Yen-Min Lee

Fully model-based methodology for simultaneous correction of extreme ultraviolet mask shadowing and proximity effects

Extreme ultraviolet (EUV) lithography is a promising candidate for high-volume manufacturing at the 22-nm half-pitch node and beyond. EUV projection lithography systems need to rely on reflective optical elements and masks with oblique illumination for image formation. It leads to undesired effects such as pattern shift and horizontal-to-vertical critical dimension bias, which are generally reported as shadowing. Rule-based approaches proposed to compensate for shadowing include changing mask topography, introducing mask defocus, and biasing patterns differently at different slit positions. However, the electromagnetic interaction between the incident light and the mask topography with complicated geometric patterns, such as optical diffraction, not only causes shadowing but also induces proximity effects. This phenomenon cannot be easily taken into account by rule-based corrections and thus imposes a challenge on a partially model-based correction flow, the so-called combination of rule- and model-based corrections. A fully model-based correction flow, which integrates an in-house optical proximity correction algorithm with rigorous three-dimensional mask simulation, is proposed to simultaneously compensate for shadowing and proximity effects. Simulation results for practical circuit layouts indicate that the fully model-based correction flow significantly outperforms the partially model-based one in terms of correction accuracy, while the total run time is slightly increased.

Electron-beam proximity effect model calibration for fabricating scatterometry calibration samples

Scatterometry has been proven to be effective in critical dimension (CD) and sidewall angle (SWA) measurements with good precision and accuracy. In order to study the effectiveness of scatterometry measurement of line edge roughness (LER), calibration samples with known LER have to be fabricated precisely. The relationship between ITRS LER specifications and the feature dimension design of the LER calibration samples is discussed. Electron-beam-direct-write lithography (EBDWL) has been widely used in nanoscale fabrication and is a natural selection for fabricating the designed calibration samples. With the increasingly demanding requirement of lithography resolution in ITRS, the corresponding LER feature of calibration samples becomes more and more challenging to fabricate, even for EBDWL. Proximity effects in EBDWL due to electron scattering can cause significant distortion of fabricated patterns from designed layouts. Model-based proximity effect correction (MBPEC) is an enhancement method for EBDWL to precisely define fine resist features. The effectiveness of MBPEC depends on the availability of accurate electron-beam proximity effect models, which are usually described by point spread functions (PSFs). In this work, a PSF in a double- Gaussian function form at a 50 kV accelerating voltage, an effective beam size, and a development threshold energy level of the resist are calibrated with EBDWL exposure tests. Preliminary MBPEC results indicate its effectiveness in calibration sample fabrication.

Direct-scatterometry-enabled lithography model calibration

Optical scatterometry is crucial to advanced nodes due to its ability of non-destructively and rapidly retrieving accurate 3D profile information.1, 2, 3 In recent years, an angle-resolved polarized reflectometry-based scatterometry which can measure critical dimensions, overlay, and focus in single shot has been developed.4, 6, 20 In principle, a microscope objective collects diffracted light, and pupil images are collected by a detector. For its application of calibrating lithography models, the pupil images are fit to a database pre-characterized usually by rigorous electromagnetic simulation to estimate dimensional parameters of developed resist profiles.5 The estimated dimensional parameters can then be used for lithography model calibration. In this work, we propose a new method which directly utilizes the pupil images to calibrate lithography models without needing dimensional parameter estimation. To test its feasibility and effectiveness by numerical simulation, a reference lithography process model is first constructed with a set of parameter values complying with ITRS. A to-be-calibrated process model is initialized with a different set of parameter values from those of the reference model. Rigorous electromagnetic simulation is used to obtain the pupil images of the developed resist profiles predicted by both process models. An optimization algorithm iteratively reduces the difference between the pupil images by adjusting the set of parameter values of the to-be-calibrated process model until the pupil image difference satisfies a predefined converging criterion. This method can be used to calibrate both rigorous first-principle models for process and equipment development and monitoring, and fast kernel-based models for full-chip proximity effect simulation and correction. Preliminary studies with both 1D and 2D aperiodic and periodic layouts indicate that when the pupil image difference is minimized, the lithography model can be accurately calibrated.

