Cascadic multigrid algorithm for robust inverse mask synthesis in optical lithography

published_or_final_versio

Inverse Lithography Physics-informed Deep Neural Level Set for Mask Optimization

As the feature size of integrated circuits continues to decrease, optical proximity correction (OPC) has emerged as a crucial resolution enhancement technology for ensuring high printability in the lithography process. Recently, level set-based inverse lithography technology (ILT) has drawn considerable attention as a promising OPC solution, showcasing its powerful pattern fidelity, especially in advanced process. However, massive computational time consumption of ILT limits its applicability to mainly correcting partial layers and hotspot regions. Deep learning (DL) methods have shown great potential in accelerating ILT. However, lack of domain knowledge of inverse lithography limits the ability of DL-based algorithms in process window (PW) enhancement and etc. In this paper, we propose an inverse lithography physics-informed deep neural level set (ILDLS) approach for mask optimization. This approach utilizes level set based-ILT as a layer within the DL framework and iteratively conducts mask prediction and correction to significantly enhance printability and PW in comparison with results from pure DL and ILT. With this approach, computation time is reduced by a few orders of magnitude versus ILT. By gearing up DL with knowledge of inverse lithography physics, ILDLS provides a new and efficient mask optimization solution

Optimization of the holographic process for imaging and lithography

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 272-297).Since their invention in 1948 by Dennis Gabor, holograms have demonstrated to be important components of a variety of optical systems and their implementation in new fields and methods is expected to continue growing. Their ability to encode 3D optical fields on a 2D plane opened the possibility of novel applications for imaging and lithography. In the traditional form, holograms are produced by the interference of a reference and object waves recording the phase and amplitude of the complex field. The holographic process has been extended to include different recording materials and methods. The increasing demand for holographic-based systems is followed by a need for efficient optimization tools designed for maximizing the performance of the optical system. In this thesis, a variety of multi-domain optimization tools designed to improve the performance of holographic optical systems are proposed. These tools are designed to be robust, computationally efficient and sufficiently general to be applied when designing various holographic systems. All the major forms of holographic elements are studied: computer generated holograms, thin and thick conventional holograms, numerically simulated holograms and digital holograms. Novel holographic optical systems for imaging and lithography are proposed. In the case of lithography, a high-resolution system based on Fresnel domain computer generated holograms (CGHs) is presented. The holograms are numerically designed using a reduced complexity hybrid optimization algorithm (HOA) based on genetic algorithms (GAs) and the modified error reduction (MER) method. The algorithm is efficiently implemented on a graphic processing unit. Simulations as well as experimental results for CGHs fabricated using electron-beam lithography are presented. A method for extending the system's depth of focus is proposed. The HOA is extended for the design and optimization of multispectral CGHs applied for high efficiency solar concentration and spectral splitting. A second lithographic system based on optically recorded total internal reflection (TIR) holograms is studied. A comparative analysis between scalar and (cont.) vector diffraction theories for the modeling and simulation of the system is performed.A complete numerical model of the system is conducted including the photoresist response and first order models for shrinkage of the holographic emulsion. A novel block-stitching algorithm is introduced for the calculation of large diffraction patterns that allows overcoming current computational limitations of memory and processing time. The numerical model is implemented for optimizing the system's performance as well as redesigning the mask to account for potential fabrication errors. The simulation results are compared to experimentally measured data. In the case of imaging, a segmented aperture thin imager based on holographically corrected gradient index lenses (GRIN) is proposed. The compound system is constrained to a maximum thickness of 5mm and utilizes an optically recorded hologram for correcting high-order optical aberrations of the GRIN lens array. The imager is analyzed using system and information theories. A multi-domain optimization approach is implemented based on GAs for maximizing the system's channel capacity and hence improving the information extraction or encoding process. A decoding or reconstruction strategy is implemented using the superresolution algorithm. Experimental results for the optimization of the hologram's recording process and the tomographic measurement of the system's space-variant point spread function are presented. A second imaging system for the measurement of complex fluid flows by tracking micron sized particles using digital holography is studied. A stochastic theoretical model based on a stability metric similar to the channel capacity for a Gaussian channel is presented and used to optimize the system. The theoretical model is first derived for the extreme case of point source particles using Rayleigh scattering and scalar diffraction theory formulations. The model is then extended to account for particles of variable sizes using Mie theory for the scattering of homogeneous dielectric spherical particles. The influence and statistics of the particle density dependent cross-talk noise are studied. Simulation and experimental results for finding the optimum particle density based on the stability metric are presented. For all the studied systems, a sensitivity analysis is performed to predict and assist in the correction of potential fabrication or calibration errors.by José Antonio Domínguez-Caballero.Ph.D

