Yiyu Shi

Thermal via allocation for 3D ICs considering temporally and spatially variant thermal power

The existing 3-D thermal-via allocation methods are based on the steady-state thermal analysis and may lead to excessive number of thermal vias. This paper develops an accurate and efficient thermal-via allocation considering the temporally and spatially variant thermal-power. The transient temperature is calculated by macromodel with a one-time structured and parameterized model reduction, which also generates temperature sensitivity with respect to thermal-via density. The proposed thermal-via allocation minimizes the time-integral of temperature violation, and is solved by a sequential quadratic programming algorithm with use of sensitivities from the macromodel. Compared to the existing method using the steady-state thermal analysis, our method in experiments is 126 times faster to obtain temperature, and reduces the number of thermal vias by 2.04 times under the same temperature bound.

A universal state-of-charge algorithm for batteries

State-of-charge (SOC) measures energy left in a battery, and it is critical for modeling and managing batteries. Developing efficient yet accurate SOC algorithms remains a challenging task. Most existing work uses regression based on a time-variant circuit model, which may be hard to converge and often does not apply to different types of batteries. Knowing open-circuit voltage (OCV) leads to SOC due to the well known mapping between OCV and SOC. In this paper, we propose an efficient yet accurate OCV algorithm that applies to all types of batteries. Using linear system analysis but without a circuit model, we calculate OCV based on the sampled terminal voltage and discharge current of the battery. Experiments show that our algorithm is numerically stable, robust to history dependent error, and obtains SOC with less than 4% error compared to a detailed battery simulation for a variety of batteries. Our OCV algorithm is also efficient, and can be used as a real-time electro-analytical tool revealing what is going on inside the battery.

Statistical multilayer process space coverage for at-speed test

Increasingly large process variations make selection of a set of critical paths for at-speed testing essential yet challenging. This paper proposes a novel multilayer process space coverage metric to quantitatively gauge the quality of path selection. To overcome the exponential complexity in computing such a metric, this paper reveals its relationship to a concept called order statistics for a set of correlated random variables, efficient computation of which is a hitherto open problem in the literature. This paper then develops an elegant recursive algorithm to compute the order statistics (or the metric) in provable linear time and space. With a novel data structure, the order statistics can also be incrementally updated. By employing a branch-and-bound path selection algorithm with above techniques, this paper shows that selecting an optimal set of paths for a multi-million-gate design can be performed efficiently. Compared to the state-of-the-art, experimental results show both the efficiency of our algorithms and better quality of our path selection.

On the preconditioner of conjugate gradient method: a power grid simulation perspective

Preconditioned Conjugate Gradient (PCG) method has been demonstrated to be effective in solving large-scale linear systems for sparse and symmetric positive definite matrices. One critical problem in PCG is to design a good preconditioner, which can significantly reduce the runtime while keeping memory usage efficient. Universal preconditioners are simple and easy to construct, but their effectiveness is highly problem-dependent. On the other hand, domain-specific preconditioners that explore the underlying physical meaning of the matrices usually work better, but are difficult to design. In this paper, we study the problem in the context of power grid simulation, and develop a novel preconditioner based on the power grid structure through simple circuit simulations. Experimental results show 43% reduction in the number of iterations and 23% speedup over existing universal preconditioners.

Efficient Decoupling Capacitance Budgeting Considering Operation and Process Variations

This paper solves the variation-aware decoupling capacitance (decap) budgeting problem. Unlike previous works which only consider worst case design, for the first time, we consider the input of both process variation and operation variation for decap budgeting. A novel stochastic current model is proposed that efficiently and accurately captures temporal correlation between clock cycles, logic-induced correlation between ports, and current variation due to process variation with spatial correlation. An iterative alternative programming algorithm that is applicable to a variety of current models is then developed. Compared with the baseline model which assumes maximum current peaks at all ports, the model considering temporal correlation reduces noise by up to 5times, and the model considering both temporal and logic-induced correlations reduces noise by up to 17times. Compared with using deterministic process parameters, considering process variation (in particular Leff variation) reduces the mean noise by up to 4times and 3sigma noise by up to 13times when both applying the current model with temporal and logic-induced correlations. Note that stochastic optimization has been used mainly for process variation in the literature, but this paper convincingly demonstrate that stochastic optimization considering operation variation is effective to reduce overdesign introduced by worst case design for power integrity. Such stochastic optimization has a wide scope of applications to design problems. To the best of our knowledge, this is the first in-depth study on decap insertion for power network design considering current correlations including process variation.

