An approach to increase efficiency of DOE based pupil shaping technique for off-axis illumination in optical lithography

Fang Zhang; Jing Zhu; Weirui Yue; Jian Wang; Qiang Song; Guohai Situ; Frank Wyrowski; Huijie Huang

doi:10.1364/OE.23.004482

1. Introduction

In projection lithography system, off axis illumination (OAI) is extensively utilized for critical dimension (CD) shrinking, depth of focus increasement and image contrast enhancement [1, 2]. Phase-only diffractive optical elements (DOEs) are adopted in pupil shaping unit (PSU) for most of the deep-ultraviolet (DUV) lithography machines to realize OAI because of their design flexibility, high-quality freeform illumination mode generation and stable output against the fluctuation of the input laser beam [3–5]. In general, the specifications of the PSU such as opening angle, azimuth angle, especially efficiency and pole balance, are the key factors since they affect the exposure performance [6, 7]. For example, high efficiency requires shorter exposure time which is directly related to the lithography’s throughput [7, 8]. Besides, the pole balance is proved to be one of the most important specifications to guarantee the required line width accuracy and depth of focus of the optical lithography [9]. However, up to now, it is not very clear that how the uniformity of the illumination mode at the pupil plane impacts the lithographic performance. Moreover, the uniformity of the illumination mode is undetermined, because it is very sensitive to the state of zoom and axicon pairs that are designed to work with DOE to compose PSU [10]. And some researchers have investigated to utilize the actual measured pupil fill for successful optical proximity correction (OPC) [11, 12]. Actually, there are specialized homogeneous unit and homogeneous compensation unit in the lithography illumination system to realize high illumination uniformity. And the uniformity of the illumination mode at the pupil plane has been proved to have little effect on the illumination uniformity [13]. Therefore, to some extent, it is reasonable to relax uniformity and increase efficiency as well as control the other key factors in the DOE design for PSU.

Several classical algorithms such as iterative Fourier transformation algorithm (IFTA) [14], simulated annealing algorithm [15] and genetic algorithm [16] have been used to design DOE. The iterative process of IFTA is repeated Fourier transform (FT) and inverse Fourier transform (IFT) along with constraints C_xy in the diffraction plane (x, y) and C_uv in the source plane (u, v). The constraint C_xy is to replace the calculated amplitude in the diffraction plane with the amplitude of the desired pattern while keeping the phase unchanged. Similarly, the constraint C_uv is to perform the same operation in the source plane. However, for a desired pattern which consists of more than one point, this algorithm is insufficient to retrieve a phase distribution which generates the desired pattern without noise in theory [17]. In order to solve the problem, some improved constraints based on IFTA have been proposed [18] and they have become the traditional constraints. Typically the goal of these improved constraints is mainly to optimize the signal noise ratio (SNR) in signal window, or to enhance fidelity, while diffraction efficiency is the secondary consideration [19, 20]. To the best of our knowledge, there were only a small number of studies that focus on the improvement of the diffraction efficiency of the DOE in lithography illumination system. However, there is still space for efficiency of the DOE to increase. Thus, in this paper we replace the strong SNR constraints with more relaxed ones, which are well suited for our purpose in optical lithography.

In this paper, the approach based on IFTA to increase pupil shaping efficiency is introduced in Section 2. Based on proposed constraints, several high efficiency DOEs which are used in high NA lithography illumination system are designed in Section 3. In Section 4, experiments are carried out to verify the proposed constraints. Some problems are discussed and the solutions are proposed in Section 5. Finally, conclusions are provided in Section 6.

2. Design method of high efficiency DOEs

In this section, an approach based on IFTA to increase pupil shaping efficiency is introduced. The iteration flowchart of the IFTA is shown in Fig. 1. As a comparison, a typical traditional constraint of IFTA discussed in the introduction is presented firstly. Then modified constraints are proposed to obtain high efficiency DOEs. Besides efficiency, pole balance is also considered in the design. It is used to evaluate the balance of energy distribution, and its definition is

P B = \frac{M a x (ε_{i}) - M i n (ε_{i})}{M a x (ε_{i}) + M i n (ε_{i})}

where, ε_i indicates the energy of the ith pole (i = 1,2 for dipole and i = 1, 2, 3, 4 for quadrupole). Pole balance is usually required to be less than 1.5% in high NA lithography illumination system. This value is restricted to be less than 1% in the design step in order to leave space for the fabrication and integration.

