EDA Solutions for Double Patterning Lithography

Expanding the optical lithography to 32-nm node and beyond is impossible using existing single exposure systems. As such, double patterning lithography (DPL) is the most promising option to generate the required lithography resolution, where the target layout is printed with two separate imaging processes. Among different DPL techniques litho-etch-litho-etch (LELE) and self-aligned double patterning (SADP) methods are the most popular ones, which apply two complete exposure lithography steps and an exposure lithography followed by a chemical imaging process, respectively. To realize double patterning lithography, patterns located within a sub-resolution distance should be assigned to either of the imaging sub-processes, so-called layout decomposition. To achieve the optimal design yield, layout decomposition problem should be solved with respect to characteristics and limitations of the applied DPL method. For example, although patterns can be split between the two sub-masks in the LELE method to generate conflict free masks, this pattern split is not favorable due to its sensitivity to lithography imperfections such as the overlay error. On the other hand, pattern split is forbidden in SADP method because it results in non-resolvable gap failures in the final image. In addition to the functional yield, layout decomposition affects parametric yield of the designs printed by double patterning. To deal with both functional and parametric challenges of DPL in dense and large layouts, EDA solutions for DPL are addressed in this thesis. To this end, we proposed a statistical method to determine the interconnect width and space for the LELE method under the effect of random overlay error. In addition to yield maximization and achieving near-optimal trade-off between different parametric requirements, the proposed method provides valuable insight about the trend of parametric and functional yields in future technology nodes. Next, we focused on self-aligned double patterning and proposed layout design and decomposition methods to provide SADP-compatible layouts and litho-friendly decomposed layouts. Precisely, a grid-based ILP formulation of SADP decomposition was proposed to avoid decomposition conflicts and improve overall printability of layout patterns. To overcome the limited applicability of this ILP-based method to fully-decomposable layouts, a partitioning-based method is also proposed which is faster than the grid-based ILP decomposition method too. Moreover, an A∗-based SADP-aware detailed routing method was proposed which performs detailed routing and layout decomposition simultaneously to avoid litho-limited layout configurations. The proposed router preserves the uniformity of pattern density between the two sub-masks of the SADP process. We finally extended our decomposition method for double patterning to triple patterning and formulated SATP decomposition by integer linear programming. In addition to conventional minimum width and spacing constraints, the proposed decomposition method minimizes the mandrel-trim co-defined edges and maximizes the layout features printed by structural spacers to achieve the minimum pattern distortion. This thesis is one of the very early researches that investigates the concept of litho-friendliness in SADP-aware layout design and decomposition. Provided by experimental results, the proposed methods advance prior state-of-the-art algorithms in various aspects. Precisely, the suggested SADP decomposition methods improve total length of sensitive trim edges, total EPE and overall printability of attempted designs. Additionally, our SADP-detailed routing method provides SADP-decomposable layouts in which trim patterns are highly robust to lithography imperfections. The experimental results for SATP decomposition show that total length of overlay-sensitive layout patterns, total EPE and overall printability of the attempted designs are also improved considerably by the proposed decomposition method. Additionally, the methods in this PhD thesis reveal several insights for the upcoming technology nodes which can be considered for improving the manufacturability of these nodes

