Source and mask optimization (SMO) has emerged as a key resolution enhancement technique for advanced optical lithography. Current SMO, however, keeps the polarization state fixed, thus limiting the degrees of freedom during the optimization procedure. To overcome this limitation, pixelated gradient-based joint source polarization mask optimization (SPMO) approaches, which effectively extend the solution space of the SMO problem by introducing polarization variables, are developed. First, the SPMO framework is formulated using an integrative and analytic vector imaging model that is capable of explicitly incorporating the polarization angles. Subsequently, two optimization methods, namely simultaneous SPMO (SISPMO) and sequential SPMO (SESPMO) are developed, both of which exploit gradient-based algorithms to solve for the optimization problem. In addition, a postprocessing method is applied to reduce the complexity of the optimized polarization angle pattern for improving its manufacturability. Illustrative simulations are presented to validate the effectiveness of the proposed algorithms. The simulations also demonstrate the superiority of the SESPMO over SISPMO in computational efficiency and improvement of image fidelity.

Gradient-based joint source polarization mask optimization for optical lithography

The disclosure relates to optical systems of a microlithographic projection exposure apparatus, and to a microlithographic exposure method. According to an aspect of the disclosure, an optical system has a light source, a ray-splitting optical element, which splits a light ray incident on this element when the projection exposure apparatus is in operation into a first partial ray and a second partial ray, with the first and the second partial ray having mutually orthogonal polarization directions, and at least one ray-deflecting optical element for generating a desired polarized illumination setting from the first partial ray and the second partial ray, wherein the ray-splitting optical element is arranged such that light incident on this ray-splitting optical element when the projection exposure apparatus is in operation has a degree of polarization of less than one.

Optical system for a microlithographic projection exposure apparatus and microlithographic exposure method

Illumination source optimization (SO) in optical lithography is generally performed under a simulation model that does not consider critical effects such as the vectorial nature of light and mask topography. When a numerical aperture becomes large and the critical dimension reaches subwavelength, the prediction of this model generally fails; therefore, the previous works based on this model become inaccurate. In order to correctly compute SO, we first propose a new source pattern representation method that has moderate parameter variations but remains complete in solution space. Then we develop a derivative-free optimization (DFO) method to optimize these parameters under a rigorous simulation model. Unlike gradient-based techniques, DFO methods do not require a closed-form formulation of the model and are independent of the form of cost function.

Illumination source optimization in optical lithography via derivative-free optimization

Polarized illumination and source mask optimization (SMO) are two prominent resolution enhancement technologies
(RETs) in immersion lithography. Recently, source-mask-polarization optimization (SMPO) has been developed to
support photolithographic process shrinks, which shows that the illumination system with arbitrary intensity and
polarization distribution of light in the pupil is emergency. In this paper, we propose a unique illumination system design
to match the target SMPO source and meet the requirement of immersion lithography at 45-16 nm node. In our designed
illumination system, the adjustable λ/2 wave plates and mirror array are introduced to produce arbitrary intensity and
polarization distribution of light in the pupil. The three λ/2 wave plates are designed to that can move freely in certain
planes perpendicular to the optical path. To produce target SMPO sources, the positions of thousands spots reflected by
adjustable mirrors array are firstly designed and optimized to approximate the target intensity distribution in the pupil
corresponding to unpolarized light. Then the target polarization states in all the spots are obtained in the pupil by
designing and optimizing the relative positions of the three wave plates. Compared with prior design method, our design
results show that the intensity distribution and polarization state of all spots in the pupil match the target SMPO source
accurately and efficiently with lower intensity lost.

Design of freeform illumination sources with arbitrary polarization for immersion lithography

A new technique is introduced to replace DOEs that are used for illumination in lithographic
projectors with polarization computer generated holograms (PCGHs) that produce both arbitrary
intensity and arbitrary polarization state in the illumination pupil. The additional capability of
arbitrary polarization state adds an additional degree of freedom for source-mask optimization.
The PCGHs are similar in design and construction to DOEs, but they incorporate polarizationsensitive
elements. Three experiments are described that demonstrate different configurations of
PCGHs deigned to produce a tangentially polarized ring. Measurements of ratio of polarization
and polarization orientation indicate that all three configurations performed well. Experimetns
are performed with visible (λ = 632.8nm) light.

Polarization holograms for source-mask optimization

An interlaced polarization computer-generated hologram (PCGH) is designed to produce specific irradiance and polarization states in the image plane. The PCGH produces a tangentially polarized annular pattern with correlated speckle, which is achieved by a novel application of the diffuser optimization method. Alternating columns of orthogonal linear polarizations illuminate an interlaced PCGH, producing a ratio of polarization of 88% measured on a fabricated sample. The demonstrated technique can be applied to designs for arbitrary irradiance and polarization states in the image plane.

Polarization synthesis by computer-generated holography using orthogonally polarized and correlated speckle patterns

An etched calcite square-wave retarder is designed, fabricated, and demonstrated as an illuminator for an interlaced polarization computer-generated hologram (PCGH). The calcite square-wave retarder enables alternating columns of orthogonal linear polarizations to illuminate the interlaced PCGH. Together, these components produce a speckled, tangentially polarized PCGH diffraction pattern with a measured ratio of polarization of 84% and a degree of linear polarization of 0.81. An experimental alignment tolerance analysis is also reported.

Square-wave retarder for polarization computer-generated holography

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Papers

Polarization holograms for source-mask optimization

Polarization synthesis by computer-generated holography using orthogonally polarized and correlated speckle patterns

Square-wave retarder for polarization computer-generated holography