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Abstract
Mask blank defect is one of the most important factors that degrades the image quality of extreme ultraviolet (EUV) lithography system, and further leads to a yield lose. In order to compensate the amplitude and phase distortions caused by the EUV mask blank defects, this paper proposes an advanced algorithm to optimize the mask absorber pattern based on genetic algorithm. First, a successive approximation correction method is used to roughly compensate the effect of mask blank defect. Then, an advanced genetic algorithm is proposed to obtain higher efficiency and compensation accuracy, which uses an adaptive coding strategy and a fitness function considering normalized image log slope of lithography image. For illustration, the proposed method is verified based on rectangular contact patterns and complex pattern with different defects. The aerial images of optimized masks are evaluated by a commercial lithography simulator. It will show that the proposed method can mitigate the impact of mask defects, and improve the fidelity of lithography print image. The simulation results also demonstrate the higher convergence efficiency and mask manufacturability can be guaranteed by the proposed method.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Extreme ultraviolet (EUV) lithography is considered as the most promising candidate for the semiconductor manufacturing at 7nm node and beyond [1]. Unlike the masks used for deep ultraviolet lithography with 193nm wavelength, EUV lithography mask are always reflective. The introduction of reflective mask has brought a series of challenges, which would introduce different impacts to the overall lithography workflow. At the technology nodes with immersion lithography, substrate fabrication and mask manufacturing are sufficiently mature, by which mask defects could be limited to acceptable levels in both of density and size [2]. Over high defect density is a major obstacle to the high volume manufacturing (HVM) in EUV lithography. In order to achieve high reflectivity, a stack comprised of about 40 bilayers of Mo and Si are used as reflective mirrors on the EUV masks [3]. As shown in Fig. 1, defects embedded in the multilayer of EUV mask could cause the deformation of multilayer and decrease the image quality of exposure [4], and thus result in a yield lose.
Fig. 1. Illustration of the (a) defect-free mask, (b) defect-free aerial image, (c) defect-free resist contour, (d) defective mask, (e) defective aerial image, and (f) defective resist contour.
In the past, extensive researches were conducted to develop novel methods or workflows, such as pattern-shifting or absorber pattern optimization, to reduce mask defect impacts as much as possible. Strategies including design-blank matching, pattern rotation and intentional pattern deformation were adopted and validated by simulations or experiments. Algorithms such as gradient descent, simulated annealing and level-set were used to improve the accuracy and efficiency of optimization [5,6]. For the pattern-shifting methods, there are strict requirements for the defect sizes. The relative position relationship between defects and mask pattern also determines whether the defects can be mitigated successfully. In order to break these restrictions, Chae et al. evaded more defects by adding a 2nd order deformation to the local patterns [7]. However, it is hard to deal with the cooperation of multiple patterns, and the non-Manhattan patterns due to the 2nd deformation is not friendly to manufacturing. Zhang et al. proposed a covariance-matrix-adaption evolution strategy to compensate for the mask defects by inserting rectangle patterns on mask with repaired results [8]. Zhang’s method modified mask pattern by applying additional patterns directly on the target pattern, which does not consider mask manufacturability. However, excessive defects cannot be compensated by merely modifying mask pattern. In addition, using pattern-shifting method indiscriminately for all kinds of defects would reduce the manufacturability [9]. At the same time, using pixelated approach to modify the absorber patterns may result in mask patterns that are not friendly to manufacturing [10]. Thus, it is necessary to explore new kinds of efficient and manufacturing-friendly methods to further improve the compensation capability of EUV mask defects.
In order to overcome the difficulties encountered in the previous works, this paper develops a mask defect compensation method based on advanced generic algorithm with higher efficiency and accuracy. The problem is formulated as follows:
Problem: Given an initial mask pattern with a defect, set up a method to accurately compensate the impact of defect. The genetic algorithm is required to achieve the maximum fitness value within a limited loop number, and the output mask should have promising manufacturability.
