Understanding lens aberration and influences to

Understanding lens aberration and influences to lithographic imaging

Bruce W. Smith and Ralph Schlief Rochester Institute of Technology, Microelectronic Engineering Department

82 Lomb Memorial Drive, Rochester, NY 14623- 1732, [email protected]

ABSTRACT

Lithographic imaging in the presence of lens aberration results in unique effects, depending on feature type, size, phase, illumination, and pupil use. As higher demands are placed on optical lithography tools, a better understanding of the influence of lens aberration is required. The goal of this paper is to develop some fundamental relationships and to address issues regarding the importance, influence, and interdependencies of imaging parameters and aberration.

Keywords: Aberrations, optical lithography, resolution enhancement

1. INTRODUCTION

It is generally true that there is no universal impact of lens aberration. This is especially so for microlithographic imaging. We have demonstrated in earlier reports how the influence of lens aberration depends on illumination method, masking approach, and specific utilization of the objective lens pupil (for a projection lithography tool using Kohler illumination) [ 1, 21. As values of kl below 0.5 are pursued, an understanding of the impact of lens aberration for specific imaging situations is important. Establishing tolerance limits and relationships for current and future conditions of optical lithography is challenging, leaving the lithographer with concerns that are not easily addressed using conventional optical description.

Historically, during the design and fabrication of an optical system, decisions about imaging capability and performance could be carried out using general modulation calculations combined with actual resist performance data. This has changed dramatically over the past few years as lithography demands have pushed imaging to levels approaching incoherent diffraction limits. Methods of image assessment now include specific feature characterization and the evalmtion of sensitivity to unique aberration types [3, 4, 51. These advanced characterization techniques can make generalizations difficult and can lead away from the development of underlying relationships. In this paper, we describe some of the fimda.mentaI relationships that govern such things as feature specific aberration sensitivity, resist capability and aberration tolerancing, illumination and masking influences, and the best utilization of an aberrated lens pupil. Additionally, we develop a predictive link between frequency plane and image plane distributions and present pupil statistics to model the primary influences of aberration on imaging. These analytical techniques and methods have been incorporated into a lithography software tool, which is also described.

2. PROXIMITY AND ABERRATION

Isolated features do not respond the same to lens aberration as dense features do. This is a classical and important example of how the impact of lens aberration depends on the geometry being imaged. Closer examination can lead to a better understanding about optical performance and limitations. Figure la shows an aerial image simulation for line/space features of size kl=O.35 at duty ratios ranging from 4: 1 to 1:4 using a perfect lens for partial coherence values from 0.5 to 0.9 (where a 1: 1 duty ratio implies equal line/space features). A high NA scalar model was used for the simulations (Prolith/2 v. 6.05d). This plot shows how NILS generally increases for more isolated features, which is expected as the corresponding pitch value increases. Figure lb shows a similar plot for an imaging system with 0.05 waves of spherical aberration, a reasonably small level but significant by today’s standards. The impact of this aberration is realized in the plot in Figure lc, where the fractional loss in NILS is shown. The impact of spherical aberration is greatest as line isolation increases and also at low levels of partial coherence. As will be

Proc. of SPIE Vol. 4000, Optical Microlithography XIII, ed. C. Progler (Mar, 2000) Copyright SPIE

294

shown, this is a direct result of phase errors between zero and higher frequency terms in the objective lens pupil. Analysis has also been carried out for other aberration types suggesting similar effects.

25 . 1

05 .

a

0.5

0 w-qcc)qcvLc) -qcuqmIs,*

c9 N cv c9 ‘aqmqnlq ~qNqCr)qd

DutlJ ratio; :X) c’) N

Duti ratio i :X) N m

Figure la&. NILS vs. duty ratio vs. partial coherence for kl=0.35 features. Duty ratio varies from 4: 1 (lines) to 1:4 (spaces). A perfect lens (a) is compared to a lens with 0.05 waves of spherical aberration (b).

