OPC model separability speeds computational lithography
04/01/2008
Executive OVERVIEW
In low k1 lithography, process integration and qualification are of little value without OPC-corrected masks. Robust separable models that permit optics and resists to be modeled independently allow accurate OPC results to be obtained much faster, shortening the qualification process for both tools and OPC. With the RET strategy decided and the necessary corrections predicted accurately, OPC-corrected masks can be ready as soon as new tools come on line, dramatically accelerating time to production.
As distinguished from traditional behavior-lumped models, separable optical proximity correction (OPC) models not only allow full-chip process window characterization for fine tuning and matching of the existing process and exposure tools, but also enable process optimization before the arrival of next-generation exposure tools, photomasks, and resist processes.
In this article, we assess multiple sets of data that demonstrate the ability of the Tachyon FEM (focus and exposure matrix) to separate the modeling of optics and resists. The optics module allows direct input of the actual illumination source map as well as focus and exposure values. Experimental wafer printing results demonstrate that FEM models calibrated to one optical setting can be extrapolated to dramatically different optical settings, with prediction accuracy commensurate with calibration accuracy.
OPC models
Model-based OPC is the engine that drives computational lithography to meet full-chip CD uniformity (CDU) requirements from manufacturing at 90nm and likely extending to 22nm and beyond. As future CDU targets become ever more stringent, the need to optimize the lithography performance at the full-chip level becomes critical and necessary. Model-based OPC, as calibrated from the existing process, must perform with reliable accuracy at full-chip for both CD correction and verification.
Conventional OPC models have been confined to the optical and resist conditions for which they have been calibrated. Such models must be recalibrated each time any of the optical settings change. To fully characterize the lithography process in advance for upcoming exposure tools, while using the existing resist processes, a fully separable lithography model is essential. Therefore, the resist, imaging tool, and mask models must stand separately, allowing, for example, existing resist and mask models to be combined with new optics models.
In practice, calibrating a trustworthy OPC model for today’s 45nm node is time consuming. Exposing wafers with a model calibration test reticle can be relatively quick (within one hour).However, it is no small task for the two subsequent steps:
1) the metrology work for the many thousands of SEM CD measurements, and still more 2D pattern extractions through the process window, followed by
2) the need for intensive engineering efforts to “clean up” the massive amount of metrology data.
These steps easily consume many weeks, if not months. However, using capable computing hardware, the actual OPC model calibration can be turned around within days. Without doubt, the overall calibration effort simply poses too much schedule risk for today’s fast-paced product development cycle. The situation could worsen if calibration needs to be repeated several more times. On the other hand, by using separable models, a generation of new, yet highly dependable models could potentially happen in minutes.
Separable OPC models
Separable models have an advantage in that each module can represent the physics and chemistry of its stage more completely, improving accuracy and reliability. Many more powerful applications become feasible even before the availability of the actual silicon data or new tools, such as enabling early decisions on low k1 imaging, scanner matching and characterization, and fast adoption or fine-tuning of ongoing manufacturing processes. The outcome improves product yield and achieves better time-to-market.
In this article, we discuss the building of separable models and the use of FEM calibration for full-chip characterization [1-8] and calibrate a base model by using only one set of FEM experimental data. With changing optical conditions, multiple sets of models are quickly generated without the use of any wafer data. These models then generate CD predictions that are compared against the corresponding wafer CD measurements. To demonstrate separable model performance, we compare root-mean-square (RMS) CD errors of the calibrated base model to those models generated without wafer calibration. Actual illumination source maps demonstrate model accuracy improvements.
Building separable models
For a model that is separable, the change for one part of the physical process should affect only the corresponding part of the model. For example, the model calibrated with annular illumination ought to predict accurately when using another type of illumination. In the three stages of lithography processing–mask, optical, and resist–the more the underlying physics and physically significant effects for each model module are incorporated, the better will be the overall models’ separability.
The implementation of the optical model must be based upon first principles and rigorous optical imaging theory. This is essential to minimize residual fitting errors that could get coupled unnecessarily into the resist model. Hopkins transmission cross-coefficient (TCC) is the preferred method to describe partially coherent imaging formation for OPC. For the best results, up to 256 TCC terms are needed to match the imaging calculated analytically from Abbe’s method (Fig. 1). For low k1 imaging, acceptable accuracy is better achieved when using a larger ambit radius (up to 3???4µm) for optical proximity calculation. Physically significant effects, such as the illumination source map, polarization expressed in Jones Pupils, and lens aberration wavefronts, need to be included to represent actual scanner optics.
The resist model needs to be physics-driven and should be well calibrated empirically. For vector imaging, the averaging of aerial images in resist and the mapping of aerial images into acid concentration have been implemented. While an optical model is good for predicting trends, a robust resist model is required in order to accurately predict CD, resolution, process window, and proximity effects.
Using the existing resist model, the impending low k1 imaging strategy, scanner matching, RET/OPC recipes, and design rules can be explored by simply swapping the optical portion of the model. By doing the homework ahead of time, the likelihood of getting the model correct the first time is much higher. This shortens the total process development and qualification cycle, speeds up RET/OPC mask tapeout, and ensures product time-to-market.
