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 Mueller matrix roots decomposition recently proposed by Chipman in [1] and its three associated families of depolarization (amplitude depolarization, phase depolarization, and diagonal depolarization) are explored. Degree of polarization maps are used to differentiate among the three families and demonstrate the unity between phase and diagonal depolarization, while amplitude depolarization remains a distinct class. Three families of depolarization are generated via the averaging of different forms of two nondepolarizing Mueller matrices. The orientation of the resulting depolarization follows the cyclic permutations of the Pauli spin matrices. The depolarization forms of Mueller matrices from two scattering measurements are analyzed with the matrix roots decomposition-a sample of ground glass and a graphite and wood pencil tip.

Mueller matrix roots depolarization parameters

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

The in-plane Mueller matrix bidirectional reflectance distribution function (MMBRDF) is measured for a Spectralon
calibration target with a reflectance of 99%. Measurements are acquired using a Mueller matrix active imaging,
goniometric polarimeter operated in the near infrared at 1550nm. The Spectralon is measured for both incident and
scattering angles from -80 degrees to 80 degrees to within 20 degrees of retro-reflection. A range of polarization states
is generated and scattered polarization states are analyzed by means of a dual rotating retarder Mueller matrix
polarimeter. Complete Mueller matrix data is measured with a high-resolution camera in image form.
Polarization scatter data is presented in Mueller matrix angular arrays. As expected the Spectralon is a strong
depolarizer and weak s-plane oriented diattenuator. It was also a weak retarder. Diattenuation and retardance are
strongest at horizontal and vertical polarizations, and weakest for circular polarization states.

Polarization scattering from a Spectralon calibration sample

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

Understanding the interaction of polarized light with materials is critical to applications such as remote
sensing, laser radar, and quality control. The availability of angular and spatial information add additional dimensions
to this understanding.
A facility is constructed for Mueller Matrix Bidirectional Reflectance Distribution (MMBRDF) imaging.
Polarized light at near infrared and visible wavelengths is scattered from samples ranging from bare metals to complex
organic structures with various textures and orientations. The resulting scattered polarized light is measured with a
Mueller matrix active imaging polarimeter.
The in-plane MMBRDF is measured for a sanded aluminum sample as a demonstration of the facility. The
aluminum is found to be a weak depolarizer, with a somewhat higher depolarization index at specular angles.
Retardance is dominated by its linear component and is close to 180° for the majority of angles. Diattenuation is weak,
especially in the specular region, and increases in the region further away from specular angles.

Polarization imaging light scattering facility

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

Polarization imaging light scattering facility

Square-wave retarder for polarization computer-generated holography