ANALYSIS OF STRAY LIGHT IN MOST COMPLEX SITUATIONS

Jean­Claude PERRIN J.C.P.C. ­ "Le Buet", Mellecey, 71640, France.­ jean­claude.perrin@jcp­consultant.com

ABSTRACT

To analyze ghost effects in optical systems including decentred coatings with thickness variations, polarized light and interactions with object and image planes is a difficult task. Thanks to a battery of tools especially developed in the last ten years and applied to many different situations, it is possible to do such jobs in a quick and elegant manner. As an example, we shall consider optical relay lenses used for photolithography. The object plane is the reticle; The image plane is the wafer.

1. INTRODUCTION.

Relay lenses used in photolithography are extremely demanding applications with respect to performances, including effects of ghosts and stray light in general. This is the case for the classical design shown on the Fig. N°1, but also and especially for new designs which are appearing as possible tradeoffs for future applications. Examples of such designs, have been described in 2006 (Ref. 1) and in several patents (Ref.2,7) They are using catadioptric designs and decentred field which have many advantages with respect to classical designs, as explained in the Ref.1. An example of such a design taken from the open literature is shown on the Fig. N°2. For such lens, and especially for catadioptric designs, it is important to analyze the stray light more in depth.

In the last ten years, we have developed methods to analyze ghosts and stray light, and applied those to many different situations and projects, ranging from infrared (3­5 µm and 8­12 µm) to far UV (157 nm). The software that we have developed is called PARASIT. The publication in Ref. 8, also available on the web site www.jcp­consultant.com, describes the basis of the method. Thanks to the experience gained in using PARASIT for many different applications, and also by comparing the results obtained using classical (time consuming) methods, the reliability and exactness of the methods used are now firmly established.

In order to deal with the problem of catadioptric lenses for photolithography, we have extended significantly this software. We describe in this paper these new developments.

2. SUMMARY OF THE PROBLEM TO SOLVE.

With respect to the photolithographic relay lens shown on the Fig. N° 1 and also to catadioptric designs of the kind described in Ref.2 to 7 and on Fig. N° 2, the problem to solve is has follows :

• Determine and classify the main ghosts contributors to stray light, taking into account the ghosts due to reticle and wafer contributions.

• Present for each of them the cartography of the stray light (for example in pseudo colour) on the effective printed area and its surroundings on the wafer plane, and the same by summation of all contributors.

• Take into account real coatings with their thickness variations and decenter.

• Take into account the polarization.

• Model annular illumination and different values of σin and σout.

• Repeat the simulations for different configurations (coatings, illuminations, baffles) and find solutions with minimum stray light.

Of major importance in this problem is the computer time. Due to the large amount of simulations which are necessary to find best compromises, the effectiveness of the method with respect to computer time is determinant.

3. METHOD USED.

A method and corresponding software has been especially developed using PARASIT (CODE V), LightTools, MATLAB and EXCEL acting together in the Active X protocol.

The advantages of using PARASIT are as follows :

• It is using only sequential ray tracing (by reconstructing corresponding files for each ghost or stray light path). The computer time is therefore optimum.

• It can take into account the coatings, with their variations of thickness. • It makes easily the classification of the ghosts on various criteria. • One of it’s routine makes the classical ray trace of selected ghost immediately. • It can take into account the emitting area of the reticle in a very flexible manner (local or total). • It can take into account the polarization. • It can model several illumination schemes (annular, dipolar, quadripolar).

The typical way in using PARASIT is to determine very quickly the leading contributors and make the full (time consuming) simulations using only a few of them. To our experience it is usual that only less than ten ghosts contribute significantly. Nevertheless, the question may arise, whether the method used in PARASIT for the first selection of ghost (based on first order analysis) is acceptable. This is especially the case for catadioptric lenses with decentred fields. For this reason we took as a rule to make first a comparison between the result obtained with PARASIT and this obtained with a standard Monte Carlo based software. We are using LightTools for this. This comparison is made on a simplified manner, taking only R­T values for coatings (ignoring real definitions) and unpolarized light. In that comparison, PARASIT is taking only a limited number of ghosts, but LightTools takes all of them. (Comparison of computer time is about 1/70).