0.99 0.97

Y 0.95 7 g 0.93

‘9 0.91

L 0.89

0.87

0.85 ~Lqcc)qcv~ ~~cu~c’>Lqd-

c9 nl Duk ratio b:X)

N c9

Figure lc. Loss is NILS with 0.05 waves of spherical aberration, increasing with line isolation and with partial coherence.

3. SIMPLE COHERENT ANALYSIS

To gain insight into the reasons for the imaging differences between dense and isolated features, their difFraction distribution in the lens pupil needs to be explored. Figure 2 depicts two mask functions - a dense line (1: 1) mask function md(x) and a more isolated line (1:4) mask function mi(X) (a duty ratio of 1:4 or greater will be used to represent line isolation). It is convenient to represent these functions using a linear systems description, the convolution of a single space function (rect) with an impulse train function (comb) with a fundamental frequency of the mask pattern (I/‘):

mP(x) = rect(x.OSp) * comb(x/p) mi(x) = rect(xdl.8p) * comb(x/p)

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where p is the mask pitch and the scaling factor in the denominator of the rect functions correlates to the spacewidth.

The diffraction patterns resulting from coherent illumination are Fourier Transforms of these masking functions:

i&(i) = OSsinc(id2) x comb(u) Mi(u) = 0.8sinc(4u/5) x comb(u)

where M(U) is the Fourier Transform of m(x) and u is spatial frequency, I/x. The magnitude values of the zero and first orders for the dense lines are 0.5 and 0.3 18 and for the isolated lines, values are 0.8 and 0.187, as shown in Figure 3 for a lens pupil collecting only these orders (pitch - ?JNA). The resulting coherent image amplitude function for the isolated lines is biased quite differently from the dense image amplitude function. Figure 4a depicts the situation where image amplitude functions at the wafer, represented as:

m&ix) = 0.5 + 0.63 7cos(21zx/p) mi’(L) = 0.8 + 0.3 ~~cos(~~x/P).

Squaring the image amplitude functions results in intensity or aerial image functions [I(x)], shown in Figure 4b:

&(-i-i) = r0.5 + 0.63 7cos(2xdp) Jz Ii(X) =[ 0.8 + 0.3 ~~cos(~YE..)]~

rect(x/O.5p)*comb(tip)

I i 1.5

rect(x/O.8p)*comb(x/p)

-05’ -055 . . Figure 2. Mask functions analyzed, (left) equal dense lines and (right) 19 isolated hes.

Figure 3. The diffraction field for dense and isolated lines showing orders collected in the lens pupil NA-Up. Zero and first order magnitude values are 0.5 and 0.3 18 for dense features and 0.8 and 0.187 for isolated features. The defocus aberration function across the lens pupil is also shown.

Proc. SPIE Vol. 4000296

e a I 21-

55% threshold Intensity

b

30% threshold,

I -0

5

I 1 I I I 1 I I I 1

.

1

Figure 4. Amplitude and aerial image (intensity) functions for dense and isolated (1:4) lines with pitch - ?JNA. The dense lines are the lower curves, the isolated lines are the upper curves. A 55% resist amplitude threshold and a 30% resist intensity threshold values are indicated.

For the isolated line case, the increased bias from the zero diffraction order compared to the first order gives rise to problems. A photoresist process is generally optimized when it samples an aerial image at a threshold point near a 30% intensity value. This correlates to a 55% amplitude threshold. This is appropriate for dense lines since it is close to the intensity bias value. For isolated lines, the situation is problematic. The isolated intensity and amplitude functions are sampled by the photoresist near image positions that will vary the most - the peak or nodal positions of the biased cosine functions. Sensitivity to image process variation for small isolated lines is now predictable. By comparison, the dense lines sampling point is near the infection point of the amplitude or intensity functions. Photoresist materials and processes have historically been tuned to dense line performance. This situation also suggests possibilities for materials to be geared more specifically for isolated line performance (which are also in use).

