Pub Date : 2020-11-06DOI: 10.1117/1.jmm.19.4.040501
A. Yen
We review the history in connection with the resolution formula of microlithography and argue that it was Abbe rather than Rayleigh who definitively stated the 0.5λNA resolution limit for the minimum pitch first, using an approach more relevant to projection imaging, and hence, this expression should be more appropriately referred to as the Abbe formula for the resolution of a projection imaging system.
{"title":"Rayleigh or Abbe? Origin and naming of the resolution formula of microlithography","authors":"A. Yen","doi":"10.1117/1.jmm.19.4.040501","DOIUrl":"https://doi.org/10.1117/1.jmm.19.4.040501","url":null,"abstract":"We review the history in connection with the resolution formula of microlithography and argue that it was Abbe rather than Rayleigh who definitively stated the 0.5λNA resolution limit for the minimum pitch first, using an approach more relevant to projection imaging, and hence, this expression should be more appropriately referred to as the Abbe formula for the resolution of a projection imaging system.","PeriodicalId":16522,"journal":{"name":"Journal of Micro/Nanolithography, MEMS, and MOEMS","volume":"1 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2020-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73788241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-20DOI: 10.1117/1.jmm.19.4.040101
H. Levinson, H. Zappe
{"title":"JM3 is Gone, Long Live JM3!","authors":"H. Levinson, H. Zappe","doi":"10.1117/1.jmm.19.4.040101","DOIUrl":"https://doi.org/10.1117/1.jmm.19.4.040101","url":null,"abstract":"","PeriodicalId":16522,"journal":{"name":"Journal of Micro/Nanolithography, MEMS, and MOEMS","volume":"80 1","pages":"040101"},"PeriodicalIF":2.3,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74224041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1117/1.JMM.19.4.041001
A. Erdmann, H. Mesilhy, P. Evanschitzky, V. Philipsen, F. Timmermans, Markus Bauer
Abstract. Next-generation extreme ultraviolet (EUV) systems with numerical apertures of 0.55 have the potential to provide sub-8-nm half-pitch resolution. The increased importance of stochastic effects at smaller feature sizes places further demands on scanner and mask to provide high contrast images. We use rigorous mask diffraction and imaging simulation to understand the impact of the EUV mask absorber and to identify the most appropriate optical parameters for high NA EUV imaging. Simulations of various use cases and material options indicate two main types of solutions: high extinction materials, especially for lines spaces, and low refractive index materials that can provide phase shift mask solutions. EUV phase masks behave very different from phase shift masks for DUV. Carefully designed low refractive index materials and masks can open up a new path toward high contrast edge printing.
{"title":"Perspectives and tradeoffs of absorber materials for high NA EUV lithography","authors":"A. Erdmann, H. Mesilhy, P. Evanschitzky, V. Philipsen, F. Timmermans, Markus Bauer","doi":"10.1117/1.JMM.19.4.041001","DOIUrl":"https://doi.org/10.1117/1.JMM.19.4.041001","url":null,"abstract":"Abstract. Next-generation extreme ultraviolet (EUV) systems with numerical apertures of 0.55 have the potential to provide sub-8-nm half-pitch resolution. The increased importance of stochastic effects at smaller feature sizes places further demands on scanner and mask to provide high contrast images. We use rigorous mask diffraction and imaging simulation to understand the impact of the EUV mask absorber and to identify the most appropriate optical parameters for high NA EUV imaging. Simulations of various use cases and material options indicate two main types of solutions: high extinction materials, especially for lines spaces, and low refractive index materials that can provide phase shift mask solutions. EUV phase masks behave very different from phase shift masks for DUV. Carefully designed low refractive index materials and masks can open up a new path toward high contrast edge printing.","PeriodicalId":16522,"journal":{"name":"Journal of Micro/Nanolithography, MEMS, and MOEMS","volume":"22 1","pages":"041001 - 041001"},"PeriodicalIF":2.3,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88833807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1117/1.JMM.19.4.043201
Manabu Hakko, Kanji Suzuki
Abstract. Background: To increase the resolution and depth of focus (DOF) of flat panel display (FPD) exposure systems, off-axis illumination (OAI) conditions are used extensively. OAI using narrowband wavelength illumination has been studied sufficiently. In contrast, new techniques that consider broadband wavelength illumination are needed because the effects of OAI differ between broadband and narrowband illumination. Aim: This paper presents a divided spectrum illumination (DSI), a new design concept that achieves both high resolution and a large DOF. Approach: The source wavelength is optimized according to the illumination angle. Results: Experimental imaging results for line and space patterns with a line width of 1.0 and a pitch of 2.0 μm demonstrate that the DSI design provides improved resolution. Exposure results also indicate that resist profiles using DSI are sufficiently sharp to retain pattern fidelity at the top of the resist. The DOF with DSI is also improved by 21% compared to that obtained with traditional OAI. Conclusions: DSI achieves both high resolution and a large DOF while maintaining high productivity.