Design for Manufacturing in IC Fabrication: Mask Cost, Circuit Performance and Convergence

Ph.DDOCTOR OF PHILOSOPH

TOWARDS EFFECTIVE DISPLAYS FOR VIRTUAL AND AUGMENTED REALITY

Virtual and augmented reality (VR and AR) are becoming increasingly accessible and useful nowadays. This dissertation focuses on several aspects of designing effective displays for VR and AR. Compared to conventional desktop displays, VR and AR displays can better engage the human peripheral vision. This provides an opportunity for more information to be perceived. To fully leverage the human visual system, we need to take into account how the human visual system perceives things differently in the periphery than in the fovea. By investigating the relationship of the perception time and eccentricity, we deduce a scaling function which facilitates content in the far periphery to be perceived as efficiently as in the central vision. AR overlays additional information on the real environment. This is useful in a number of fields, including surgery, where time-critical information is key. We present our medical AR system that visualizes the occluded catheter in the external ventricular drainage (EVD) procedure. We develop an accurate and efficient catheter tracking method that requires minimal changes to the existing medical equipment. The AR display projects a virtual image of the catheter overlaid on the occluded real catheter to depict its real-time position. Our system can make the risky EVD procedure much safer. Existing VR and AR displays support a limited number of focal distances, leading to vergence-accommodation conflict. Holographic displays can address this issue. In this dissertation, we explore the design and development of nanophotonic phased array (NPA) as a special class of holographic displays. NPAs have the advantage of being compact and support very high refresh rates. However, the use of the thermo-optic effect for phase modulation renders them susceptible to the thermal proximity effect. We study how the proximity effect impacts the images formed on NPAs. We then propose several novel algorithms to compensate for the thermal proximity effect on NPAs and compare their effectiveness and computational efficiency. Computer-generated holography (CGH) has traditionally focused on 2D images and 3D images in the form of meshes and point clouds. However, volumetric data can also benefit from CGH. One of the challenges in the use of volumetric data sources in CGH is the computational complexity needed to calculate the holograms of volumetric data. We propose a new method that achieves a significant speedup compared to existing holographic volume rendering methods

Image simulation for biological microscopy: microlith

Image simulation remains under-exploited for the most widely used biological phase microscopy methods, because of difficulties in simulating partially coherent illumination. We describe an open-source toolbox, microlith (https://code.google.com/p/microlith), which accurately predicts three-dimensional images of a thin specimen observed with any partially coherent imaging system, including coherently illuminated and incoherent, self-luminous specimens. Its accuracy is demonstrated by comparing simulated and experimental bright-field and dark-field images of well-characterized amplitude and phase targets, respectively. The comparison provides new insights about the sensitivity of the dark-field microscope to mass distributions in isolated or periodic specimens at the length-scale of 10nm. Based on predictions using microlith, we propose a novel approach for detecting nanoscale structural changes in a beating axoneme using a dark-field microscope.Comment: current: 17 pages, 8 figures, expanded to include biological simulations; previous version: 7 pages, 2 figures; related website: https://code.google.com/p/microlit