The connection to aberration sensitivity is now a logical step. If any perturbation exists that will influence the diffraction orders within the lens pupil, it would be expected that the effects may be more noticeable for small isolated lines than for small dense lines. Aberration in the lens pupil causes phase error in the diffraction orders that are collected by the lens. A phase error in the zero diffraction order alone is of no consequence since it has no frequency content. As more than the zero order exists in the lens pupil however, phase error will impact order interference and ultimately the integrity of the resulting image. To demonstrate this point, symmetrical aberration is considered. Defocus and spherical aberrations are examples of symmetrical aberration, as is astigmatism if considered along a single axis. The impact described using a defocus aberration (p*, shown in Figure 3) can be shown to be common across other symmetrical aberration types. If we consider defocus and its influence on coherent diffraction orders, we recognize the phase error in the first diffraction order measured against the phase of the zero diffraction order. For a peak defocus aberration, Ad, the impact on first diffraction orders at the edge of the lens pupil will be a corresponding phase error. For a real and even function, this can be a simple cosine amplitude dependence of the aberration leading to a modulation of the first diffraction order:

md’(x) = 0.5 + cos(Ad)O. 63 ~cos(~xx..) mi’(i) = 0.8 + COS(A~) 0.3 ~~COS(~ZU’JJ)

As an example, we will consider 0.10 waves of peak defocus aberration or 0.628 radians of phase error. The cosine projection of this aberration onto the first order results in an effective amplitude loss corresponding to cos(O.628) = 0.809. Figure 5 shows the image results for dense and for isolated lines. Since the defocus phase error impacts the first diffraction order with respect to the zero order, the biasing factor for either case does not change but demodulation of the first order cosines does occur This will have the most significant


1: 1 amplitude I:4 amplitude

2 2

15 . 15 .

1 1

05 . 05 . --a-w-- c-

0 I I I I I I I I I I I I I I I I 0 1 1

Figure 5. Image amplitude and intensity for dense and isolated features, showing the impact of 0.1 waves of defocus aberration.

impact in situations when the resulting image is not sampled near the inflection point of the biased cosine (which is the bias value itself). In the case of small dense lines, 0.1 waves of defocus may still produce useful images since it may have little impact at the resist threshold point. For small isolated lines, however, the resist is likely sampled at a position in the image that varies significantly with defocus, making useful imaging unlikely. Other generalizations can also be made. The analysis suggests that an isofocal point could exist for dense lines, where a feature would remain a near constant size through focus. This is unlikely as feature isolation increases. It could also be concluded that dense features would exhibit a resemblance of an “iso-aberration” point where imaging would be least sensitive to aberrations. This would also be more difficult for isolated features.

For this example, features have been exarnined with corresponding pitch values near UNA (with first diffraction orders just within the lens pupil). The isolated line size is therefore substantially smaller than the dense line size. For isolated lines equal in size to the dense lines, higher diflkaction orders may be collected. This would reduce the impact of the zero order weighting (since it would be weighted against more than just the first orders) and reduce the sensitivity to aberration, including defocus. Figure 6 shows a summary of aerial images with and without defocus aberration. Three conditions are shown: dense lines on a pitch itlvA &=OS), 1:4 isolated lines on a pitch MtA, and 1:3 semi-isolated lines on a pitch 2;t/NA. Aberration introduced for each case is 0.1 waves of defocus.

This type of analysis leads to some useful insight. Although defocus aberration has been studied, generalizations made can be extended to higher aberration orders as long as the specific character of the aberration is taken into account. Although not shown here, a similar analysis was carried out for 3rd order coma, resulting is similar conclusions regarding image placement error and line isolation. The analysis shown here is based on coherent illumination. Increasing partial coherence reduces the discrete character of d.i@action orders and lessens the impact of defocus and aberration (see for instance Reference 6). From this analysis, it can be seen why simple biasing will not gain much with respect to isolated line performance. If a line is biased, the zero diffraction order weighting can be reduced.


