We describe and analyze a method by which an optical polarization state is mapped to an image sensor. When placed in a Bayesian framework, the analysis allows a priori information about the polarization state to be introduced into the measurement. We show that when such a measurement is applied to a single photon, it eliminates exactly one fully polarized state, offering an important insight about the information gained from a single photon polarization measurement.
Star Test Polarimetry is a method of inferring polarization information in a single irradiance measurement from the shape of a point spread function [1]. We present the optical design of an image sampling polarimeter that utilizes a stress engineered optical element to image the polarization states of scattered light collected by a lens across a given field. In our scheme, an intermediate image is sampled by a pinhole array and a relay system projects the polarization dependent point spread functions to a CCD. In this way, we show polarization mapping of a sample using a single irradiance image.
Abstract. Wafer chucks are used in advanced lithography systems to hold and flatten wafers during exposure. To minimize defocus and overlay errors, it is important that the chuck provide sufficient pressure to completely chuck the wafer and remove flatness variations across a broad range of spatial wavelengths. Analytical and finite element models of the clamping process are presented here to understand the range of wafer geometry features that can be fully chucked with different clamping pressures. The analytical model provides a simple relationship to determine the maximum feature amplitude that can be chucked as a function of spatial wavelength and chucking pressure. Three-dimensional finite element simulations are used to examine the chucking of wafers with various geometries, including cases with simulated and measured shapes. The analytical and finite element results both demonstrate that geometry variations with short spatial wavelengths (e.g., high-frequency wafer shape features) present the greatest challenge to achieving complete chucking. The models and results presented here can be used to provide guidance on wafer geometry and chuck designs for advanced exposure tools.
Reducing focus errors during optical lithography patterning is crucial for minimizing defects and for achieving the desired critical dimension uniformity (CDU). Factors that contribute to lithography defocus originate from both within and outside the exposure tools. Wafer geometry and topography have been shown to be a major contributor to the focus budget, but decoupling wafer issues from scanner tooling / chuck signatures is far from trivial. In this paper we will review how the use of flatness metrology in a 22nm manufacturing environment improved our ability to measure focus errors as well as enabled the decoupling of error between tooling and wafer sources. We will also review several examples of experimental datasets demonstrating how this wafer shape measurement technique has provided unique insight to the nature of topography based focus error, as well as provide a valuable learning mechanism for driving improvement in process cycles of learning.
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