Abstract:In several optical systems, a specific Point Spread Function (PSF) needs to be generated. This can be achieved by shaping the complex field at the pupil. The Extended Nijboer-Zernike (ENZ) theory relates complex Zernike modes on the pupil directly to functions in the focal region. In this paper, we introduce a method to engineer a PSF using the ENZ theory. In particular, we present an optimization algorithm to design an extended depth of focus with high lateral resolution, while keeping the transmission of light high (over 60%). We also have demonstrated three outcomes of the algorithm using a Spatial Light Modulator (SLM). 145-148 (1965). 6. G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento 9, 426-438 (1952). 7. H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001). 8. C. J. R. Sheppard, "Synthesis of filters for specified axial properties," J. Mod. Opt. 43, 525-536 (1996)

We demonstrate a method to obtain within an arbitrary numerical aperture (NA) the entire scattering matrix of a scatterer by using focused beam coherent Fourier scatterometry. The far-field intensities of all scattered angles within the NA of the optical system are obtained in one shot. The corresponding phases of the field are obtained by an interferometric configuration. This method enables the retrieval of the maximum available information about the scatterer from scattered far-field data contained in the given NA of the system.

In the semiconductor industry, the performance and capabilities of the lithographic process are evaluated by measuring specific structures. These structures are often gratings of which the shape is described by a few parameters such as period, middle critical dimension, height, and side wall angle (SWA). Upon direct measurement or retrieval of these parameters, the determination of the SWA suffers from considerable inaccuracies. Although the scattering effects that steep SWAs have on the illumination can be obtained with rigorous numerical simulations, analytical models constitute a very useful tool to get insights into the problem we are treating. In this paper, we develop an approach based on analytical calculations to describe the scattering of a cliff and a ridge with steep SWAs. We also propose a detection system to determine the SWAs of the structures.

In optical metrology, grating-like structures are used as tools to evaluate the performance of lithographic techniques. In particular, several shape parameters characterize those structures. One of them, termed side-wall angle, suffers from a considerable high error estimation. Using mathematical optimization, we investigated whether a properly shaped beam could increase the ability to detect tiny changes of this angle in the case of a cliff-like structure. This paper describes the theoretical formulation used to calculate the optimized beam and compares its performance with the case of a plane wave. The results indicate that the sensitivity increases by several folds by using the optimized solution. Still, such an optimization process needs to be extended to the more general vectorial case.

Finding a fast and precise method to measure the side-wall angle of periodic (or non-periodic) structures is still a very challenging problem in lithographic applications. For this reason, over the years, many techniques have been proposed to circumvent this limitation, with the final goal to give the most precise geometrical description of particular targets. Recently, the investigation of the optical angular momentum, which is encoded in the light's spiral spectrum, has brought new ways to acquire information about objects. In this work, we built an optical setup to put forward a new method to detect the side-wall angle in a fast and reliable way. The novelty of this work is the use of the spiral spectrum of a light beam for angle measurements, i.e. the light transmitted by a particular structure is projected onto properly tailored spatial modes and only the most sensitive mode to the side wall angle is detected and processed.