Programmable lithography engine (ProLE) grid-type supercomputer and its applications

As minimum feature size shrinks to a metal pitch of 21 nm, the current extreme ultra violet (EUV) lithographic tool with a numeric aperture (NA) of 0.33 will face resolution limit for some critical layers. High NA (0.55) EUV with anamorphic optics or EUV double patterning (DP) at 0.33 NA are being considered for the next generation of lithographic technology. Both the high NA EUV system and EUV DP will enhance resolution relative to current EUV single patterning (SP). Nevertheless, in order to be able to compare EUV DP and High NA EUV processes, important lithographic factors including image contrast, mask three dimension (M3D) effects, process variation band, stochastic effects and local critical dimension uniformity need to be investigated to understand their contributions to process variations. This study was carried out using rigorous lithographic model simulations in Sentaurus Lithography, where strong M3D effects in EUVL are computed physically. We have simulated patterns with both isomorphic and anamorphic optical proximity corrections (OPC) using the rigorous model. The study focuses on 3nm node Via layer designs. These vias need to connect to metal features which have pitches of 21 nm. Simulation results using 0.33 NA SP, 0.33 NA DP, and 0.55 NA anamorphic SP are presented. The benefit of using an alternative mask absorber and a thinner resist as well as the impact of stochastic effects have also been explored. Although a 0.55 NA EUV is expected to produce a superior image to 0.33 NA EUV and to have less impact from overlay errors and stochastic effects, an analysis of process margins of 0.33 NA EUV SD and DP versus 0.55 NA anamorphic systems helps to better understand the benefits, challenges and optimal insertion point for introducing High-NA EUV.

Improvements in compact lithography models and compute resources have allowed EDA suppliers to keep up with the accuracy and turnaround time (TAT) requirements for each new technology node. Compact lithography models are derived from the Hopkins method to calculate the image at the wafer. They consist of the pre-calculated optical kernel set that includes properties of projection and source optics as well as resist effects. The image at the wafer is formed by the convolution of optical kernel set with the mask transmission. The compact model is used for optical proximity correction (OPC) and lithography rule checking (LRC) due to its excellent turnaround time in full chip applications. Leading edge technology nodes, however, are inherently more sensitive to process variation and typically contain more low contrast areas, sometimes resulting in marginal hotspots. In these localized areas, it is desirable to have access to more predictive first principle lithography simulation. The Abbe method for lithography simulation includes full 3D resist models that solves from first principles the reaction/diffusion equation of the post exposure bake to provide the highest accuracy. These rigorous models have the ability to provide added insight into 3D developed profile in resist at the wafer level to assist in the application of OPC and disposition of hotspots found by LRC using compact models. This paper will explore the benefits of a tightly integrated rigorous lithography simulation during LRC hotspot detection step of the post OPC flow. Multiple user flows will be addressed along with methods for automating the flows to maximize the imaging predictability where needed while keeping the impact to turn around time to a minimum.

We have previously reported the exact convolution-based analytical solution to the problem of an elastic resist shrinkage during post-exposure baking (PEB). In contrast to the PEB problem, the elastic shrinking during development in general does not admit a strict analytical solution. Here we use a numerical finite element method (FEM) to compare a two-step development/shrinking model to the results of simultaneously solving full set of the development equations with the elastic deformations being accounted for. We also report existence of a strict analytical solution for the shrinking of line and space resist patterns; this constitutes a special 2D shrinking case. The results of analytical and numerical solutions are compared, and are shown to agree. In the final section we formulate novel Elastic Compact Model (ECM) that mechanistically captures shrink-induced biases for the resist walls of arbitrary 2D resist patterns. The model is fast and can be used for the full-chip optical proximity corrections (OPC). The accuracy of ECM is analyzed using typical OPC layouts by comparing to FEM results, rigorous simulations, and SEM measurements.