{"title":"Resolution enhancement with source-wavelength optimization according to illumination angle in optical lithography","authors":"Manabu Hakko, Kanji Suzuki","doi":"10.1117/1.JMM.19.4.043201","DOIUrl":"https://doi.org/10.1117/1.JMM.19.4.043201","url":null,"abstract":"Abstract. Background: To increase the resolution and depth of focus (DOF) of flat panel display (FPD) exposure systems, off-axis illumination (OAI) conditions are used extensively. OAI using narrowband wavelength illumination has been studied sufficiently. In contrast, new techniques that consider broadband wavelength illumination are needed because the effects of OAI differ between broadband and narrowband illumination. Aim: This paper presents a divided spectrum illumination (DSI), a new design concept that achieves both high resolution and a large DOF. Approach: The source wavelength is optimized according to the illumination angle. Results: Experimental imaging results for line and space patterns with a line width of 1.0 and a pitch of 2.0 μm demonstrate that the DSI design provides improved resolution. Exposure results also indicate that resist profiles using DSI are sufficiently sharp to retain pattern fidelity at the top of the resist. The DOF with DSI is also improved by 21% compared to that obtained with traditional OAI. Conclusions: DSI achieves both high resolution and a large DOF while maintaining high productivity.","PeriodicalId":16522,"journal":{"name":"Journal of Micro/Nanolithography, MEMS, and MOEMS","volume":"1 1","pages":"043201 - 043201"},"PeriodicalIF":2.3,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83130986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1117/1.JMM.19.4.044401
K. Hattori, Daisuke Matsushima, Kensuke Demura, Masaya Kamiya
Abstract. Background: Although the wet cleaning process has been widely used in semiconductor device manufacturing due to its convenience, it faces theoretical limits. That is, when the size of the objected particle is smaller than 100 nm, it is buried in the stagnant layer where there is substantially no fluid flow. Aim: Only small particles below the stagnant layer (<100 nm) is removed without any damage to the fine patterns or substrate: pattern collapse, critical dimension shift, and optical property shift. Approach: Utilizing unique characteristics of water: volume expansion when freezing, solid (ice) is lighter than liquid (water), and particles adhered the substrate is peeled off from the substrate and rise to the water surface along with the surrounding ice. Results: By repeating the cycle of cooling, thawing, and rinsing, polystyrene sphere particle of 80 nm in diameter can be removed with high particle removal efficiency (PRE >90 % ) and no negative influences on the pattern or substrate. Conclusions: A new cleaning method for very small (<100 nm) particles is proposed with high PRE and low damage. This method is thought to be applied to every process if water can infiltrate into the gap between the particles and the substrate.
