Diffractive phase-shift lithography photomask operating in proximity printing mode

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)A phase shift proximity printing lithographic mask is designed, manufactured and tested. Its design is based on a Fresnel computer-generated hologram, employing the scalar diffraction theory. The obtained amplitude and phase distributions were mapped into discrete levels. In addition, a coding scheme using sub-cells structure was employed in order to increase the number of discrete levels, thus increasing the degree of freedom in the resulting mask. The mask is fabricated on a fused silica substrate and an amorphous hydrogenated carbon (a:C-H) thin film which act as amplitude modulation agent. The lithographic image is projected onto a resist coated silicon wafer, placed at a distance of 50 mu m behind the mask. The results show a improvement of the achieved resolution - linewidth as good as 1.5 mu m - what is impossible to obtain with traditional binary masks in proximity printing mode. Such achieved dimensions can be used in the fabrication of MEMS and MOEMS devices. These results are obtained with a UV laser but also with a small arc lamp light source exploring the partial coherence of this source. (C) 2010 Optical Society of America18161638716405Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP_BrasilCNPq_Brasi

Doctor of Philosophy

dissertationOptics is an old topic in physical science and engineering. Historically, bulky materials and components were dominantly used to manipulate light. A new hope arrived when Maxwell unveiled the essence of electromagnetic waves in a micro perspective. On the other side, our world recently embraced a revolutionary technology, metasurface, which modifies the properties of matter-interfaces in subwavelength scale. To complete this story, diffractive optic fills right in the gap. It enables ultrathin flat devices without invoking the concept of nanostructured metasurfaces when only scalar diffraction comes into play. This dissertation contributes to developing a new type of digital diffractive optic, called a polychromat. It consists of uniform pixels and multilevel profile in micrometer scale. Essentially, it modulates the phase of a wavefront to generate certain spatial and spectral responses. Firstly, a complete numerical model based on scalar diffraction theory was developed. In order to functionalize the optic, a nonlinear algorithm was then successfully implemented to optimize its topography. The optic can be patterned in transparent dielectric thin film by single-step grayscale lithography and it is replicable for mass production. The microstructures are 3?m wide and no more than 3?m thick, thus do not require slow and expensive nanopatterning techniques, as opposed to metasurfaces. Polychromat is also less demanding in terms of fabrication and scalability. The next theme is focused on demonstrating unprecedented performances of the diffractive optic when applied to address critical issues in modern society. Photovoltaic efficiency can be significantly enhanced using this optic to split and concentrate the solar spectrum. Focusing through a lens is no news, but we transformed our optic into a flat lens that corrects broadband chromatic aberrations. It can also serve as a phase mask for microlithography on oblique and multiplane surfaces. By introducing the powerful tool of computation, we devised two imaging prototypes, replacing the conventional Bayer filter with the diffractive optic. One system increases light sensitivity by 3 times compared to commercial color sensors. The other one renders the monochrome sensor a new function of high-resolution multispectral video-imaging

An alternating direction method of multipliers for inverse lithography problem

We propose an alternating direction method of multipliers (ADMM) to solve an optimization problem stemming from inverse lithography. The objective functional of the optimization problem includes three terms: the misfit between the imaging on wafer and the target pattern, the penalty term which ensures the mask is binary and the total variation regularization term. By variable splitting, we introduce an augmented Lagrangian for the original objective functional. In the framework of ADMM method, the optimization problem is divided into several subproblems. Each of the subproblems can be solved efficiently. We give the convergence analysis of the proposed method. Specially, instead of solving the subproblem concerning sigmoid, we solve directly the threshold truncation imaging function which can be solved analytically. We also provide many numerical examples to illustrate the effectiveness of the method

Modeling, design and optimization of computer-generated holograms with binary phases