0.60

0.30

0.00

- Dense ---- Dense defocus - I:4 pitch VNA ---- I:4 pitch VNA defocus ~ I:3 pitch 2VNA - - - - I:3 pitch I/NA defocus

Figure 6. Comparison of aerial images of dense and isolated features with and without aberration.

In order to print to size, however, additional exposure is needed, which will move the resist thresholding point in the opposite direction. The use of optical proximity correction can be useful however since additional frequency information is actually added in the lens pupil to reduce the weighting of the zero order. A combination of biasing and OPC usually proves to be most practical. It is also interesting to realize how feature type might influence lens performance goals. For dense features, the lens NA is most important in order to print as small a pitch as possible. If only dense features are printed, the sensitivity to aberration may be less important that achieving high NA. For more isolated line structures, NA becomes less importance since these features will likely be set on a larger total pitch than dense lines would be. Aberrations are, however, very critical. This may suggest different lens criteria for different applications. Although not discussed in detail here, it becomes evident that resist process modifications can greatly influence process capability and aberration sensitivity. In summary, a principle goal for a robust imaging process is to match the inflection point of an amplitude image with the resist process thresholding point. As a process gets closer to this goal, its tolerance to aberrations will improve.

3. PREDICTIVE MODELING - APPLICATIONS IN IMAGING

The fundamental description so far has been useful to help understand the role of aberrations in lithographic imaging. To anaIyze more realistic situations, further description is needed. The frequency description of aberration influence can be extended to situations of partial coherence, phase shift masking, modified illumination, and optical proximity correction (OPC) and this description can be used to develop predictive models.

Pupil metrics have recently been introduced to help predict the capability of an imaging system in the presence of lens aberration [ 1, 21. Descriptive statistics have been developed that measure the phase variance in the lens pupil as it is weighted by diffraction energy. Variance, RMS, or similar measurements are made across the utilized pupil where a weighted pupil can be defined as:

Weighted pupil = W(p, 8) x [M(u, v) *S(u, v)] x H(u, v)

where W(p,8) is the aberration function, M(u,v) is the mask diffraction pattern, S(u,v) is the illumination function, and H(u,v) is the pupil function. A weighted variance or PMS OPD measurement has proven useful for instance during the illumination or phase masking design [ 11.


Although useful for evaluating resolution enhancement methods where zero difRaction order is limited, a simple weighted calculation of RMS OPD is not suflicient to describe general imaging performance and such calculations can sometimes be misleading. The shortcomings of using a simple RMS calculation are realized using an example similar to the one in the previous section where UNA pitch features are imaged with 0.10 waves of defocus aberration. As partial coherence increases, the weighted RMS OPD measurement could suggest that isolated line performance suffer less consequence from aberration than dense lines do, which is counterintuitive and does not occur.

3.1 Predictive modeling using frequency term evaluation

The problem with attempting to use a simple weighted pupil RMS OPD calculation is that the zero diffraction order overwhelms the pupil phase measurement. Image modulation and image placement responses depend on phase differences between frequency terms. This was shown earlier for a coherent case where the phase error in the first diffraction order is measured against the phase of the zero diffraction order. This description is valid also for non-coherent conditions and where mask and illumination structure is more complex. A weighted pupil function is shown in Figure 7a for dense k&).4 features imaged with a partial coherence value of 0.7. The full pupil aberration is shown in Figure 7b, which is based on a real lens file with full pupil RMS OPD of 0.0377 waves, a reasonable good lens from an aberration standpoint. The pupil weighted RMS OPD is 0.0356, a value slightly lower than that for full pupil use but any interpretation beyond this generalization is difficult. By separating the frequency terms from the zero diffraction order, additional description should be possible.