Lithography aware physical design and layout optimization for manufacturability

textAs technology continues to scale down, semiconductor manufacturing with 193nm lithography is greatly challenging because the required half pitch size is beyond the resolution limit. In order to bridge the gap between design requirements and manufacturing limitations, various resolution enhancement techniques have been proposed to avoid potentially problematic patterns and to improve product yield. In addition, co-optimization between design performance and manufacturability can further provide flexible and significant yield improvement, and it has become necessary for advanced technology nodes. This dissertation presents the methodologies to consider the lithography impact in different design stages to improve layout manufacturability. Double Patterning Lithography (DPL) has been a promising solution for sub-22nm node volume production. Among DPL techniques, self-aligned double patterning (SADP) provides good overlay controllability when two masks are not aligned perfectly. However, SADP process places several limitations on design flexibility and still exists many challenges in physical design stages. Starting from the early design stage, we analyze the standard cell designs and construct a set of SADP-aware cell placement candidates, and show that placement legalization based on this SADP awareness information can effectively resolve DPL conflicts. In the detailed routing stage, we propose a new routing cost formulation based on SADP-compliant routing guidelines, and achieve routing and layout decomposition simultaneously. In the case that limited routing perturbation is allowed, we propose a post-routing flow based on lithography simulation and lithography-aware design rules. Both routing methods, one in detailed routing stage and one in post routing stage, reduce DPL conflicts/violations significantly with negligible wire length impact. In the layout decomposition stage, layout modification is restricted and thus the manufacturability is even harder to guaranteed. By taking the advantage of complementary lithography, we present a new layout decomposition approach with e-beam cutting, which optimizes SADP overlay error and e-beam lithography throughput simultaneously. After the mask layout is defined, optical proximity correction (OPC) is one of the resolution enhancement techniques that is commonly required to compensate the image distortion from the lithography process. We propose an inverse lithography technique to solve the OPC problem considering design target and process window co-optimization. Our mask optimization is pixel based and thus can enable better contour fidelity. In the final physical verification stage, a complex and time-consuming lithography simulation needs to be performed to identify faulty patterns. We provide a classification method based on support vector machine and principle component analysis that detects lithographic hotspots efficiently and accurately.Electrical and Computer Engineerin