{"title":"Particle and pattern discriminant freeze-cleaning method","authors":"K. Hattori, Daisuke Matsushima, Kensuke Demura, Masaya Kamiya","doi":"10.1117/1.JMM.19.4.044401","DOIUrl":"https://doi.org/10.1117/1.JMM.19.4.044401","url":null,"abstract":"Abstract. Background: Although the wet cleaning process has been widely used in semiconductor device manufacturing due to its convenience, it faces theoretical limits. That is, when the size of the objected particle is smaller than 100 nm, it is buried in the stagnant layer where there is substantially no fluid flow. Aim: Only small particles below the stagnant layer (<100 nm) is removed without any damage to the fine patterns or substrate: pattern collapse, critical dimension shift, and optical property shift. Approach: Utilizing unique characteristics of water: volume expansion when freezing, solid (ice) is lighter than liquid (water), and particles adhered the substrate is peeled off from the substrate and rise to the water surface along with the surrounding ice. Results: By repeating the cycle of cooling, thawing, and rinsing, polystyrene sphere particle of 80 nm in diameter can be removed with high particle removal efficiency (PRE >90 % ) and no negative influences on the pattern or substrate. Conclusions: A new cleaning method for very small (<100 nm) particles is proposed with high PRE and low damage. This method is thought to be applied to every process if water can infiltrate into the gap between the particles and the substrate.","PeriodicalId":16522,"journal":{"name":"Journal of Micro/Nanolithography, MEMS, and MOEMS","volume":"105 1","pages":"044401 - 044401"},"PeriodicalIF":2.3,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85896721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1117/1.JMM.19.4.044001
R. Kizu, I. Misumi, A. Hirai, S. Gonda
Abstract. Background: Conventional scanning electron microscopy (SEM) that is used for 2D top-view metrology, a classical line edge roughness (LER) measurement technique, is incapable of measuring 3D structures of a nanoscale line pattern. For LER measurements, SEM measurement generates a single line-edge profile for the 3D sidewall roughness, although the line-edge profile differs at each height in the 3D sidewall. Aim: To develop an evaluation method of SEM-based LER measurement techniques and to verify how the 3D sidewall shape is reflected in the SEM’s 2D result. Approach: Direct comparison by measuring an identical location of a line pattern by SEM and an atomic force microscopy (AFM) with the tip-tilting technique that is capable of measuring the 3D sidewall. The line pattern has vertical stripes on the sidewall due to its fabrication process. Measured line edge profiles were analyzed using power spectral density, height-height correlation function, and autocorrelation function. Results: Line edge profiles measured by SEM and AFM were well matched except for noise level. Frequency and scaling analyses showed that SEM profile contained high noise and had lost a property of self-affine fractals in contrast to AFM. Conclusions: In the case of the line pattern with vertical stripes on the sidewall, SEM profile is generally consistent with 3D sidewall shape. The AFM-based LER measurement technique is useful as LER reference metrology to evaluate other LER measurement techniques.
{"title":"Direct comparison of line edge roughness measurements by SEM and a metrological tilting-atomic force microscopy for reference metrology","authors":"R. Kizu, I. Misumi, A. Hirai, S. Gonda","doi":"10.1117/1.JMM.19.4.044001","DOIUrl":"https://doi.org/10.1117/1.JMM.19.4.044001","url":null,"abstract":"Abstract. Background: Conventional scanning electron microscopy (SEM) that is used for 2D top-view metrology, a classical line edge roughness (LER) measurement technique, is incapable of measuring 3D structures of a nanoscale line pattern. For LER measurements, SEM measurement generates a single line-edge profile for the 3D sidewall roughness, although the line-edge profile differs at each height in the 3D sidewall. Aim: To develop an evaluation method of SEM-based LER measurement techniques and to verify how the 3D sidewall shape is reflected in the SEM’s 2D result. Approach: Direct comparison by measuring an identical location of a line pattern by SEM and an atomic force microscopy (AFM) with the tip-tilting technique that is capable of measuring the 3D sidewall. The line pattern has vertical stripes on the sidewall due to its fabrication process. Measured line edge profiles were analyzed using power spectral density, height-height correlation function, and autocorrelation function. Results: Line edge profiles measured by SEM and AFM were well matched except for noise level. Frequency and scaling analyses showed that SEM profile contained high noise and had lost a property of self-affine fractals in contrast to AFM. Conclusions: In the case of the line pattern with vertical stripes on the sidewall, SEM profile is generally consistent with 3D sidewall shape. The AFM-based LER measurement technique is useful as LER reference metrology to evaluate other LER measurement techniques.","PeriodicalId":16522,"journal":{"name":"Journal of Micro/Nanolithography, MEMS, and MOEMS","volume":"5 1","pages":"044001 - 044001"},"PeriodicalIF":2.3,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81135078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-04DOI: 10.1117/1.jmm.19.3.030101
H. Levinson
JM3 Co-Editor-in-Chief Harry Levinson introduces new guidelines regarding materials for lithography.