Fig. 1 The iteration flowchart of IFTA which is repeated Fourier transform (FT) and inverse Fourier transform (IFT) along with constraints C_xy in the diffraction plane (x, y) and C_uv in the source plane (u, v). The constraints C_xy and C_uv are to replace the calculated amplitudes with the ideal ones in corresponding planes, while keeping the phases unchanged. f₀(x,y) is the initial field distribution of the desired pattern. The phase of f₀(x,y) is arbitrary if only the intensity of the desired pattern is concerned.

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The typical constraint of the traditional IFTA is expressed by Traditional constraint:

C_{x y} [f_{j} (x, y)] = {\begin{matrix} s_{j} | f (x, y) | \exp [i φ_{j} (x, y)] \begin{matrix} x, y \in S W \end{matrix} \\ f_{j} (x, y) \begin{matrix} x, y \in N W \end{matrix} \end{matrix}

where, |f(x, y)| is the amplitude of desired pattern, φ_j(x, y) is the phase of f_j(x, y), SW and NW indicate the signal window and noise window respectively whose definitions can be found in Fig. 2(a), s_j is a scale factor [17]. There are three freedoms in the Traditional constraint, i.e. phase freedom, amplitude freedom and scale factor [17, 21]. The phase freedom refers to the SW, while the amplitude freedom refers to the NW where is opened to contain noise. The scale factor s_j is defined as

s_{j} = \frac{\int_{S R} | f (x, y) | | f_{j} (x, y) | d x d y}{\int_{S R} {| f (x, y) |}^{2} d x d y}

in reference [17]. It can be adjusted to balance the efficiency and SNR of SW, but its adjustment capacity is limited according to our observation.

Fig. 2 The definitions of (a) signal window (SW), noise window (NW), and (b) opening angle, orientation angle. M × M, S × S and s × s are used to represent the sampling number of diffractive window, outer and inner diameter of the SW.

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Applying the phase freedom to SW means that the amplitude of the desired pattern is restricted. And this SNR constraint will inevitably limit the efficiency. Efficiency is the percentage of the energy of input light that is diffracted into the SW. In order to increase efficiency, more light should be diffracted into the SW and a direct way to achieve this is to relax the amplitude restraint in the SW. An effective method to release the amplitude constraint in the SW is to set C_xy as Constraint 1:

C_{x y} [f_{j} (x, y)] = {\begin{matrix} f_{j} (x, y) \begin{matrix} x, y \in S W \end{matrix} \\ 0 \begin{matrix} x, y \in N W \end{matrix} \end{matrix}

The light field including amplitude and phase is freedom in the SW while severely repressed in the NW according to Eq. (4). Due to the amplitude freedom in the SW, the increase of the efficiency is expected, but this freedom does not meet our requirement because it may lead to two problems: 1) The pole balance could not be guaranteed; 2) The intensity distribution of the generated pattern in the SW is completely unable to be controlled. Therefore it is necessary to add some restrictions into Constraint 1 to solve these problems.

Pole balance is directly related to the energy of each pole. Thus the energy of each pole should be adjusted to be equivalent in iterations in order to ensure pole balance. Accordingly, calculate the energy ε_ij of the ith pole in jth iteration, and the average energy $\bar{ε_{j}}$ of them. And then the Constraint 1 is adjusted to Constraint 2:

C_{x y} [f_{j} (x, y)] = {\begin{matrix} \sqrt{\frac{\bar{ε_{j}}}{ε_{i j}}} f_{i j} (x, y) \begin{matrix} x, y \in P_{i} \end{matrix} \\ 0 \begin{matrix} x, y \in N R \end{matrix} \end{matrix}