Design automation algorithms for advanced lithography

In circuit manufacturing, as the technology nodes keep shrinking, conventional 193 nm immersion lithography (193i) has reached its printability limit. To continue the scaling with Moore's law, different kinds of advanced lithography have been proposed, such as multiple patterning lithography (MPL), extreme ultraviolet (EUV), electron beam lithography (EBL) and directed self-assembly (DSA). While these new technologies create enormous opportunities, they also pose great design challenges due to their unique process characteristics and stringent constraints. In order to smoothly adopt these advanced lithography technologies in integrated circuit (IC) fabrication, effective electronic design automation (EDA) algorithms must be designed and integrated into computer-aided design (CAD) tools to address the underlying design constraints and help the circuit designer to better facilitate the lithography process. In this thesis, we focus on algorithmic design and efficient implementation of EDA algorithm for advanced lithography, including directed self-assembly (DSA) and self-aligned double patterning (SADP), to conquer the physical challenges and improve the manufacturing yield. The first advanced lithography technology we explore is self-aligned double patterning (SADP). SADP has the significant advantage over traditional litho-etch-litho-etch (LELE) double patterning in its ability to eliminate overlay, making it a preferable DPL choice for the 14 nm technology node. As in any DPL technology, layout decomposition is the key problem. While the layout decomposition problem for LELE DPL has been well studied in the literature, only a few attempts have been made for the SADP layout decomposition problem. This thesis studies the SADP decomposition problem in different scenarios. SADP has been successfully deployed in 1D patterns and has several applications; however, applying it to 2D patterns turns out to be much more difficult. All previous exact algorithms were based on computationally expensive methods such as SAT or ILP. Other previous algorithms were heuristics without a guarantee that an overlay-free solution can be found even if one exists. The SADP decomposition problem on general 2D layout is proven to be NP-complete. However, we show that if we restrict the overlay, the problem is polynomial-time solvable, and present an exact algorithm to determine if a given 2D layout has a no-overlay SADP decomposition. When designing the layout decomposition algorithms, it is usually useful to take the layout structure into consideration. As most of the current IC layouts adopt a row-based standard cell design style, we can take advantage of its characteristics and design more efficient algorithms compared to the algorithms for general 2D patterns. In particular, the fixed widths of standard cells and power tracks on top and bottom of cells suggest that improvements can be made over the algorithms for general decomposition problem. We present a shortest-path based polynomial time SADP decomposition algorithm for row-based standard cell layout that efficiently finds decompositions with minimum overlay violations. Our proposed algorithm takes advantage of the fixed width of the cells and the alternating power tracks between the rows to limit the possible decompositions and thus achieve high efficiency. The next advanced lithography technology we discuss in the thesis is directed self-assembly (DSA). Block copolymer directed self-assembly (DSA) is a promising technique for patterning contact holes and vias in 7 nm technology nodes. To pattern contacts/vias with DSA, guiding templates are usually printed first with conventional lithography (193i) that has a coarser pitch resolution. Contact holes are then patterned with DSA process. The guiding templates play the role of defining the DSA patterns, which have a finer resolution than the templates. As a result, different patterns can be obtained through controlling the templates. It is shown that DSA lithography is very promising in patterning contacts/vias in 7 nm technology node. However, to utilize DSA for full-chip manufacturing, EDA for DSA must be fully explored because EDA is the key enabler for manufacturing, and the EDA research for DSA is still lagging behind. To pattern the contact layer with DSA, we must ensure that all the contacts in the layout require only feasible DSA templates. Nevertheless, the original layout may not be designed in a DSA-friendly way. However, even with an optimized library, infeasible templates may be introduced after the physical design phase. We propose a simulated-annealing (SA) based scheme to perform full-chip level contact layer optimization. According to the experimental results, the DSA conflicts in the contact layer are reduced by close to 90% on average after applying the proposed optimization algorithm. It is a current trend that industry is transiting from the random 2D designs to highly regular 1D gridded designs for sub-20 nm nodes and fabricating circuit designs with print-cut technology. In this process, the randomly distributed cuts may be too dense to be printed by single patterning lithography. DSA has proven its success in contact hole patterning, and can be easily expanded to cut printing for 1D gridded designs. Nevertheless, the irregular distribution of cuts still presents a great challenge for DSA, as the self-assembly process usually forms regular patterns. As a result, the cut layer must be optimized for the DSA process. To address the above problem, we propose an efficient algorithm to optimize cut layers without hurting the original circuit logic. Our work utilizes a technique called `line-end extension' to move the cuts and extend the functional wires without changing the original functionality of the circuit. Consequently, the cuts can be redistributed and grouped into valid DSA templates. Multiple patterning lithography has been widely adopted for today's circuit manufacturing. However, increasing the number of masks will make the manufacturing process more expensive. By incorporating DSA into the multiple patterning process, it is possible to reduce the number of masks and achieve a cost-effective solution. We study the decomposition problem for the contact layer in row-based standard cell layout with DSA-MP complementary lithography. We explore several heuristic-based approaches, and propose an algorithm that decomposes a standard cell row optimally in polynomial-time. Our experiments show that our algorithm is guaranteed to find a minimum cost solution if one exists, while the heuristic cannot or only finds a sub-optimal solution. Our results show that the DSA-MP complementary approach is very promising for the future advanced nodes. As in any lithography technique, the process variation control and proximity correction are the most important issues. As the DSA templates are patterned by conventional lithography, the patterned templates are prone to deviate from mask shapes due to process variations, which will ultimately affect the contacts after the DSA process even for the same type of template. Therefore, in order to enable the DSA technology in contact/via layer printing, it is extremely important to accurately model and detect hotspots, as well as estimate the contact pitch and locations during the verification phase. We propose a machine learning based design automation framework for DSA verification. A novel DSA model and a set of features are included. We implemented the proposed ML-based flow and performed extensive experiments on comparing the performances of learning algorithms and features. The experimental results show that our approach is much more efficient than the traditional approach, and can produce highly accurate results

