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Guest Editors Alan Brodie and Martha I. Sanchez introduce the JM3 Special Section on Masks and Lithography in the Era of Multi-beam Mask Writers.

Extreme ultraviolet lithography (EUV) materials and processes are constantly evolving and maturing, making sub-30 nm pitch single-exposure yield feasible. Characterization methodologies for stochastic variations are well-documented at this stage, with most employing critical dimension scanning electron microscopy (CDSEM) and a form of defect inspection to quantify line edge roughness (LER), local critical dimension uniformity and patterning failures. In this paper, the link between LER and stochastic defectivity is explored at a deeper level, as we probe the possibility of nucleating stochastic failures with programmed LER structures at 30 nm pitch using CDSEM, optical inspection and electrical yield data. First, we characterize LER post-develop and post-etch using unbiased LER measurements. Second, we study the defectivity and optical characteristics of the programmed LER pattern post hard mask open using optical inspection. Specifically, we measure the optical noise induced by programmed LER, the inspection performance in terms of defect capture and nuisance rate, and the predictive capability of optical inspection through a comparison of defectivity with electrical yield data.

In roll-to-roll digital maskless lithography (R2R DML) equipment, it is difficult to achieve high quality, owing to surface deformation that affects the pattern position. To address this issue, we simulated the patterning results of R2R DML to analyze the relationship between positional errors and pattern quality. Errors perpendicular to the pattern direction exhibited a 1.3–2 times greater effect on the linewidth and line edge roughness compared to those parallel to this direction. We confirmed that positioning errors could lead to defects in which the photoresists were not fully exposed. Finally, through simulations, we found that the effect of positional errors could be reduced by controlling the array spot separation length.

Two earlier publications showed that mask defectivity contributes to the stochastics of the EUVL-printed image on wafer. The present contribution gives more insights into the methodology and resist models used therein. In addition, an extended study of two types of mask roughness is presented, comprising mask absorber line-edge roughness and rippling of the multilayer mirror on the mask. For both, it is shown that contributions to stochastics are larger than expected purely from normalized intensity log-slope considerations. As a second topic, printability of local defects is readdressed at smaller pitches and more state-of-the-art illumination settings, in preparation to a genuine study of mask defectivity contribution to wafer printing stochastics at high-NA EUV lithography. First results for one-dimensional mask patterns indicate an influence of the anamorphic characteristic of high-NA imaging, showing a different behavior for vertical and horizontal orientations.

Standard samples with programmed micro-defects were fabricated for evaluating the defect detection capability of the next generation of pattern inspection tools. A 1.5-nm protrusion programmed defect and a 4-nm-wide (

Directed self-assembly (DSA) is one of the candidates for next generation lithography. Over the past years, many papers and presentation have been reported regarding DSA, and Tokyo Electron Limited (TEL is a registered trademark or a trademark of Tokyo Electron Limited in Japan and /or other countries.) also has presented the evaluation results and the advantages of each1-10. Polystyrene-b-polymethyl methacrylate (PS-b-PMMA) has been used in many report because the polymerization technology is established and it is easy to form vertical patterns. In addition, the chemical epitaxy flow for PS-b-PMMA has established well to improve defectivity, line edge roughness and line width roughness. On the other hand, it is difficult to achieve less than 24nm pitch pattern by PS-b-PMMA because of the low chi parameter. In this paper, the combination process of DSA and SADP (self-aligned double pattern) is proposed for further small pitch pattern by PS-b- PMMA and latest results are reported.

The authors present latent image characterization in photoresists by means of extreme ultraviolet (EUV) spectroscopic reflectometry. The optical constants of photoresists before and after exposure are measured in the EUV spectral range. Latent images are investigated in the form of periodic line gratings. The investigation is performed by the analysis of spectroscopic reflectance curves in the wavelength range from 5 nm to 20 nm at grazing incidence angles. Through an analysis of the reflectance curves based on rigorous electromagnetic modeling, a characterization of parameters of interest of the latent image is evaluated. This includes the latent image profile, surface topography and stochastic-related parameters such as line edge roughness.