For the applications of amplitude and phase freedoms in the SW and energy control of each pole in Constraint 2, the DOE designed by this constraint for high NA lithography illumination system is expected to achieve high efficiency and better pole balance despite the intensity distribution of the generated pattern in the SW is still uncontrolled. As presented in the introduction, efficiency and pole balance are the key factors that affect the exposure performance in DUV lithography system, and the uniformity of the illumination mode at the pupil plane has little effect on the illumination uniformity. Besides, the source used in DUV lithography is an excimer laser. The emitted spatially partially coherent light will smooth the pattern generated at the pupil plane. Therefore there is no reason to say that pattern lack of fidelity is not satisfied with the actual demand. Nevertheless, let us put aside this argument and concentrate on exploiting methods to control the intensity distribution of the generated pattern.

Just like the Traditional constraint, the amplitude in the SW is fixed by the desired one. The amplitude in the SW should be controlled in iterations in order to obtain better intensity distribution. An improvement based on Constraint 2 to control the intensity distribution is presented below:

(1) Calculate the intensity distribution I_ij of the ith pole in jth iteration.
(2) Subtract $\sqrt{I_{i j}}$ from the amplitude of f_ij(x,y), set the values greater than 0 to 0, and then take the absolute values as the amplitude and the phase of f_ij(x,y) as phase to generate the field distribution ${f^{'}}_{i j} (x, y)$ .
(3) Add a factor $α$ ( $α \in (0, 1]$ ) to adjust the field distribution in each pole, i.e., $α f_{i j} (x, y) + (1 - α) {f^{'}}_{i j} (x, y)$ . And then calculate the energy $ε_{i j}^{'}$ of each pole and the average value $\bar{ε_{j}^{'}}$ of them after adjustment.
(4) The constraint which can control the intensity distribution is Constraint 3: $C_{x y} [{\bar{g}}_{j} (x, y)]= {\begin{matrix} \sqrt{\frac{\bar{ε_{j}^{'}}}{ε_{i j}^{'}}} [α f_{i j} (x, y) + (1 - α) {f^{'}}_{i j} (x, y)] \begin{matrix} x, y \in P_{i} \end{matrix} \\ \begin{matrix} 0 & x, y \in N R \end{matrix} \end{matrix}$

In fact, Constraint 3 is the general expression of the method to increase efficiency of DOE, because Constraint 2 is just a special case of Constraint 3 with α = 1. When Applying Constraint 3 to design DOE used in high NA lithography illumination system, the intensity distribution of the generated pattern in the SW is expected to be controlled and the control degree is related to α. Pole balance can also be guaranteed for the energy control in the Constraint 3, but the efficiency may decrease for the control of amplitude in the SW.

3. Design results of high efficiency DOEs

As illustration and verification, several DOEs are designed using the modified constraints discussed in the previous section. Without loss of generality, top hat dipole and quadrupole are chosen as the desired patterns.

The wavelength of the input beam is 193.368nm and the level of phase quantization is 8. The outer and inner divergence half angles of DOEs to be designed are 1.433° and 0.143°. The opening angle is 20°. The divergence and opening angles are the same for the two modes. The orientations of two poles (P1, P2) of dipole are 0°, 180° with respect to the x-axis. The orientations of four poles (P1, P2, P3 and P4) of quadrupole are 0°, 90°, 180° and 270° with respect to the x-axis. The definitions of opening and orientation angles are indicated in Fig. 2(b).

The achieved efficiencies and pole balances are shown in Fig. 3. And the patterns generated by the designed DOEs are shown in Fig. 4. The dipoles’ efficiency and pole balance of the designed DOEs are shown in Fig. 3(a). The pattern shown in Fig. 4(a) is generated by the DOE designed by the Traditional constraint. The diffractive efficiency is 88.27% and the pole balance is 0.11%. The intensity distribution which is extremely similar with the desired one looks gratifying. The intensity distribution of the pattern generated by the DOE designed by Constraint 1 is shown in Fig. 4(b). The efficiency achieved is 91.97% and the pole balance is 2.49%. The efficiency has about 3.5% increase compared to the one achieved by the Traditional constraint. But the poles are seriously imbalanced and the generated pattern is clear edge collapse. The efficiency and pole balance are 91.93% and 0.03% when the energy control constraint is used to design the DOE. There is a great improvement in pole balance with almost no decline in efficiency. The intensity distribution of the pattern generated by the DOE designed by Constraint 3 with α = 0.8 is shown in Fig. 4(d). The efficiency is 90.83% and the pole balance is 0.15%. The efficiency increases about 2.6% and the control of the intensity distribution is effective.

