Illumination optimization of periodic patterns for maximum process window

Microelectronic Engineering 61–62 (2002) 57–64 www.elsevier.com / locate / mee

Illumination optimization of periodic patterns for maximum process window Robert Socha*, Mark Eurlings, Frank Nowak, Jo Finders ASML TDC, Veldhoven, The Netherlands

Abstract A rigorous computationally fast technique for optimizing the illumination is demonstrated based on Hopkins imaging formulation for partial coherent imaging. The technique optimizes the illumination by changing selecting areas of the illuminator, which enhance the pattern dependent diffraction orders. The illumination is also maximized for largest process window by increasing the normalized image log slope (NILS) and by increasing the depth of focus (DOF). For a 110-nm DRAM isolation pattern with 220-nm pitch the optimized illumination is an elliptical dipole element. This elliptical dipole element has the largest NILS through focus for the 110-nm main feature width and for the end of line. Simulation results with this elliptical dipole element show that the DOF is 0.6 mm. Experiments were done with a 358 dipole element, which approximates the elliptical dipole element. These experiments demonstrated that the 110-nm DRAM isolation pattern is resolvable with 0.4-mm DOF.  2002 Published by Elsevier Science B.V.

1. Theory One of the methods for lowering the k1 factor is by optimizing the illumination. In optimizing the process, often the illuminator is not considered or the illumination is copied from a previous generation. It is well known that by modifying the illumination one can increase the process window. Several techniques for modifying the illuminator to optimize the illumination have been described [1–3]. This paper describes a different technique for illumination optimization based on Hopkins imaging formulation for partial coherent imaging. In Hopkins formulation, the source is integrated over first in which the transmission cross coefficient (TCC) is created. The TCC is the autocorrelation of the illumination pupil with the projection pupil and with the complex conjugate of the projection pupil. Multiplying the TCC with the diffraction orders of the reticle optimizes the illumination. Since the diffraction orders are pattern dependent, the illumination is pattern dependent. Furthermore, it is * Corresponding author. ASML, 4800 Great America Parkway, Suite 400, Santa Clara, CA 95054, USA. Tel.: 11-408-8550509; fax: 11-408-855-0549. E-mail address: [email protected] (R. Socha). 0167-9317 / 02 / $ – see front matter PII: S0167-9317( 02 )00516-6

 2002 Published by Elsevier Science B.V.

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possible to optimize the illumination to maximize NILS through depth of focus (DOF) or to minimize aberration sensitivity. The illumination is optimized based on Hopkins imaging formulation where the TCC is defined in Eq. (1) [4]. The TCC is the autocorrelation of illumination source, Js , and the projection pupil, K. TCC(m,n, p,q;z) 5

EE ]]] 2 2 œa 1 b

S

ml nl , s Js (a, b )K a 1 ]], b 1 ]]; z Px NA Py NA

S

D

D

pl ql 3 K* a 2 ]], b 2 ]]; z da db Px NA Py NA

(1)

Since the TCC is an autocorrelation, the TCC is a four-dimensional function where m and p are the diffraction orders in the x direction and n and q are the orders in the y direction. The pupil coordinates of the source to optimize, Js , are a and b. The TCC is band limited with the largest diffraction order in the x direction (m and p) being NA(1 1 s )Px /l and in the y direction (n and q) being NA(1 1 s )Py /l where NA is the numerical aperture, s is the maximum outer s of the illumination source Js (a, b ), Px is the pitch in the x direction, Py is the pitch in the y direction and l is the wavelength of the exposure system. From the TCC, a term is defined called the diffraction order cross coefficients (DOCC) which weights the TCC by the diffraction order, T. The DOCC therefore gives more importance to the diffraction orders that the pattern creates. DOCCsm,n, p,qd 5 Tsm,ndT *s 2 p, 2 qdTCCsm,n, p,qd

(2)

Based on the DOCC, areas of the illuminator that are most important can be visualized with Jopt , which is function of six variables a, b, m, n, p, and q. The formula for Jopt is shown in Eq. (3) where Js (a, b ) is the initial illumination profile which is assumed to be a circ function with maximum radius of s where s is the largest outer s on the exposure tool, e.g. s 5 0.92 for the ASML / 750.

S

ml nl Joptsa, b,m,n, p,qd 5 Tsm,ndT *s 2 p, 2 qd Jssa, bdK a 1 ]], b 1 ]] Px NA Py NA

S

pl ql 3 K* a 2 ]], b 2 ]] Px NA Py NA

D

D (3)

The intensity is the inverse Fourier transform of the DOCC, which is shown in Eq. (4). From the intensity, the metrics that improves the process window can be deduced. It has been shown the exposure latitude (EL) is proportional to the normalized image log slope (NILS) [5]. By increasing the NILS, the EL increases. The NILS is defined in Eq. (5) where the NILS is proportional to the norm of the gradient of the intensity. Therefore by increasing the gradient of the intensity the NILS increases and consequently the EL.

