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Mask defects, especially multilayer defects, are a major

roadblock to EUV lithography adoption in high volume

manufacturing. Although the defect density and size are

reduced annually, the current progress is far from

sufficient.

The defects in the blank are difficult to repair without

damaging the blank itself. Therefore, the mitigation of

mask blank defects is considered a well working

alternative proposition. Several mitigation methods, such

as mask floor planning, pattern shifting1,2 and absorber

modification3, have been proposed. There is no reliable

method which can repair all EUV blank defects. For

better defect mitigation, several combination methods

are proposed. Elayat et al.4 provided a cost-benefit

assessment of different defect mitigation methods. It is

demonstrated that the most promising methods are

pattern shifting and its combination with other methods.

The optimal shift of pattern shifting needs to be

determined when combined with other mitigation

methods. Two methods for determining the optimal shift

are presented in this study. The first method involves the

mitigation of the impact of all defects as much as

possible. For this method, a merit function is proposed to

determine the optimal shift in pattern shifting. The

second method attempts to cover as many defects as

possible. A merit function is also proposed. These two

methods are then compared.

INTRODUCTION

MODELING ASSUMPTIONS AND PARAMETERS

Real-coded Binary-Coded

Mean 53.7 155.5

Variance 224.2333333 12759.16667

Observations 10 10

Hypothesized Mean Difference 0

df 9

t Stat -2.825228375

P(T<=t) one-tail 0.009938311

t Critical one-tail 1.833112933

P(T<=t) two-tail 0.019876621

t Critical two-tail 2.262157163

Real-coded Binary-Coded

Mean 53.7 155.5

Variance 224.2333333 12759.16667

Observations 10 10

Hypothesized Mean Difference 0

df 9

t Stat -2.825228375

P(T<=t) one-tail 0.009938311

t Critical one-tail 1.833112933

P(T<=t) two-tail 0.019876621

t Critical two-tail 2.262157163

Real-coded Binary-Coded

Mean 53.7 155.5

Variance 224.2333333 12759.16667

Observations 10 10

Hypothesized Mean Difference 0

df 9

t Stat -2.825228375

P(T<=t) one-tail 0.009938311

t Critical one-tail 1.833112933

P(T<=t) two-tail 0.019876621

t Critical two-tail 2.262157163

Laboratory of Information Optics and Opto-Electronic Technology, Shanghai Institute of Optics and Fine Mechanics,

Chinese Academy of Sciences, Shanghai 201800, China.

Sikun Li, Xiangzhao Wang, Xiaolei Liu, Heng Zhang

Optimal shift of pattern shifting for mitigation of mask defects in extreme ultraviolet lithography

ACKNOWLEDGEMENT

CONCLUSIONS

Two methods have been proposed to determine the

optimal pattern shift. Compared with the reference

without shifting, both the minimum impact method and

the maximum number method decrease the impact of

defects. Neglecting complexity, and compared with the

maximum number method, the minimum impact

method is more likely to succeed in the mitigation of

defects. The comparisons of those methods with

different defect sizes and amounts show that the

reduction of defects with large FWHM in the blank is

essential for successful defect mitigation.

REFERENCE

[1] P. Yan, Y. Liu, M. Kamna, G. Zhang, R. Chen, and F.

Martinez, Proc. SPIE 8322, 83220Z (2012).

[2] A. Wagner, M. Burkhardt, A. B. Clay, and J. P.

Levin, J. Vac. Sci. Technol. B 30, 051605 (2012).

[3] C. H. Clifford, T. T. Chan, and A. R. Neureuther, J.

Vac. Sci. Technol. B 29, 011022 (2011).

[4] Elayat, P. Thwaite, and S. Schulze, Proc. SPIE

8522, 85221W (2012).

The authors appreciate the insightful suggestions of

Dr. Andreas Erdmann from Fraunhofer IISB. This work

was supported by the National Natural Sciences

Foundation of China under Grant Nos. 61474129,

61275207, 61205102 and 61405210.

MINIMUM IMPACT METHOD

Defect impact:

First, the blank defects considered in the following are

multilayer defects after smoothing deposition process.

We assume that the blank defects are all Gaussian

defects. Furthermore, we assume that the inspection tool

provides the exact locations and sizes of the defects. The

size of the defect is described by height and full width at

half maximum (FWHM). In the simulation, the locations

and sizes of defects in the blank are generated by

adopting uniform random number.

Fig. 7 (a) The overlap of permitted regions, (b) (c) the collections of the shifts with the maximum overlap number (white region).