Fig. 3 The efficiencies and pole balances of the designed DOEs for high NA lithography illumination system. The far field intensity distributions of the designed DOEs are (a) dipole and (b) quadrupole. The α equals to 0.8 in Constraint 3.

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Fig. 4 The far field intensity distributions of the designed DOEs for high NA lithography illumination system. These patterns are generated by the DOEs which are designed by (a, e) Traditional constraint, (b, f) Constraint 1, (c, g) Constraint 2 and (d, h) Constraint 3 (α = 0.8).

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The quadrupoles’ efficiency and pole balance of the designed DOEs are shown in Fig. 3(b), and the diffraction patterns are shown in Fig. 4(e-h). The diffractive efficiency and pole balance of the DOE designed by the Traditional constraint are 85.73% and 0.74%. The efficiencies of the DOEs designed by Constraint 1 and Constraint 2 both have about 5% increase compared to the one achieved by the Traditional constraint. The efficiency has about 3.3% increase when applying Constraint 3 with α = 0.8 to control the intensity distribution. The pole balances of the DOEs designed by Constraint 2 and Constraint 3 are both less than 1%, while the pole balance of the DOE designed by Constraint 1 is 4.1%.

4. Experiments

For the demonstration of the proposed method, several experiments are carried out where a reflective type spatial light modulator (SLM) is adopted to represent DOEs. The utilized SLM (HOLOEYE Leto, with 1920 × 1080 pixels of 6.4μm in size) works under visible laser light illumination. Therefore the DOEs are designed under such condition.

The experimental setup is shown in Fig. 5. The beam emitted from a He-Ne laser is coupled into the single mode fiber and comes out at the other end. The wavelength of the light emitted from the laser is 632.8nm. With close approximation we can take it as a point source since we only use the paraxial region set by a diaphragm. The expander is a Fourier transform lens and it converts light outputted from the fiber to a collimated beam. A diaphragm with circular aperture is used to adjust the beam size. A beam splitter is used to split the incoming laser beam into two parts, one of which is sent into a power meter to detect the energy fluctuation, the other shined on the reflective SLM. A polarizer is utilized to adjust the polarization state of the laser beam impinging onto the SLM, on which the designed DOEs are displayed. The beam is then reflected by the SLM and Fourier transformed by using a focal length = 125mm Fourier transform lens. At the back focal plane of the Fourier transform lens, a CCD camera is placed to record the diffraction patterns produced by the DOEs. And the number of pixels and the size of pixels of the CCD camera are 1280 × 1024 and 5.2μm.

Fig. 5 Experimental setup where the SLM is used to represent DOEs.

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In our designs for experiments, the level of quantization of the DOEs is 8. The outer and inner divergence half angles of the designed diffraction patterns are 0.71° and 0.06°. The opening angle is 20°. The orientations of the two poles (P1, P2) of dipole are 0°, 180°. The orientations of the four poles (P1, P2, P3 and P4) of quadrupole are 0°, 90°, 180° and 270°. The efficiencies and pole balances of the designed DOEs for the experiments are demonstrated in Table 1. And the simulated patterns are shown in Fig. 6. The efficiencies of the designed DOEs for the experiments are consistent with the DOEs designed for high NA lithography illumination system. The pole balances of the DOEs designed by Traditional constraint, Constraint 2 and Constraint 3 are all less than 1.0% except the ones designed by Constraint 1. The far field intensity distributions of the DOEs designed by Constraint 3 are controlled to close to the desired ones compared with those designed by Constraint 1 and Constraint 2.