QuickYield: an efficient global-search based parametric yield estimation with performance constraints

With technology scaling down to 90nm and below, many yield-driven design and optimization methodologies have been proposed to cope with the prominent process variation and to increase the yield. A critical issue that affects the efficiency of those methods is to estimate the yield when given design parameters under variations. Existing methods either use Monte Carlo method in performance domain where thousands of simulations are required, or use local search in parameter domain where a number of simulations are required to characterize the point on the yield boundary defined by performance constraints. To improve efficiency, in this paper we propose QuickYield, a yield surface boundary determination by surface-point finding and global-search. Experiments on a number of different circuits show that for the same accuracy, QuickYield is up to 519X faster compared with the Monte Carlo approach, and up to 4.7X faster compared with YENSS, the fastest approach reported in literature.

On the Efficacy of Through-Silicon-Via Inductors

Through-silicon-vias (TSVs) can potentially be used to implement inductors in 3-D integrated systems for minimal footprint and large inductance. However, different from conventional 2-D spiral inductors, TSV inductors are fully buried in the lossy substrate, thus suffering from low quality factors. In this paper, we systematically examine how various process and design parameters affect their performance. A few interesting phenomena that are unique to TSV inductors are observed. We then propose a novel shield mechanism utilizing the microchannel, a technique conventionally used for heat removal, to reduce the substrate loss. The technique increases the quality factor and inductance of the TSV inductor by up to 21× and 17×, respectively. Finally, since full-wave simulations of 3-D structures are time-consuming, we develop a set of compressed sensing-based design strategies for microchannel-shielded TSV inductors, which only requires a minimal number of simulations. It enables us to implement microchannel-shielded TSV inductors of up to 5.44× reduced area compared with spiral inductors of the same design specs (quality factor, inductance, and frequency). To the best of our knowledge, this is the very first in-depth study on TSV inductors to make them practical for high-frequency applications. We hope our study shall point out a new and exciting research direction for 3-D integrated circuit designers.

An Analytical Placement Framework for 3-D ICs and Its Extension on Thermal Awareness

In this paper, we present a high-quality analytical 3-D placement framework. We propose using a Huber-based local smoothing technique to work with a Helmholtz-based global smoothing technique to handle the nonoverlapping constraints. The experimental results show that this analytical approach is effective for achieving tradeoffs between the wirelength and the through-silicon-via (TSV) number. Compared to the state-of-the-art 3-D placer ntuplace3d, our placer achieves more than 20% wirelength reduction, on average, with a similar number of TSVs. Furthermore, we extend this analytical 3-D placement framework with thermal awareness. While 2-D thermal-aware placement simply follows uniform power distribution to minimize temperature, we show that the same criterion does not work for 3-D ICs. Instead, we are able to prove that when the TSV area in each bin is proportional to the lumped power consumption of that bin and the bins in all tiers directly above it, the peak temperature is minimized. Based on this criterion, we implement thermal awareness in our analytical 3-D placement framework. Compared with a TSV oblivious method, which only results in an 8% peak temperature reduction, our method reduces the peak temperature by 34%, on average, with slightly less wirelength overhead. These results suggest that considering the thermal effects of TSVs is necessary and effective during the placement stage.

Circuit simulation based obstacle-aware Steiner routing

Steiner routing is a fundamental yet NP-hard problem, in VLSI design and other research fields. In this paper, we propose to model the routing graph by an RC network with routing terminals as input ports and Hanan nodes as output ports. We show that the faster an output reaches its peak, the higher the possibility for the correspondent Hanan node to be a Steiner point. Iteratively adding one or multiple selected Steiner points to build and improve Steiner trees leads to 1-cktSteiner and Blocked-cktSteiner (in short, B-cktSteiner) algorithms, respectively. When there are no routing obstacles, 1-cktSteiner obtains similar wirelength compared with the best existing algorithm FastSteiner. Both are less than 1% worse than the exact solution, but 1-cktSteiner is up to 11.3times faster than FastSteiner. Compared with the fastest existing heuristic FLUTE, B-cktSteiner has similar runtime but up to 1.9% shorter wirelength. Different from FastSteiner and FLUTE which are only applicable to non-obstacle cases, 1-cktSteiner and B-cktSteiner can be applied to routing with obstacles with minimal runtime increase. Compared with the best existing obstacle-avoiding algorithm An-OARS Man, 1-cktSteiner has similar runtime and reduces wirelength by 6.12%. and B-cktSteiner has an average speedup of 352times with a similar wirelength

Fast analysis of structured power grid by triangularization based structure preserving model order reduction

In this paper, a triangularization based structure preserving (TBS) model order reduction is proposed to verify power integrity of on-chip structured power grid. The power grid is represented by interconnected basic blocks according to current density, and basic blocks are further clustered into compact blocks, each with a unique pole distribution. Then, the system is transformed into a triangular system, where compact blocks are in its diagonal and the system poles are determined only by the diagonal blocks. Finally, projection matrices are constructed and applied for compact blocks separately. The resulting macromodel has more matched poles and is more accurate than the one using flat projection. It is also sparse and enables a two-level analysis for simulation time reduction. Compared to existing approaches, TBS in experiments achieves up to 133times and 109times speedup in macromodel building and simulation respectively, and reduces waveform error by 33times