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Computational lithography and resolution enhancement techniques
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.
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With the introduction of the NXE:3400B scanner, ASML has brought extreme ultraviolet lithography (EUV) to high-volume manufacturing (HVM). The high-EUV power of >200 W being realized with this system satisfies the throughput requirements of HVM, but also requires reconsideration of the imaging aspects of spectral purity, both from the details of the EUV emission spectrum and from the deep-ultraviolet (DUV) emission. We present simulation and experimental results for the spectral purity of high-power EUV systems and the imaging impact of this, both for the case of with and without a pellicle. Also, possible controls for spectral purity will be discussed, and an innovative method will be described to measure imaging impact of varying conversion efficiency (CE) and DUV. It will be shown that CE optimization toward higher source power leads to reduction in relative DUV content, and the small deltas in EUV source spectrum for higher power do not influence imaging. It will also be shown that resulting variations in DUV do not affect imaging performance significantly, provided that a suitable reticle black border is used. In summary, spectral purity performance is found to enable current and upcoming nodes of EUV lithography and to not be a bottleneck for further increasing power of EUV systems to well above 250 W.
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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.
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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.
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In extreme ultraviolet (EUV) lithography, chemistry is driven by secondary electrons. A deeper understanding of these processes is needed. However, electron-driven processes are inherently difficult to experimentally characterize for EUV materials, impeding targeted material engineering. A computational framework is needed to provide information for rational material engineering and identification at a molecular level. We demonstrate that density functional theory calculations can fulfill this purpose. We first demonstrate that primary electron energy spectrum can be predicted accurately. Second, the dynamics of a photoacid generator upon excitation or electron attachment are studied with ab-initio molecular dynamics calculations. Third, we demonstrate that electron attachment affinity is a good predictor of reduction potential and dose to clear. The correlation between such calculations and experiments suggests that these methods can be applied to computationally screen and design molecular components of EUV material and speed up the development process.
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Background: Molecular logic circuits have great potential applications. DNA logic circuit is an important research direction of DNA computing in nanotechnology. DNA self-assembly has become a powerful tool for building nanoscale structures. The combination of different self-assembly methods is an interesting topic.
Aim: Two different self-assembly methods are combined to realize large-scale logic circuit. A basic logical unit is extended to complex logic circuits by self-assembly.
Approach: The complex logic circuit is solved by combining nanoparticles. One DNA strand attached to nanoparticle maps to a logical unit. Just as the combination between logical units can form logic circuits, the combination between nanoparticles can be used to structure logic circuits. On a larger-scale logic circuits, this is done by attaching the assembled nanoparticles to an origami template. Different logical values are mapped into different DNA initiators.
Results: After the reaction is over, the nanoparticles are dynamically separated from the DNA origami template, indicating that the result is true. The nanoparticles remain on the DNA origami template, indicating that the result is false. The simulation results show that this self-assembly model is highly feasible for complex logic circuits.
Conclusions: The model combines two different self-assembly methods to realize large-scale logic circuits. Compared with previous models, this model implements a larger logic circuit on one origami template. This method can be used to construct more complex nanosystems and may have potential applications in molecular engineering.
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