Standard cell optimization and physical design in advanced technology nodes

Integrated circuits (ICs) are at the heart of modern electronics, which rely heavily on the state-of-the-art semiconductor manufacturing technology. The key to pushing forward semiconductor technology is IC feature-size miniaturization. However, this brings ever-increasing design complexities and manufacturing challenges to the $340 billion semiconductor industry. The manufacturing of two-dimensional layout on high-density metal layers depends on complex design-for-manufacturing techniques and sophisticated empirical optimizations, which introduces huge amounts of turnaround time and yield loss in advanced technology nodes. Our study reveals that unidirectional layout design can significantly reduce the manufacturing complexities and improve the yield, which is becoming increasingly adopted in semiconductor industry [61, 89]. The lithography printing of unidirectional layout can be tightly controlled using advanced patterning techniques, such as self-aligned double and quadruple patterning. Despite the manufacturing benefits, unidirectional layout leads to more restrictive solution space and brings significant impacts on the IC design automation ow for routing closure. Notably, unidirectional routing limits the standard cell pin accessibility, which further exacerbates the resource competitions during routing. Moreover, for post-routing optimization, traditional redundant-via insertion has become obsolete under unidirectional routing style, which makes the yield enhancement task extremely challenging. Regardless of complex multiple patterning and design-for-manufacturing approaches, mask optimization through resolution enhancement techniques remains as the key strategy to improve the yield of the semiconductor manufacturing processes. Among them, Sub-Resolution Assist Feature (SRAF) generation is a very important method to improve lithographic process windows. Model-based SRAF generation has been widely used to achieve high accuracy but it is time-consuming and hard to obtain consistent SRAFs. This dissertation proposes novel CAD algorithms and methodologies for standard cell optimization and physical design in advanced technology nodes, which ultimately reduces the design cycle and manufacturing cost of IC design. First, a standard cell pin access optimization engine is proposed to evaluate the pin accessibility of a given standard cell library. We further propose novel pin access planning techniques and concurrent pin access optimizations to efficiently resolve the routing resource competitions, which generates much better routing solutions than state-of-the-art, manufacturing-friendly routers. To systematically improve the manufacturing yield in the post-routing stage, a global optimization engine has been introduced for redundant local-loop insertion considering advanced manufacturing constraints. Finally, we propose the first machine learning-based framework for fast yet consistent SRAF generation with the high quality of results.Electrical and Computer Engineerin

Improved Physical Design for Manufacturing Awareness and Advanced VLSI

Increasing challenges arise with each new semiconductor technology node, especially in advanced nodes, where the industry tries to extract every ounce of benefit as it approaches the limits of physics, through manufacturing-aware design technology co-optimization and design-based equivalent scaling. The increasing complexity of design and process technologies, and ever-more complex design rules, also become hurdles for academic researchers, separating academic researchers from the most up-to-date technical issues.This thesis presents innovative methodologies and optimizations to address the above challenges. There are three directions in this thesis: (i) manufacturing-aware design technology co-optimization; (ii) advanced node design-based equivalent scaling; and (iii) an open source academic detailed routing flow.To realize manufacturing-aware design technology co-optimization, this thesis presents two works: (i) a multi-row detailed placement optimization for neighbor diffusion effect mitigation between neighboring standard cells; and (ii) a post-routing optimization to generate 2D block mask layout for dummy segment removal in self-aligned multiple patterning.To achieve advanced node design-based equivalent scaling, this thesis presents two improved physical design methodologies: (i) a post-placement flop tray generation approach for clock power reduction; and (ii) a detailed placement approach to exploit inter-row M1 routing for congestion and wirelength reduction.To address the increasing gap between academia and industry, this thesis presents two works toward an open source academic detailed routing flow: (i) a complete, robust, scalable and design ruleaware dynamic programming-based pin access analysis framework; and (ii) TritonRoute – the open source detailed router that is capable of delivering DRC-clean detailed routing solutions in advanced nodes.This thesis concludes with a summary of its contributions and open directions for future research