In this study, we developed a methodology to evaluate scanning electron microscopy (SEM)-based line edge roughness (LER) metrology. In particular, we used a metrological tilting atomic force microscopy (tilting-mAFM) as LER reference metrology. We analyzed the height-height correlation function (HHCF) of SEM line-edge profiles combining averaging and unbiased correction methods. The direct comparison of our method with tilting-mAFM enabled a precise evaluation of the SEM-based LER metrology. We demonstrated that a combination of unbiased HHCF and averaging methods with appropriate condition enabled relatively precise measurement of three roughness parameters. We observed that, for precise roughness evaluation, reducing noise in the line-edge profiles is important before performing the HHCF analysis and unbiased correction.

This paper extends the 2019 findings, that local defects on an EUV mask are trigger points for stochastic failures on the printed wafer, to a simulation study of non-local mask deficiencies. These relate to shortcomings of a larger area nature where the reticle deviates from an ideal reticle or fails specification. These include aspects such as global CD error, absorber slope, contamination effects, line edge roughness, and multilayer roughness. The presented results suggest that mask specifications may need refinement, specifically for roughness type deficiencies, in order to help mitigate the mask contribution in the stochastics of wafer printing by EUV lithography.

We investigated the contribution ratio of process fidelity and beam accuracy in patterning with the multi-beam mask writing system. A beam pitch-related line edge profile may occur, which impacts on line edge roughness (LER) in the multi-beam writing system. The printability of beam image into the final etched pattern depends on the mask process, therefore, we need to understand quantitatively the printability of beam placement errors on LER with the actual mask process. We examined how the patterning characteristics are modified in each step of the mask process. The printability of beam placement errors largely depend on the period of errors, rather than the amplitude of errors. These results can optimize the writing strategy in multi-beam mask writing.

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.

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. We study the response of a CD-SEM to sidewall roughness (SWR) by simulation. We generate random rough lines and spaces, where the SWR is modelled 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. We find that, 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 2 less than the true on-wafer roughness. The effect can be accurately modelled 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.

The manufacturing of semiconductor devices using extreme ultraviolet (EUV) lithography started in 2019. A high numerical aperture tool under development is capable of resolving 8 nm line-and-space optical images and will extend the application of EUV lithography. However, resist materials have not been yet applicable to the production with 8 nm resolution. In this study, the relationships among the half-pitch of line-and-space patterns (resolution), chemical gradient [an indicator of line edge roughness (LER)], and sensitivity were investigated in the sub-10 nm half-pitch region for chemically amplified EUV resists. The chemical gradient was simulated on the basis of their sensitization and reaction mechanisms. The relationship was formulated as a function of total sensitizer concentration (the sum of photoacid generator and photodecomposable quencher concentrations) and the thermalization distance of secondary electrons. The effect of thermalized electrons was well incorporated into the trade-off relationships between resolution, LER, and sensitivity. (147/150)

Pitch uncertainty and line edge roughness are among the critical quality attributes of a pitch standard and normally the analyses of these two parameters are separate. The analysis of self-traceable Cr atom lithography nano-gratings shows a positive relevance and sensitivity between LER and evaluated standard deviation of pitch. Therefore, LER can be used as an aided pre-evaluation parameter for the pitch calculation method, such as the gravity center method or the zero-crossing points method. The optimization of the nano-grating evaluation method helps to obtain the accurate pitch value with fewer measurements and provide a comprehensive characterization of pitch standards.

We examine the impact of line-edge roughness (LER) on the variability in the on-current and saturation threshold voltage of ultrascaled FinFET devices via quantum-mechanical transport simulation. We obtain a realistic model of LER by decomposing the LER into short- $\lambda $ and long- $\lambda $ fluctuations, and we consider their separate influences on device performance. We show that the long- $\lambda $ fluctuations lead to greater device variability than the short- $\lambda $ fluctuations, and we explain the difference between the two cases via the influence of fluctuating quantum confinement arising from the LER. Finally, we consider devices in which the long- $\lambda $ fluctuations of the two fin edges are correlated and demonstrate that this correlation significantly improves the variability. Thus, we show the continued need for fabrication technology either to reduce the amplitude of the long- $\lambda $ fluctuations or to ensure the long- $\lambda $ fluctuations between the sidewalls of ultrascaled FinFET devices are correlated.