Weighted Pupil OPD Weighted Pupil OPD Weighted Pupil OPD 1 . . . .._..-.._.._...._-.......-....-.......- _..._.__._.____._.._.----.--.--..---.-.... _....-........_._.._.-......-....-....-... . . . . .._.........._..-........--......-..-. _........._...............-...---...-.---- .._...._........_...*.........-........... _.-.._-..--._...-.._.-..--..-..---..--..-- . . .._............_._.--..-......-.-..--..-

0.6

0.4

02

- > 0

02

0.4

06

0.0 0 8 .-.~~-.-.-.-.~.-.-~-.-.~~~.-.~.~~-.-.-.~.~.~.-~~.~~-.-~-.-.-~-.-~-.-~-~-.-~-.-~-.-. .-.-.-.-.'.-.-~-.-.-.-.'.‘~-~-.-~-.-.-.-~~.-.-~-.~.-.-.~.-~-.-.-~-~-~-.-.-.-.-.-.-~ .-..-..-...---.-.......-.-.-.-.-.-----.-.--...--.-...-.-.-.-.-...-...-.-.....-.-... ------.---..---.............---..---..-..- ..__.._.._......__..-...--....-.-.-....... . . .._.._.............-.-.......-...-.-....

-1 4 _._.__....=~____..._=_..__.._._.-.-..____. ----*---- ---~*~'~ ..-..........--.-..... -1 05 05 I .05 IY 05 1 -1 0.5 05 1

Figure 7a The separation of weighted diffraction orders for dense kl-0.4 features imaged with a partial coherence value of 0.7 in an aberrated lens.

Lens Pupil OPD .:-

:.’ ,:‘: . .

: __ ,:: _.i _.: _.:-.. I..

Figure 7b. Full pupil aberration plot (OPD in waves) used for imaging example.

To further explore the idea of performing pupil statistics on individual weighted orders, individual aberration terms are considered. Typically, 37 Zernike polynomials are used to describe an aberrated pupil with 37 associated Zemike coefficient terms. Eight of these coefficients will be used for this analysis, specifically even terms: defocus (24), astigmatism (Z5), spherical (Z9), 5th order astigmatism (212), and 5* order spherical (216) and odd terms : x-coma (27) x-3 point (ZlO), and 5th order x-coma (214). LensMapper [7] imaging and aberration analysis software was used for modeling and statistical analysis of J~=0.5 geometry (1: 1) using a 248nm wavelength, and a 0.62NA lens , with a partial coherence value of 0.7. Mean and RMS OPD values were calculated for individual orders and are plotted in Figures 8a and 8b. The mean wavefront aberration plot (Figure 8a) shows that there is a large difference between the first


di.B?action orders and the zero order for defocus, astigmatism, and spherical. Figure 9 is a plot of the differences between the mean of the first diffraction orders and the mean of the zero order. This plot gives insight into the sensitivity of this specific imaging situation to each individual aberration. Even aberrations result in equivalent effects for both first diffraction orders while odd aberrations result in asymmetry between the orders. The value of this description can be realized when these results are compared to data presented from earlier work based on full aerial image simulation [i], shown in Figure 10. This plot shows the sensitivity to focus shift for these same aberrations under similar imaging condition. Comparison of kI=0.5 results shows good correlation. Since focus shift does not describe asymmetrical deviations, additional testing using the simulation method is required to capture the full effect of odd aberrations. This information is already contained in the frequency plane analysis. The frequency plane or weighted pupil method described here provides quick, interactive assessment of the sensitivity to aberrations.

Mean wavefront aberration

5 -0.015

6 -0.02

-0.025

-0.03 24 z5 27 Z9 ZIO 212 214 Z16

Zernike #

RMS wavefront aberration

24 25 27 z9 ZIO 212 214 Z16

Zernike #

Figure 8. Mean wavefront aberration and RMS wavefront aberration plots of individual diffraction orders.