L’hologramme généré par ordinateur (HGO) a été démontré à jouer un rôle important depuis son invention par Lohmann dans les années 1960 dans de nombreuses applications telles que l’ingénierie du front d'onde, l’éclairage structuré et l’affichage optique, etc. Dans le travail de thèse ci-présent, la modélisation, la conception et l’optimisation d’HGO avec des phases binaires sont étudiées. Nous avons examiné un système pratique de projection d’image avec certaines spécifications de travail, par exemple, une distance de travail de 40 cm, une profondeur de champ de 10 cm et un angle de diffraction de 53 degré pour une longueur d’onde de travail de 632 nm, et ensuite conçu et optimisé un hologramme de phase binaire en passant par une recherche directe binaire pour ce système d’image. L’hologramme a été fabriqué par la lithographie à faisceau d’électrons. Pour atteindre l’angle de diffraction requis, nous avons discuté de l’architecture optique dans le système de projection d’image holographique. L’HGO conçu et le système de projection d’image holographique ont été validés expérimentalement par reconstruction optique. Étant donné que les pixels finiront par se regrouper pour former des ouvertures polygonales en hologramme, qui peut être vu clairement dans le processus de recherche directe binaire, nous avons proposé une nouvelle approche pour la conception directe des ouvertures polygonales basée sur la disposition triangulaire en HGO de grande taille en pixels. La diffraction de l’ouverture a été calculée par la transformation analytique d’Abbe. L’image reconstruite peut être exprimée comme une addition cohérente de motifs de diffraction à partir de tous les bords droits d’orientations et de longueurs différentes. Une optimisation en deux étapes comprenant l’algorithme génétique avec la recherche locale de codage des phases binaires des ouvertures, suivie par la recherche directe de co-sommets flottants des ouvertures triangulaires élémentaires a été développée. Nous avons en outre proposé une disposition d’ouverture quadrilatérale, qui fournit plus de degrés de liberté et peut former des ouvertures polygonales plus diverses en hologrammes. L’algorithme génétique parallèle avec la recherche locale a été adopté dans une première étape pour assigner des phases binaires, et la recherche directe a ensuite été utilisée pour optimiser des emplacements de co-sommets d'ouvertures quadrilatérales lors de la deuxième étape. Trois schémas différents pour l'algorithme en deux étapes ont été discutés pour fournir des moyens flexibles afin d’équilibrer la performance de l’optimisation et la durée nécessaire.The computer-generated hologram (CGH) has been demonstrated to play an important role, since its invention by Lohmann in 1960s, in many applications such as wavefront engineering, structured illumination and optical display, etc. In this thesis, the modeling, design and optimization of CGH with binary phases are studied. We considered a practical projection image system with certain working specification, e.g. working distance of 40 cm, depth of field of 10 cm and a diffraction angle of 53 degree for 632 nm working wavelength, and then designed and optimized a binary-phase hologram by direct binary search for this image system. The hologram was fabricated by E-beam lithography. To achieve the required diffraction angle, we discussed the optical architecture in holographic projection image system. The designed CGH and holographic projection image system were validated experimentally by optical reconstruction. Since the pixels will eventually cluster to form polygonal apertures in hologram, which can be seen clearly during the process of direct binary search, we proposed a new approach to directly design polygonal apertures based on triangular layout in CGH of a large number of pixels. The diffraction of aperture was calculated by analytical Abbe transform. The reconstructed image can be expressed as a coherent addition of diffraction patterns from all the straight edges of different orientations and lengths. A two-step optimization including genetic algorithm with local search for encoding binary phases of apertures, followed by direct search for floating covertices of the elementary triangular apertures was developed. We further proposed a quadrilateral aperture layout, which provides more degrees of freedom and can form more diverse polygonal apertures in holograms. The parallel genetic algorithm with local search was adopted to assign binary phases in the first step, and direct search was then used to optimize of locations of covertices of quadrilateral apertures in the second step. Three different schemes for the two-step algorithm were discussed to provide flexible ways to balance the optimization performance and time cost.Résumé en espagno

Robust source and mask optimization compensating for mask topography effects in computational lithography