High NA and Ultra-High NA (NA>1.0) applications for low k₁ imaging strongly demand the adoption of polarized illumination as a resolution enhancement technology since proper illumination polarization configuration can greatly improve the image contrast hence pattern printing fidelity and the effectiveness of optical proximity correction (OPC). However, current OPC/RET modeling software can only model the light source polarization of simple types, such as TE, TM, X, Y, or sector polarization with relatively simple configuration. Realistic polarized light used in scanners is more complex than the aforementioned simple ones. As a result, simulation accuracy and quality of the OPC result will be compromised by the simplification of the light source polarization modeling in the traditional approach. With ever shrinking CD error budget in the manufacturing of IC's at advanced technology nodes, more accurate and comprehensive illumination source modeling for lithography simulations and OPC/RET is needed. On the other hand, for polarized illumination to be fully effective, ideally all the components in the optical lithography system should not alter the polarization state of light during its propagation from illuminator to wafer surface. In current OPC modeling tools, it is typically assumed that the amplitude and polarization state of the light do not change as it passes through the projection lens pupil, i.e. the polarization aberration of projection lens pupil is ignored. However, in reality, the projection lens pupil of the scanner does change the amplitude and the polarization state to some extent, and ignorance of projection pupil induced polarization state and amplitude changes will cause CD errors un-tolerable at the 45nm device generation and beyond. We developed an OPC-deployable modeling approach to model arbitrarily polarized light source and arbitrarily polarized projection lens pupil. Based on polarization state vector descriptions of a general illumination source, this modeling approach unifies optical simulations of unpolarized, partially polarized, and completely polarized illuminations. The polarization aberration imposed by the projection lens pupil is modeled via Jones matrix format, and it is applicable to arbitrary polarization aberrations imposed by any components in the lithography system that can be characterized in Jones matrix format. Numerical experiments were performed to study CD impact from illumination polarization and projection lens pupil polarization aberrations, and up to several nanometers impact on optical proximity effect (OPE) was observed, which is not negligible given the extremely stringent CD error budget at 45nm node and beyond. Based on an experimentally measured Jones matrix pupil which intrinsically provides a much better approximation to the physical scanner projection pupil, we propose a more physics-centric methodology to evaluate the optical model accuracy of OPC simulator.

Due to the sub-wavelength lithography, manufacturing sub-90 nm feature sizes require intensive use of resolution-enhancement techniques, among which optical proximity correction (OPC) is the most popular technique in industry. Considering the OPC effects during routing can significantly alleviate the cost of post-layout OPC operations. In this paper, we present an efficient, accurate, and economical analytical formula for intensity computation and develop the first modeling of post-layout OPC based on a quasi- inverse lithography technique. Extensive simulations with SPLAT, the golden lithography simulator in academia and industry, show that our intensity formula has high fidelity. Incorporating the OPC costs computed by the quasi-inverse lithography technique for our post-layout OPC modeling into a router, the router can be guided to maximize the effects of the correction. Compared with a rule- based OPC method, the experimental results show that our approach can achieve 14% and 16% reductions in the maximum and average layout distortions, respectively.

As an important resolution enhancement technique (RET), alternating aperture phase shift masks (AAPSM) has been widely adopted in 90 nm technology node and beyond. Mask topographical effect due to the 3D nature of the shifter features is becoming an increasingly important factor in lithography modeling. Rigorous 3D modeling of PSM is very computationally demanding thus impractical for full chip optical proximity correction (OPC). Here we introduce an alternative approach employing boundary layers to effectively approximate the 3D mask effect. We will present the model calibration versus real wafer data using the boundary layers and the corresponding OPC correction flow.

In previous work we combined fast aerial image simulation with a closed-loop Optical Proximity Correction (OPC) control system to generate pre-compensated mask geometries which account for pattern transfer distortion effects at small feature sizes. We also presented the variable- threshold resist (VTR) model in which an image-dependent threshold is used to calculate linewidths directly from the image intensity. The model parameters can be determined by `tuning' the model with linewidth measurements from chosen sample sites on the wafer. In this paper, we present verify our OPC approach experimentally by showing after etch SEM wafers of corrected and uncorrected designs. In doing so, we show that (1) OPC can eliminate bridging effects in uncorrected designs, (2) VTR model is fairly insensitive to process variations and (3) mask writing effects are important and cannot be ignored.