Aberration sensitivity ASMUZeiss data, 0.08 waves, 0.5 sigma*

-0.015 ’ 24 25 27 Z9 ZIO 212 214 Z16

Zernike # 24 z5 27 z9 ZIO 212 214 Z16

Zernike #

Figure 9. Aberration sensitivity analysis using Figure 10. Full aerial image analysis of aberration frequency plane or pupil description. The sensitivity for comparison. Good agreement exists differences between the first diffraction order across all terms. Only symmetrically analysis is mean and zero order mean are plotted. possible.


3.2 Evaluating the effects of sigma, OAI, and PSM

The method of image assessment and aberration evaluation described here can be extended to situations involving optimization of partial coherence, designing of phase shift masking, or customizing of illumination. A few examples can illustrate this.

3.2.1 The effect of partial coherence on imaging with aberrations

The influence of partial coherence on aberration effects is demonstrated for 130nm dense lines (1:l) imaged using a 248nm wavelength and a 0.67 NA lens with the aberration description of Figure 7. Weighted pupil plots are shown in Figure 11 for sigma values from 0.7 to 0.9. Table 1 shows the statistics on the individual orders for a single partial coherence condition. Figure 12 shows how the calculated RMS and mean OPD values vary with partial coherence. Minimization of the impact of aberration results with reduced average phase of the first diffraction order, suggesting increased levels of partial coherence for this situation.

0.8~ Weighted Pupil OPD 0.9cr Weighted Pupil OPD 1 1

0.6 0.6

0.6 0.6

0.4 0.4

0.2 0.2

> 0 > 0

-cl2 -a2

-a4 -a4

-a6 -a6

-a6 -a6

-1 -1 -1 -a6 -a6 -a4 -a2 0 0.2 0.4 0.6 0.6 1 -1 -a6 -a6 -a4 -a2 0 0.2 0.4 0.6 04 1 -1 -as -a6 -a4 -a2 0 0.2 0.4 0.7 0.6 1

U U U

Figure 11. Weighted pupil plots for three levels of partial coherence. Mask lines size is 13Onm (1: l), wavelength is 248nm and NA is 0.67.

I 0.003 !G of 0.002

3 3 0.006 0.006 - - 9 9 g g 0.005 0.005 - - ti ti g g 0.004 0.004 - -

E 0.003 - !G of 0.002 - --

---a---RMS

0.004 g

- 0.001 0.001 4 l + + IAvgl IAvgl -- -- I I m I . - I . 0.002 0.0°2

0.000 0.000 I I I I I I 0.000 0.000

0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 Partial Coherence (sigma) Partial Coherence (sigma)

0.012 T 5

0.010 z

0.008 % x

0.006 i

0.004 g -

0.008 0.008 I 0.016 0.016 o*oo7 0.007

~""-------*~~~~~~ - 0.014 0.4

Figure 12. Plot of RMS and mean OPD vs. partial coherence factor for the +first diffraction order of Figure 11 with sigrna values from 0.5 to 0.9.


LENSMAPPER PUPILSTATISTICS (XOrientation)(Waves)

Order Mean RMS PV X-Asym Y-Asym 0 0.004387 0.032701 0.13995 -0.00939 -0.0002 Table 1. +I -0.00651 0.00726 0.046355 -0.00327 -0.00651 Pupil

statistics on individual -1 -0.00324 0.028826 0.13184 -0.00327 0.003242 orders for a partial +2 0 0 0 0 0 coherence factor of -2 0 0 0 0 0 0.9.