Table 1. The pole balances and efficiencies (increments) of design and experimental results in the experiments.

View Table

Fig. 6 The simulated far field intensity distributions of the designed DOEs for experiments. These patterns are generated by the DOEs which are designed by (a, e) Traditional constraint, (b, f) Constraint 1, (c, g) Constraint 2 and (d, h) Constraint 3 (α = 0.8).

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In the experiments, the patterns captured by the CCD camera are shown in Fig. 7. The intensity distributions are consistent with the designed results except for the zero orders. The zero order is unexpected to our optical system for the very strong energy density. However, the zero order is indeed exist for fabrication errors of DOE and calibration errors and fill factor of SLM. A simple method to eliminate zero order is to add a stop at the pupil plane. But in the data processing the zero orders are removed from the detected datum when calculating efficiencies and pole balances.

Fig. 7 The intensity distributions captured by the CCD camera in the experiments. These patterns correspond to the DOEs which are designed by (a, e) Traditional constraint, (b, f) Constraint 1, (c, g) Constraint 2 and (d, h) Constraint 3 (α = 0.8).

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The pole balance is easy to obtain by referring to its definition while the efficiency is not. This is because it is almost impossible to obtain the absolute energy value from the CCD camera. That is to say, the efficiency gained by dividing the relative energy abstracted from the CCD camera by the energy obtained from the power meter is a relative value. Therefore, an increment value is adopted to evaluate efficiency increase and it is defined as

Δ η_{k} = \frac{η_{T} - η_{k}}{η_{T}} \begin{matrix} (k = 1, 2, 3) \end{matrix}

where, η_T is the relative efficiency of the DOE designed by Traditional constraint, and η_k is the relative efficiency of DOE designed by the Constraint k (k = 1, 2, 3).

The experimental results show that the pole balances of the DOEs designed by Constraint 2 and Constraint 3 are less than 1.5%. The dipoles’ efficiency increment of the DOEs designed by the three high efficiency constraints are 7.28%, 5.34% and 3.19%. And the quadrupoles’ efficiency increment of the DOEs designed by the three high efficiency constraints are 13.43%, 11.94% and 10.92%.

5. Discussion

This paper focused on exploiting a design method to increase the efficiency of DOE used in high NA lithography. In general, the diffractive efficiency of DOE is also related to many other factors, including the desired pattern, spatial sampling and phase quantization. Therefore, it is important to show how to choose spatial sampling and phase quantization in the proposed method. Although there have been several studies discussing the influence of the desired pattern [22, 23] and spatial sampling [24] of DOE on efficiency upper bounds. But these results cannot be applied directly for the case in this paper, because their upper bounds are only valid for optimizing a special signal with high SNR. Regarding the pupil shaping in this paper, SNR requirement is relaxed and the efficiency is the main specification. Nevertheless, the diffractive efficiency is positively correlated with the number of spatial sampling and the level of phase quantization from theory. But they cannot be increased indefinitely especially for the DOE used in the deep ultraviolet light. Therefore, we try to find the relationship of efficiency to spatial sampling for the proposed method in this paper. The attempting results indicate that efficiency increases with the sampling number, and the increase trend becomes weaker when the sampling number reaches a threshold. The sampling number of all the designed DOEs in this paper is adopted following this rule. And the sampling number of DOEs for dipole and quadrupole in the same section is same. In addition, the influence of phase quantization on efficiency is sinc²(1/Z), where sinc(1/Z) is defined as sin(π/Z)/(π/Z) [25, 26]. Z is the level of phase quantization which must be positive integer power of 2. It is observed that the phase quantization decreases efficiency and the impact reduces with a larger level. When Z equates to 8, the effect on efficiency is 94.96%. And when 16, the effect is 98.72%. But at present the level of phase quantization is chosen as 8, because the efficiency increasement for higher quantization level is less than the decreasement from fabrication errors.