In our previous conference paper, we proposed an EUV mask defect compensation method based on genetic algorithm [11]. Firstly, the mask pattern was roughly corrected according to the edge placement error (EPE), which was referred to as the successive approximation correction method. Then, the approximate correction result was used to generate the initial population of the following modified genetic algorithm to greatly reduce the iteration number. In particular, an adaptive coding strategy was introduced, which adjusted the segment lengths and segment number during the optimization process to enrich the diversity of individuals. In addition, the normalized image log slope (NILS) was considered in the fitness function to improve the contrast of the lithography aerial image. The optimized mask pattern obtained by this method is edge-based, which is more friendly to manufacturing than the pixelated mask pattern.
In this paper, we make further exploration based on our former work in [11]. The previous work mainly focused on the optimization of simple lithography mask layouts, including the one-dimensional line-space pattern and square contact pattern. In addition, it only comes with a few comparisons with other algorithms. In semiconductor manufacturing, the rectangular contact patterns are more commonly used in Contact layers, and some complex two-dimensional mask layouts are extensively used in Metal layers. In order to prove the robustness of the proposed method, this paper studies the optimization of rectangular contact patterns and complex mask pattern to compensate the mask defects. Besides, the influence of different positions and sizes of mask defects on the compensation performance is discussed. In order to demonstrate the superiority of the proposed algorithm, comparisons with different kinds of genetic algorithms are conducted. The results also show that the proposed successive approximation correction and adaptive coding methods can improve the performance of convergence speed and compensation accuracy.
The remaining content of this paper is organized as follow: Fundamental of mask modification and genetic algorithm are introduced in Section 2. The whole workflow and advancement of the proposed method are described in Section 3. Lithography simulations based on multiple masks with different defects are provided in Section 4. The compensation capacity of the proposed method is proved by the results with different defect parameters. Furthermore, simulations based on complex layout patterns are also provided. Section 5 gives the conclusion of this work.
2. Mask modification based on genetic algorithm
There are two major methods to compensate the defects by mask optimization: one is to modify the mask pattern directly, the other is to cover the defect with absorber. Modifying the mask pattern directly is a general and wide-used method to compensate the lithographic influence caused by defects. Commonly, buried mask blanket defects are phase defects. That means the compensation results in focus may not be found in through focus. This limits the depth of focus (DOF) of the repaired mask. The goal of covering the defect with absorber is to transform phase defects into amplitude defects. However, this method increases the difficulty of compensating defects in focus. Besides, a small-sized isolated absorber is required, which would seriously affect the manufacturability of mask pattern. At the same time, this method also needs to know the location, size and shape of defects in advance. According to [12], We believed that the former method could guarantee the manufacturability of the final mask pattern.
The genetic algorithm is a computational model to simulate the natural selection and genetic mechanism of Darwin’s biological evolution theory. In the genetic algorithm, a set of individuals compose a population, which represent the possible solutions to the appointed problems. A genetic algorithm begins with the initialization step to create the population with random or specific genes. These genes can be mapped to the individuals in the population, and the individuals represent the mask patterns in this paper. Then, a certain fitness function is utilized to calculate the fitness value of each individual to achieve the evaluation results. Based on these results, individuals with the best fitness will be selected as survivals in the population. Following that, these remaining individuals multiply through cross-over and mutation operations to obtain a new population in the next generation. The process of “evaluation-selection-crossover-mutation” will be looped until the stop criteria is satisfied, which could be the maximum loop number or a target fitness value. In the applications of mask modification, genes are used to encode the movement of segments along the mask boundaries. The individuals thus formed can correspond to a certain mask pattern and its lithography image. The workflow of the proposed genetic algorithm is described in Fig. 2
For genetic algorithms, it is vital to select a proper initial population. Especially in this paper, where defects would have a serious impact on the lithography image, and improper initial population would result in a great lost in convergence rate. Therefore, a rough correction is used to generate the initial population for the genetic algorithm. On the basis of the rough correction, adaptive encoding method will be applied to obtain more potential individuals. Genetic operators including selection, crossover and mutation will be used to generate the new population.