No DC -0.00488 0.021062 0.13184 -0.00327 -0.00327 Full 0.002654 0.035592 0.20841 -0.00952 -0.00112

3.2.2 Evaluating custom illumination

Designing off-axis and custom illumination requires consideration of the distribution of diffraction energy in the pupil. Defocus and aberration needs to be accounted for during the design stage since the minimization of their effects is a primary goal. As an example, Figure 13 shows 248nm illumination of 150nm dense lines with strong quadrupole illumination (0,=0.7 and 0,=0.2). Since zero diffraction energy does not exist in this instance where the illumination has been optimized for these features, statistics on the entire weighted pupil are most useful. In this example, an additional metric is included. The asymmetry statistic measures the difference in the pupil and between diffraction orders along various directions in the pupil [ 11. Figure 13 shows asymmetry results along an X direction.

Wavefrontaberration 0.03

0.025

F 0.02

5 m 0.015 0

.- L

G 0.01

E 0.005 E .- 3 0 k 2 -0.005 a

Figure 13. Full pupil statistics for strong quadrupole illumination of 15Onm dense lines.

24 z5 27 Z9 ZIO 212 214 Zl6

Zernike #

3.2.3 Evaluating phase shift masking

Strong phase shift masking utilizes specific portions of a lens pupil. Figure 14 shows the differences in pupil utilization for a binary mask vs. a strong alternating phase shift mask for imaging 130nm dense features at 248nm with 0.67NA. The diffraction energy for this phase shift mask case does not distribute diffraction energy into the center of the pupil, similar to the situation with strong quadrupole illumination. The sensitivity to individual aberration types is shown in Figure 15 where the impact from


defocus is significantly reduced, as expected with this mask type. The sensitivity to odd aberration types, especially 3-point, is increased substantially. Although this evaluation is unique to the specific imaging situation, it has generally be demonstrated that phase shift masking is most sensitive to these aberration

weighted Pupil OPD ,........:..... . -. . . . . . . . . . . . . . . i

._:._ . . 1‘ . . . . . . . . . . . . -..... I . . . . . . . j i f ; i i i f i i

i : : : : ; : i : i i . . . . . . . . . . . . . 3 . . . . . ..I . . . . . . . . . . . . i . . . . . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . i

: ; : i i : : : : i : : : o1 i : ; : : : : : : : . . . . i . i . . . . . . . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L . . . . . . . .

Weighted Pupil OPD

-1 03 ae -0.4 -02 0 0.2 0.4 0.6 0.e 1 ll

Figure 14. Weighted pupil plots for 130nm dense geometry using binary (left) and alternating phase shift (right) masking.

-1

-0 c

-1

0.03 1

0.025

0.02

Mean wavefront aberration

2 0.015 > m s 0.01

z 0.005 E 0

& -0.005 z 0 -0.01

Figure 15. Full pupil statistics for strong phase shift masking of 130nm features.

-0.015

-0.02 -0.025 ’ I

24 z5 27 z9 ZIO 212 214 Z16

Zernike #

3.2.4 Evaluating optical proximity correction

When using OPC assist features, a pair of sub-resolution bars is placed on either size of an isolated feature so that the cosinusoidal frequency distribution in the lens coincides with the frequency positions of dense line diffraction orders. As this cosine function is added to the diffraction pattern for the isolate feature, the diffraction pattern more closely resembles that of the dense features, reducing proximity effects. Figure 16 demonstrates the effect that assist features have on the distribution of a mask diffraction field. Optimization of OPC is most appropriately carried out with the consideration of aberration. Figure 17 shows for example how OPC assist features used with isolated spaces features can improve depth of focus by reducing sensitivity to the defocus aberration. As the number of assist pairs are added, RMS OPD across the pupil is decreased. The separation distance of the assist features is determined to minimize the


defocus aberration. This separation corresponds to a distance of NA/I or an equivalent frequency of UNA in the lens pupil. Further optimization is possible as other aberrations are considered.

2.00 -

4.00 -

6.00 -

8.00 - a

Figure 16. The distribution of difEaction energy in a lens pupil for (a) dense lines, (b) an isolated line and (c) an OPC assisted isolated line.