A methodology is described wherein a calibrated model-based ‘Virtual’ Variable Shaped Beam (VSB) mask writer process simulator is used to accurately verify complex Optical Proximity Correction (OPC) and Inverse Lithography Technology (ILT) mask designs prior to Mask Data Preparation (MDP) and mask fabrication. This type of verification addresses physical effects which occur in mask writing that may impact lithographic printing fidelity and variability. The work described here is motivated by requirements for extreme accuracy and control of variations for today’s most demanding IC products. These extreme demands necessitate careful and detailed analysis of all potential sources of uncompensated error or variation and extreme control of these at each stage of the integrated OPC/ MDP/ Mask/ silicon lithography flow. The important potential sources of variation we focus on here originate on the basis of VSB mask writer physics and other errors inherent in the mask writing process. The deposited electron beam dose distribution may be examined in a manner similar to optical lithography aerial image analysis and image edge log-slope analysis. This approach enables one to catch, grade, and mitigate problems early and thus reduce the likelihood for costly long-loop iterations between OPC, MDP, and wafer fabrication flows. It moreover describes how to detect regions of a layout or mask where hotspots may occur or where the robustness to intrinsic variations may be improved by modification to the OPC, choice of mask technology, or by judicious design of VSB shots and dose assignment.

For the patterning of sub-100 nm contact holes, thermal reflow is suggested as a good method of resolving the cost problems of resolution-enhancement technology and the new lithography technology. However, it is difficult to use this process in lithography process because the optical proximity effect of thermal reflow is quite severe. In this study, the optical proximity effects before and after thermal reflow are described. Resist reflow is modeled and simulated for a top-view image. For repeated contacts and random contacts, thermal reflow biases are modeled and compensated for pattern arrays. Simulation results agree well with the experiment results in a small error range according to baking temperature, time, and pitch size. For the optical proximity correction of thermal reflow, two-stage corrections, and model-based optical proximity corrections before and after thermal reflow, are described. The model-based optical proximity correction before thermal reflow can be required using pull-simulated images rather than an aerial image as pattern critical dimension shrinks down to sub-100 nm. The possibility of thermal reflow for the formation of a sub-100 nm pattern is shown by simulating a model-based optical proximity correction of a 45 nm contact hole.

With the continued shrink of integrated circuit fabrication groundrules, the achievement of good critical dimension (CD) control becomes more and more dependent on optical proximity correction (OPC). Current simulation capabilities involve a first principle aerial image simulation algorithm, such as the transmission cross coefficient (TCC) algorithm, and a resist model, which captures the dynamics of the chemical amplification and the developing process. In the past few years, it has been found that the key photolithographic parameters, such as, the exposure latitude (EL) and the mask error factor (MEF) for the dense features can be very accurately simulated by the algorithm in which the latent image are made by simple Gaussian diffusion of the aerial image. However, more detailed comparison between the simulation and experiment in isolated features, or two-dimensional features indicates that the current modeling algorithm is still not good enough. This may have resulted in the fact that even advanced model based OPC may require hundreds, even more than a thousand experimental data points for model building. In addition, the model made with such endeavor does not usually extend well beyond the minimum groundrule, which can cause sub-groundrule test structures to fail. We have studied one process parameter of the photoresists, the MEF, and we found that a single Gaussian can not explain well the CD behavior and it seems that such difference varies with different resists. The effective diffusion length of some resists are found to vary with line to space ratio within a dense pitch.