3. Advanced genetic algorithm
Different from the traditional methods, three major improvements are adopted: Firstly, the proposed genetic algorithm uses a successive approximation correction to increase the convergence speed. Then, the adoption of adaptive coding could provide abundant potentials of individuals. Finally, this proposed genetic algorithm also uses an innovative fitness function where the NILS is involved to obtain better lithography image. These three points will be described in this section.
3.1 Successive approximation correction
Regarding to the genetic algorithm, selecting a fine initial population would accelerate the algorithm greatly. At the beginning of the algorithm, the defective masks would result in poor aerial images, which probably lead to empty print images. Therefore, a rough correction is needed to rapidly generate the initial population for the genetic algorithm.
A successive approximation correction is proposed to implement the rough correction. As shown in Fig. 2, the mask boundaries are first divided into segments with a fixed length. In each iteration, the segments are moved according their local EPEs. Typically, the movement step equals half of the local EPE or a given maximum movement step when the local EPE cannot be measured. After several iterations, this correction would obtain a mask pattern with smaller overall EPE. Based on this correction result, the initial population of genetic algorithm is generated.
After this rough correction, the result of print image contour usually seems acceptable. However, because the movement of each segment only considers its local EPE, the results need to be further optimized. This successive approximation correction process results in a good guess of the initial population, and thus improves the convergence rate of the genetic algorithm.
3.2 Adaptive encoding method
Fragmentation is the operation that breaks the pattern edges into smaller segments, and the segments can be moved forward or backward during the following optimization. The number of additional vertices on the mask pattern produced by the segment movement will greatly affect the algorithm speed.
Although a fragmentation is done in the successive approximation correction, segments represented by this gene are fixed, which limits the potential of individuals. Therefore, an adaptive encoding method is proposed to increase the degrees of freedom in fragmentation. In the advanced genetic algorithm with adaptive coding, the movement step and length of each segment are optimized according to its feature type (edge, convex corner or concave corner). An example of random individual is shown in Fig. 3. In Fig. 3(a), the length of each segment is the same. After setting different values for the movement and length of segments, the individual is modified as shown in Fig. 3(b).
However, tuning the lengths of segments may not always get better results. Long segments count against fine compensation of mask defects, while short segments count against manufacturability. In the genetic algorithm, the length of each segment is limited within in the range of $[{{l_{\min }}\textrm{,}{l_{\max }}} ]$ by splitting or merging segments, as shown in Fig. 4(b). According to Ref. [13], the minimum segment length is determined as 4nm on the wafer scale to maintain basic manufacturability. In the next Section, the critical dimension (CD) on wafer is 22nm, and thus the ${l_{\min }}$ and ${l_{\max }}$ are set as 4nm and 12nm respectively.
In this approach, initial segments with equal length could be adopted at the beginning. In the process of optimization, the algorithm gradually selects the individual with the best segmentation according to the fitness function. This avoids the influence of fixed segmentation on the compensation results.
3.3 Fitness function
The investigation of an appropriate fitness function is a crucial step for genetic algorithm. After decoding individuals to the mask patterns, lithography simulations are used to verify the capability of defect compensation. The design of fitness function is considered from the following aspects: (1) The compensation of the print image; (2) The compensation of the aerial image; (3) The compensation of local edges; (4) Weighting of the above three parts. These aspects evaluate the compensation from the entirety to locality. We select the difference in aerial image, the difference in print image and NILS at the edge of the pattern closest to the defect location to describe the first three aspects, and weighting parameters to adjust the weight of each part. The fitness function is formulated as following:
4. Simulation and discussion
4.1 Simulation settings
For a given EUV substrate, firstly, defects on multilayer are inspected, and then characterized by the height and the full width at half maximum (FWHM) at the top and bottom of the multilayer, as shown in Fig. 5. As the printed images are defined by the absorber above the stack, the pattern of the absorber is generally modified to compensate the impact of mask defects. Large defects which are considered as irreparable are usually evaded by pattern-shifting [4]. Then, the pattern shapes of absorbers are adjusted to cover the rest defects to compensate the imaging deformation.
