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Double patterning technology: process-window analysis in a many-dimensional space

We consider a memory device that is printed by double patterning (litho-etch-litho-etch) technology wherein positive images of 1/4-pitch lines are printed in each patterning step. We analyze the errors that affect the width of the spaces. We propose a graphical method of visualizing the many-dimensional process-window for double patterning. Controlling the space-width to ±10% of half-pitch is not possible under the worst combination of errors. Statistical analysis shows that overlay and etch bias are the most significant contributors to the variability of spaces. 3σ[space-width] = 17% and 11% of nominal space can be achieved for 3σ[Overlay] = 6 nm and 3 nm, respectively, for a 40-nm half pitch array printed using NA=0.93.

A rigorous method to determine printability of a target layout

We present a necessary condition for an arbitrary 2-dimensional pattern to be printable by optical projection lithography. We call a pattern printable if it satisfies a given set of edge-placement tolerances for a given lithography model and process-window. The test can be made specific to a lithography model, or it can be made generic for a wavelength and numerical aperture. In the generic form, if a pattern is found to be not printable, the conclusion is valid for all RET technologies except for non-linear techniques such as litho-etch-litho-etch double-patterning and multi-photon lithography. The test determines printability of a target layout without applying RET/OPC.

Model-based assist feature generation

We optimize a continuous-tone photomask to meet a set of edge-placement tolerances and 2-D image fidelity requirements, for a set of dose and defocus values. The resulting continuous tone mask, although not realizable, indicates where to place assist features and their polarity. This algorithm derives assist features from first principles: when the mask is optimized for best focus, the optimal continuous-tone photomask does not have any features that resemble assist features. When the mask is optimized for best focus and a defocus condition, the optimal continuous-tone photomask spontaneously grows assist features. The continuous-tone photomask also has features that can be identified as phase windows. Polygonal, quantized assist features are extracted from the optimal continuous-tone photomask.

Enabling process window improvement at 45nm and 32nm with free-form DOE illumination

We present a method for optimizing a free-form illuminator implemented using a diffractive optical element (DOE). The method, which co-optimizes the source and mask taking entire images of circuit clips into account, improves the common process-window and 2-D image fidelity. We compare process-windows for optimized standard and free-form DOE illuminations for arrays and random placements of contact holes at the 45 nm and 32 nm nodes. Source-mask cooptimization leads to a better-performing source compared to source-only optimization. We quantify the effect of typical DOE manufacturing defects on lithography performance in terms of NILS and common process-window.

Model-based assist features

We present a model-based method of generating and optimizing sub-resolution assist features. Assist feature generation is based on a focus sensitivity map derived from a cost function that minimizes the variations in the printed pattern with respect to focus change. We also demonstrate a method to generate mask-friendly SRAF polygons from the focus sensitivity map. After model-based placement, assist features and the main polygons are optimized together by moving their edge segments. One of the optimization goals is that side-lobes and assist features should not print. This is enforced by computing image on a two dimensional grid. We demonstrate the process window improvement for a contact layer example.

Sequential PPC and process-window-aware mask layout synthesis

We present a full-chip implementation of model-based process and proximity compensation. Etch corrections are applied according to a two-dimensional model. Lithography is compensated by optimizing a cost function that expresses the design intent. The cost function penalizes edge placement errors at best dose and defocus as well as displacement of the edges in response to a specified change in a process parameter. This increases immunity to bridging in low contrast areas.

Calibration of e-beam and etch models using SEM images

Mask Process Compensation (MPC) corrects proximity effects arising from e-beam lithography and plasma etch processes that are used in the photomask manufacturing. Accurate compensation of the mask process requires accurate, predictive models of the manufacturing processes. Accuracy of the model in turn requires accurate calibration of the model. We present a calibration method that uses either SEM images of 2-dimensional patterns, or a combination of SEM images and 1D CD-SEM measurements. We describe how SEM images are processed to extract the contours, and how metrology and process variability and SEM alignment errors are handled. Extracted develop inspection (DI) and final inspection (FI) contours are used to calibrate e-beam and etch models. Advantages of the integrated 2D+1D model calibration are discussed in the context of contact and metal layers.

Algorithm for determining printability and colouring of a target layout for double patterning

An algorithm is presented which performs a model-based colouring of a given layout for double patterning. The algorithm searches the space of patterns which can be printed with a particular wavelength and numerical aperture, and seeks to find a pair of patterns which combine to produce the desired target layout. This is achieved via a cost function which encodes the geometry of the layout and allowable edge placement tolerances. If the layout is not printable by double patterning, then the algorithm provides a closest solution and indicates hotspots where the target is not feasible.

Metrology for stepper illumination pupil profile

A technique for measuring the profile of the illumination in the pupil of a lithography projector is presented. The technique is based on exposing pinhole patterns on a wafer at different dose and defocus settings, and processing the scanning electron microscopy (SEM) images of the printed pinholes. The latent image intensity at the edges of the resist patterns equals the dose-to-clear. This establishes a multitude of equations, each of which states that the latent image intensity at a particular field location, dose, and defocus is known. The intensity distribution in the pupil of the illuminator is obtained by solving a large system of such equations, subject to the constraint that the intensity distribution is non-negative. An image processing algorithm based on nonlinear diffusion is used for finding coordinates of points on the edges of resist in SEM images. The results of the inversion for 193-nm stepper with 0.55/0.85 annular illumination and numerical aperture of 0.75 at five exposure field locations are presented.

PPC model build methodology: sequential litho and etch verification

We present a methodology for building through-process, physics-based litho and etch models which result in accurate and predictive models. The litho model parameters are inverted using resist SEM data collected on a set of test-structures for a set of exposure dose and defocus conditions. The litho model includes effects such as resist diffusion, chromatic aberration, defocus bias, lens aberrations, and flare. The etch model, which includes pattern density and particle collision effects, is calibrated independently of the litho model, using DI and FI SEM measurements. Before being used for mask optimization, the litho and etch models are signed-off using a set of verification structures. These verification structures, having highly two-dimensional geometries, are placed on the test-reticle in close vicinity to the calibration test-structures. Using through-process DI and FI measurement and images from verification structures, model prediction is compared to wafer results, and model performance both in terms of accuracy and predictability is thus evaluated.