In order to compare the proposed constraints and the traditional constraint in more details, the efficiency and pole balance are studied versus the optimization iteration number. There are four iterative procedures in the DOE design when the traditional constraint of IFTA is used [18]. In the first step, only the phase freedom is applied. And the efficiency increases clearly in this step. The amplitude freedom is adopted in the second step where the SNR will be significantly improved. The third step is soft quantization [27]. The soft quantization is an effective method to solve stagnation problem in iterative quantization. The last step is directly quantization. In this paper, the iteration numbers of the four procedures are 300, 200, 50 and 200 respectively for the DOEs designed by the traditional method. And the efficiency trends of the DOEs designed for high NA lithography illumination system by the traditional method are shown in Fig. 8. From Fig. 8, we can see the efficiency rises rapidly in the first step. It has a drastic decline in the second step. Then it fluctuates with small amplitude in the third step. Finally, the efficiency is at a standstill state in the last step.

Fig. 8 The efficiency trends of the designed DOEs for high NA lithography illumination system. The far field intensity distributions of the designed DOEs for lithography illumination system are (a) dipole and (b) quadrupole.

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For the high efficiency constraints which are different from the traditional one, the first two steps are merged in this paper. The iteration numbers of the three procedures are 500, 50 and 200 respectively. The efficiency trends of the designed high efficiency DOEs for high NA lithography illumination system are also shown in Fig. 8. It is obvious that the efficiencies are larger than the traditional one in every step.

The pole balance trends in the DOEs design for high NA lithography illumination system are shown in Fig. 9. The pole balance trends of Traditional constraint, Constraint 2 and Constraint 3 are always less than 1% in the iterations.

Fig. 9 The pole balance trends of the designed DOEs for high NA lithography illumination system. The far field intensity distributions of the designed DOEs for lithography illumination system are (a) dipole and (b) quadrupole.

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Actually, the asymmetry of the patterns generated by the designed DOEs may have an impact on the final exposure performance. But this problem can be easily solved by the mixed multi-region design principle, where every region of a DOE is designed individually, rather than simply repeated [28]. Here we choose a DOE which generates dipole in the far field to explain the specific operations. In order to solve the problem of asymmetry, one designed region is rotated and radially reversed as indicated in Fig. 10. Then the designed region and its rotated replica and radially reversed regions are formatted as a secondary region to compose a complete DOE. The pattern generated by the mixed multi-region DOE is symmetry for the compensation function of its secondary region.

Fig. 10 One of the implementations based on the mixed multi-region design method to solve the problem of pattern asymmetry.

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The overall performance of each pole has been controlled in the algorithm, and we found it satisfying the requirement for high NA lithography machine. The lithography simulations are almost focused on the influence of the overall pupil fill. However, how the uniformity of the illumination mode at the pupil plane impacts the lithographic performance is still lack of study. In order to quantify the appropriateness of the proposed approach for lithographic imaging, the effect of actual pupil uniformity on the final exposure performance is worthy of further study. Nevertheless, the proposed method can provided an approach to produce high efficiency OAI not only in optical lithography but also in optical fields requiring functional illumination such as optical microscopy.

6. Conclusions

This paper presents an approach to increase efficiency of DOE-based pupil shaping technique for off-axis illumination in optical lithography. The efficiency of the OAI is the main criteria in the DOE design. A general modified constraint based on IFTA is proposed for DOE design to achieve high efficiency and ensure low pole balance at the same time. The main idea is to apply amplitude and phase freedoms in the signal window with controlling energy of each pole.

By applying the amplitude and phase freedoms in the signal window and controlling the energy of each pole, we observed clearly efficiency increase and pole balance retention. The achieved efficiencies of DOEs designed by this proposed constraint for high NA lithography illumination system are 91.93% for dipole and 90.72% for quadrupole which have about 3.7% and 5% increase compared to those obtained from the traditional constraint. The achieved pole balances are 0.03% for dipole and 0.72% for quadrupole. By adjusting α in the general high efficiency constraint expression, the intensity distributions of the generated patterns can be controlled to some extent. When α = 0.8, the achieved efficiencies of DOEs designed for high NA lithography illumination system are 90.83% for dipole and 89.05% for quadrupole. And the pole balances are also less than 1%. The efficiencies have a little decrease, but the intensity distributions of the generated patterns are controlled to close to the desired ones. The pole balances achieved are all satisfied the 90nm and 45nm optical lithography systems.