In this paper, we calculate the diffraction field of mask by commercial simulator Sentaurus Lithography (S-Litho) using waveguide method. The default lithography simulation parameters settings are shown in Table 1, with some parameters using the default values of the simulator. All dimensions in this work are defined and shown on the wafer scale for uniformity. The actual size of defects and absorbers on the mask scale could be calculated based on the demagnification factor of lithography system. Simulations for different types of mask patterns are studied in this work (Table 2). The influence of different defect sizes and positions are also studied.
Table 1. Parameter settings for lithography simulation
Table 2. Mask settings (wafer scale /nm)
4.2 Simulations with different defect sizes
In order to simplify the optimization flow and reduce the complexity of simulation, contact pattern is mainly used in the simulations. Defects are characterized by Gaussian shapes and preset in different sizes and positions on the mask. The center of mask is defined as the coordinate origin. The x and y coordinates represent the position of defect. In order to reduce the influence of exposure intensity distribution on the neighboring patterns, the ratio of CD to pitch in the x direction is 1:3 instead of 1:2. All defects are located in the center or left side of the contact hole. The illumination intensity threshold is set to make the CD in the middle of contact for the defect-free mask equals to the target CD, which represents the standard.
The defect located on the edge of contact is selected to analyze the influence of different defect sizes on the same position, and to evaluate the maximum compensation capability of the proposed algorithm. The reason that the defect position is chosen on the edge of the contact is that the contact edge defect has more serious influences on the aerial image in contrast to the defect in the corner. Specific defect parameters and the repaired results are shown in Tables 3, 4, and 5. Five different sizes are selected at the same mask position. For each mask pattern, the corresponding repaired mask is shown. For each pattern, the contour of print image is shown as the black curve overlapped with the aerial image, and the red circle on the repaired mask stands for the defect area. In these simulations, we use pattern error (PE) to describe the quality of imaging results. According to a given unit pixel (1nm×1nm in this paper) and threshold, each aerial image could generate a corresponding print image. The sum of pixels different from the print image corresponding to a pattern and the print image corresponding to defect-free pattern is recorded as its PE. A lower PE means the print image is closer to that of defect-free case.
Table 3. Parameters of defects (wafer scale /nm)
Table 4. Simulation results with different defect sizes
Table 5. Measurement results for different defect sizes
It can be inferred that the print image shrinks along with the increment of defect size, which poses greater challenges to the defect compensation. Affected by the defect, the target mask CD cannot be fully recovered. With a tolerance of 10% in CD, a repaired CD within the range from 19.8 nm to 24.2 nm is considered acceptable. Judging from the repaired masks, defect #1 and #2 could be repaired well. Both of them have approximate 3% loss in CD. A drop of performance emerges from defect #3 and #4. From the corresponding contour images, it can be observed that the impact caused by these two defects can be still repaired normally. All these above four correction cases could meet the requirement of 10% CD loss, and further reach 5% CD loss. The repaired result of defect #5 is a little over the limit of 10% CD loss (19.8 nm expected). It can be observed from the aerial images that intensity distribution is not satisfactory at the defect location. Thus, defect #5 is considered irreparable defect. The limit of repairable defect size is between the defect #4 and defect #5. Defects beyond this limit should be regarded as irreparable since the defect area would be always less than the threshold.
4.3 Simulations with different defect positions
Next, the influence of defect position is studied. According to the simulation results in the previous section, defect #2 is selected as a typical repairable defect. Three typical defect locations are chosen: center, edge and corner of the contact, which represents several possible situations. The edge and corner are chosen in the opposite direction to the shadow effect. So, the lithography imaging is more influenced by the defect when compensating the shadow effect by the shifting mask. Simulation results of are shown in Table 6 and Table 7.