We compared a simulator's predictions with the critical dimension (CD) value measured on the wafer. We used sub resolution assist features (SRAF) in the experiment to keep the focus margin, the minimum size of the mask was small and comparable with the absorber's thickness. Therefore, it seems that we need a rigorous model and a variety of parameters for high prediction accuracy. We investigated the prediction error and found its behavior was not complicated. The dependence of the prediction errors was related to the space until the next feature, but the relationship was not linear; rather, it went up and down periodically like a Bessel function. This fact gave us the idea that it might be possible to improve the simulation accuracy by using a special convolution kernel but not a Gaussian function. We used a complementary kernel and tried to find a suitable shape to match the prediction error. The convolution kernel consisted of a complex number in order to represent phase change and amplitude loss. The kernel was applied to the simulator's mask plain. The results showed a significant improvement in simulation accuracy and a reduction in the route mean square (RMS) of the CD fitting error for all features with or without SRAFs. We used this model for optical proximity correction (OPC) and verified its accuracy with a printed wafer image. The range of the final CD variation of 40 nm line on the wafer was 1.9 nm, and the model also showed good agreement with the experimental two-dimensional feature shape.

As technology nodes in integrated circuit manufacturing continue to shrink, the impact of wafer and reticle stage vibrations on lithographic imaging quality has become increasingly pronounced. Focusing on extreme ultraviolet lithography for contact hole patterns, this work systematically investigates the influence of stage vibrations on imaging performance with a rigorous lithographic imaging model and numerical simulations. Dynamic stage vibrations are incorporated into a conventional static imaging model to establish a more realistic dynamic imaging framework, and optical proximity correction (OPC) is used to emulate advanced-node process characteristics across different patterns. Results indicate that, as the target feature size decreases, the sensitivity of imaging to vibration increases significantly, and larger vibration amplitudes lead to a clearly nonlinear degradation of imaging quality. A comparative analysis of imaging performance and vibration robustness for different critical dimensions shows that bright-field masks exhibit slightly inferior vibration tolerance, whereas dark-field masks provide superior robustness for dense patterns. Building on these findings, an OPC optimization strategy incorporating moving standard deviation is proposed, offering a feasible approach to mitigating the adverse effects of stage vibrations on lithographic imaging.

A scanning electron microscope (SEM) is the metrology tool used to accurately characterize very fine structures on wafers, usually by extracting one critical dimension (CD) per SEM image. This approach for optical proximity correction (OPC) modeling requires many measurements resulting in a lengthy cycle time for data collection, review, and cleaning, and faces reliability issues when dealing with critical two-dimensional (2-D) structures. An alternative to CD-based metrology is to use SEM image contours for OPC modeling. To calibrate OPC models with contours, reliable contours matched to traditional CD-SEM measurements are required along with a method to choose structure and site selections (number, type, and image space coverage) specific to a contour-based OPC model calibration. The potential of SEM contour model-based calibration is illustrated by comparing two contour-based models to reference models, one empirical model and a second rigorous simulation-based model. The contour-based models are as good as or better than a CD-based model with a significant advantage in the prediction of complex 2-D configurations with a reduced metrology work load.

A rigorous and efficient distillation column model for engineering and training simulators

Computer Aided Engineering (CAE) software has become an essential element in design, simulation, manufacturing and even marketing in the automotive industry as well as in other major manufacturing companies. Multi-physics simulation of IC engines may be one of the most challenging areas both technically and scientifically, since it requires sound basis and experience for diverse physical phenomena. There are quite a few commercial softwares currently available for various elements of CAE, which require substantial investment cost for licensing, personnel and computing facilities. There is a current consensus for the need of low cost CAE based on open sources through which professionals may contribute to new modeling features and validation through a free access web-based platform. There are several high quality open sources available under General Public Licence (GNU-GPL) which allow free utilization and development. Some of them have features as competitive as their commercial counterparts, whereas their interface in general may not be as user-friendly as most commercial software. In this work, we introduce a web-based platform with selected open source programs and their performance will be shown for some example cases. All these programs are downloadable, while remote job access and post-processing can be performed by cloud computing facilities.