David Z. Pan

Layout decomposition for double patterning lithography

As minimum feature size and pitch spacing further decrease, triple patterning lithography (TPL) is a possible 193nm extension along the paradigm of double patterning lithography (DPL). However, there is very little study on TPL layout decomposition. In this paper, we show that TPL layout decomposition is a more difficult problem than that for DPL. We then propose a general integer linear programming formulation for TPL layout decomposition which can simultaneously minimize conflict and stitch numbers. Since ILP has very poor scalability, we propose three acceleration techniques without sacrificing solution quality: independent component computation, layout graph simplification, and bridge computation. For very dense layouts, even with these speedup techniques, ILP formulation may still be too slow. Therefore, we propose a novel vector programming formulation for TPL decomposition, and solve it through effective semidefinite programming (SDP) approximation. Experimental results show that the ILP with acceleration techniques can reduce 82% runtime compared to the baseline ILP. Using SDP based algorithm, the runtime can be further reduced by 42% with some tradeoff in the stitch number (reduced by 7%) and the conflict (9% more). However, for very dense layouts, SDP based algorithm can achieve 140× speed-up even compared with accelerated ILP.

Redundant-via enhanced maze routing for yield improvement

Redundant via insertion is a good solution to reduce the yield loss by via failure. However, the existing methods are all post-layout optimizations that insert redundant via after detailed routing. In this paper, we propose the first routing algorithm that considers feasibility of redundant via insertion in the detailed routing stage. Our routing problem is formulated as maze routing with redundant via constraints. The problem is transformed to a multiple constraint shortest path problem, and solved by Lagrangian relaxation technique. Experimental results show that our algorithm can find routing layout with much higher rate of redundant via than conventional maze routing.

Buffer block planning for interconnect-driven floorplanning

We study buffer block planning for interconnect-driven floorplanning in deep submicron designs. We first introduce the concept of feasible region (FR) for buffer insertion, and derive closed-form formula for FR. We observe that the FR for a buffer is quite large in general even under fairly tight delay constraints. Therefore, FR gives us a lot of flexibility to plan for buffer locations. We then develop an effective buffer block planning (BBP) algorithm to perform buffer clustering such that the overall chip area and the buffer block number can be minimized. To the best of our knowledge, this is the first in-depth study on buffer planning for interconnect-driven floorplanning with both area and delay consideration.

Pushing ASIC performance in a power envelope

Power dissipation is becoming the most challenging design constraint in nanometer technologies. Among various design implementation schemes, standard cell ASICs offer the best power efficiency for high-performance applications. The flexibility of ASICs allow for the use of multiple voltages and multiple thresholds to match the performance of critical regions to their timing constraints, and minimize the power everywhere else. We explore the trade-off between multiple supply voltages and multiple threshold voltages in the optimization of dynamic and static power. The use of multiple supply voltages presents some unique physical and electrical challenges. Level shifters need to be introduced between the various voltage regions. Several level shifter implementations will be shown. The physical layout needs to be designed to ensure the efficient delivery of the correct voltage to various voltage regions. More flexibility can be gained by using appropriate level shifters. We discuss optimization techniques such as clock skew scheduling which can be effectively used to push performance in a power neutral way.

True process variation aware optical proximity correction with variational lithography modeling and model calibration

Optical proximity correction (OPC) is one of the most widely used resolution enhancement techniques (RET) in nanometer designs to improve subwavelength printability. Conventional model-based OPC assumes nominal process conditions without considering process variations because of the lack of variational lithography models. A simple method to improve OPC results under process variations is to sample multiple process conditions across the process window, which requires long run times. We derive a variational lithography model (VLIM) that can simulate across the process window without much run-time overhead compared to the conventional lithography models. To match the model to experimental data, we demonstrate a VLIM calibration method. The calibrated model has accuracy comparable to nonvariational models, but has the advantage of taking process variations into consideration. We introduce the variational edge placement error (VEPE) metrics based on the model, a natural extension to the edge placement error (EPE) used in conventional OPC algorithms. A true process-variation aware OPC (PVOPC) framework is proposed used the VEPE metric. Due to the analytical nature of VLIM, our PVOPC is only about 2 to 3× slower than the conventional OPC, but it explicitly considers the two main sources of process variations (exposure dose and focus variations) during OPC. Thus our post-PVOPC results are much more robust than the conventional OPC ones, in terms of both geometric printability and electrical characterization under process variations.

