Algorithms for DFM in electronic design automation

As the dimension of features in integrated circuits (IC) keeps shrinking to fulfill Moore’s law, the manufacturing process has no choice but confronting the limit of physics at the expense of design flexibility. On the other hand, IC designs inevitably becomes more complex to meet the increasing demand of computational power. To close this gap, design for manufacturing (DFM) becomes the key to enable an easy and low-cost IC fabrication. Therefore, efficient electronic design automation (EDA) algorithms must be developed for DFM to address the design constraints and help the designers to better facilitate the manufacture process. As the core of manufacturing ICs, conventional lithography systems (193i) reach their limit for the 22 nm technology node and beyond. Consequently, several advanced lithography techniques are proposed, such as multiple patterning lithography (MPL), extreme ultra-violet lithography (EUV), electron beam (E-beam), and block copolymer directed self-assembly (DSA); however, DFM algorithms are essential for them to achieve better printability of a design. In this dissertation, we focus on analyzing the compatibility of designs and various advanced lithography techniques, and develop efficient algorithms to enable the manufacturing. We first explore E-Beam, one of the promising candidates for IC fabrication beyond the 10 nm technology node. To address its low throughput issue, the character projection technique has been proposed, and its stencil planning can be optimized with an awareness of overlapping characters. 2D stencil planning is proved NP-Hard. With the assumption of standard cells, the 2D problem can be partitioned into 1D row ordering subproblems; however, it is also considered hard, and no efficient optimal solution has been provided so far. We propose a polynomial time optimal algorithm to solve the 1D row ordering problem, which serves as the major subroutine for the entire stencil planning problem. Technical proofs and experimental results verify that our algorithm is efficient and indeed optimal. As the most popular and practical lithography technique, MPL utilizes multiple exposures to print a single layout and thus allows placement of features within the minimum distance. Therefore, a feasible decomposition of the layout is a must to adopt MPL, and it is usually formulated as a graph k-coloring problem, which is computationally difficult for k > 2. We study the k-colorability of rectangular and diagonal grid graphs as induced subgraphs of a rectangular or diagonal grid respectively, since it has direct applications in printing contact/via layouts. It remains an open question on how hard it is to color grid graphs due to their regularity and sparsity. In this dissertation, we conduct a complete analysis of the k-coloring problems on rectangular and diagonal grid graphs, and particularly the NP-completeness of 3-coloring on a diagonal grid graph is proved. In practice, we propose an exact 3-coloring algorithm for those graphs and conduct experiments to verify its performance and effectiveness. Besides, we also develop an efficient algorithm for model based MPL, because it is more expensive but accurate than the rule based decomposition. As one of the alternative lithography techniques, block copolymer directed self-assembly (DSA) is studied. It has emerged as a low-cost, high- throughput option in the pursuit of alternatives to traditional optical lithography. However, issues of defectivity have hampered DSA’s viability for large-scale patterning. Recent studies have shown the copolymer fill level to be a crucial factor in defectivity, as template overfill can result in malformed DSA structures and poor LCDU after etching. For this reason, the use of sub-DSA resolution assist features (SDRAFs) as a method of evening out template density has been demonstrated. In this dissertation, we propose an algorithm to place SDRAFs in random logic contact/via layouts. By adopting this SDRAF placement scheme, we can significantly improve the density unevenness and the resources used are also optimized. We also apply our knowledge in coloring grid graphs to the problem of group-and-coloring in DSA-MPL hybrid lithography. We derive a solution to group-3-coloring and prove the NP-completeness of grouping-2-coloring

Advances in Unconventional Lithography

The term Lithography encompasses a range of contemporary technologies for micro and nano scale fabrication. Originally driven by the evolution of the semiconductor industry, lithography has grown from its optical origins to demonstrate increasingly fine resolution and to permeate fields as diverse as photonics and biology. Today, greater flexibility and affordability are demanded from lithography more than ever before. Diverse needs across many disciplines have produced a multitude of innovative new lithography techniques. This book, which is the final instalment in a series of three, provides a compelling overview of some of the recent advances in lithography, as recounted by the researchers themselves. Topics discussed include nanoimprinting for plasmonic biosensing, soft lithography for neurobiology and stem cell differentiation, colloidal substrates for two-tier self-assembled nanostructures, tuneable diffractive elements using photochromic polymers, and extreme-UV lithography

A study of optical propagation in polymer liquid crystal nanocomposites for photolithography applications