Moreover, we are using Matlab in order to present PARASIT and LightTools results in the same manner using Matlab graphics

Doing this comparison shows that the PARASIT assumptions are quite acceptable for classical lenses of Fig.N°1, and limiting the number of ghosts to less than ten is usually sufficient to get an accurate result.

This is not the case for catadioptric lenses with decentred field. The LightTools analyses put in evidence some ghost path which can not be detected in PARASIT, because they do not correspond to classical double reflections ghosts. An example is shown on the Fig.N°5 : light can go back directly to the wafer ignoring two mirrors, after double reflections first on a surface of the lens, second on a mirror. In that case, the solution consist in introducing those path (typically four in the design that we have studied) in PARASIT, in order to take them into account in the last step (the step which gives the final quantitative result). This can be done easily in PARASIT.

When an exact correspondence of LightTools and PARASIT results is obtained, PARASIT only is used to model exactly the coatings with their imperfections, and to define best configurations.

4. EXAMPLES OF RESULTS

For reasons of confidentiality, some figures are limited to the classical relay lens only.

o Fig. N°1 is a typical relay lens for phoptilithography. Typical magnification is x4, with NA ranging from 0.75 to about 1.6 (new generation immersion lithography).

o Fig. N°2 is an example of a new generation catadioptric design taken in the open literature. o Fig. N°3 is one of the standard output of PARASIT. This table shows the EXCEL classification of the main contributors to

stray light. o Fig. N°4 is also a typical outputs from PARASIT. It shows the classical ray traces of a ghost which can produce significant

stray light. o Fig. N°5 is an illustration of a possible path of a ghost in a catadioptric design which do not correspond to a classical

double reflection ghost.

o Fig. N°6, 7, 8 and 9 shows for comparison the results obtained with PARASIT and LightTools with exactly the same hypotheses.

o Fig. N°10 shows a typical PARASIT result of analysis of stray light on the wafer, including coatings with their imperfections.

The table on Fig. N°3 is a classification of the ghosts with respect to their corresponding stray light ratios (maximum value on the corresponding image of the ghost). This has been done for three small emitting regions on the reticle centred at YOB = 0 , 10 and 20 mm. The two first column REFL1 and REFL2 give the number of the surfaces which correspond to the ghost. The Fig. N°4 is obtained from one ghost and using these two numbers and can be done for each ghost, if necessary.

Fig. N° 6 and 7 are Matlab representations of the results obtained with PARASIT (Fig. N°6) and LightTools (Fig.N°7) and both along the Y axis (Fig.N°8). Both results are represented on the same manner in logarithmic scale and pseudo colour, on the useful area of the wafer. The PARASIT simulation is using less than ten ghosts, but LightTools use all of them. Exact definitions of coatings have not been used in this comparison, only R­T values. To obtain those figures, we have assumed that the emitting area on the wafer is a small circular area located at some YOB value on Y axis. The annular aspect of the ghosts appears clearly. This is due to the values of σin and σout which have been chosen for the illuminator. The noisy aspect of the LightTools figure is due to the fact that the number of Monte­Carlo runs have been limited to save the computer time. Nevertheless, time necessary to obtain the Fig. N° 7 is about 70 times this of the Fig. N°6. The aspect of both figures is about the same, except for four ghosts which appear in LightTools, and not in PARASIT. Path corresponding to those ghosts are of the sort represented on the Fig.N°5. A lot of energy is present because one of the reflection is on a mirror with 100% reflection. Such ghost can be very dangerous. The result obtained with PARASIT after introducing those path is shown on the Fig.N°9. Now Fig.N°7 and 9 agree perfectly.

The Fig. N°10 has been obtained with PARASIT only, taking into account the exact definitions of coatings, including possible defects. To obtain this figure, the reticle is emitting uniformly on its all useful area. What is represented is the wafer rectangular useful area (called printed zone on the figure), and it’s neighbour on a circular area. By this way, PARASIT is ready to model the system taking all into account including the coatings with thickness variations and decenter, with a reasonnable computer time. Making such a simulation is not possible with LightTools, and probably not with any other software.