Mueller matrix ellipsometry (MME) is applied to characterize lithographic patterns with natural line edge roughness (LER). A computationally efficient approach based on effective medium approximation is proposed to model the effects of LER in MME measurements. We present both the theoretical and experimental results on lithographic patterns with realistic LER which demonstrate that MME in combination with the proposed effective modeling method is capable of quantifying LER amplitudes. Quantitative comparisons between the MME and scanning electron microscopy measured results also reveal the strong potential of this technique for in-line nondestructive line roughness monitoring.

We investigate the effects of Line Edge Roughness (LER) of electrode lines on the uniformity of Resistive Random Access Memory (ReRAM) device areas in cross-point architectures. To this end, a modeling approach is implemented based on the generation of 2D cross-point patterns with predefined and controlled LER and pattern parameters. The aim is to evaluate the significance of LER in the variability of device areas and their performances and to pinpoint the most critical parameters and conditions. It is found that conventional LER parameters may induce &gt, 10% area variability depending on pattern dimensions and cross edge/line correlations. Increased edge correlations in lines such as those that appeared in Double Patterning and Directed Self-assembly Lithography techniques lead to reduced area variability. Finally, a theoretical formula is derived to explain the numerical dependencies of the modeling method.

The optimization problem of reducing EUV line edge roughness (LER) of a given feature, subject to the tolerance constraints on a CD of this feature at nominal EUV process conditions and several off-nominal conditions, is formulated. A stochastic rigorous Monte-Carlo EUV resist model is employed to solve this stochastic optimization problem. Several options for optimization algorithms, suitable for the solution of the formulated EUV LER optimization problem, are presented and discussed, along with the results of their tests.

The LER and LWR of subtractively patterned Si and SiN waveguides was calculated after each step in the process. It was found for Si waveguides that adjusting the ratio of CF4:CHF3 during the hard mask open step produced reductions in LER of 26 and 43% from the initial lithography for isolated waveguides patterned with partial and full etches, respectively. However for final LER values of 3.0 and 2.5 nm on fully etched Si waveguides, the corresponding optical loss measurements were indistinguishable. For SiN waveguides, introduction of C4H9F to the conventional CF4/CHF3 measurement was able to reduce the mask height budget by a factor of 5, while reducing LER from the initial lithography by 26%.

With the extreme ultraviolet (EUV) lithography, the performance limit of chemically amplified resists has recently been extended to 16-and 11-nm nodes. However, the line edge roughness (LER) and the line width roughness (LWR) are not reduced automatically with this performance extension. In this paper, to investigate the impacts of the EUVL mask and the EUVL exposure process on LER, EUVL is modeled using multilayer-thin-film theory for the mask structure and the Monte Carlo (MC) method for the exposure process. Simulation results demonstrate how LERs of the mask transfer to the resist and the exposure process develops the resist LERs.

The left side and right side line edge roughnesses (LER) of a line are compared for different conditions, such as through pitch, through critical dimension (CD), from horizontal to vertical line direction, from litho to etch. The investigation shows that the left and right side LER from lithography process are the same, however, the metrology can cause a 4-25% increase in the measured right side LER. The LER difference is related to the CDSEM e-beam scan direction.

In the simulation of secondary electron yields (SEY) and secondary electron microscopy (SEM) images, there is always the question: "are we using the correct scattering cross-sections?". The three scattering processes of interest are quasi-elastic phonon scattering, elastic Mott scattering and inelastic scattering using the dielectric function model. We have artificially scaled the scattering cross-sections, such that the probability for events associated with a particular model is either increased or decreased. The influence of this adjustment on the calculated SEYs and simulated SEM images is then evaluated. At first we have investigated the influence on the calculated SEY of pure and infinitely thick silicon. We have observed that the influence of the acoustic phonon scattering cross-sections is seen all the way up to the incident primary electron energy of 10keV. We have extended the analysis to the simulation of SEM images of three dimensional rough lines of PMMA located on a silicon substrate. We conclude that the scaling of the scattering cross-sections affects the contrast of the SEM images, but not the roughness characterization of the lines, i.e. the 3ź of the line edge roughness (LER), correlation length and roughness exponent. Display Omitted We have performed a sensitivity analysis by scaling scattering cross-sections.Acoustic phonon scattering plays a significant role in the calculation of SEYs.Scaling of cross-sections affects SEM image contrast, but not LER characterization.

