of pitchis 120 nm. The image displacement variation range at certain pitch

is obtained by finding out the maximum and minimum image dis-placements and calculating their absolute difference. The sign ofthe image displacement is taken into account when the maximum

B. Peng et al. / Optics Communications 283 (2010) 2309–2317 2315

image displacement and minimum image displacement are foundout. The simulated variation ranges of image displacements underthe four typical illuminations are shown in Fig. 5, and the calcula-tion results of image displacement variation ranges under dipoleand conventional illuminations are also added in Fig. 5 to make acomparison. Fig. 5 shows the PROLITH simulation results are ingood agreement with the calculation results by Hopkins theoryof partial coherent imaging. The difference is no more than0.70 nm (0:0036k) in dipole illumination case and no more than0.49 nm (0:0025k) in conventional illumination case. The imagedisplacement variation range under conventional illumination isthe smallest among the four typical illuminations. The image dis-placement variation range under annular illumination is similarwith that under quadrupole illumination. The image displacementunder dipole illumination is the largest through the whole pitch

Fig. 8. Aberration distributions of Z7, Z10 and Z14. (a) and (b) 2D and 3D distributions forZ14.

variation range and is significantly larger than other three cases.The explanation for the above results is as below. The light passesthe exit pupil experiences different phase delays, which averageout the image displacement. When different illuminations areused, two factors decided by the illumination profile influencethe image displacement: (1) the size and (2) the location of illumi-nated area in the exit pupil. Compared with other illuminations, di-pole illumination leads to smaller illuminated area in the exitpupil, which reduces the average effect and makes the final imagedisplacement more sensitive to the phase error in a specific area.As the image displacement usually decrease as r (partial coherenceor center sigma) increases, it usually reaches maximum whenr = 0.3, and minimum when r = 0.8. When r = 0.3, dipole illumina-tion appropriately positions the left part and the right part of theilluminated area in regions with large positive and large negative

Z7. (c) and (d) 2D and 3D distributions for Z10. (e) and (f) 2D and 3D distributions for

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Z7 Z10 Z14 Z7 Z10 Z14 Z7 Z10 Z14

Group1 Group2 Group3M

agni

tude

(λ)

Input

Output

Fig. 10. Comparison of the input and output wavefront errors.

2316 B. Peng et al. / Optics Communications 283 (2010) 2309–2317

phase errors, respectively. When r = 0.8, the symmetrical illumi-nated area by dipole illumination moves to the edge of the exitpupil, where the left part and right part of illuminated area expe-rience large negative and large positive phase errors, respectively.Therefore, dipole illumination leads to large positive image dis-placement and large negative image displacement when r = 0.3and r = 0.8, respectively. Due to the relative small illuminated areaand appropriate location of the illuminated area, dipole illumina-tion offers largest image displacement variation range in the fourtypical illuminations. According to the above simulation, the pitchwith the largest image displacement variation range is 1080 nm.This result is the same with the theoretical analysis. The structureof the mark is shown in Fig. 6, where w = 720 nm and p = 1080 nm.Mark A is used to measure Z7, Z10 and Z14, and mark B is used tomeasure Z8, Z11 and Z15.

3.2. Evaluation of the measurement method under dipole illumination

In the present technique, odd aberrations are extracted from theimage displacement of the Alt-PSM mark. The measurement accu-racy of odd aberrations is related with the measurement accuracyof image displacement and the variation range of the sensitivity ofthe aberration. Define MA as the measurement accuracy of Zi, OAas the overlay accuracy of the lithographic tool, ðSiÞmax and ðSiÞmin

as the maximum and minimum values of sensitivity of Zi. Theirrelationship can be expressed as:

Fig. 9. The correlation between image displacement and Z7 within the range of 0–0.05kwith a step of 0.1.

MAi /OA

ðSiÞmax � ðSiÞmin

�� �� : ð20Þ

According to Eq. (18), the variation range of the sensitivity isproportional to the variation range of image displacement, thusthe measurement accuracy can be evaluated by the image dis-placement variation range. Using lithographic simulator PROLITH,the image displacements under dipole illumination and conven-tional illumination are simulated. In the simulation, the redesignedmark with 360 nm linewidth and 1080 nm pitch is used, and theamount of Z7, Z10 and Z14 are set to be 0:05k. The variation range

at (a) NA = 0.5, (b) NA = 0.6, (c) NA = 0.7 and (d) NA = 0.8. r is varied from 0.3 to 0.8