Technology devices today are rapidly growing in complexity while shrinking in physical size as exemplified by the ultra slim laptops and music players currently available on the market. With the downsizing of packaging and the increase in components, innovative new lithography techniques designed to push the density limit of the digital functions on a chip are becoming more available. Though many di erent forms of lithography exist, all with individual benefits, there currently exists no photolithography tool that can completely eliminate alignment error over a series of exposures; a tool that can bring the industry into the next phase of nanometer photo-patterning. The device that can achieve this goal is designed using digitally adaptable polymer light-valve films to spatially control exposure transmission creating a photomask with an arbitrary and dynamically adjustable pattern.This thesis presents the fundamental engineering behind the design of this novel photomasking application that uses a nanostructured composite. The material used is holographically-formed polymer-dispersed liquid crystal (H-PDLC) film and it is a photosensitive material formed with an interference pattern to contain layers of liquid crystal molecules held in a polymer matrix. With control over individual regions of film in a patterned electrode configuration, areas can be user defined as opaque or transmissive to resist exposing light. When used in a photomasking application, the light and dark fields can be real-time adjusted for rapid mask debugging, mask testing, and multiple exposures with no realignment. To truly understand the microscopic optical behavior of this device, aspects of propagation through the nanostructured film are investigated. Diffractive and edge interference effects are simulated and measured. In addition to this study, transmissive wavefront, scattering, coherence, intensity, and absorption are examined to assess factors limiting imaging due to transmission through the nanostructured thin film. To this point, there have been no investigations into imaging through an H-PDLC as it pertains to patterning photoresist, and limited studies regarding optical propagation within the film. Shown in this work is compelling evidence not only of the practicality of a liquid crystal adaptable photomask but also a study of the optical transmission properties within this type of thin film.Ph.D., Electrical Engineering -- Drexel University, 200

Analog design for manufacturability: lithography-aware analog layout retargeting

As transistor sizes shrink over time in the advanced nanometer technologies, lithography effects have become a dominant contributor of integrated circuit (IC) yield degradation. Random manufacturing variations, such as photolithographic defect or spot defect, may cause fatal functional failures, while systematic process variations, such as dose fluctuation and defocus, can result in wafer pattern distortions and in turn ruin circuit performance. This dissertation is focused on yield optimization at the circuit design stage or so-called design for manufacturability (DFM) with respect to analog ICs, which has not yet been sufficiently addressed by traditional DFM solutions. On top of a graph-based analog layout retargeting framework, in this dissertation the photolithographic defects and lithography process variations are alleviated by geometrical layout manipulation operations including wire widening, wire shifting, process variation band (PV-band) shifting, and optical proximity correction (OPC). The ultimate objective of this research is to develop efficient algorithms and methodologies in order to achieve lithography-robust analog IC layout design without circuit performance degradation

Optically Induced Nanostructures

Nanostructuring of materials is a task at the heart of many modern disciplines in mechanical engineering, as well as optics, electronics, and the life sciences. This book includes an introduction to the relevant nonlinear optical processes associated with very short laser pulses for the generation of structures far below the classical optical diffraction limit of about 200 nanometers as well as coverage of state-of-the-art technical and biomedical applications. These applications include silicon and glass wafer processing, production of nanowires, laser transfection and cell reprogramming, optical cleaning, surface treatments of implants, nanowires, 3D nanoprinting, STED lithography, friction modification, and integrated optics. The book highlights also the use of modern femtosecond laser microscopes and nanoscopes as novel nanoprocessing tools

Orbital angular momentum of of electron states with reduced rotational symmetry

Vortex states are interesting fundamental quantum states whilst also finding many uses in photon optics. In 2010, propagating electron vortices were experimentally produced for the first time leading to the emergence of the field of electron phase shaping. This thesis details the production of electron states containing orbital angular momentum which produce a C-shaped intensity in the focal plane. This C-shaped intensity has a diameter of approximately 10 nm and can be used to lithographically pattern nanometre scale split rings. The broken rotational symmetry also allows rotations to be viewed. The design theory and orbital angular momentum analysis of the C-shaped states is presented. Experimental results of the first production of C-shaped electrons are then shown. The C-shaped electron beams have been applied to lithographic patterning and future potential applications of C-shapes for both electrons and photons are discussed. Photons have been shown to be able to couple total angular momentum,both spin and orbital contributions, to the orbital motion of two dimensional plasmon modes in chiral structures. The similar transfer of orbital angular momentum between propagating electron and plasmon modes has not yet been shown. This thesis provides the design of two dimensional spiral structures to support plasmon oscillations containing orbital angular momentum. Simulated electromagnetic fields show the addition of a spiralling boundary can allow eigenmodes with orbital angular momentum. In addition, the first analysis and electron energy loss experimental investigation of free space electron states containing OAM with flat chiral thin film structures supporting two dimensional surface plasmon modes is presented, showing some initial evidence of an energy signal dependent on the sign of topological charge

Maskless nanolithography and imaging with diffractive optical arrays

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.Includes bibliographical references (p. 221-228).Semiconductor lithography is at a crossroads. With mask set costs in excess of one million dollars, long mask turn-around times, and tools that are characterized by their inflexibility and skyrocketing costs, there is a need for a new paradigm in lithography. The work presented in this thesis, Zone-Plate-Array Lithography (ZPAL), bypasses some of the most pressing problems of current lithography equipment by developing a maskless lithography tool that will be scalable, flexible and cost-effective. It is the departure from a century-old tradition of refractive optics, in combination with the use of advanced micromechanics and fast computing, that enables ZPAL to open up a new application space in lithography. This thesis addresses in detail all levels of the ZPAL system, from the micromechanics, to the diffractive optics, to the control system. Special emphasis is placed on the design, fabrication and characterization of high-numerical-aperture diffractive optical elements for lithography and imaging. The results achieved provide conclusive evidence that diffractive optics in general, and zone plates in particular, are capable of state-of-the-art lithography.by Darío Gil.Ph.D

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