Algorithms for Cell Layout

Cell layout is a critical step in the design process of computer chips. A cell is a logic function or storage element implemented in CMOS technology by transistors connected with wires. As each cell is used many times on a chip, improvements of a single cell layout can have a large effect on the overall chip performance. In the past years increasing difficulty to manufacture small feature sizes has lead to growing complexity of design rules. Producing cell layouts which are compliant with design rules and at the same time optimized w.r.t. layout size has become a difficult task for human experts. In this thesis we present BonnCell, a cell layout generator which is able to fully automatically produce design rule compliant layouts. It is able to guarantee area minimality of its layouts for small and medium sized cells. For large cells it uses a heuristic which produces layouts with a significant area reduction compared to those created manually. The routing problem is based on the Vertex Disjoint Steiner Tree Packing Problem with a large number of additional design rules. In Chapter 4 we present the routing algorithm which is based on a mixed integer programming (MIP) formulation that guarantees compliance with all design rules. The algorithm can also handle instances in which only part of the transistors are placed to check whether this partial placement can be extended to a routable placement of all transistors. Chapter 5 contains the transistor placement algorithm. Based on a branch and bound approach, it places transistors in turn and achieves efficiency by pruning parts of the search tree which do not contain optimum solutions. One major contribution of this thesis is that BonnCell only outputs routable placements. Simply checking the routability for each full placement in the search tree is too slow in practice, therefore several speedup strategies are applied. Some cells are too large to be solved by a single call of the placement algorithm. In Chapter 7 we describe how these cells are split up into smaller subcells which are placed and routed individually and subsequently merged into a placement and routing of the original cell. Two approaches for dividing the original cell into subcells are presented, one based on estimating the subcell area and the other based on solving the Min Cut Linear Arrangement Problem. BonnCell has enabled our cooperation partner IBM to drastically improve their cell design and layout process. In particular, a team of human experts needed several weeks to find a layout for their largest cell, consisting of 128 transistors. BonnCell processed this cell without manual intervention in 3 days and its layout uses 15% less area than the layout found by the human experts

Layout decomposition for triple patterning lithography

Nowadays the semiconductor industry is continuing to advance the limits of physics as the feature size of the chip keeps shrinking. Products of the 22 nm technology node are already available on the market, and there are many ongoing research studies for the 14/10 nm technology nodes and beyond. Due to the physical limitations, the traditional 193 nm immersion lithography is facing huge challenges in fabricating such tiny features. Several types of next-generation lithography techniques have been discussed for years, such as {\em extreme ultra-violet} (EUV) lithography, {\em E-beam direct write}, and {\em block copolymer directed self-assembly} (DSA). However, the source power for EUV is still an unresolved issue. The low throughput of E-beam makes it impractical for massive productions. DSA is still under calibration in research labs and is not ready for massive industrial deployment. Traditionally features are fabricated under single litho exposure. As feature size becomes smaller and smaller, single exposure is no longer adequate in satisfying the quality requirements. {\em Double patterning lithography} (DPL) utilizes two litho exposures to manufacture features on the same layer. Features are assigned to two masks, with each mask going through a separate litho exposure. With one more mask, the effective pitch is doubled, thus greatly enhancing the printing resolution. Therefore, DPL has been widely recognized as a feasible lithography solution in the sub-22 nm technology node. However, as the technology continues to scale down to 14/10 nm and beyond, DPL begins to show its limitations as it introduces a high number of stitches, which increases the manufacturing cost and potentially leads to functional errors of the circuits. {\em Triple pattering lithography} (TPL) uses three masks to print the features on the same layer, which further enhances the printing resolution. It is a natural extension for DPL with three masks available, and it is one of the most promising solutions for the 14/10 nm technology node and beyond. In this thesis, TPL decomposition for standard-cell-based designs is extensively studied. We proposed a polynomial time triple patterning decomposition algorithm which guarantees finding a TPL decomposition if one exists. For complex designs with stitch candidates, our algorithm is able to find a solution with the optimal number of stitches. For standard-cell-based designs, there are additional coloring constraints where the same type of cell should be fabricated following the same pattern. We proposed an algorithm that is guaranteed to find a solution when one exists. The framework of the algorithm is also extended to pattern-based TPL decompositions, where the cost of a decomposition can be minimized given a library of different patterns. The polynomial time TPL algorithm is further optimized in terms of runtime and memory while keeping the solution quality unaffected. We also studied the TPL aware detailed placement problem, where our approach is guaranteed to find a legal detailed placement satisfying TPL coloring constraints as well as minimizing the {\em half-perimeter wire length} (HPWL). Finally, we studied the problem of performance variations due to mask misalignment in {\em multiple patterning decompositions} (MPL). For advanced technology nodes, process variations (mainly mask misalignment) have significant influences on the quality of fabricated circuits, and often lead to unexpected power/timing degenerations. Mask misalignment would complicate the way of simulating timing closure if engineers do not understand the underlying effects of mask misalignment, which only exists in multiple patterning decompositions. We mathematically proved the worst-case scenarios of coupling capacitance incurred by mask misalignment in MPL decompositions. A graph model is proposed which is guaranteed to compute the tight upper bound on the worst-case coupling capacitance of any MPL decompositions for a given layout