Table 6. Simulation results for different defect positions
Table 7. Measurement results for different defect positions
Obviously, the defect in the center position has the largest impact on the imaging, and the average intensity of its repaired aerial image is the lowest. However, its print image after correction has smaller pattern error than the case with a corner defect. Although the maximum intensity of the repaired aerial image is closer to the defect-free case, the corner defect is harder to be repaired than the edge defect. From the distribution and intensity of the repaired aerial images, it is observed that the defect on the edge is the easiest to be fixed.
4.4 Comparisons between proposed method and traditional genetic algorithm
As an advanced genetic algorithm, the successive approximation correction and the adaptive encoding method are used in this work. To prove the advantages of the proposed algorithm, several experiments are conducted. According to the experiments above, defect #2 is selected as the typical repairable defect, which is placed at different locations
As shown in Fig. 6, three different algorithms are compared in terms of accuracy and convergence rate. In each case, the successive approximation correction (SAC) is applied in the first 20 generations of the proposed method. Compared to the traditional genetic algorithm with fixed-length coding, the proposed adaptive coding has little help in the rate of convergence, but provides better compensation accuracy. When it comes to the proposed algorithm, the successive approximation correction accelerates the convergence, and a better result is achieved. For different defect locations, the convergence curves show the same trend.
Fig. 6. Comparison between different algorithms with different defects at the (a) center (b) edge and (c) corner.
4.5 Optimization for complex mask pattern
To validate the competence of the proposed algorithm, a comparison of different version of genetic algorithm is furtherly discussed with complex mask pattern on a much larger area. The pitch is 240 nm on the wafer scale, which corresponds to 960 nm on the mask scale. The defect is located at the center of the mask. Other parameters of the defect are shown in Table 8. The repaired aerial image shows that the proposed genetic algorithm can effectively compensate the defect in the complex mask pattern. The repaired mask is depicted in Fig. 7(e). It also shows that the mask features far from the defect are not modified during the optimization, since their print images are not influenced by the defect.
Fig. 7. Defect compensation for complex mask pattern. (a) defect-free aerial image (b) defective aerial image (c) repaired aerial image (d) intial mask (e) repaired mask.
Table 8. Defect setting for complex mask pattern
4.6 Comparison between proposed genetic algorithm and related work
In order to compare the practical performance of this proposed algorithm, we follow the way of Ref. [8] to build another version of genetic algorithm to compensate defects. Table 9 shows the comparison of the proposed method and the related method. It shows that lower pattern error is achieved by the proposed genetic algorithm under the same condition, and the convergence speed of the proposed method is much higher.
Table 9. Comparison between proposed genetic algorithm and related work
5. Conclusion
In this paper, an advanced genetic algorithm is proposed to compensate the influence of EUV mask blank defects on the lithography imaging quality. Firstly, the successive approximation correction is proposed to generate the initial population of the genetic algorithm. Then, an adaptive coding method is developed to enrich the diversity of individuals and guarantee their manufacturability. Finally, the NILS is involved in the fitness function of genetic algorithm to get better repaired image results. Simulations with different defects are carried out. It shows that the aerial image and print image of defective mask can be repaired well if the defect size and position are constrained within a certain range. Comparison with the traditional genetic algorithm demonstrates an improvement in convergence speed and compensation accuracy by using the adaptive coding and successive approximation correction. Compared with the related work, the proposed method can converge much faster.
However, the current work only considers the modifications of main mask patterns. In addition, the overlapped process window is not considered. Future work will study the insertion methods of sub-resolution assist features to increase the process window of critical mask patterns.
Funding
National Natural Science Foundation of China (61804174); National Key Research and Development Program of China (2019YFB2205005); Beijing Municipal Natural Science Foundation (4182021); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2021115) .
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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