Improved crosstalk modeling for noise constrained interconnect optimization

This paper presents a much improved, highly accurate yet efficient crosstalk noise model, the 2-pie model, and applies it to noise-constrained interconnect optimizations. Compared with previous crosstalk noise models of similar complexity, our 2-pie model takes into consideration many key parameters, such as coupling locations (near-driver or near-receiver), and the coarse distributed RC characteristics for victim net. Thus, it is very accurate (less than 6% error on average compared with HSPICE simulations). Moreover, our model provides simple closed-form expressions for both peak noise amplitude and noise width, so it is very useful for noise-aware layout optimizations. In particular, we demonstrate its effectiveness in two applications: (i) Optimization rule generation for noise reduction using various interconnect optimization techniques; (ii) Simultaneous wire spacing to multiple nets for noise constrained interconnect minimization.

RADAR: RET-aware detailed routing using fast lithography simulations

This paper attempts to reconcile the growing interdependency between nanometer lithography and physical design. We first introduce the concept of lithography hotspots and the edge placement error (EPE) map to measure the overall printability and manufacturing effort. We then adapt fast lithography simulation models to generate EPE map. Guided by the EPE map, we develop effective RET-aware detailed routing (RADAR) techniques that can handle full-chip capacity to enhance the overall printability while maintaining other design closure. RADAR is implemented in an industry strength detailed router, and tested using some 65nm designs. Our experimental results show that we can achieve up to 40% EPE reduction with reasonable CPU time.

A High-Performance Droplet Routing Algorithm for Digital Microfluidic Biochips

In this paper, we propose a high-performance droplet router for a digital microfluidic biochip (DMFB) design. Due to recent advancements in the biomicro electromechanical system and its various applications to clinical, environmental, and military operations, the design complexity and the scale of a DMFB are expected to explode in the near future, thus requiring strong support from CAD as in conventional VLSI design. Among the multiple design stages of a DMFB, droplet routing, which schedules the movement of each droplet in a time-multiplexed manner, is one of the most critical design challenges due to high complexity as well as large impacts on performance. Our algorithm first routes a droplet with higher by passibility which is less likely to block the movement of the others. When multiple droplets form a deadlock, our algorithm resolves it by backing off some droplets for concession. The final compaction step further enhances timing as well as fault tolerance by tuning each droplet movement greedily. The experimental results on hard benchmarks show that our algorithm achieves over 35 x and 20 x better routability with comparable timing and fault tolerance than the popular prioritized A* search and the state-of-the-art network-flow-based algorithm, respectively.

BoxRouter 2.0: architecture and implementation of a hybrid and robust global router

In this paper, we present BoxRouter 2.0, a hybrid and robust global router with discussion on its architecture and implementation. As high performance VLSI design becomes more interconnect-dominant, efficient congestion elimination in global routing is in greater demand. Hence, we propose BoxRouter 2.0 which has strong ability to improve routability and minimize the number of vias with blockages, while minimizing wirelength. BoxRouter 2.0 is improved over [1], but can perform multi-layer routing with 2D global routing and layer assignment. Our 2D global routing is equipped with two ideas: robust negotiation-based A* search for routing stability, and topology-aware wire ripup for flexibility. After 2D global routing, 2D-to-3D mapping is done by the layer assignment which is powered by progressive via/blockage-aware integer linear programming. Experimental results show that BoxRouter 2.0 has better routability with comparable wirelength than other routers on ISPD07 benchmark, and it can complete (no overflow) ISPD98 benchmark for the first time in the literature with the shortest wirelength.

TSV stress aware timing analysis with applications to 3D-IC layout optimization

As the geometry shrinking faces severe limitations, 3D wafer stacking with through silicon via (TSV) has gained interest for future SOC integration. Since TSV fill material and silicon have different coefficients of thermal expansion (CTE), TSV causes silicon deformation due to different temperatures at chip manufacturing and operating. The widely used TSV fill material is copper which causes tensile stress on silicon near TSV. In this paper, we propose systematic TSV stress aware timing analysis and show how to optimize layout for better performance. First, we generate a stress contour map with an analytical radial stress model. Then, the tensile stress is converted to hole and electron mobility variations depending on geometric relation between TSVs and transistors. Mobility variation aware cell library and netlist are generated and incorporated in an industrial timing engine for 3D-IC timing analysis. It is interesting to observe that rise and fall time react differently to stress and relative locations with respect to TSVs. Overall, TSV stress induced timing variations can be as much as ± 10% for an individual cell. Thus as an application for layout optimization, we can exploit the stress-induced mobility enhancement to improve timing on critical cells. We show that stress-aware perturbation could reduce cell delay by up to 14.0% and critical path delay by 6.5% in our test case.