In this paper, first we clarify the differences between Contact Edge Roughness (CER) and Line Edge Roughness (LER) emanating from the circular form of the contact edge. Then, we investigate the effects of these differences on the characterization of the spatial and frequency aspects of CER: We define the height-height correlation function for a circular contact hole, use its shape to understand low-frequency deformations of contact holes from the ideal circle, generate model contact holes with predetermined CER and deformations, and finally study the relation between CER and Critical Dimension (CD) variation of the contact holes on a wafer.

Modeling the lithography process with stochastic principles enables the consideration of resist material and process effects variability on critical dimensions and line-edge or line-width roughness of printed features. These principles are applied for a resist system where polymer and photo-acid-generator (PAG) are blended, and for the same system with the PAG molecules bonded on the main polymer chain. Three-dimensional chain-like models of resist and PAG are considered and examples of their effect on critical dimensions and on resist edge roughness are presented. Comparison with experimental results from the literature proves the validity of the current approach and suggests that it can be used for the prediction of the resist resolution and low roughness capabilities.

Optical scatterometry has established itself as one of the mainly applied methods for CD metrology besides CD-SEM during the recent years. However, grating imperfections such as line edge roughness have been largely neglected in scatterometry models so far. Since imperfections of the perfect periodicity would yield large unit cells in a fully rigorous computation of the scatterograms an approximative method has to be used instead. To that end we propose a fieldstitching method which introduces virtual lateral Kirchhoff-boundaries.

To establish a method of measuring interconnect line-edge roughness (LER), low-k line patterns were observed and electric field concentration was simulated on the basis of observation results. Wedge-shaped LERs were observed at the edges of low-k lines, and the bottom and the top widths of the average wedge feature were 60 and 7 nm (or smaller), respectively. Simulation showed that LER causes serious electric field concentration, which may cause the degradation of time-dependent dielectric breakdown (TDDB) lifetime at 100-nm-pitch Cu/low-k interconnects. The maximum electric field strength depends on the conventional LER metric 3Rq, but depends more strongly on the wedge angle, the curvature of the tip. That is, other metrics such as wedge angle can predict fatal electric field concentration caused by LER than the conventional metric 3Rq.

We developed a novel chemically amplified resist to increase sensitivity and reduce line edge roughness (LER) in extreme ultraviolet (EUV) lithography. This resist consists of a base resin of which a photochemical acid generator (PAG) is bonded to the side chain this is called the PAG-bonded resist. Under EUV exposure, an E0 sensitivity of 1.9 mJ/cm2 and a low outgassing pressure of 2.5×10-6 Pa were achieved. Resolution and LER were obtained by electron beam (EB) exposure. Under EB exposure, an LER of 2.1 nm (3σ) for a 100 nm line and space (L/S) pattern was achieved by the PAG-bonded base resin. In addition, we improved this resist and an LER of 4.0 nm (3σ) for a 50 nm L/S pattern was achieved under EB exposure. These results demonstrate that the novel resist system has a good advantage in terms of high sensitivity and low LER.

A study has been completed to investigate the imaging performance with the industry standard 6% attenuated phase shift mask. Several test structures were used to investigate the effects on line edge roughness (LER) based on the polarization state of the illuminator. The use of a high NA (>1NA) immersion exposure system was employed to study the imaging characteristics.

We have designed and synthesized a molecular resist material, which has no distribution of the protecting groups and have evaluated its performance as a molecular resist with EB and EUV exposure tool. The molecular resist attained a resolution of sub-45nm patterning at an exposure dose of 12mJ/cm^2. It was found that controlling the distribution of the protecting groups in a molecular resist material has a great impact on improving line edge roughness (LER). Low LER values of 3.1nm (inspection length: L=620nm) and 3.6nm (L=2000nm) were achieved with this molecular resist using Extreme UltraViolet (EUV) lithography tool.

A method for direct and non-destructive sidewall scanning of nano- and micro-structures is presented. The measurements are performed with a kind of novel 'assembled cantilever probe (ACP)'. Such ACPs consist of four parts: substrate, cantilever, extension(s) and probe tip(s). The tip(s) located at the free end of the extension may extend horizontally. As a benefit, the ACPs are capable of probing in a direction perpendicular to sidewalls. The bending, torsion or deformation of the cantilever is detected when the tip is brought into contact, intermittent contact or non-contact, with sidewalls. Investigations show that the ACPs have a low measurement noise at a subnanometre level. Measurement examples performed at the sidewalls of microtrenches, microgears and line edge roughness samples are given in this paper.