B. Peng et al. / Optics Communications 283 (2010) 2309–2317 2317

of NA is 0.5–0.8, and the variation range of r is 0.3–0.8. Accordingto the simulation results, the image displacement variation rangesof Z7, Z10 and Z14 increase from 10.8 nm, 2.1 nm, 22.1 to 20.5 nm,6.3 nm, 30.3 nm, when conventional illumination is replaced by di-pole illumination. The image displacements measured at multipleillumination settings are shown in Fig. 7. Overlay accuracy of thelithographic tool is assumed to be 1 nm. Using Eqs. (18) and (20),the sensitivity variation range and measurement accuracy can becalculated. The results are shown in Table 1. It is clear that themeasurement accuracies for Z7, Z10 and Z14 increase significantlycompared with the results with the same mark under conventionalillumination. Among these three aberrations, the image displace-ment variation range of Z10 has the largest increase. It can be com-prehended by analyzing the aberration distribution of three typesof aberrations. The aberration distributions of Z7, Z10 and Z14 areshown in Fig. 8. As can be seen from the figure, the aberration dis-tribution of Z10 is flatter in the center part of the pupil, comparedwith those of Z7 and Z14. In order to effectively sample the largephase delay that is mainly distributed at the edge of the exit pupil,the illuminated area must be confined in relatively small area.Therefore, dipole illumination is extremely advantageous for themeasuring three-foil.

Besides measurement accuracy, other factors like linearity be-tween Zernike coefficient and image displacement also must beconsidered to evaluate the validation of the present technique.Except third-order x coma Z7, all the other aberrations are assumedto be zero. The correlation between image displacement and Z7

within the range of 0–0.05k is presented in Fig. 9. As Fig. 9 shows,the image displacement is well linearly related with Z7 under eachillumination setting used in the measurement process. Furthersimulation indicates that the image displacements are also welllinearly related with Z10 and Z14 within the range of 0–0.05k,respectively. Typically, individual aberration of current litho-graphic projection optics is below 0.004k, which is included inthe linear range. Therefore, the consideration of linearity wouldnot be an obstacle for the application of measurement method un-der dipole illumination. Besides, the image contrast of the pro-posed Alt-PSM mark under dipole illumination is better than thatunder conventional illumination, which is advantageous for reduc-ing the overlay measurement error of lithographic tools.

The impact of phase error of the Alt-PSM marks on aberrationsensitivities is simulated to investigate the systematic error ofthe measurement technique. From the simulation results, the sen-sitivity variation caused by phase error up to ±5� is approximately0.03. This variation is not completely ignorable for the presentmeasurement technique. Therefore the systematic error causedby phase error of the Alt-PSM marks should be corrected beforeaberration calculation.

The crosstalk between different Zernike coefficients mightinfluence measurement result. An aberrated wavefront with upto 37th order Zernike coefficients is essential to evaluate the per-formance of our technique. However, in all aberrations, even aber-rations only induce shift of best focus. They do not contribute toimage displacement when the mark is illuminated symmetrically.The influence of Z2 can be eliminated by relative image displace-ment measurement. The influence of higher order odd aberrations(Z19, Z23, Z26, Z30 and Z34) on image displacement is negligibleaccording to the simulation results. Taking these factors out ofour consideration, three groups of aberrated wavefronts with Z7,Z10 and Z14 are input to investigate the measurement results ofthe present method. When the image displacement data are col-lected, the individual aberrations are calculated using the least

square method. The results are shown in Fig. 10. According tothe simulation results, the absolute error for Z7 is less than0:0011k, the absolute error for Z10 is less than 0:0030k, the absoluteerror for Z14 is less than 0:0008k. The result shows that the presenttechnique is not vulnerable to the influence of crosstalk betweendifferent Zernike coefficients. Due to the reason of symmetry, allthe results of Z8, Z11 and Z15 are the same with Z7, Z10 and Z14,but the directions of the measurement mark and the dipole illumi-nation need to be rotated by 90�.

4. Conclusion

A novel odd aberration measurement technique based on dipoleillumination is proposed. The influence of illumination profile onthe measurement accuracy is analyzed. Both the calculation resultsby Hopkins theory of partial coherent imaging and simulationresults by PROLITH show dipole illumination offers the bestperformance for odd aberration measurement. Using the litho-graphic simulator PROLITH, the measurement accuracies of Z7,Z10 and Z14 are obtained. According to the simulation results, themeasurement accuracy of odd aberrations under dipole illumina-tion increases significantly compared with previous techniquesoperated under conventional illumination.

Acknowledgements

This work was supported by a Grant from the Key Basic ResearchProgram of Science and Technology Commission of ShanghaiMunicipality No. 07JC14056, International Cooperation ProgramProject of Shanghai Municipal Science & Technology Commissionunder Grant 08520704200, National Natural Science Foundationof China under Grant 60878029, 60938003 and Shanghai Rising-Star Program under Grant 08QB14005. The authors would like tothank NERCLE (National Engineering Research Center for Litho-graphic Equipment, China) for the support of this work.

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