# Artificial evolution for the optimization of lithographic process conditions

Künstliche Evolution für die Optimierung von Lithographischen Prozessbedingungen

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**Abstract**

Miniaturization is a driving force both for the performance and for cost reductions of semiconductor devices. It is therefore carried on at an enormous pace. Gordon Moore proposed and later refined an estimation stating that the minimization of costs would lead to a doubling of the density of integrated circuits every two years. And in fact, this time scale---known as Moore's law---is still aspired at by the major players in the industry. Photolithography, one of the key process steps, has to keep up with this pace. In the past, the introduction of new technologies, including a smaller wavelength of the illumination system or higher numerical apertures (NA) of the projector, has led to a relatively straightforward downscaling approach. Today, optical lithography is confined to argon fluoride excimer lasers with a wavelength of 193 nanometers and an NA of 1.35. The introduction of next generation lithography approaches such as extreme ultraviolet lithography have been delayed and will not be applicable until several years from now. Further scaling hence leads to dramatically decreases process margins since patterns with dimensions of only a fraction of the wavelength have to be lithographically created. In this work, computational methods are devised that are suited to drastically improve process conditions and hence to push resolution beyond former limitations. The lithographic process can be broadly grouped into the stepper components: the illumination system, the photomask, the projection system and the wafer stack. As shown in this dissertation, each element exhibits a number of parameters that can be subjected to optimization. To actually enhance resolution, however, a rigorous simulation and computation regime has to be established. The individual ingredients are discussed in detail in this thesis. Accordingly, the models required to describe the lithography process are introduced and discussed. It is shown that the numerical and algorithmic implementation can be regarded as a compromise between exactness and computation time. Both are critical to obtain predictive, yet feasible approaches. Another complication is the multi-scale and multi-physics nature of the first principle process models. Although it is sometimes possible to derive individual optimization-tailored, reduced models, such an approach is often prohibitive for a concise co-optimization of multiple aspects. In this work, we thus examine an approach that allows for a direct integration of first principle models. We investigate the use of evolutionary algorithms (EAs) for that purpose. These types of algorithms can be characterized as flexible optimization approaches that mimic evolutionary mechanisms such as selection, recombination and mutation. Many variants of related techniques exist, of which a number are considered in this dissertation. One chapter of this thesis is dedicated to the discussion of different representations and genetic operators, including motivations of the choices made for the following studies. The lithographic process is characterized not only by a large number of parameters but can also be evaluated by a wide range of criteria, some of which may be conflicting or incommensurable---such as figures of merits like performance and manufacturability. We therefore apply a multi-objective genetic algorithm (GA) that is specifically tailored to identifying ideal compromise solutions. The characteristics of multi-objective optimization, especially when performed with evolutionary algorithms, are discussed in this thesis. There is no such thing as a universal optimizer. EAs, for example, can be considered highly flexible, but they fail to intensively exploit local information. In an attempt to get the best of both worlds, we combine evolutionary with local search routines. We thoroughly discuss our approach to these hybrid techniques and present a number of benchmark tests that demonstrate their successful applications. The majority of optimization problems in lithography are characterized by computationally expensive fitness evaluations. The reduction of the number of candidate solutions is therefore critical to maintain a feasible optimization procedure. To this end, we devised a function approximation approach based on an artificial neural network. Specifically, the GA population constitutes the training pattern for the network. The resulted output is the approximated fitness function. While the global search using the GA is still conducted on the exact search space, the local search is carried out on this approximation, leading to a much reduced runtime. The efficiency and feasibility of this approach is demonstrated by a number of benchmark tests. The algorithms, frameworks and programs developed in the scope of this work are deployed as software modules that are available through the computational lithography environment Dr.LiTHO of the Fraunhofer IISB. The general software structure is briefly discussed. In order to achieve feasible optimization runtimes, rigorous distribution and parallelization techniques need to be employed. For this dissertation, a number of different approaches are devised and discussed in this thesis. A variety of application examples demonstrate the benefits of the devised methods. In a first set of examples, source/mask optimization problems are formulated and solved. In contrast to related work, which is mainly aimed at developing models that are specifically tailored to the underlying optimization routines, the direct approach proposed here is capable of directly employing models that are typically used in lithography simulation. A multitude of results using different problem representations is presented. Additional model options including mask topography effects are demonstrated. It is shown that the approach is not restricted to simplistic aerial image-based evaluations but is able to take the process windows and thin-film effects into account. Moreover, an extension to future resolution enhancement techniques, for example, constructively using projector aberrations, is also demonstrated. In another example series, three-dimensional mask optimizations are performed. There, the topography including the materials of the photomask absorber are subjected to optimization. Drastically improved configurations compared to both standard optical and EUV absorbers under various illumination conditions are obtained. In order to cover all aspects of the lithography process, the last section of this thesis is devoted to the optimization of the wafer stack. As an example, the anti-reflective coating applied at the bottom of the resist to reduce standing waves in the resist profile is optimized. Different configurations including single and bi-layer coating systems are examined and optimized for, especially for double patterning applications. Significant improvements in comparison to standard stacks are shown and discussed. The thesis finally concludes with a discussion on the different optimization strategies and the optimization and simulation infrastructure developed for this work. Advantages and challenges of the methodology are highlighted and future directions and potentials are demonstrated.