Inspecting the structure of the through silicon via (TSV) with high aspect ratio is important because they are used for 3D IC stacking. In reflectometry, simulation of near field data for TSV hole arrays is used to investigate reflection spectrum for TSV with different geometry parameters such as depth and top critical dimension. We investigate simulation results of electromagnetic field data for different TSV array using the finite-difference time-domain (FDTD) method. Near field simulation data are stored as n by n complex matrices, where n represent the number of simulation region grid points. The matrices are large in dimension, and it is necessary to compress a huge data set by looking for the dominant singular value terms to keep the information as much as possible. We find that the singular value terms shrink fast in the first few terms. It is shown that after using singular value decomposition to compress near field data, the far field reflectivity spectrum is still close to the accurate results. We propose to use data after singular value decomposition for data analysis to investigate the TSV parameters mapping to the near field data.
Understanding the electromagnetic properties of the 3D through silicon via (TSV) with high aspect ratio is important for the 3D IC stacking and packaging. The electromagnetic simulations were used to explore the TSV with different model parameters, such as top critical dimension, bottom critical dimension, hole depth, sidewall slope, sidewall roughness, curvature of the base, and light wavelength. A model is proposed to parameterize TSV structure features. The simulation results corresponding to these model parameters are discussed.
The availability of metrology solutions, one of the critical factors to drive leading-edge semiconductor devices and processes, has been confronted with difficulties in advanced nodes. For developing new metrology solutions, high-quality test structures fabricated at specific sizes are needed. Electron-beam direct-write lithography has been utilized to manufacture such samples. However, it can encounter significant-resolution difficulties and may require complicated process optimization in sub-10-nm nodes. Therefore, we investigate the feasibility and patterning control of metrology test structures fabricated by helium ion beam (HIB) direct milling and HIB direct-write lithography, where HIB has the sub-nm resolution in nature. Results show that features down to 5 nm are resolvable without any resolution enhancement technique by HIB direct milling. For HIB direct-write lithography, features down to International Roadmap for Devices and Systems 1.5-nm node are also resolvable without optimization from the lithography simulation. Furthermore, patterns beyond the 1.5-nm node can be achievable with the help of the proximity effect correction technique. Preliminary results demonstrate that HIB direct milling and HIB direct-write lithography can be a promising alternative for fabricating pit-type programmed defects (PDs) and bump-type PDs, respectively. In conclusion, HIB is suggested to be a potential tool to fabricated test structures for developing advanced metrology solutions in sub-7-nm nodes.
The availability of metrology solutions, one of the key factors to drive leading edge semiconductor devices and processes, can be confronted with difficulties in the advanced node. For developing new metrology solutions, high quality test structures fabricated at specific sizes are needed. Conventional resist-based lithography have been utilized to manufacture such samples. However, it can encounter significant resolution difficulties or requiring complicated optimization process for advanced technology node. In this work, potential of helium ion beam direct milling (HIBDM) for fabricating metrology test structures with programmed imperfection is investigated. Features down to 5 nm are resolvable without implementing any optimization method. Preliminary results have demonstrated that HIBDM can be a promising alternative to fabricate metrology test structures for advanced metrology solutions in sub 10 nm node.
Accurate and fast kernel-based proximity effect correction (PEC) models are indispensable to full-chip proximity effect simulation and correction. The attempt to utilize optical scatterometers for PEC model calibration instead of scanning electron microscopes is primarily motivated by the fact that scatterometry can be faster, more stable, and more informative if carefully implemented. Conventional scatterometry measures periodic patterns and retrieves their dimensional parameters by solving inverse problems of optical scattering with predefined libraries of the periodic patterns. PEC model parameters can be subsequently calibrated with the retrieved dimensional parameters. However, measuring only periodic patterns limits the usage of scatterometry, and the dimensional reconstruction is prone to generate estimation errors for patterns with complex three-dimensional geometry. Previously, we have proposed directly utilizing scattering light for PEC model calibration without the need for the intermediate step of retrieving the dimensional parameters. By iteratively comparing scattered light from predefined calibration patterns measured by a scatterometer to that predicted by the corresponding scattering and lithography models, PEC model parameters can be effectively calibrated with standard numerical optimization algorithms and one-dimensional periodic patterns. In this work, two-dimensional periodic circuit layouts are designed and utilized to study the applicability and potential limitations of the proposed method on the lithography of practical circuit designs.
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.
KEYWORDS: Calibration, Lithography, Optical proximity correction, Data modeling, Signal processing, Scatterometry, Process control, Photomasks, Process modeling, Systems modeling
Fast and robust metrologies for retrieving large amount of accurate wafer data is the key to meet the ever stricter semiconductor manufacturing process control such as critical dimension (CD) and overlay as the industry moving towards 22 nm or smaller designs. Scatterometry emerges due to its non-destructivity and rapid availability for accurate wafer data. In this paper we simulate the ability of a new scatterometry method to show its accurate control over lithography model and OPC model calibrations. The new method directly utilizes scattering signals of scatterometry to control the process instead of using numerically analyzed dimensional parameters such as CD and side wall angle (SWA). The control can be achieved by optimizing the scattering signal of one process by tuning numerical aperture (NA), sigma, or lens aberration to match the signal of the target process. In this work only sigma is used for optimization. We found that when the signals of both processes are matched with minimized optimization error, CD of the grating profiles on the wafers are also minimized. This result enables valid lithography process control and model calibration with the new method.
KEYWORDS: Calibration, Line edge roughness, Scatterometry, Point spread functions, Process modeling, Scanning electron microscopy, Metrology, Scattering, Semiconducting wafers, Cadmium
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.
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.
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.
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.
When EUV light is used to inspect mask defects, the reflective photons reveal information for both the mask structure
and the mask defects. The number of reflective photons has to be enough for generating sufficient detector signals. A
modeling technique based on Feynman path integral is utilized to calculate the number of reflective extreme-ultraviolet
(EUV) photons scattered from photomask surfaces. For a 2D semicircular silicon defect, the capability of predicting the
moving direction for each reemitting photon and the intensity of photons in different direction has been demonstrated.
The Finite-Difference Time-Domain (FDTD) method is used to study the scattering effects of extreme ultraviolet (EUV)
mask. It requires significant amounts of memory and computation time as the fine grid size is needed for simulation.
Theoretically, the accuracy can be increased as the mesh size is decreased in FDTD simulation. However, it is not easy
to get the accurate simulation results for the multilayer (ML) structures by FDTD method. The transmission line theory
is used to calculate the equivalent refractive index for EUV mask ML to simulate the ML as one layer of bulk artificial
material. The reflectivities for EUV light with the normal incidence and small-angle oblique incidence in the bulk
artificial material and EUV mask ML are simulated by FDTD method. The Fresnel's equation is used to evaluate the
numerical errors for these FDTD simulations, and the results show good agreement between them. Using the equivalent
refractive index material for EUV multilayer mask can reduce the computation time and have the accuracy with tolerable
numerical errors. The ML structure with periodic surface roughness is also studied by this method, and it shows that only
half of computation time is needed to substitute ML to a bulk equivalent refractive index material in FDTD simulations.
This proposed method can accelerate the simulations of EUV mask designs.
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.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.