21:1 space 0.05h w/l pair w/2 pairs w/3 pairs defocus hINA spacing l/2/3 h/NA spacing l/2/3 h/NA spacing

Weighted Pupil OPD a05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . .._

r ; f i ; aac . . . . . . . . . . . . . . . . . . . .

I

$PJJ).2~8x.. . . . . . j.. . . . . . . . . . . . . . . . . . .

oo3 . . . . . . . . . . . . . . . . . . . . i.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I

Weighted Pupil OPD o E. ......... ...... .. . ............. ..... . .......... ...... .....................

f ; ; f 1 O,M . ;.

i l

~ *mo235x .; . . . . . . . . . . . . . . .

o,m . . . . . . . . . . . . . . . . . . . . _I ..;... .,

o,a ,.............; . . ..~.................... {

.iy~ _____, i :

..,.,...._,__. ___

; 1 i d , O.D, ::‘................... f. i _..._.____.~.. @.,,

5 A._ :

: ;f;$ &$I 8 v- ;.z .

: 0 ‘,.zRNG-~,<-..T: /+.,‘~ 1 I .A; < d/.2, ,<z.;‘, SC, ~.x<:,%.,- ‘$‘ >* ;p

i

‘r’ ‘pug&g $?y+J~& tcic i; I$ 5

; &-), p - ~~..~~~.Ps- . . . . . . . . . .

-0.02

-0.03

-0.04

-o.ffi -1 -0.5 05 1

Weighted Pupil OPD Weighted Pupil OPD

. . . . . _. . . . . .

m;-” ’ 0.5 '. 0" 0.5 1

U

Wei@ted Pupil OPD oa5 .................. ..~ .................... . ........................................ .

Figure 17. The effect of assist features on the distribution of diEaction orders in a lens with defocus aberration. The weighted pupil OPD is plotted and RMS OPD is shown for an isolated space and a space with one to three pairs of assist features, spaced VNA in the pupil.


4. CONCLUSIONS

Some generalization about imaging with aberration can be made based on the concepts discussed. The pupil statistics presented become useful prediction methods if the consequences to imaging are considered. More specifically, statistics on frequency terms weighted against a zero order can be predictive. The fundamental frequency is in most situations most important. Partial coherence can reduce the overall impact of aberration by spreading diffraction orders but the opposite may be true for PSM and strong OAI. In general, small dense line geometry is more robust to aberration than small isolated geometry, leading to the possibility of different lens performance criteria depending on application. Resist thresholding is an important factor in maximizing imaging tolerance to aberration and modifications to resist materials and processes have the potential for significant consequence. For lithographic applications, defocus aberration will always be the greatest concern as imaging is carried out over topography and through a resist layer.

As optical lithography continues its extension toward smaller kl values, there is also an increasing need for user interaction with illumination design, phase mask optimization, and OPC customization. All of this should be carried out with the knowledge and an understanding of the sensitivity to aberration. LensMapperTM, an imaging design, evaluation, and optimization tool has been developed to assist the user with these activities [7].

5. REFERENCES

[l] B. W. Smith, “Variations to the influence of lens aberration invoked with PSM and OAI,“SPlE 3679 (1999), 30.

[2] B. W. Smith, J.S. Petersen, “Influences of OAI on optical lens aberration,” J. Vat. Sci. Technol. B 16(6) (1998) 3405.

[3] D. Flagello et al, “Towards a comprehensive control of full-field image quality in optical photolithography,” SPIE 305 1 (1997) 673.

[4] C. Progler, D. Wheeler, “Optical lens specifications from the user’s perspective,” SPlE 3334 (1998) 257.

[5] B. Smith et al, “Aberration evaluation and tolerancing of 193nm lithography objective lenses,” SPIE 3334 (1998) 269.

[6] B. W. Smith, “Revalidation of the Rayleigh resolution and DOF limits,” SPIE 3334 (1998), 142. [7] LensMappei? is a product and trademark of Lithographic Technology Corp. (LTC), B.W. Smith

(2000).


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