For the difficulty and long period of fabrication of DOEs, a SLM who works under visible light is adopted to represent DOEs in the experiments. And the DOEs are designed again under such condition. The experimental results are consistent with the design ones.

Acknowledgments

This work was supported by International Science & Technology Cooperation Program of China under Grant 2011DFR10010, National Natural Science Foundation of China under Grant 61377005, Science and Technology Commission of Shanghai Municipality under Grant 14YF1406300, Chinese Academy of Sciences Visiting Professorship for Senior International Scientist under Grant 2013T1G0041 and the Recruitment Program for Global Young Experts.

References and links

1. M. D. Himel, R. E. Hutchins, J. C. Colvin, M. K. Poutous, A. D. Kathman, and A. S. Fedor, “Design and fabrication of customized illumination patterns for low k1 lithography: a diffractive approach,” Proc. SPIE 4691, 1436–1442 (2001). [CrossRef]

2. H. J. Levinson, Principles of lithography (SPIE, 2005), Chap. 8.

3. Q. Tan, Y. Yan, and G. Jin, “Statistic analysis of influence of phase distortion on diffractive optical element for beam smoothing,” Opt. Express 12(14), 3270–3278 (2004). [CrossRef] [PubMed]

4. L. Y. Tan, J. J. Yu, J. Ma, Y. Q. Yang, M. Li, Y. J. Jiang, J. F. Liu, and Q. Q. Han, “Approach to improve beam quality of inter-satellite optical communication system based on diffractive optical elements,” Opt. Express 17(8), 6311–6319 (2009). [CrossRef] [PubMed]

5. A. J. Caley, M. J. Thomson, J. S. Liu, A. J. Waddie, and M. R. Taghizadeh, “Diffractive optical elements for high gain lasers with arbitrary output beam profiles,” Opt. Express 15(17), 10699–10704 (2007). [CrossRef] [PubMed]

6. Z. Hu, J. Zhu, B. Yang, Y. Xiao, A. Zeng, and H. Huang, “Test of diffractive optical element for DUV lithography system using visible laser,” Proc. SPIE 8557, 855709 (2012). [CrossRef]

7. J. E. Childers, T. Baker, T. Emig, J. Carriere, and M. D. Himel, “Advanced testing requirements of diffractive optical elements for off-axis illumination in photolithography,” Proc. SPIE 7430, 74300S (2009). [CrossRef]

8. U. Stamm, J. Kleinschmidt, K. Gabel, H. Birner, I. Ahmad, D. Bolshukhin, J. Brudermann, T. D. Chinh, F. Flohrer, S. Gotze, G. Hergenhan, D. Klopfel, V. Korobotchko, B. Mader, R. Muller, J. Ringling, G. Schriever, and C. Ziener, “High power sources of EUV lithography - State of the art,” Proc. SPIE 5448, 722–736 (2004). [CrossRef]

9. K. Welch, A. Fedor, D. Felder, J. Childers, and T. Emig, “Improvements to optical performance in diffractive elements used for off-axis illumination,” Proc. SPIE 7430, 743005 (2009). [CrossRef]

10. A. Engelen, R. Socha, E. Hendrickx, W. Scheepers, F. Nowak, M. van Dam, A. Liebchen, and D. Faas, “Implementation of pattern specific illumination pupil optimization on Step & Scan systems,” Proc. SPIE 5377, 1323–1333 (2004). [CrossRef]

11. C. Bodendorf, R. E. Schlief, and R. Ziebold, “Impact of measured pupil illumination fill distribution on lithography simulation and OPC models,” Proc. SPIE 5377, 1130–1145 (2004). [CrossRef]

12. Y. Granik and K. Adam, “Analytical approximations of the source intensity distributions,” Proc. SPIE 5992, 599255 (2005). [CrossRef]

13. F. Zhang, J. Zhu, B. X. Yang, L. H. Huang, X. B. Hu, Y. F. Xiao, and H. J. Huang, “Off-line inspection method of microlens array for illumination homogenization in DUV lithography machine,” Proc. SPIE 9046, 904619 (2013). [CrossRef]

14. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 2(35), 237–246 (1972).