Efficient scattering simulations for equivalent extreme ultraviolet mask multilayer structures by modified transmission line theory and finite-difference time-domain method

The modified transmission line theory is used to calculate equivalent refractive indices of the extreme ultraviolet (EUV) mask multilayer (ML) over wavelengths from 13.35 to 13.65 nm for finite-difference time-domain (FDTD) simulation. Generally speaking, a fine mesh requiring huge memory and computation time are necessary to get accurate results in an FDTD simulation. However, it is hard to get accurate results for ML simulation due to the thin thickness of each layer. By means of an equivalent refractive index, the ML can be treated as one layer with the bulk effective material. Using FDTD simulations, we study the reflectivities of 40 Mo/Si ML and bulk material cases. The ML structure and bulk material with periodic excessive surface roughness as well as patterned with periodic contact holes are also studied by using two- and three-dimensional FDTD simulations. The simulation cases for a single wavelength and for a full-bandwidth EUV light source with a 6 ML system are studied. The results from each simulation show that the root mean square error between ML simulations and the bulk material simulations are confined within 3.3%, and all cases indicate that the FDTD computation time of bulk material is about half as compared with a 40-ML simulation.

A fully model-based methodology for simultaneously correcting EUV mask shadowing and optical proximity effects with improved pattern transfer fidelity and process windows

Extreme ultraviolet (EUV) lithography is one of the promising candidates for device manufacturing with features smaller than 22 nm. Unlike traditional optical projection systems, EUV light needs to rely on reflective optics and masks with an oblique incidence for image formation in photoresist. The consequence of using a reflective projection system can result in horizontal-vertical (H-V) bias and pattern shift, which are generally referred as shadowing. Approaches proposed to compensate for shadowing effect include changing mask topography, modifying mask focus, and biasing features along the azimuth angle, which are all rule-based. However, the complicated electromagnetic interaction between closely placed circuit patterns can not only induce additional optical proximity effect but also change the shadowing effect. These detailed phenomena cannot be completely taken into account by the rule-based approaches. A fully model-based approach, which integrates an in-house model-based optical proximity correction (OPC) algorithm with rigorous three-dimensional (3D) EUV mask simulation, is proposed to simultaneously compensate for shadowing and optical proximity effects with better pattern transfer fidelity and process windows. Preliminary results indicate that this fully model-based approach outperforms rule-based ones, in terms of geometric printability under process variations.

Supplementary zones-surrounded Fresnel zone plate with enhanced optical resolution

The supplementary zones surrounding an ordinary Fresnel zone plate (FZP) are utilized to improve the optical resolution at focus. Based on the Fresnel–Kirchhoff diffraction formula, an optimization model is used to design the supplementary zones-surrounded FZP (SZFZP). We justified this optimization model by comparing the numerical simulations and experimental measurements in the visible light region. As expected, the comparison shows a good fit between the simulation and measurement. Mostly, both results showed that the optical resolution and the focal intensity in the visible light region are improved by applying the optimized SZFZP. Afterwards, this model is used to design the SZFZP for applications in extreme ultraviolet (EUV) light. At this point, we demonstrated the ability to fabricate the optimized SZFZP in the EUV region. In addition, we simulated the focusing properties for the designed SZFZP. Consequently, the numerical results for EUV light focused by the designed SZFZP exhibited better performances in optical resolution and intensity.

Optical scatterometry system for detecting specific line edge roughness of resist gratings subjected to detector noises

The Fourier scatterometry model was used to measure the ZEP 520A electron beam resist lines with specific line edge roughness (LER). By obtaining the pupils via an objective lens, the angle-resolved diffraction spectrum was collected efficiently without additional mechanical scanning. The concavity of the pupil was considered as the weight function in specimen recognition. A series of white noises was examined in the model, and the tolerant white noise levels for different system numerical apertures (NAs) were reported. Our numerical results show that the scatterometry model of a higher NA can identify a target with a higher white noise level. Moreover, the fabricated ZEP 520A electron beam resist gratings with LER were measured by using our model, and the fitting results were matched with scanning electron microscope measurements.