Design Techniques for Lithography-Friendly Nanometer CMOS Integrated Circuits

The Integrated Circuits industry has been a major driver of the outstanding changes and improvements in the modern day technology and life style that we are observing in our day to day life. The continuous scaling of CMOS technology has been one of the major challenges and success stories. However, as the CMOS technology advances deeply into the deep sub-micron technology nodes, the whole industry (both manufacturing and design) is starting to face new challenges. One major challenge is the control of the variation in device parameters. Lithography variations result from the industry incapability to come up with new light sources with a smaller wavelength than ArF source (193 nm wavelength). In this research, we develop better understanding of the photo-lithography variations and their effect on how the design gets patterned. We investigate the state-of-the-art mask correction and design manipulation techniques. We are focusing in our study on the different Optical Proximity Correction (OPC) and design retargeting techniques to assess how we can improve both the functional and parametric yield. Our goal is to achieve a fast and accurate Model Based Re-Targeting (MBRT) technique that can achieve a better functional yield during manufacturing by establishing the techniques to produce more lithography-friendly targets. Moreover, it can be easily integrated into a fab's PDK (due to its relatively high speed) to feedback the exact final printing on wafer to the designers during the early design phase. In this thesis, we focus on two main topics. First is the development of a fast technique that can predict the final mask shape with reasonable accuracy. This is our proposed Model-based Initial Bias (MIB) methodology, in which we develop the full methodology for creating compact models that can predict the perturbation needed to get to an OPC initial condition that is much closer to the final solution. This is very useful in general in the OPC domain, where it can save almost 50% of the OPC runtime. We also use MIB in our proposed Model-Based Retargeting (MBRT) flow to accurately compute lithography hot-spots location and severity. Second, we develop the fast model-based retargeting methodology that is capable of fixing lithography hot spots and improving the functional yield. Moreover, in this methodology we introduce to the first time the concept of distributed retargeting. In distributed MBRT, not only the design portion that is suffering from the hot-spot is moving to get it fixed but also the surrounding designs and design fragments also contribute to the hot-spot fix. Our proposed model-based retargeting methodology also includes the multiple-patterning awareness as well as the electrical-connectivity-awareness (via-awareness). We used Mentor Graphics Calibre Litho-API c-based programing to develop all of the methodologies we explain in this thesis and tested it on 20nm and 10nm nodes

Algorithms and Architectures for Some Problems in Multibeam Electron Beam Lithography and SEM Metrology

The original Moore’s law has slowed down. It has become unfeasible to double the number of transistor per unit area on integrated circuits every 18 to 24 months. However, the continuous need for computation power is driving the semiconductor industry towards innovative solutions to reduce integrated circuit sizes. Multibeam mask writers and accurate scanning electron microscopy (SEM) metrology are two such innovative solutions. Multibeam mask writers enable next-generation integrated circuit fabrication technologies like extreme ultraviolet lithography (EUV). However, the digital communication capacity constraints limit the widespread adoption of multibeam mask writers. In the first part of this dissertation thesis, we present a study of multibeam systems and offer improvements to increase their communication capacity. We propose improvements to the communication datapath architecture, compression algorithms, and the decompression architecture to improve the communication capacity. In the second part of this thesis, we attempt to improve scanning electron microscopy (SEM) metrology using deep learning techniques. Poisson noise, edge effects, and instrument errors frequently corrupt SEM images. Significant improvements in SEM metrology will enable next-generation lithography. To attain metrology improvements, we first create simulated datasets of SEM images and then train multiple deep convolution neural networks on these datasets. Our deep convolution neural networks exhibit superior performance in comparison with previous techniques. Particularly, we demonstrate improvements to nanostructure roughness measurements like line edge roughness (LER), which determine the quality of fabrication processes. Overall, this thesis work attempts to improve the semiconductor manufacturing process using architectural and algorithmic improvements

