Optimizing lithographic techniques with predictive modeling
Lithography is a key step in the fabrication of micro- and nanoelectronic circuits. It transfers a designed pattern into a thin (photo)polymer or photoresist layer on the top surface of a semiconductor wafer. For over 30 years, optical projection lithography has been the standard technology for patterning microelectronic circuits. In the mid 1970s, systems with an operating wavelength of 436nm formed patterns with a minimal feature size of 2000nm. Now, optical lithography at a wavelength of 193nm generates features as small as 45nm.
This tendency to print features much smaller than the wavelength of light used has tremendously increased lithographic process complexity. Scientists must account for more and more physical and chemical effects to optimize the formation of images and resist profiles. Therefore, modeling and simulation of lithographic processes has become mandatory for developing and perfecting new processes.
The simulation of lithographic processes typically involves two different steps: image formation and resist processing (shown schematically in Figure 1). The process starts with a mask layout. The first simulation step describes the projection imaging of the mask and can be considered a bandpass filter. The letters are clearly resolved in the projected ‘aerial image.’ However, this process blurs fine details of the mask, such as line ends. Lithography simulation accurately and efficiently describes this filtering process in terms of the projection system optical parameters—wavelength λ, numerical aperture (NA), polarization, and coherence properties.
Increasingly smaller features require rigorous modeling of light diffraction from sub-wavelength size objects. Researchers use numerical methods to efficiently model the electromagnetic field. Recently, we reported simulation times of less than 30min on a standard personal computer for a 245λ × 245λ × 6λ simulation area.1 The code is parallelized, and computing times scale down nearly linearly with the number of available central processing units (CPUs).
The second step in the simulation describes chemical modification of the photoresist during exposure, baking, and chemical development. Semi-empirical models can describe the concentration of important chemical species inside the resist and their impact on the solubility of the resist in the final development step. Even more advanced modeling approaches—such as Markov chains—are required to account for the finite size and limited concentration of chemical species, and their statistical impact on the resist profile, especially on line-edge roughness.
To enhance this process, we designed a development and research lithography simulator (Dr.Litho).2 It combines advanced optical and chemical models for predictive simulation of optical projection lithography, and uses many tools to evaluate and optimize the processes. Moreover, the open architecture of Dr.Litho facilitates the integration of additional extensions and third-party modules, as well as for user-specific process steps.
We have also used lithography simulation to evaluate new patterning strategies and materials. Our simulation of different double-exposure and double-patterning strategies supported material development in the European MD3 project.3 For instance, we compared photoresist profiles and lithographic process windows for the transistor poly-layer of a six transistor static random access memory cell. We compared different lithography options, including a standard single exposure, and interference assisted lithography in combination with various double-exposure and patterning options.4 We also used simulation to explore the capabilities and limitations of extreme UV lithography.
Others5 have reported results in a relatively new area of advanced lithography: source and mask optimization. We have used lithography simulation in combination with sophisticated optimization techniques to find new, non-intuitive mask layouts, and illumination geometries to improve the printing of a given target layout.6 Computational lithography is considered one of the most important resolution enhancement techniques.
The simulation models and algorithms we originally developed for semiconductor fabrication are becoming increasingly important for other areas of micro- and nanotechnology as well. For example, contact and proximity printing with a so-called mask aligner is a cost-efficient alternative to optical projection printing for many microsystems applications. Lithography simulation helps explore the technology's limits and develop process enhancements. Figure 3 shows a simulation result for a contact printing of 400nm dense lines and spaces in comparison with a scanning electron microscope (SEM) photograph of an actual printing result on an SÜSS MicroTec Mask Aligner.
Simulation has become a standard technique for the development and optimization of projection lithography for semiconductor fabrication. It is a training tool for researchers and process engineers. It is also used for the evaluation and comparison of different technology options, for extensive parameter and sensitivity studies, and increasingly as a design and process optimization tool.
Dr.Litho enables the simulation of other lithographic techniques such as optical near field, interference, plasmonic, and e-beam lithography. Combining simulation with experiments is needed to extract relevant modeling parameters for photoresists. Application-specific methods should also be developed to help optimize processes for micro- and nanosystems. Using lithography and device/system simulations with flexible optimization tools can lay the groundwork for micro- and nanosystems fabrication. Our next steps will focus on the modeling of alternative photoresist materials and processes, as well as combining lithography simulation with metrology.
In 1988, Andreas Erdmann received his PhD in applied optics from the Friedrich-Schiller University in Jena, Germany. In 1995 he joined the Fraunhofer Institute for Silicon Technology. Since 1999 he has headed the lithography simulation group in the Semiconductor Technology Simulation Department. His interests include simulation of optical lithography, computational electrodynamics, microelectronic process technology and modern optics. He has helped develop several advanced lithography simulators.
Tim Fühner earned a master's in computer science at the University of Erlangen-Nuremberg, Germany in 2002. His thesis focused on the improvement of a genetic algorithm-based machine learning system. He has also investigated the application of soft-computing approaches to the modeling of crystal growth processes and to various lithography simulation related problems, including source/mask optimization. He is the project leader and co-author of Dr. Litho.