JM3联合主编Harry Levinson介绍了关于光刻材料的新指南。
{"title":"Lithography materials guidelines","authors":"H. Levinson","doi":"10.1117/1.jmm.19.3.030101","DOIUrl":"https://doi.org/10.1117/1.jmm.19.3.030101","url":null,"abstract":"JM3 Co-Editor-in-Chief Harry Levinson introduces new guidelines regarding materials for lithography.","PeriodicalId":16522,"journal":{"name":"Journal of Micro/Nanolithography, MEMS, and MOEMS","volume":"3 1","pages":"030101"},"PeriodicalIF":2.3,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84703708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.1117/1.JMM.19.3.034002
L. van Kessel, T. Huisman, C. W. Hagen
Abstract. Background: Line-edge roughness (LER) is often measured from top-down critical dimension scanning electron microscope (CD-SEM) images. The true three-dimensional roughness profile of the sidewall is typically ignored in such analyses. Aim: We study the response of a CD-SEM to sidewall roughness (SWR) by simulation. Approach: We generate random rough lines and spaces, where the SWR is modeled by a known power spectral density. We then obtain corresponding CD-SEM images using a Monte Carlo electron scattering simulator. We find the measured LER from these images and compare it to the known input roughness. Results: For isolated lines, the SEM measures the outermost extrusion of the rough sidewall. The result is that the measured LER is up to a factor of 2 less than the true on-wafer roughness. The effect can be modeled by making a top-down projection of the rough edge. Our model for isolated lines works fairly well for a dense grating of lines and spaces as long as the trench width exceeds the line height. Conclusions: In order to obtain and compare accurate LER values, the projection effect of SWR needs to be taken into account.
{"title":"Understanding the influence of three-dimensional sidewall roughness on observed line-edge roughness in scanning electron microscopy images","authors":"L. van Kessel, T. Huisman, C. W. Hagen","doi":"10.1117/1.JMM.19.3.034002","DOIUrl":"https://doi.org/10.1117/1.JMM.19.3.034002","url":null,"abstract":"Abstract. Background: Line-edge roughness (LER) is often measured from top-down critical dimension scanning electron microscope (CD-SEM) images. The true three-dimensional roughness profile of the sidewall is typically ignored in such analyses. Aim: We study the response of a CD-SEM to sidewall roughness (SWR) by simulation. Approach: We generate random rough lines and spaces, where the SWR is modeled by a known power spectral density. We then obtain corresponding CD-SEM images using a Monte Carlo electron scattering simulator. We find the measured LER from these images and compare it to the known input roughness. Results: For isolated lines, the SEM measures the outermost extrusion of the rough sidewall. The result is that the measured LER is up to a factor of 2 less than the true on-wafer roughness. The effect can be modeled by making a top-down projection of the rough edge. Our model for isolated lines works fairly well for a dense grating of lines and spaces as long as the trench width exceeds the line height. Conclusions: In order to obtain and compare accurate LER values, the projection effect of SWR needs to be taken into account.","PeriodicalId":16522,"journal":{"name":"Journal of Micro/Nanolithography, MEMS, and MOEMS","volume":"750 1","pages":"034002 - 034002"},"PeriodicalIF":2.3,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78790931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.1117/1.JMM.19.3.034001
Jennifer Church, Luciana Meli, Jing Guo, M. Burkhardt, C. Mack, A. de Silva, K. Petrillo, M. Breton, R. Bonam, R. Lallement, E. Miller, B. Austin, S. Matham, N. Felix
Abstract. Background: With aggressive scaling of single-expose (SE) extreme ultraviolet (EUV) lithography to the sub-7-nm node, stochastic variations play a prominent role in defining the lithographic process window (PW). Fluctuations in photon shot noise, absorption, and subsequent chemical reactions can lead to stochastic failure, directly impacting electrical yield. Aim: Fundamental characterization of the mode and magnitude of these variations is required to define the threshold for failure. Approach: A complementary series of techniques is enlisted to probe the nature and modulation of stochastic variation in SE EUV patterning. Unbiased line edge roughness (LER), local critical dimension uniformity (LCDU), and defect inspection techniques are employed to monitor the frequency of stochastic variations leading to failures in line/space (L/S) and via patterning. Results: When characterizing different resists and illumination conditions, there is no change in unbiased LER or via LCDU with increasing critical dimension (CD). Stochastic defect density is correlated with CD for both L/S and via arrays, and there is a strong correlation with L/S electrical yield data. Conclusions: Traditional 3σ LER and via LCDU measurements are not sensitive enough to define and improve PW. For PW centering and yield improvement, stochastic defect inspection is a necessity.
