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While the VLSI community cares about designs with high yields under process variations, expensive computational costs make conventional yield optimization methods for analog circuits inefficient for industrial applications. In this article, an efficient yield optimization method via the freeze–thaw Bayesian optimization technique is proposed for analog circuits. The yield analysis is integrated into the exploration process of the Bayesian optimization. With a specified Gaussian process regression method, the flexible freeze–thaw Bayesian optimization technique is utilized to automatically guide the search in the design space and control the accuracy of yield analysis in the process space. A performance optimization problem is formulated and solved to mine prior knowledge, and a further speed up is achieved. Experimental results show that the proposed method can gain a $2.47\times $ – $5.73\times $ speedup compared with the state-of-the-art methods, without loss of accuracy. [ABSTRACT FROM AUTHOR]

With the aggressive and amazing scaling of the feature size of semiconductors, hotspot detection has become a crucial and challenging problem in the generation of optimized mask design for better printability. Machine learning techniques, especially deep learning, have attained notable success on hotspot detection tasks. However, most existing hotspot detectors suffer from suboptimal performance due to two-stage flow and less efficient representations of layout features. What is more, most works can only solve simple benchmarks with apparent hotspot patterns like ICCAD 2012 Contest benchmarks. In this article, we first develop a new end-to-end hotspot detection flow where layout feature embedding and hotspot detection are jointly performed. An attention mechanism-based deep convolutional neural network (CNN) is exploited as the backbone to learn embeddings for layout features and classify the hotspots simultaneously. The experimental results demonstrate that our framework achieves accuracy improvement over prior arts with fewer false alarms and faster inference speed on much more challenging benchmarks. [ABSTRACT FROM AUTHOR]

In this article, to accurately estimate the rare failure rates for large-scale circuits (e.g., SRAM) where process variations are modeled as truncated normal distributions in high-dimensional space, we propose a novel truncated scaled-sigma sampling (T-SSS) method. Similar to scaled-sigma sampling (SSS), T-SSS distorts the truncated normal distributions by a scaling factor, resulting in an analytical model for failure rate estimation. By drawing random samples from the distorted distribution and estimating a sequence of scaled failure rates, we can solve all unknown model coefficients and predict the original failure rate by extrapolation. The accuracy of T-SSS is further assessed by estimating its confidence interval (CI) based on resampling. Our numerical results demonstrate that the proposed T-SSS method can achieve superior accuracy over the state-of-the-art method without increasing the computational cost. [ABSTRACT FROM AUTHOR]

As the circuit feature size continuously shrinks down, hotspot detection has become a more challenging problem in modern design for manufacturability flows. Developed deep learning techniques have recently shown their superiorities on hotspot detection tasks. However, existing hotspot detectors can only handle defect detection from one small layout clip each time, thus, may be very time-consuming when dealing with a large full-chip layout. In this article, we develop a new end-to-end framework that can detect multiple hotspots in a large region at a time and promise a better hotspot detection performance. We design a joint auto-encoder and inception module for efficient feature extraction. A two-stage classification and regression framework is designed to detect hotspot with progressive accurate localization, which provides a promising performance improvement. Experimental results show that our framework enables a significant speed improvement over existing methods with higher accuracy and fewer false alarms. [ABSTRACT FROM AUTHOR]