Adaptive Aberration Correction for Holographic Projectors

This work builds up on the greatest minds of Cambridge Holography: Adrian Cable, Edward Buckley, Jonathan Freeman, and Christoph Bay. Cable and Buckley, developed an OSPR algorithm which was the first to provide high-quality real-time hologram generation using general-purpose hardware while Freeman designed a method to correct arbitrary aberrations. As ingenious as the method was, the calculations were extensively lengthy. Addressing this issue, a variant of OSPR suited for correcting spatially-varying aberration is presented. The algorithm combines the approaches of Cable, Buckley and Freeman to provide real-time hologram generation while incorporating various corrections (aberration, distortion, and pixel shape envelope). A high-performance implementation on a mid-range GPU achieved hologram generation up to 12 fps. Following topic studied is an adaptive optical correction. This work attempts to construct a set of methods, forming an automated testbed for holographic projectors. Each model, after exiting the production line is placed on such testbed, having all of its imperfections characterized. Once calibrated, each model is able to display highest-quality image throughout its life-span. An application of this work to industry was carried in collaboration with Dr Phillip Hands (University of Edinburgh) and LumeJET. Three demonstrators are constructed intending for a cost-effective system for holographic lithography. They are characterized using the developed testbed. Using the supersampled Adaptive OSPR algorithm, the diffraction limit was surpassed 2.75 times allowing to increase the patterning area. This combines approaches of Cable, Buckley, Freeman and Bay to achieve a wide field-of-view and high pixel-count replay field using off-the-shelf components. This thesis is finished describing the work on 3D holography carried with Penteract28. It is shown that the 2D hologram in the presence of spatially-varying aberrations is mathematically equivalent to a 3D hologram. The same implementation of the algorithm can be used to provide real-time 3D hologram generation.Scholarship from the Engineering and Physical Sciences Research Council (EPSRC) awarded and administrated by the Centre for Doctoral Training (CDT) in Integrated Photonic and Electronic Systems (IPES

Limitations of Proximity Lithography Printing:Simulations, Experiments, and Applications

Photolithography is one of the earliest technologies used to transfer patterns to a substrate. It is also known as optical lithography since it uses light to transfer the pattern. The main exposure techniques exist in the industry are projection printing, contact printing, and proximity printing. Projection printing technology uses optical elements between mask and wafer to project the feature on the mask to the wafer. This is very expensive and delivers the highest resolution. In contact printing, the mask and wafer are in contact with each other and in proximity printing, the mask is kept at some proximity distance away from the wafer. Proximity printing is an easy and cost effective printing technique because the damage to the mask will be less and also no optical elements between mask and wafer are used. The main drawback of the proximity printing is the diffraction effect caused by the proximity gap between mask and wafer, which limits the resolution. The main objective of this thesis is to study the limitations of proximity printing and to increase its resolution. To study the limitations, different types of design strategies and verification methods are used in the thesis. First is the simulation technique which is performed with GenISys Layout LAB. This is specially designed for proximity printing. The software gives the aerial image and final resist pattern as output. The most interesting and important aspect is the second verification technique which is the experimental setup. A measurement setup has been built to study the light propagation from different masks and to study the aerial image at different proximity gaps. The setup is known as High Resolution Interference Microscopy (HRIM). The setup is basically a Mach- Zehnder interferometer having different light sources, sample plane and reference arm which are used according to the samples. The final verification is achieved using the mask aligner. Both the simulation and experiments are carried out using a special illumination optics called MO exposure optics from Süss MicroOptics. The thesis mainly focuses on the rule based optical proximity correction a technique which is a simple method for mass production. Correction structures are designed for one dimensional and two dimensional features in amplitude masks. Adding lines near the edge to improve the edge slope will be discussed as the one dimensional correction. The different intensity cutting planes and the comparison between simulation and experimental results will be discussed along with that. A unified correction structure is designed to solve corner rounding problem and will be studied as the two dimensional study. The structure is defined to print different line widths at single proximity gap on single exposure. Usually, all the structures in the amplitude mask are studied with their aerial image intensities at different proximity gaps. But, here the study extends to phase evaluation also. The measurement technique can measure both intensity and phase evolution from the mask structures. Phase evolution from amplitude correction features will be discussed and how the phase modulates the intensity patterns is also studied. The role of fundamental principles like phase singularities, phase shifts are also discussed to find its effects on proximity printing structures. The study also leads to the intensity and phase propagation from phase shifting mask (PSM) . The structure evaluated is a group of corners in PSM