Ultra thin ultrafine-pitch chip-package interconnections for embedded chip last approach

Ever growing demands for portability and functionality have always governed the electronic technology innovations. IC downscaling with Moore s law and system miniaturization with System-On-Package (SOP) paradigm has resulted and will continue to result in ultraminiaturized systems with unprecedented functionality at reduced cost. The trend towards 3D silicon system integration is expected to downscale IC I/O pad pitches from 40µm to 1- 5 µm in future. Device- to- system board interconnections are typically accomplished today with either wire bonding or solders. Both of these are incremental and run into either electrical or mechanical barriers as they are extended to higher density of interconnections. Alternate interconnection approaches such as compliant interconnects typically require lengthy connections and are therefore limited in terms of electrical properties, although expected to meet the mechanical requirements. As supply currents will increase upto 220 A by 2012, the current density will exceed the maximum allowable current density of solders. The intrinsic delay and electromigration in solders are other daunting issues that become critical at nanometer size technology nodes. In addition, formation of intermetallics is also a bottleneck that poses significant mechanical issues. Recently, many research groups have investigated various techniques for copper-copper direct bonding. Typically, bonding is carried out at 400oC for 30 min followed by annealing for 30 min. High thermal budget in such process makes it less attractive for integrated systems because of the associated process incompatibilities. In the present study, copper-copper bonding at ultra fine-pitch using advanced nano-conductive and non-conductive adhesives is evaluated. The proposed copper-copper based interconnects using advanced conductive and non-conductive adhesives will be a new fundamental and comprehensive paradigm to solve all the four barriers: 1) I/O pitch 2) Electrical performance 3) Reliability and 4) Cost. This thesis investigates the mechanical integrity and reliability of copper-copper bonding using advanced adhesives through test vehicle fabrication and reliability testing. Test vehicles were fabricated using low cost electro-deposition techniques and assembled onto glass carrier. Experimental results show that proposed copper-copper bonding using advanced adhesives could potentially meet all the system performance requirements for the emerging micro/nano-systems.M.S.Committee Chair: Prof. Rao R Tummala; Committee Member: Dr. Jack Moon; Committee Member: Dr. P M Ra

Nanofabricated Neural Probe System for Dense 3-D Recordings of Brain Activity

Computations in brain circuits involve the coordinated activation of large populations of neurons distributed across brain areas. However, monitoring neuronal activity in the brain of intact animals with high temporal and spatial resolution has remained a technological challenge. Here we address this challenge by developing dense, three-dimensional (3-D) electrode array system for electrophysiology. The front-end of the system is composed of nanofabricated neural probes with ultrathin shanks that are engineered to minimize tissue damage. The probes are connected via flexible cables to custom PCBs that multiplex the electrophysiological signals. This system architecture decouples the front-end both mechanically and thermally from the PCB which carries all active electronics for signal conditioning and multiplexing. This system was validated in vivo with hippocampal recordings from head-fixed mice. The culmination of these efforts was a 3-D array with 1024 sites packed within 0.6 mm3 of tissue that yielded the densest electrophysiological recordings to date