Separable models are predictive. From a set of limited pattern gauges and shapes, the model can be calibrated by sampling CDs in a constraint FEM form. The model is expected to be capable of achieving the same level of accuracy to the full-chip layout for the entire process window area. Figure 2 demonstrates this behavior by comparing the RMS CD errors between the fitted (black) and the predicted ones (red).
Experimental assessments
To assess the model separability associated with the Tachyon, we have devised a number of wafer printing experiments in the ASML demo lab in Veldhoven, IMEC, and the Albany research center. Using the model-building and calibration methods previously described, the actual wafer printing performance of separable models was checked by comparing the predicted vs. the on-wafer measured values of the RMS resist CD errors. The data here shows the performance improvement in the ability of the model to predict results when using the actual illumination source map vs. the parameterized model, as well as how the model can handle various NA and illumination settings derived from a fitted base model. More extended reports covering 3D mask topography effects and Jones Pupil calculations for the latest scanner tools will be published later.
 Figure 3. Model accuracy improvement when using an actual illumination source map (red) vs. a parameterized setting (blue). |
Figure 3 presents our findings for the improvement in model accuracy when using an actual illumination source map (red) instead of a parameterized setting (blue). In every test case, RMS CD errors are all consistently lower when using the measured illumination source maps. In terms of model separability, the differences in RMS between the base model (on the left side of Fig. 3) and the rest of models generated without fitting are all in the subnanometer range.
Figure 4 summarizes the experimental conditions and the outcome of the RMS CD errors for both the fitted base model and those for the experimental values. The exposure tool used in the experiment is the ASML 1700i. The same resist process was used for all exposures. The base model is fitted with NA = 1.15 and annular illumination (σi/σo = 0.64/0.90); the RMS resist CD error for the fitted model is 0.95nm. Using the fitted base model, we explored the model’s ability to predict by using two different NA and illumination settings, respectively. The experimental NA settings are 1.1 and 1.2 with the same annular illumination of the base model. As for the illumination experiment, one illumination is annular (σi/σo = 0.59/0.85) and the other is a quasar (σi/σo/degree = 0.64/0.90/30). The NA is the same as the base model at 1.15. No wafer data were used to calibrate the new models.
 Figure 5. NA exploration with the same annular illumination (σi/σ0 =0.64./0.90): a) base model of NA=1.15 and b)models with different NA setting of 1.1 and 1.2 |
Using the base model, calibrated at NA=1.15 to explore two different NA settings (1.1 and 1.2) with the same annular illumination, the model prediction performance in terms of RMS errors for resist CD–comparing the prediction and the measurements–are 1.07nm and 0.96nm, respectively. If the same NA of 1.15 is used, but with two separate illuminations (another annular and a quasar-30), the model predicts RMS errors of 1.07nm and 1.28nm, respectively. Compared to the base model RMS error at 0.95nm, the differences are well within subnanometer range.
Figure 5 shows through-pitch RMS CD error scatter plots for the three NA settings, comparing the model error trends of the base model calibrated at NA = 1.15 to predictions at NA settings of 1.1 and 1.2, all with the same annular illumination as noted in Fig. 4. The trends are remarkably similar with subnanometer RMS differences for all pitch settings. This is additional evidence of a well-behaved, separable model. Similar plots are shown in Fig. 6, which compares model errors of the base model calibrated at one illumination setting to predictions at two different illumination settings, yet all have the same NA setting of 1.15 (as in Fig. 4). The model error trends for the entire pitch range are all in very good agreement and with RMS differences in the subnanometer range from the predicted to the fitted.
Conclusion
On-wafer printing experiments have successfully confirmed model separability for different types of applications using multiple scanner-resist processes. Separable models for computational lithography can dramatically accelerate time to production. If an existing resist process can be used for a new scanner imaging condition, trustworthy models–with any scanner settings–will be readily available in minutes, not weeks. The model can employ accurate tool parameters measured at the factory before the exposure tool is delivered. The early availability of accurate models enables decisions about design rules, RET strategy, and OPC development to occur in parallel. Many more options can be explored and better optimized solutions can be obtained.
Acknowledgments
The authors wish to thank Jeroen Meessen of ASML Veldhoven who performed SEM metrology, and Michael M. Crouse of ASML Albany, NY, for carrying out wafer exposure experiments. Tachyon is a trademark of Brion Technologies, an ASML company.
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Hua-Yu Liu received her masters in chemistry from California State U. of San Jose and is VP, advanced technologies and applications, at Brion Technologies, an ASML company, 4211 Burton Dr., Santa Clara, CA 95054 USA; ph 408/653-0132, e-mail [email protected].
Jiong Jiang is a senior engineer in the Model Product Engineering Group at Brion Technologies.
Qian Zhao is a senior engineer in the Model Product Engineering Group at Brion Technologies.
J. Fung Chen received MS degrees in lithography, imaging science, and optical instrumentation from Rochester Institute of Technology. He co-invented scattering bars for OPC and is VP of research and development at Brion Technologies.
Robert Socha received his BSEE in electrical engineering from the U. of Michigan at Ann Arbor, and his MS and PhD in electrical engineering from the U. of California at Berkeley. He is a Fellow at ASML, Tempe, AZ USA.
Jo Finders is a Fellow at ASML, Veldhoven, Netherlands.