OOOOe F ix

Isx,yd 5

m

n

p

Ge F

2p ]sm1pd Px

iy

GDOCCsm,n, p,qd

2p ]sn1qd Py

(4)

q

NILS ; CDuu=sln Iduu 5 CD

CD UU]1I =IUU 5 ]] uu=Iuu ~ uu=Iuu I

(5)

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By maximizing the NILS, a weighting function, w NILS , is created for each of the diffraction orders as shown in Eq. (6). When w NILS is small, these orders are less important in maximizing the EL. For example, the zero order does not contribute to the modulation and reduces the EL. For the zero order, w NILS in Eq. (6) is zero. Therefore areas of the illuminator that enhance the zero order are eliminated. Furthermore, when w NILS is larger, these orders are more important in maximizing the EL. The larger orders contribute the most to modulation. Eq. (6) enhances these larger orders, consequently improving the NILS and the EL. ]]]]] ]]]]]]] ≠I 2 ≠I 2 m1p 2 n1q 2 ] 1 ] ⇒ w NILS 5 ]] 1 ]] ≠x ≠y Px Py

œS

œU U U U

uu=Iuu 5

D S

D

(6)

Taking the derivative of the TCC in Eq. (6) with respective to focus, z, and equating it to zero can also maximize the depth of focus (DOF). In Eq. (1), only the projection pupil, K, is a function of focus. The derivative of the TCC with respect to focus is given by g in Eq. (7). Eq. (7) equals zero when d [g(a, b,m,n, p,q)] is satisfied. This Dirac delta function, d, however, will result in discrete sampling points in the pupil. Since discrete points in the pupil cannot be manufactured, other functions are considered. These other functions include a gaussian function and a cusp function in Eq. (8). The illumination apertures in this paper were created with the cusp function. ]]]]]]]]]]] ml 2 nl 2 gsa, b,m,n, p,qd 5 2 1 2 a 1 ]] 2 b 1 ]] Px NA Py NA ]]]]]]]]]]] pl 2 ql 2 1 1 2 a 2 ]] 2 b 2 ]] Px NA Py NA

Fœ S

D S

D S

œ S

D

DG

w focussa, b,m,n, p,qd 5 1 2u g(a, b,m,n, p,q)u

(7) (8)

The optimized illuminator, Jtot (a, b ), is calculated by summing over the discrete diffraction orders m, n, p, and q in Eq. (9). To further increase the process window, an integral equation for the intensity in Eq. (4) can be solved, where Jtot represents an initial starting point of the illuminator, and the integral equation is bounded by the constraints given by Eqs. (6) and (7).

OOOOw

Jtotsa, bd 5

m

n

p

q

sm,n, p,qdw focussa, b,m,n, p,qd Joptsa, b,m,n, p,qd

NILS

(9)

2. Simulation results This technique is applied to a DRAM isolation layer. In Fig. 1 the mask pattern of the isolation layer is shown for a 220-nm pitch with a linewidth of 110 nm. The illumination is optimized for an ASML / 750 which is KrF tool having a NA of 0.7 and maximum outer sigma, s, of 0.92. Using the illumination technique outlined above, the optimized illumination, Jtot , was calculated and is shown in Fig. 2. In Fig. 2, white areas of the pupil are the most important for maximizing the NILS of the central line through focus, and black areas are the least important for maximizing the NILS through focus. Three ways to implement the illuminator in Fig. 2 are with standard CADISSE (customer application defined illumination source shaping element) elements, dipole 908 and dipole 358.

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Fig. 1. 110-nm DRAM isolation pattern to optimize the illumination for maximum process window.

However, a customized binary elliptical dipole element can also be manufactured with a diffractive optical element (DOE) as shown in Fig. 2. The process window with these three binary implementations (358 dipole, 908 dipole, and elliptical dipole) was simulated for the 110-nm isolation design and compared to annular illumination. In Fig. 3, simulation results when imaging into the photoresist are shown for the custom elliptical dipole source. The resist cross-section simulation results are taken at the x 5 0.375 mm cut plane. The Bossung plot shows that the CD at the bottom of the cross-section is nearly iso-focal with over 0.6 mm DOF. In Fig. 4, simulation results for top down imaging show the end of line (EOL) printing where the aerial image is shown at a 0.4 intensity threshold level. Fig. 4 indicates that the end of line has little pull back through focus; however, a hammerhead or serifs at the end of line would help with squaring the end of line profile. In Fig. 5, simulations for the resist cross-section are shown for the 358 dipole element. These simulation results show that the 358 dipole element is also nearly iso-focal with over 0.6-mm DOF. In Fig. 6, the top down aerial images are also shown. These top down images, however, have greater pull back compared to the elliptical dipole. This indicates that the 358 dipole element is more susceptible to end of line shortening. Since the exposure latitude is related to the NILS, simulations were done to calculate the NILS through focus for the main feature with target width of 110 nm and for the end of line with target width of 500 nm. Maximizing the EOL NILS helps to prevent the end of line shortening in the

Fig. 2. Optimized illumination source for isolation pattern in Fig. 1 with possible binary implementations: CADISSE elements, 908 and 358 dipole, and a custom elliptical dipole.