Refractive Index and Effective Thickness Measurement System for the RGB Color Filter Coatings With Absorption and Scattering Properties

During the manufacturing processes of the thin-film transistor liquid-crystal display (TFT-LCD) panel, red, green, and blue (RGB) color filter coatings undergo the layer-adding process which causes the rough surfaces between the layers. The rough surfaces make acquiring an accurate measurement of the optical properties and thickness (n, k, d) much more difficult because the scattering effects occur. The effective layer-included model is considered in determining the (n, k, d) by including effective layers to reside between and above the multilayer (ML). To show the feasibility of the effective layer-included model, we examined the model by fitting the (n, k, d) for different virtual systems which contain different kinds of scatters reside between and above it. Our findings show that the fitted (n, k, d) can be closer to the assumed (n, k, d) by using the effective layer-included model rather than the standard model. Also, the tolerance of initial assigned (n, k, d) regions to obtain the accurate results are investigated. Further, both models are used to determine the (n, k, d) of the fabricated RGB color filter samples. In the experimental measurements, all reflection and transmission signals are measured by utilizing the in-house variable angle spectroscopic ellipsometry (VASE) system. Consequently, the thicknesses determined from effective layer-included model are closer to the thicknesses measured from profilometry (Alpha-step 100). Also, the transmissions under 0 °, 15 °, and 30 ° illuminations calculated from the fitted (n, k, d) through the effective layer-included model are closer to the VASE measurements rather than the standard model for each sample. We conclude that the effective layer-included model can be used to determine the accurate (n, k, d) of RGB color filter coatings with rough surface.

Void-based photonic crystal mirror with high reflectivity and low dissipation for extreme-ultraviolet radiation

Abstract. The effects of void-based photonic crystal mirrors on reflectivity and dissipation for extreme-ultraviolet (EUV) radiation at near-normal illumination are studied. The mirrors are based on a multilayer coating comprising alternating layers of molybdenum (Mo) and silicon (Si) with 40 periods. By embedding voids in silicon films instead of molybdenum films, we found that the reflectivities of the mirror are increased and the absorptions of the mirror are decreased with the increments of the voids. On the other hand, the reflectivities of the mirror are decreased and the absorptions are increased by embedding voids in the molybdenum films, with the increments of the voids. Compared to the standard designs of 40 Mo/Si multilayer mirrors, which are currently used in most EUV or soft x-ray applications, the reflectivity of the void-based photonic crystal mirror in our study can reach from 73.43 to 83.24% and the absorption can decline from 26.18 to 16.80%. In consideration of EUV bandwidth, the effects of illumination angles in the six-mirror projection system, the intermixing layers, and the variation of the coated absorber thickness on the reflection properties are studied. The proposed concept can be used in next-generation EUV lithography and soft x-ray optical systems.

Solution-Refined Method for Electrostatic Potential Distribution of Large-Scale Electron Optics

The solution-refined method is developed to solve electrostatic fields of the electron-beam direct-write lithography system. The prediction of accurate electron trajectories and the geometry of the developed photoresist patterns rely on high-resolution electrostatic fields in the whole system. Considering fabrication errors, such electrostatic fields cannot be solved using a cylindrical symmetry. Thus, this problem is a multiscale problem that requires a huge computer memory to solve. In our cases, the minimum number of grids of 1 nm length are applied and the total memory required approaches 75 Gbyte. Since the proposed solution-refined technique has a tradeoff with computational time, fewer central processing units (CPUs) are needed to solve this system because each CPU that solves the problem exceeds its available storage memory. The proposed technique can be used to solve the electron-beam direct-write lithography system at higher resolution and the problems exceed the available storage memory.