Multi-objective optimization of lithographic process conditions using a genetic algorithm

Student:Sebastian Seifert
Title:Multi-objective optimization of lithographic process conditions using a genetic algorithm
Type:diploma thesis
Advisors:Kókai, G.; Fühner, T.; Wilke, P.
State:submitted on October 23, 2006

Commonly optimization problems in an engineering context are of multi-{}objective nature. The merit of a solution is not given by a single criterion, but by a number of (often incommensurable) properties. For example, it may be desirable to improve both the quality of an item and its production feasibility. These attributes are not comparable. Even more, they are likely to be contradictory: Increase in quality often requires a higher effort in production.
Most conventional optimization techniques, however, rely on a scalar merit value. Thus, the problem has to be reduced to one objective. Usually this is done by aggregating multiple merits using a weighted sum. This approach has two main disadvantages:

  • Finding appropriate weights is non-trivial and may be very time consuming.
  • Solutions on convex search fronts cannot be found. With designated multi-objective approaches, such as multi-{}objective genetic algorithms (MOGAs), optimization is not directed by a one-best value but by a frontier, a number of indistinguishably well performing solutions Thus facilitating the formulation of the optimization problem and preventing a pre-induced or perverse bias, caused by weights.

Micro-lithography is one of the critical process steps for the production of logic and memory devices in microelectronics. Complex and yet very small circuit layouts can be created by imaging a photo mask onto a photo-{}sensitive layer (photo resist) on top of the wafer. The Lithograpy Simulation Group at Fraunhofer IISB develops models that describe these lithographic processes. As these models yield predictive simulations, they cannot only be used to optimize existing processes but also to develop entirely new settings. A common problem in lithography simulation is to determine appropriate mask geometries and optical process parameters in order to obtain a desired intensity distribution in the photo resist. In the general case, this problem cannot be solved analytically. Therefore, a genetic algorithm (GA) is used to perform this optimization task. Thus allowing for a semi-automated search for ideal process conditions. Both mask and illumination geometries are generated with very little pre-adjustments; yielding highly innovative solutions.
As drawback, however, this optimization problem involves very many incompatible fitness criteria such as producibility of the photo mask, feasibility of the illumination set-{}up, and numerous properties that determine the imaging performance. Combining these objectives and finding appropriate weights is critical, as it has a significant impact on both the convergence behavior and the properties of resulted solutions. Thus, weights have to be selected very carefully, which is a fairly complex and time consuming procedure.


This work aims at integrating a multi-objective approach into the genetic algorithm that has been developed at IISB, and at tailoring this approach to the automatic optimization of micro-{}lithography mask and illumination settings.
In a first step, an intensive literature research should be conducted in order to investigate on the characteristics (advantages and shortcomings)of the approaches. The most promising approaches should be integrated intothe present GA and compared using bench-mark tests. The MOGA integration should be realized modularly. That is, it should be possible to easily select any of the implemented approaches (e.g., by editing a configuration file). Further on, the interaction of presently used GA operators and extensions (e.g., linkage learning) is to be thoroughly studied. Finally, the approaches are to be applied to the optimization of mask and illumination settings. In a first survey, the feasibility and the performance of the multi-objective approaches (in comparison to the former scalar approach) is to be studied and future directions should be proposed. In addition to the genetic algorithm, a comprehensive simulation environment, which can be controlled using the Python programming language, will be available for this task. Furthermore, numerous powerful computers, including access to the RRZE Linux cluster, will allow for large-scale studies.


  • Tim Fühner and Andreas Erdmann, Improved mask and source representations for automatic optimization of lithographic process conditions using a genetic algorithm Proc. SPIE 5754, 2005.
  • Kalyanmoy Deb, Multi-Objective Optimization Using Evolutionary Algorithms, 2001
  • Andreas Erdmann and Wolfgang Henke, Simulation of Optical Lithography. Optics and Optoelectronics - Theory, Devices, and Applications, 1999.
  • Georges Harik, "Learning Gene Linkage to Efficiently Solve Problems of Bounded Difficulty Using Genetic Algorithms.", 1997
  • Harry Levinson, "Principles of Lithography", 1997.
  • Python Python Homepage
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