High numerical aperture imaging in homogeneous thin films.

摘要

This dissertation investigates imaging phenomena by lenses of high relative numerical aperture (NA) in the first layer of a homogeneous thin film stack. The imaging is described by a high NA model that combines elements of vector imaging theory with traditional thin-film optics. Various examples are studied with an emphasis on analyzing the polarization effects of the illumination. Experiments are shown that verify aspects of the model. A brief review of the development of high NA imaging theory is given. The use of the Debye approximation dominates most of the previous work. Investigation of imaging in thin films has been limited to the area of micro-photolithography, where verification studies are done in photoresist. High NA imaging in films is described in terms of matrix formalism. The image is based on the Debye approach in which the vector field is characterized as a plane wave decomposition for each Cartesian component of the electric field, E. This is used to describe propagation from object to entrance pupil, from entrance pupil to exit pupil, and from exit pupil to thin-film stack. If the first film of the stack is located at or near focus, the amplitude and phase of each plane wave, weighted by factors due to polarization, aberration and object diffraction, are used as input into thin-film equations to calculate the local field volume. The image distribution within the film is described by the absorbed electric energy distribution, which is proportional to |E|². The overall effect of the film is shown to significantly reduce vector effects and asymmetries in the image. This is mainly due to the reduction of NA in the film by refraction. The image of a tri-bar object with an extreme NA of 0.95 is simulated. The differences between two orthogonal polarizations are shown to be small. This is attributed to the large contribution due to the central zone of the pupil. The behavior is shown to be similar to three-beam interference. Modification of this simulation with a annular pupil results in image behavior that is very similar to two-beam interference with increased image differences between two polarizations. Two-beam and three-beam interference is shown to be derived from the general imaging equation, resulting in concise analytic vector equations. Experimental verification in photoresist film is shown using a cross-sectioning technique that highlights the image distribution. Structural artifacts within the simulated image are identified in experimental scanning electron microscope photographs. Large differences are seen between S and P polarized illumination.