UC Berkeley

Next generation extreme ultraviolet (EUV) optical systems are moving to higher resolution optics to accommodate smaller length scales targeted by the semiconductor industry. As the numerical apertures (NA) of the optics become larger, it becomes increasingly difficult to characterize aberrations due to experimental challenges associated with high-resolution spatial filters and geometrical effects caused by large incident angles of the test wavefront.

This dissertation focuses on two methods of wavefront metrology for high resolution optical systems.

The first method, lateral shearing interferometry (LSI), is a self-referencing interferometry where the test wavefront is incident on a low spatial frequency grating, and the resulting interference between the diffracted orders is used to reconstruct the wavefront aberrations. LSI has many advantages over other interferometric tests such as phase-shifting point diffraction interferometry (PS/PDI) due to its experimental simplicity, stability, relaxed coherence requirements, and its ability to scale to high numerical apertures.

While LSI has historically been a qualitative test, this dissertation presents a novel quantitative investigation of the LSI interferogram. The analysis reveals the existence of systematic aberrations due to the nonlinear angular response from the diffraction grating that compromises the accuracy of LSI at medium to high NAs. In the medium NA regime (0.15 < NA < 0.35), a holographic model is presented that derives the systematic aberrations in closed form, which demonstrates an astigmatism term that scales as the square of the grating defocus. In the high NA regime (0.35 < NA), a geometrical model is introduced that describes the aberrations as a system of transcendental equations that can be solved numerically. The characterization and removal of these systematic errors is a necessary step that unlocks LSI as a viable candidate for high NA EUV optical testing.

The second method is a novel image-based reconstruction that characterizes the aberrations of an optical system with arbitrary numerical aperture and illumination coherence. In this method a known pattern is imaged by the test optic at several planes through focus. A computer model is created that iterates through possible sets of wavefront aberrations until the through-focus series of aerial images matches the aerial images from the experiment. Although the sample space of Zernike coefficients is non-convex, a hybrid algorithm consisting of pattern search and simulated annealing methods is used to search for the global minimum.

The computation of aerial images from a partially coherent optical system is expedited with a novel decomposition of the Hopkins equation known as the Reduced Optical Coherent Sum (ROCS). In this method, the Hopkins integral is described by an operator S which maps the space of pupil aberrations directly to the space of aerial images. This operator is shown to be semipositive definite and well-approximated by a truncated sum of its spectral components. The ROCS decomposition has a customizable error bound allowing one to tradeoff aerial image fidelity for significant speed improvements. For aerial image errors of 1-3%, the ROCS algorithm can compute aerial images up to 15 times faster than the Hopkins integration.

The ROCS-based wavefront test is extremely versatile since it is applicable in nearly all optical systems that measure aerial image intensity regardless of numerical aperture or illumination coherence and requires little or no experimental modifications. This test is used to characterize the field-dependent aberrations of the SEMATECH Berkeley Actinic Inspection Tool (AIT), and the results match an independent analysis of the astigmatism aberrations to within lambda/20 rms.