Handling the complexity of routing problem in modern VLSI design

In VLSI physical design, the routing task consists of using over-the-cell metal wires to connect pins and ports of circuit gates and blocks. Traditionally, VLSI routing is an important design step in the sense that the quality of routing solution has great impact on various design metrics such as circuit timing, power consumption, chip reliability and manufacturability etc. As the advancing VLSI design enters the nanometer era, the routing success (routability issue) has been arising as one of the most critical problems in back-end design. In one aspect, the degree of design complexity is increasing dramatically as more and more modules are integrated into the chip. Much higher chip density leads to higher routing demands and potentially more risks in routing failure. In another aspect, with decreasing design feature size, there are more complex design rules imposed to ensure manufacturability. These design rules are hard to satisfy and they usually create more barriers for achieving routing closure (i.e., generate DRC free routing solution) and thus affect chip time to market (TTM) plan. In general, the behavior and performance of routing are affected by three consecutive phases: placement phase, global routing phase and detailed routing phase in a typical VLSI physical design flow. Traditional CAD tools handle each of the three phases independently and the global picture of the routability issue is neglected. Different from conventional approaches which propose tools and algorithms for one particular design phase, this thesis investigates the routability issue from all three phases and proposes a series of systematic solutions to build a more generic flow and improve quality of results (QoR). For the placement phase, we will introduce a mixed-sized placement refinement tool for alleviating congestion after placement. The tool shifts and relocates modules based on a global routing estimation. For the global routing phase, a very fast and effective global router is developed. Its performance surpasses many peer works as verified by ISPD 2008 global routing contest results. In the detailed routing phase, a tool is proposed to perform detailed routing using regular routing patterns based on a correct-by-construction methodology to improve routability as well as satisfy most design rules. Finally, the tool which integrates global routing and detailed routing is developed to remedy the inconsistency between global routing and detailed routing. To verify the algorithms we proposed, three sets of testcases derived from ISPD98 and ISPD05/06 placement benchmark suites are proposed. The results indicate that our proposed methods construct an integrated and systematic flow for routability improvement which is better than conventional methods

Netlist Decomposition and Candidate Generation for Analog IC Routing

Netlist decomposition and candidate generation is a non-conventional approach in the routing stage of the place and route (PnR) flow. While there has been significant research and advancement in the digital domain for automation with respect to this as well as other techniques, very little work has been done in the analog domain due to its complex constraints and specific requirements. With this proposed method, the most common requirements of Analog circuits are taken into consideration to provide candidate routes for netlists of analog Integrated Chips (IC). Netlist decomposition is an important stage of breaking down multi-pin nets into two-pin nets by adding additional nodes for each net. The proposed method takes into account blockages and constraints such as symmetry and bends to develop a new algorithm using Steiner trees and Hanan grids to generate optimal Steiner points. This method also breaks down multi-pin nets to 3-pin nets which reduces the wirelength and computations significantly. The decomposed net segments are run through Dijkstra algorithm to generate multiple candidates and an Integer Linear programming (ILP) solver is used to pick the best candidates that follow all the constraints and design rules. The experimental results show that overall wirelength is reduced by 5.16% while using 3-pin net decomposition when compared to 2-pin net decomposition. There is also a reduction in the number of metal layers used and the number of Steiner points generated. The method shows lesser computations when compared to other decomposition techniques as it avoids multiple reroutes to obtain Design Rule Check (DRC) clean routes