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Fig. 3. Simulation results with the custom elliptical dipole source imaging into the photoresist. The resist cross-section simulation results are taken at the x 5 0.375 mm cut plane. The Bossung plots show that the CD at the bottom of the cross-section is nearly iso-focal with over 0.6-mm DOF.

isolation pattern. The NILS through focus is plotted for the main feature along the x 5 0.375 mm cut line in Fig. 7, and the NILS through focus is plotted for the EOL along the y 5 0.22 mm cut line in Fig. 8. For the main feature in Fig. 7, the custom elliptical dipole source and dipole 358 have approximately the same main feature NILS. The dipole 908, however, has significantly lower main feature NILS, and the annular does not resolve with significant process window. For the end of line

Fig. 4. Simulation results with the custom elliptical dipole source. The aerial image is shown above at a 0.4 intensity threshold level.

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Fig. 5. Simulation results with the 358 dipole source imaging into the photoresist. The resist cross-section simulation results are taken at the x 5 0.375 mm cut plane. The Bossung plots show that the CD at the bottom of the cross-section is approximately the same as the custom elliptical dipole source in Fig. 3.

NILS in Fig. 8, the dipole 908 has the best EOL NILS with the custom elliptical dipole source slightly less than dipole 908. The dipole 358, however, has the worst EOL NILS through focus. The custom source has the highest NILS for both the main feature and the EOL as compared to the other sources.

Fig. 6. Simulation results with the 358 dipole source. The aerial image is shown above at a 0.4 intensity threshold level.

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Fig. 7. NILS plotted for the main feature along the x 5 0.375 mm cut line. The custom elliptical dipole source and dipole 358 have approximately the same NILS while the dipole 908 has significant lower NILS and the annular does not resolve with significant process window.

3. Experimental results In addition to the simulations, experiments to print 110-nm DRAM isolation pattern in Fig. 1 were conducted with the two CADISSE dipole sources, dipole 908 and dipole 358. The depth of focus for the experiments are shown in Fig. 9 with top down CD SEM images at best energy through focus. The

Fig. 8. NILS plotted for the end of line (EOL) along y 5 0.22 mm cut line. The dipole 908 has the best NILS with the custom elliptical dipole source slightly less than dipole 908. The custom source has the highest NILS for both the main feature and the EOL as compared to the other sources.

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Fig. 9. Experimental results at best energy showing the DOF. The DOF with dipole 908 is |0.3 mm and the DOF with dipole 358 is |0.4 mm. The largest loss of DOF is due to resist thickness loss.

DOF with dipole 908 is |0.3 mm and the DOF with dipole 358 is |0.4 mm. The largest loss of DOF is due to resist thickness loss. The experiments show that printing the 110-nm isolation pattern with sufficient DOF is feasible with strong off axis illumination. In the future, further experiments are planned to examine custom illumination sources and to examine the custom illumination in the presence of optical proximity correction.

4. Conclusions and future work The illumination is often a neglected element in minimizing the k1. The illumination has a lot of potential for increasing the process window for periodic patterns such as DRAM, SRAM, FPGA, Flash memory, and ROM codes. Software to optimize the illumination and hardware to implement the optimized illumination is currently being coded at ASML Masktools. In addition to optimizing the illumination for a particular pattern, optimizing the illumination and mask simultaneously as shown by Rosenbluth has greater promise in maximizing the process window for periodic patterns. In addition to periodic patterns, the combination of assist features and illumination optimization can optimize the process windows for logic designs. For logic designs, the assist features eliminate some pitches, and the illumination can optimize the process windows for these fewer pitches.

References [1] M. Burkhardt et al., Illuminator design for the printing of regular contact patterns, Microelectron. Eng. 41 (1998) 91. [2] T.S. Gau et al., The customized illumination aperture filter for low k1 photolithography process, Proc. SPIE 4000 (2000) 271. [3] A. Rosenbluth et al., Optimum mask and source patterns to print a given shape, Proc. SPIE 4346 (2001) 486. [4] M. Born, E. Wolf, in: Principles of Optics, 7th Edition, Cambridge University Press, 1999, p. 604. [5] C.A. Mack et al., Lumped parameter model of the photolithographic process, in: Kodak Microelectronics Seminar Proceedings, 1986, p. 228.