5. ANNEX : NOTES CONCERNING PARASIT

The Ref.8 is presenting the methods used in PARASIT and gives some examples. This annex describes in more detail the improvements made to PARASIT since 2003, to deal with the problem.

PARASIT is mainly a CODE V macro based on the principle of selection of ghost in two steps, in order to make the full and time consuming calculation (third step) only with the main contributors. The first step is based on first order analysis, the second step is based on a real ray trace by constructing the file of each ghost’s path which has been selected after the first step. By this way, the second step eliminates the selected ghosts which are not physically possible (due to apertures, decentrations, etc…) and makes a rough estimation of the stray light ratio for each of them. The third step uses only the selected ghost after step 2 to make a full Monte Carlo analysis using the LUM routine of CODE V. The core of PARASIT is a CODE V macro which is constructing the sequential file of selected ghost and set reference rays. This macro has been modified in order to take into account the definitions of coatings. The coatings must be defined both in transmission and in reflection, and corresponding .mul files constructed. Thicknesses variations and decentrations can be taken into account with THV.

Coatings and polarisation are taken into account in the third step, because LUM does it (but at the expense of increased computer time). For this reason, PARASIT has been modified in order to keep also the former option. Coatings can be defined by their R­T values (in that case polarisation is not taken into account and computer time is reduced) or they can be defined by their .mul files.

More flexibility has been given to define the source in the third step. Typically, it is a circular source of small diameter located on the object plane (reticle). Various shapes can be given now to the source. It also can be a customer’s file.

PARASIT is now working together with EXCEL and Matlab using the Application Programming Interface (API) built into CODE V. EXCEL is now the main command and control tool for PARASIT and access to CODE V results using the Microsoft Windows Component Object Model (COM). EXCEL also uses Matlab’s routines using the same protocol (EXCEL LINK).

ACKNOWLEDGMENTS

The author would like to thank Daniel Kraehmer and Vladimir Kamenov for helpful discussions and support, and Carl Zeiss SMT AG for permission to publish.

REFERENCES

[1] A. Epple, Extreme Ring Fields in Microlithography. International Optical Design Conference 2006 (SPIE proceeding N° 6342).

[2] Catadioptric optical system and exposure apparatus having the same. Patent N° US 6,985,286 B2

[3] Catadioptric reduction lens. Patent N° US 2004/0263955

[4] Microlithographic reduction projection catadioptric objective. Patent N° US 6,636,350 B2

[5] Catadioptric projection objective with geometric bean splitting. Patent N° US 6,995,930 B2

[6] Projection optical system, exposure apparatus ans exposure method. Patent N° US 6,909,492 B2

[7] Yasuhiro Ohmura, The Optical Design for Microlithographic Lenses. International Optical Design Conference 2006 (SPIE proceeding N° 6342).

[8] J­C. Perrin. Methods for rapid evaluation of the stray light in optical systems. Optical Design and Engineering Conference 2003 (SPIE proceeding N° 5249).

[9] CODE V Reference manual.

CODE V is a trademark of ORA – Matlab is a trademark of MathWorks – EXCEL is a trademark of Microsoft.

Fig. N° 1 : Typical lens for photolithography.

Fig. N° 2 : Example of a catadioptric design of new generation for photolithography.

Fig. N° 3 : Classification of the ghosts according to the stray light ratio.

First reflexion

Second reflexion

Fig. N° 4: Ray trace of a classical double reflection ghost.

Second reflection (mirror)

First reflection

Fig. N° 5: Possible ray path of an unconventional double reflection ghost.

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PARASIT­LightTools comparison 1 ­ Result of PARASIT

Fig. N° 6: Analysis of stray light due to ghost using PARASIT.

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PARASIT­LightTools comparison 2 ­ Result of LightTools

Fig. N° 7: Analysis of stray light due to ghost using LightTools.

PARASIT­LightTools comparison 3 10

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Fig. N°8: PARASIT­LightTools comparison along Y axis

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Fig. N° 9: Analysis of stray light due to ghost using PARASIT including unconventional ghosts (To be compared to Fig. N° 7)

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Area analyzed on the wafer

Printed zone

Fig. N°10 : Analysis of stray light on the wafer using PARASIT (printed zone and surroundings), including coatings with their imperfections.