Netlist Decomposition and Candidate Generation for Analog IC Routing

Netlist decomposition and candidate generation is a non-conventional approach in the routing stage of the place and route (PnR) flow. While there has been significant research and advancement in the digital domain for automation with respect to this as well as other techniques, very little work has been done in the analog domain due to its complex constraints and specific requirements. With this proposed method, the most common requirements of Analog circuits are taken into consideration to provide candidate routes for netlists of analog Integrated Chips (IC). Netlist decomposition is an important stage of breaking down multi-pin nets into two-pin nets by adding additional nodes for each net. The proposed method takes into account blockages and constraints such as symmetry and bends to develop a new algorithm using Steiner trees and Hanan grids to generate optimal Steiner points. This method also breaks down multi-pin nets to 3-pin nets which reduces the wirelength and computations significantly. The decomposed net segments are run through Dijkstra algorithm to generate multiple candidates and an Integer Linear programming (ILP) solver is used to pick the best candidates that follow all the constraints and design rules. The experimental results show that overall wirelength is reduced by 5.16% while using 3-pin net decomposition when compared to 2-pin net decomposition. There is also a reduction in the number of metal layers used and the number of Steiner points generated. The method shows lesser computations when compared to other decomposition techniques as it avoids multiple reroutes to obtain Design Rule Check (DRC) clean routes

Intelligent approaches to VLSI routing

Very Large Scale Integrated-circuit (VLSI) routing involves many large-size and complex problems and most of them have been shown to be NP-hard or NP-complete. As a result, conventional approaches, which have been successfully used to handle relatively small-size routing problems, are not suitable to be used in tackling large-size routing problems because they lead to \u27combinatorial explosion\u27 in search space. Hence, there is a need for exploring more efficient routing approaches to be incorporated into today\u27s VLSI routing system. This thesis strives to use intelligent approaches, including symbolic intelligence and computational intelligence, to solve three VLSI routing problems: Three-Dimensional (3-D) Shortest Path Connection, Switchbox Routing and Constrained Via Minimization. The 3-D shortest path connection is a fundamental problem in VLSI routing. It aims to connect two terminals of a net that are distributed in a 3-D routing space subject to technological constraints and performance requirements. Aiming at increasing computation speed and decreasing storage space requirements, we present a new A* algorithm for the 3-D shortest path connection problem in this thesis. This new A*algorithm uses an economical representation and adopts a novel back- trace technique. It is shown that this algorithm can guarantee to find a path if one exists and the path found is the shortest one. In addition, its computation speed is fast, especially when routed nets are spare. The computational complexities of this A* algorithm at the best case and the worst case are O(Ɩ) and 0(Ɩ3), respectively, where Ɩ is the shortest path length between the two terminals. Most importantly, this A\u27 algorithm is superior to other shortest path connection algorithms as it is economical in terms of storage space requirement, i.e., 1 bit/grid. The switchbox routing problem aims to connect terminals at regular intervals on the four sides of a rectangle routing region. From a computational point of view, the problem is NP-hard. Furthermore, it is extremely complicated and as the consequence no existing algorithm can guarantee to find a solution even if one exists no matter how high the complexity of the algorithm is. Previous approaches to the switch box routing problem can be divided into algorithmic approaches and knowledge-based approaches. The algorithmic approaches are efficient in computational time, but they are unsucessful at achieving high routing completion rate, especially for some dense and complicated switchbox routing problems. On the other hand, the knowledge-based approaches can achieve high routing completion rate, but they are not efficient in computation speed. In this thesis we present a hybrid approach to the switchbox routing problem. This hybrid approach is based on a new knowledge-based routing technique, namely synchronized routing, and combines some efficient algorithmic routing techniques. Experimental results show it can achieve the high routing completion rate of the knowledge-based approaches and the high efficiency of the algorithmic approaches. The constrained via minimization is an important optimization problem in VLSI routing. Its objective is to minimize the number of vias introduced in VLSI routing. From computational perspective, the constrained via minimization is NP-complete. Although for a special case where the number of wire segments splits at a via candidate is not more than three, elegant theoretical results have been obtained. For a general case in which there exist more than three wire segment splits at a via candidate few approaches have been proposed, and those approaches are only suitable for tackling some particular routing styles and are difficult or impossible to adjust to meet practical requirements. In this thesis we propose a new graph-theoretic model, namely switching graph model, for the constrained via minimization problem. The switching graph model can represent both grid-based and grid less routing problems, and allows arbitrary wire segments split at a via candidate. Then on the basis of the model, we present the first genetic algorithm for the constrained via minimization problem. This genetic algorithm can tackle various kinds of routing styles and be configured to meet practical constraints. Experimental results show that the genetic algorithm can find the optimal solutions for most cases in reasonable time

