Browsing by Subject "Photolithography"

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    A level set method for an inverse problem arising in photolithography
    (2009-08) Tuzel, Vasfiye Hande
    Photolithography is a key process used in the semiconductor industry during the fabrication of integrated circuits. It is the process in which a given circuit layout pattern is transferred onto a substrate by employing a mask. The role of the mask is to block out the ultraviolet light exposure on certain areas on the substrate, hence allowing the emergence of specific patterns after chemical post-processing. Designing the perfect mask that takes into account all optical effects, especially at nanometer resolutions, is a challenging task. In this thesis, we formulate this as an inverse problem, i.e. finding the mask that produces the desired pattern. In order to do this, we first introduce the forward problem of calculating the light intensity at the substrate, given the initial mask. We then formulate a variational problem, which minimizes the mismatch between the desired mask and the one predicted by the model. The variational problem is solved using a level-set approach. Our results show that we can successfully produce masks that match the desired patterns with an error less than 2%. We believe our algorithm can enable further automation of the mask design process, and help manufacturers design better layouts at nanometer scales.
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    Recognition and assembly at multiple length-scales.
    (2010-05) Olmsted, Brian Keith
    Many molecular materials capable of crystallizing into an ordered solid state may assume multiple packing arrangements. This behavior is called polymorphism and is common among organic molecules such as pharmaceuticals and dyes. Controlling the nucleation of specific polymorphic crystals is not well understood, but is tantamount to the development and manufacture of new industrial products. One phenomena that has been observed to influence crystal orientation, growth rate, and morphology is epitaxy. Epitaxy refers to a condition by which a crystalline substrate presents a similar two-dimensional lattice to a crystalline plane of a nucleating species, resulting in a condition that lowers the energy barrier to nucleation and results in a preferential orientation of crystal growth on the substrate. Therefore, epitaxial nucleation may provide routes to selectively nucleate polymorphs and attain control over otherwise unpredictable crystallization events. The literature provides several examples of epitaxial relationships between a substrate and a crystal overlayer in fields involving inorganic crystals as well as organic crystals, and because epitaxy relies on geometric comparisons between lattice parameters, computational prediction of epitaxy is an active area of research. Our laboratories have developed software; named GRACE, to attempt to predict epitaxial relationships and this software has been used to verify epitaxy reported in the literature. One particularly useful feature of GRACE is its ability to handle a library of substrates and screen them against a corresponding database of crystal structures available as candidate crystal overlayers. In this capacity GRACE allows large libraries of substrates and crystals to be reduced to an experimentally manageable size, whereby combinatorial crystallizations can be tested for selective nucleation arising from epitaxial interfaces. This research also focuses on other aspects of nucleation that are not yet fully understood. Epitaxial interfaces are by definition, abrupt. However, a specialized class of crystals involving a domain that completely overgrows a core crystal by epitaxial mechanisms has revealed a zone of intermixing spanning close to a micron. In situ Atomic Force Microscopy (AFM) reveals the mechanisms for these observations and provides insight into how epitaxial interfaces behave mechanistically. Notably, it was revealed that process conditions between phases of growth in the formation of core-shroud heterocrystals may yield controllable interfacial thicknesses between crystalline domains, It was also discovered that the propensity for abrupt, epitaxial interfaces may be limited by the thermodynamic behavior of specific crystal interfaces under conditions of near-equilibrium. Although the use of in situ AFM is excellent for the study of crystal growth, the mass-transfer limitations at crystallizing interfaces inside an (AFM) fluid cell are not directly discernable and the assumption is typically made that conditions in the bulk solution are the same inside the cell. By implementing computational fluid dynamic (CFD) simulations for flow and mass transport, in situ AFM was studied to determine how the different conditions at the crystal surface are in comparison to the bulk solution outside the cell. The geometry of the internal volume of the AFM fluid cell imparts specific fluid flow and mass transport limitations on the environment directly at the area of investigation for crystal growth and in some cases may have significant ramifications for the appropriate correlation of bulk solution variables to crystal growth variables. The results of the CFD calculations indicate that differences are significant, though usually minor and these results may prove useful for future fluid cell design. Finally, photolithographic techniques were employed to produce millions of micron-sized particles with shapes mimicking molecular contours and other crystallographically significant contours to study how symmetry and packing originates at the micron length-scale. Although much is known about assembly at the molecular level for symmetry and packing, the assembly of anisotropic particles at longer length scales, which involve different interactive forces, has not been studied. This work concludes by performing preliminary work in elucidating the general behavior towards symmetry and packing in two-dimensions of micron-sized particles by using gravitational gradients and dielectrophoresis.