{"title":"Fundamental characterization of stochastic variation for improved single-expose extreme ultraviolet patterning at aggressive pitch","authors":"Jennifer Church, Luciana Meli, Jing Guo, M. Burkhardt, C. Mack, A. de Silva, K. Petrillo, M. Breton, R. Bonam, R. Lallement, E. Miller, B. Austin, S. Matham, N. Felix","doi":"10.1117/1.JMM.19.3.034001","DOIUrl":"https://doi.org/10.1117/1.JMM.19.3.034001","url":null,"abstract":"Abstract. Background: With aggressive scaling of single-expose (SE) extreme ultraviolet (EUV) lithography to the sub-7-nm node, stochastic variations play a prominent role in defining the lithographic process window (PW). Fluctuations in photon shot noise, absorption, and subsequent chemical reactions can lead to stochastic failure, directly impacting electrical yield. Aim: Fundamental characterization of the mode and magnitude of these variations is required to define the threshold for failure. Approach: A complementary series of techniques is enlisted to probe the nature and modulation of stochastic variation in SE EUV patterning. Unbiased line edge roughness (LER), local critical dimension uniformity (LCDU), and defect inspection techniques are employed to monitor the frequency of stochastic variations leading to failures in line/space (L/S) and via patterning. Results: When characterizing different resists and illumination conditions, there is no change in unbiased LER or via LCDU with increasing critical dimension (CD). Stochastic defect density is correlated with CD for both L/S and via arrays, and there is a strong correlation with L/S electrical yield data. Conclusions: Traditional 3σ LER and via LCDU measurements are not sensitive enough to define and improve PW. For PW centering and yield improvement, stochastic defect inspection is a necessity.","PeriodicalId":16522,"journal":{"name":"Journal of Micro/Nanolithography, MEMS, and MOEMS","volume":"217 1","pages":"034001 - 034001"},"PeriodicalIF":2.3,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73012797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. Source mask and polarization optimization (SMPO) is a promising extension of the widely used resolution enhancement technology, source mask optimization (SMO), to further enhance chip manufacturability beyond 28-nm node. Our work is aimed to develop an efficient gradient-based SMPO method by employing the hybrid Hopkins–Abbe imaging model to fulfill the goal. In addition to source and mask variables, the model is adapted to also include polarization variables to realize the optimization. Compact formulas for forward and backward model application are derived. The computation benefits from precomputed transmission cross coefficients and features high efficiency. Validity of the method is confirmed by case studies. For dense array pattern case, the optimal source and polarization can be found analytically. SMPO optimized results match well with the theoretical expectations. In addition, process window, mask error enhancement factor, and normalized image log-slope for the studied cases all get improved over the counterpart SMO results, which employ commonly used polarization. Runtime analysis shows the method is computationally efficient. Our work provides a valid way to optimize polarization together with source and mask.
{"title":"Gradient-based source mask and polarization optimization with the hybrid Hopkins–Abbe model","authors":"M. Ding, Zhiyuan Niu, Fang Zhang, Linglin Zhu, Weijie Shi, Aijun Zeng, Huijie Huang","doi":"10.1117/1.JMM.19.3.033201","DOIUrl":"https://doi.org/10.1117/1.JMM.19.3.033201","url":null,"abstract":"Abstract. Source mask and polarization optimization (SMPO) is a promising extension of the widely used resolution enhancement technology, source mask optimization (SMO), to further enhance chip manufacturability beyond 28-nm node. Our work is aimed to develop an efficient gradient-based SMPO method by employing the hybrid Hopkins–Abbe imaging model to fulfill the goal. In addition to source and mask variables, the model is adapted to also include polarization variables to realize the optimization. Compact formulas for forward and backward model application are derived. The computation benefits from precomputed transmission cross coefficients and features high efficiency. Validity of the method is confirmed by case studies. For dense array pattern case, the optimal source and polarization can be found analytically. SMPO optimized results match well with the theoretical expectations. In addition, process window, mask error enhancement factor, and normalized image log-slope for the studied cases all get improved over the counterpart SMO results, which employ commonly used polarization. Runtime analysis shows the method is computationally efficient. Our work provides a valid way to optimize polarization together with source and mask.","PeriodicalId":16522,"journal":{"name":"Journal of Micro/Nanolithography, MEMS, and MOEMS","volume":"21 1","pages":"033201 - 033201"},"PeriodicalIF":2.3,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82125715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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