Fig. 1 Schematic of the mask blank, layout and margin

The number of residual defects by the

maximum number method is less than that

of the minimum impact method (Figs. 8 and

9). However, the residual impact of every

defect by the minimum impact method is

small, and the residual impact of some

defects by the maximum number is very

large, especially defect No. 18. Compared

with Fig. 8, the open region in the defect

region of No. 18 in Fig. 9 is much closer to

the peak of the defect. Given the high

height of No. 18 defect, its residual impact

may not be mitigated or compensated by

other methods. Considering the absorber

modification method as an example,

compensating the residual impact of this

defect is unsuccessful.

In addition, all sizes

reported here are at mask

scale, and magnification is 4×.

The mask layout consists of

patterns of square reflective

regions. According to the

application of EUV lithography,

the pattern size in the

simulations is 64 nm, and pitch

is 400 nm.

Considering the accuracy of the mask writer, 10 nm

errors are included in the simulation. Normally, because

the blank is always a little larger than the layout, a

certain margin is kept between the layout and blank

boundaries, allowing to shift the layout relative to the

blank( Fig. 1). A layout without shifting means that the

layout is positioned at the center of the blank. In our

approach, the sizes of the layout and the blank are

limited to 40 μm×40 μm and 41 μm×41 μm, respectively.

1

2 2

( ) ( , , ) ( , , , ) ,

| ( , , ) | ( ) ( )( , , )

0

1 ( , )( , , , )

0

N

defect pattern

i defect i

d i i idefect

pattern

D s A i x y A i s x y dxdy

h i x y x x y y FWHMA i x y

others

x y open regionA i s x y

others

Fig. 3 (a) The relative position of the blank and layout after shifting, (b) the three-dimensional topography of the defect, and (c) the effective region for computation of the impact.

Fig. 4 The error tolerance

The merit function of the optimal shift is

described as follows:

s: Max [Te(s)] after Max [Nd(s)], when Min [D(s)],

where Nd(s) is the number of defects covered

completely, Te(s) is the error tolerance(Fig.4),

D(s) is the residual impact after shifting.

Fig. 5 The residual impact with different shifts (There are 20 defects in the blank).

The residual impact D(s) with different shifts is shown in Fig. 5. the

maximum height and maximum FWHM of defects are 10 nm and 200 nm,

respectively. In this case, the residual impact without shifting is

1.067×105, the minimum residual impact after shifting is 6.032×103, and

two minimum impact shifts are (17, 294) nm and (17, 694) nm,

respectively. The number of uncovered defect is 8.

MAXIMUM NUMBER METHOD

Fig. 6 The definition of overlap

of the permitted regions.

The merit function is described as

s: Max [Te(s)] after Min [D(s)], when Max [Nd(s)]

Fig. 2 The phase perturbation (a) and change of amplitude (b) of

the multilayer reflection coefficient caused by a multilayer defect.

The PR of each defect in the blank is determined

by

1, ( , , ) ( , , , ) 0

( )0, ( , , ) ( , , , ) 0

defect pattern

defect i

defect i

defect pattern

defect i

A i x y A i s x y dxdy

PR sA i x y A i s x y dxdy

In Fig. 7, the maximum number of covered defects is 16. The optimal shifts

are (70, 317) nm and (70, 717) nm. The residual impact of both is 2.0614×104,

which is higher than the result of the minimum impact method. Compared

with the minimum impact method, the amount of defects uncovered is

reduced; however, the residual impact of some defects is higher. The highest

is 1.87×104, which is almost three times that of the residual impact of all

defects by the minimum impact method.

COMPARISON OF THE PROPOSED METHODS

Fig. 8 The residual defects after optimally shifting by the minimum impact method

Fig. 9 The residual defects after optimally shifting by the maximum number method (h is the peak height of the defect, w is the FWHM of the defect, the white bordered squares are the open regions, and other part of the defects is under the absorber).

Fig. 10 The residual impact (a) and the residual defects amount (b) as the maximum FWHM increases from 50 nm to 500 nm with an increment of 50 nm.

Fig. 11 The residual impact (a) and the residual defects amount (b) as the maximum height increases from 5 nm to 10 nm with an increment of 0.5 nm.

Given the random generation of defect sizes, the

increase in the maximum FWHM and maximum height

will raise the possibility of generating larger defects.

With the increase of the maximum FWHM, both the

residual impact and the amount of residual defects

generally increase (Fig. 10). However, with the increase

of the maximum height in Fig. 11, the increase of the

residual impact and the amount of residual defects is

not obvious. In pattern shifting, the defect regions

determined by FWHM of defects are covered more

difficultly as the FWHM increases. Therefore, in view of

the mitigation of blank defects, reduction of defects

with large FWHM is of higher priority.

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