Mask topography effects need to be taken into consideration for a more accurate solution of source mask optimization (SMO) in advanced optical lithography. However, rigorous 3D mask models generally involve intensive computation and conventional SMO fails to manipulate the mask-induced undesired phase errors that degrade the usable depth of focus (uDOF) and process yield. In this work, an optimization approach incorporating pupil wavefront aberrations into SMO procedure is developed as an alternative to maximize the uDOF. We first design the pupil wavefront function by adding primary and secondary spherical aberrations through the coefficients of the Zernike polynomials, and then apply the conjugate gradient method to achieve an optimal source-mask pair under the condition of aberrated pupil. We also use a statistical model to determine the Zernike coefficients for the phase control and adjustment. Rigorous simulations of thick masks show that this approach provides compensation for mask topography effects by improving the pattern fidelity and increasing uDOF.published_or_final_versio

Pupil wavefront manipulation for the compensation of mask topography effects in optical nanolithography

As semiconductor optical lithography is pushed to smaller dimensions, resolution enhancement techniques have been required to maintain process yields. For some time, the customization of illumination coherence at the source plane has allowed for the control of diffraction order distribution across the projection lens pupil. Phase shifting at the mask plane has allowed for some phase control as well. However, geometries smaller than the imaging wavelength introduce complex wavefront effects that cannot be corrected at source or mask planes. Three dimensional mask topography effects can cause a pitch dependent defocus (δBF), which can decrease the useable depth of focus (UDOF) across geometry of varying density. Wavefront manipulation at the lens pupil plane becomes necessary to provide the degrees of freedom needed to correct for such effects. The focus of this research is the compensation of such wavefront phase error realized through manipulation of the lens pupil plane, specifically in the form of spherical aberration. The research does not attempt to improve the process window for one particular feature, but rather improve the UDOF in order to make layouts with multiple pitches possible for advanced technology nodes. The research approach adopted in this dissertation includes rigorous simulation, analytical modeling, and experimental measurements. Due to the computational expense of rigorous calculations, a smart genetic algorithm is employed to optimize multiple spherical aberration coefficients. An analytical expression is formulated to predict the best focus shifts due to spherical aberration applied in the lens pupil domain. Rigorously simulated trends of best focus (BF) through pitch and orientation have been replicated by the analytical expression. Experimental validation of compensation using primary and secondary spherical aberration is performed using a high resolution wavefront manipulator. Subwavelength image exposures are performed on four different mask types and three different mask geometries. UDOF limiting δBF is observed on the thin masks for contact holes, and on thick masks for both one directional (1D) and two directional (2D) geometries. For the contact holes, the applied wavefront correction decreases the δBF from 44 nm to 7 nm and increases the UDOF to 109 nm, an 18% improvement. For the 1D geometries on a thick mask, the through pitch UDOF is increased from 59 nm to 108 nm, an 83% improvement. Experimental data also shows that an asymmetric wavefront can be tuned to particular geometries, providing a UDOF improvement for line ends under restricted processing conditions. The experimental data demonstrates that pupil wavefront manipulation has the capability to compensate for mask topography induced δBF. This dissertation recommends that corrective spherical aberration coefficients be used to decrease pitch dependent best focus, increase process yield, and ultimately expand the design domain over parameters such as mask materials and mask feature densities. The effect of spherical aberration applied in the pupil plane is to provide a wavefront solution that is equivalent to complex multiple-level mask compensation methods. This will allow the advantages of thicker masks to be explored for further applications in semiconductor optical lithography

Continuous phase-shift lithography with a roll-type mask and application to transparent conductor fabrication

We report the development of a near-field optical nanolithography method using a roll-type phase-shift mask. Sub-wavelength resolution is achieved using near-field exposure of photoresist through a cylindrical phase mask, allowing dynamic and high throughput continuous patterning. As an application, we present the fabrication of a transparent electrode in the form of a metallic wire grid by using the roller-based optical lithography method. To fabricate a mesh-type metal pattern, a specific phase-shift mask was designed and critical experimental parameters were also studied. As a result, a transparent conductor with suitable properties was achieved with a recently built cylindrical phase-shift lithography prototype designed to pattern on 100 mm 2 of substrate area.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98604/1/0957-4484_23_34_344008.pd