It is reviewed that research and development of resist for extreme ultraviolet lithographic in University of Hyogo. It is focused on the mitigation of the development of high sensitive and low line edge roughness EUV resist. To achieve high sensitivity, it is found that cyclo(1,3-per-fluoropropanedisulfone) imidate employed as an anion of PAG is beneficial in EUV exposure to achieve high sensitivity. To achieve low LER and high sensitivity simultaneously, PAG bonded resist is proposed. We demonstrate Eo sensitivity of higher than 2 mJ/cm2 under EUV exposure. PAG bonded resist which has LER of around 2.0 nm and 6.8 μC/c2 are demonstrated. Furthermore, design concept of low outgassing resist is introduced.

We studied an imaging method for side wall surface of high aspect ratio structure in semiconductor devices by atomic force microscope (AFM). This method is based on conventional AFM methods (for example, contact mode AFM, non-contact mode AFM, tapping mode AFM, and so on) and is equipped with sample inclination mechanism using new XYZ scanner. As experimental results, we demonstrated that the inclination AFM method is very suitable to get detailed structure such as etching scratches on side walls with nanometer resolution.

Extreme ultraviolet lithography (EUVL) is considered to be the most promising option to continue with the aggressive scaling required in high-volume manufacturing (HVM) of integrated circuits. One of the main challenges, however, is the development of EUV resists that fulfill the strict sensitivity, resolution, and line-edge roughness specifications of future nodes. Here, we present our EUV resist screening results of a wide range of EUV resists in their developmental phase from our collaborators from around the world. Furthermore, we have carried out extensive experiments to improve the processing parameters of the resists as well as to identify the optimal wafer pre-treatment methods in order to optimize the adhesion of the resist to the substrate. We show that even though significant improvements in performance of chemically amplified resists have been achieved, pattern collapse is still the major process-limiting factor as the resolution decreases below 14 nm half-pitch (HP).

In order to improve line width roughness (LWR) of chemically amplified resists (CARs) without trade-offs with other lithographic performances such as exposure latitude (EL) and sensitivity, we investigated effects of the spatial fluctuation of sensitivity on LWR of ArF resists. Compared a statistical model with experiments, it was clarified that LWR of ArF resists was caused by the fluctuation of sensitivity due to the fluctuation of the PAG and quencher concentration. Furthermore, we developed novel photoactive materials such as a transparent PAG and an nPAG-1Aminewhich were predicted to be useful for reducing the statistical fluctuation of sensitivity by the theoretical model. LWR was successfully improved using these photoactive materials. This study not only provided new insight into the root cause of LWR, but also proved efficacy of the theory-based material design. Keywords: ArF lithography, chemically amplified resist material, line width roughness (LWR), line edge roughness (LER), statistical fluctuation of sens itivity, transparent photo acid generator, nPAG-1Amine

Lack of progress in reducing linewidth roughness of lithographic features has led to investigations of the use of post-lithography process smoothing techniques. But it remains unclear whether such postprocessing will sufficiently reduce the detrimental effects of feature roughness. Thus, there is a need to understand the efficacy of post-processing on not just roughness reduction, but on the negative device impacts of roughness. This work derives model equations of how roughness impacts lithographic performance, and incorporates smoothing using post-processing. These models clearly show that post-process smoothing works best by increasing the correlation length. Increasing the correlation length is very effective at reducing high-frequency roughness that impacts within-feature variations, but is not very effective at reducing low-frequency roughness that impacts feature-tofeature variations. It seems that post-process smoothing is not a substitute for reducing the initial roughness of resist features.

A frequency domain 3 sigma LER characterization methodology combining the standard deviation and power spectral density (PSD) methods is proposed. In the new method, the standard deviation is calculated in the frequency domain instead of the spatial domain as in the conventional method. The power spectrum of the LER is divided into three regions: low frequency (LF), middle frequency (MF) and high frequency (HF) regions. The frequency region definition is based on process visual comparisons. Three standard deviation numbers are used to characterize the LER in the three frequency regions. Pattern wiggling can be detected quantitatively with a wiggling factor which is also proposed in this paper.