15. S. Kirkpatrick, C. D. Gelatt Jr, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983). [CrossRef] [PubMed]

16. N. Yoshikawa, M. Itoh, and T. Yatagai, “Quantized phase optimization of two-dimensional Fourier kinoforms by a genetic algorithm,” Opt. Lett. 20(7), 752–754 (1995). [CrossRef] [PubMed]

17. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. 7(6), 961–969 (1990). [CrossRef]

18. O. Ripoll, V. Kettunen, and H. P. Herzig, “Review of iterative Fourier-transform algorithms for beam shaping applications,” Opt. Eng. 43(11), 2549–2556 (2004). [CrossRef]

19. M. Skeren, I. Richter, and P. Fiala, “Iterative Fourier transform algorithm: comparison of various approaches,” J. Mod. Opt. 49(11), 1851–1870 (2002). [CrossRef]

20. H. Kim, B. Yang, and B. Lee, “Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements,” J. Opt. Soc. Am. A 21(12), 2353–2365 (2004). [CrossRef] [PubMed]

21. F. Wyrowski, “Diffraction efficiency of analog and quantized digital amplitude holograms: analysis and manipulation,” J. Opt. Soc. Am. 7(3), 383–393 (1990). [CrossRef]

22. F. Wyrowski, “Upper bound of the diffraction efficiency of diffractive phase elements,” Opt. Lett. 16(24), 1915–1917 (1991). [CrossRef] [PubMed]

23. U. Krackhardt, J. N. Mait, and N. Streibl, “Upper bound on the diffraction efficiency of phase-only fanout elements,” Appl. Opt. 31(1), 27–37 (1992). [CrossRef] [PubMed]

24. V. Arrizón and M. Testorf, “Efficiency limit of spatially quantized Fourier array illuminators,” Opt. Lett. 22(4), 197–199 (1997). [CrossRef] [PubMed]

25. H. Dammann, “Blazed synthetic phase-only holograms,” Optik (Stuttg.) 31(1), 95–104 (1970).

26. F. Wyrowski, “Efficiency of quantized diffractive phase elements,” Opt. Commun. 92(1-3), 119–126 (1992). [CrossRef]

27. F. Wyrowski, “Iterative quantization of digital amplitude holograms,” Appl. Opt. 28(18), 3864–3870 (1989). [CrossRef] [PubMed]

28. Z. Hu, J. Zhu, B. Yang, Y. Xiao, A. Zeng, and H. Huang, “Mixed multi-region design of diffractive optical element for projection exposure system,” Optik (Stuttg.) 124(22), 5573–5576 (2013). [CrossRef]

Modes	Parameters		Traditional constraint	Constraint 1	Constraint 2	Constraint 3(α = 0.8)
Dipo	Design	Efficiency (%)	88.28	92.13	92.08	90.98
	Design	Pole balance (%)	0.01	3.45	0.40	0.03
	Experiment	Efficiency (%, increment)	-	7.28	5.34	3.19
	Experiment	Pole balance (%)	0.21	3.87	0.85	0.50
Quad	Design	Efficiency (%)	85.81	90.73	90.65	89.13
	Design	Pole balance (%)	0.70	23.34	0.60	0.76
	Experiment	Efficiency (%, increment)	-	13.43	11.94	10.92
	Experiment	Pole balance(%)	1.11	22.16	1.19	1.18

An approach to increase efficiency of DOE based pupil shaping technique for off-axis illumination in optical lithography

Abstract

1. Introduction

2. Design method of high efficiency DOEs

3. Design results of high efficiency DOEs

4. Experiments

5. Discussion

6. Conclusions

Acknowledgments

References and links

Cited By

Figures (10)

Tables (1)

Equations (7)

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