Using ant colony optimization for routing in microprocesors

Power consumption is an important constraint on VLSI systems. With the advancement in technology, it is now possible to pack a large range of functionalities into VLSI devices. Hence it is important to find out ways to utilize these functionalities with optimized power consumption. This work focuses on curbing power consumption at the design stage. This work emphasizes minimizing active power consumption by minimizing the load capacitance of the chip. Capacitance of wires and vias can be minimized using Ant Colony Optimization (ACO) algorithms. ACO provides a multi agent framework for combinatorial optimization problems and hence is used to handle multiple constraints of minimizing wire-length and vias to achieve the goal of minimizing capacitance and hence power consumption. The ACO developed here is able to achieve an 8% reduction of wire-length and 7% reduction in vias thereby providing a 7% reduction in total capacitance, compared to other state of the art routers

Graphics Processing Unit-Based Computer-Aided Design Algorithms for Electronic Design Automation

The electronic design automation (EDA) tools are a specific set of software that play important roles in modern integrated circuit (IC) design. These software automate the design processes of IC with various stages. Among these stages, two important EDA design tools are the focus of this research: floorplanning and global routing. Specifically, the goal of this study is to parallelize these two tools such that their execution time can be significantly shortened on modern multi-core and graphics processing unit (GPU) architectures. The GPU hardware is a massively parallel architecture, enabling thousands of independent threads to execute concurrently. Although a small set of EDA tools can benefit from using GPU to accelerate their speed, most algorithms in this field are designed with the single-core paradigm in mind. The floorplanning and global routing algorithms are among the latter, and difficult to render any speedup on the GPU due to their inherent sequential nature. This work parallelizes the floorplanning and global routing algorithm through a novel approach and results in significant speedups for both tools implemented on the GPU hardware. Specifically, with a complete overhaul of solution space and design space exploration, a GPU-based floorplanning algorithm is able to render 4-166X speedup, while achieving similar or improved solutions compared with the sequential algorithm. The GPU-based global routing algorithm is shown to achieve significant speedup against existing state-of-the-art routers, while delivering competitive solution quality. Importantly, this parallel model for global routing renders a stable solution that is independent from the level of parallelism. In summary, this research has shown that through a design paradigm overhaul, sequential algorithms can also benefit from the massively parallel architecture. The findings of this study have a positive impact on the efficiency and design quality of modern EDA design flow

Electromigration modeling and layout optimization for advanced VLSI

textElectromigration (EM) is a critical problem for interconnect reliability in advanced VLSI design. Because EM is a strong function of current density, a smaller cross-sectional area of interconnects can degrade the EM-related lifetime of IC, which is expected to become more severe in future technology nodes. Moreover, as EM is governed by various factors such as temperature, material property, geometrical shape, and mechanical stress, different interconnect structures can have distinct EM issues and solutions to mitigate them. For example, one of the most prominent technologies, die stacking technology of three-dimensional (3D) ICs, can have different EM problems from that of planer ICs, due to their unique interconnects such as through-silicon vias (TSVs). This dissertation investigates EM in various interconnect structures, and applies the EM models to optimize IC layout. First, modeling of EM is developed for chip-level interconnects, such as wires, local vias, TSVs, and multi-scale vias (MSVs). Based on the models, fast and accurate EM-prediction methods are proposed for the chip-level designs. After that, by utilizing the EM-prediction methods, the layout optimization methods are suggested, such as EM-aware routing for 3D ICs and EM-aware redundant via insertion for the future technology nodes in VLSI. Experimental results show that the proposed EM modeling approaches enable fast and accurate EM evaluation for chip design, and the EM-aware layout optimization methods improve EM-robustness of advanced VLSI designs.Electrical and Computer Engineerin