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: Electron beam lithography, Monte Carlo methods, Line edge roughness, Computer simulations, Critical dimension metrology, Transistors, Optical simulations, Diffusion, Optimization (mathematics), Point spread functions
Low-energy electron beam lithography is one of the promising next-generation lithography technology solutions for the 21-nm half-pitch node and beyond because of fewer proximity effects, higher resist sensitivity, and less substrate damage compared with high-energy electron beam lithography. To achieve high-throughput manufacturing, low-energy electron beam lithography systems with writing parameters of larger beam size, larger grid size, and lower dosage are preferred. However, electron shot noise can significantly increase critical dimension deviation and line edge roughness. Its influence on patterning prediction accuracy becomes nonnegligible. To effectively maximize throughput while meeting patterning fidelity requirements according to the International Technology Roadmap for Semiconductors, a new method is proposed in this work that utilizes a new patterning prediction algorithm to rigorously characterize the patterning variability caused by the shot noise and a mathematical optimization algorithm to determine optimal writing parameters. The new patterning prediction algorithm can achieve a proper trade-off between computational effort and patterning prediction accuracy. Effectiveness of the new method is demonstrated on a static random-access memory circuit. The corresponding electrical performance is analyzed by using a gate-slicing technique and publicly available transistor models. Numerical results show that a significant improvement in the static noise margin can be achieved.
As integrated circuit design dimensions continue to shrink, previously ignored three-dimensional (3-D) mask effects have become significant for the accurate prediction and correction of proximity effects. Optical proximity correction (OPC) process models must consequently take into account 3-D mask effects. The state-of-the-art model-based OPC methodology, which is called delta-chrome OPC (DCOPC), needs the repeated computation of the mask perturbation to facilitate its convergence. The increasing complexity of OPC process models challenges this DCOPC methodology because each computation of the mask perturbation becomes prohibitively expensive. In this study, a new model-based OPC methodology, which is called non-delta-chrome OPC (non-DCOPC), is proposed without introducing any mask perturbations. It only requires image intensity information to achieve convergence using classical control techniques, and its effectiveness is demonstrated, showing that the run time with and without considering 3-D mask effects can be significantly improved. In addition, the correction accuracy of the DCOPC and non-DCOPC methodologies without considering 3-D mask effects is quite comparable. However, the correction accuracy considering 3-D mask effects can be slightly improved by the non-DCOPC methodology.
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.
A model-based proximity effect correction methodology is proposed and tested for electron-beam-direct-write
lithography. It iteratively modulates layout geometry by feedback compensation until the correction error converges. The
energy intensity distribution is efficiently calculated by fast convolving the modulated layout with a point-spread
function which models electron beam shape and proximity effects primarily due to electron scattering in resist. The
effectiveness of this methodology is measured by iteration numbers required for meeting the patterning fidelity
specifications. It is examined versus process parameters including acceleration voltage and resist thickness with several
regular mask geometries and practical design layouts.
Delta-chrome optical proximity correction (OPC) has been widely adopted in lithographic patterning for semiconductor
manufacturing. During the delta-chrome OPC iteration, a predetermined amount of chrome is added or subtracted from
the mask pattern. With this chrome change, the change of exposure intensity error (IE) or the change of edge placement
error (EPE) between the printed contour and the target pattern is then calculated based on standard Kirchhoff
approximation. Linear approximation is used to predict the amount of the proper chrome change to remove the
correction error. This approximation can be very fast and effective, but must be performed iteratively to capture
interactions between chrome changes. As integrated circuit (IC) design shrinks to the deep sub-wavelength regime,
previously ignored nonlinear process effects, such as three-dimensional (3D) mask effects and resist development effects,
become significant for accurate prediction and correction of proximity effects. These nonlinearities challenge the deltachrome
OPC methodology. The model response to mask pattern perturbation by linear approximation can be readily
computed but inaccurate. In fact, computation of the mask perturbation response becomes complex and expensive. A
non-delta-chrome OPC methodology with IE-based feedback compensation is proposed. It determines the amount of the
proper chrome change based on IE without intensive computation of mask perturbation response. Its effectiveness in
improving patterning fidelity and runtime is examined on a 50-nm practical circuit layout. Despite the presence and the
absence of nonlinear 3D mask effects, our results show the proposed non-delta-chrome OPC outperforms the deltachrome
one in terms of patterning fidelity and runtime. The results also demonstrate that process models with 3D mask
effects limit the use of delta-chrome OPC methodology.
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.
KEYWORDS: Monte Carlo methods, Scattering, Electron beam lithography, Silicon, Data modeling, Polymethylmethacrylate, Laser scattering, Direct write lithography, Computer simulations, Backscatter
Accelerating voltage as low as 5 kV for operation of the electron-beam micro-columns as well as solving the
throughput problem is being considered for high-throughput direct-write lithography for the 22-nm half-pitch node and
beyond. The development of efficient proximity effect correction (PEC) techniques at low-voltage is essential to the
overall technology. For realization of this approach, a thorough understanding of electron scattering in solids, as well as
precise data for fitting energy intensity distribution in the resist are needed. Although electron scattering has been
intensively studied, we found that the conventional gradient based curve-fitting algorithms, merit functions, and
performance index (PI) of the quality of the fit were not a well posed procedure from simulation results. Therefore, we
proposed a new fitting procedure adopting a direct search fitting algorithm with a novel merit function. This procedure
can effectively mitigate the difficulty of conventional gradient based curve-fitting algorithm. It is less sensitive to the
choice of the trial parameters. It also avoids numerical problems and reduces fitting errors. We also proposed a new PI to
better describe the quality of the fit than the conventional chi-square PI. An interesting result from applying the proposed
procedure showed that the expression of absorbed electron energy density in 5keV cannot be well represented by
conventional multi-Gaussian models. Preliminary simulation shows that a combination of a single Gaussian and double
exponential functions can better represent low-voltage electron scattering.
Model-based Optical Proximity Correction (MBOPC) has become one of the most important resolution enhancement
technologies (RETs), which can effectively improve the image fidelity and process robustness. MBOPC is performed by
iteratively shifting the polygon edges of mask patterns until convergence requirements are achieved. In this paper, we
specifically discuss the design of feedback controllers to improve MBOPC convergence. Effective controller design rules
are derived from the OPC results of several circuit layouts. Meanwhile, resist models also significantly affect MBOPC
convergence. Two kinds of resist model have been proposed for MBOPC such as constant threshold resist model (CTRM)
and variable threshold resist model (VTRM). We propose a novel CTRM, called pattern-based optimal threshold
determination (PBOTD). By normalized mean square error (NMSE) formulation, appropriate threshold values with
minimum NMSE can be determined to improve image fidelity, and effectively decrease iterations required. The
effectiveness of applying both optimized controller and PBOTD is demonstrated on a 90-nm SRAM cell.
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.