Bayesian optimization is a promising methodology for analog circuit synthesis. However, the sequential nature of the Bayesian optimization framework significantly limits its ability to fully utilize real-world computational resources. In this article, we propose an efficient parallelizable Bayesian optimization algorithm via multiobjective acquisition function ensemble (MACE) to further accelerate the optimization procedure. By sampling query points from the Pareto front of the probability of improvement (PI), expected improvement (EI), and lower confidence bound (LCB), we combine the benefits of state-of-the-art acquisition functions to achieve a delicate tradeoff between exploration and exploitation for the unconstrained optimization problem. Based on this batch design, we further adjust the algorithm for the constrained optimization problem. By dividing the optimization procedure into two stages and first focusing on finding an initial feasible point, we manage to gain more information about the valid region and can better avoid sampling around the infeasible area. After achieving the first feasible point, we favor the feasible region by adopting a specially designed penalization term to the acquisition function ensemble. The experimental results quantitatively demonstrate that our proposed algorithm can reduce the overall simulation time by up to $74\times $ compared to differential evolution (DE) for the unconstrained optimization problem when the batch size is 15. For the constrained optimization problem, our proposed algorithm can speed up the optimization process by up to $15\times $ compared to the weighted EI-based Bayesian optimization (WEIBO) approach, when the batch size is 15. [ABSTRACT FROM AUTHOR]

Layout hotspot detection is of great importance in the physical verification flow. Deep neural network models have been applied to hotspot detection and achieved great successes. The layouts can be viewed as binary images. The binarized neural network (BNN) can thus be suitable for the hotspot detection problem. In this article, we propose a new deep learning architecture based on BNNs to speed up the neural networks in hotspot detection. A new binarized residual neural network is carefully designed for hotspot detection. Experimental results on ICCAD 2012 and 2019 benchmarks show that our architecture outperforms previous hotspot detectors in detecting accuracy and has an 8 × speedup over the best deep learning-based solution. Since the BNN-based model is quite computationally efficient, a good tradeoff can be achieved between the efficiency and performance of the hotspot detector by applying ensemble learning approaches. Experimental results show that the ensemble models achieve better hotspot detection performance than the original with acceptable speed loss. [ABSTRACT FROM AUTHOR]

Dummy filling is widely applied to significantly improve the planarity of topographic patterns for the chemical mechanical polishing process in VLSI manufactures. The main challenge of dummy filling is balancing multiple objectives, such as fill amounts, planarity, parasitic capacitance, etc. An obvious drawback of traditional rule-based dummy filling methods is pattern densities, instead of post-chemical mechanical polishing (CMP) topographies, being included in optimization objectives. Although the quality of post-CMP topography strongly depends on pattern features of layouts, especially the density uniformity, however, experimental results show that chip surface variations are not exactly the same as density variations. In this article, a unified dummy fill insertion optimization framework is proposed, integrated with the multiple starting points-sequential quadratic programming (MSP-SQP) optimization solver, where all objectives are considered without approximation. Inside this framework, a full-chip CMP simulator is first integrated to evaluate the planarity of the chip surface. By selecting the initial points smartly with heuristic prior knowledge, the proposed method can be effectively accelerated. The effectiveness of the proposed algorithm is verified with the average 25.8% improvement of quality compared with rule-based methods. [ABSTRACT FROM AUTHOR]

In this article, a novel asymptotic probability approximation (APA) method is proposed to estimate the overall rare probability of correlated failure events for complex circuits containing a large number of replicated cells (e.g., SRAM bit-cells). The key idea of APA is to approximate the overall circuit failure rate based on a set of carefully defined failure events. An efficient hierarchical subset simulation (H-SUS) method is developed to calculate the aforementioned failure rate and a statistical methodology is further proposed to estimate the confidence interval of APA. Our numerical experiments demonstrate that APA can accurately and reliably estimate the overall failure rate of correlated rare failure events involving more than 20 000 independent random variables. [ABSTRACT FROM AUTHOR]

In this article, we propose an efficient correlated Bayesian inference (CBI) method to estimate the system-level failure rates for large-scale circuit systems over multiple process corners. The key idea is to encode the correlations of circuit performances among the different corners into the prior distributions of several carefully defined failure events. The hyper-parameters of these distributions can be learned from a few simulation samples via Bayesian inference and, next, the system-level failure rates over different corners can be simultaneously estimated by taking into account these prior distributions. An iteratively constrained inference method is further developed to guarantee the numerical stability of the proposed method and legalize all estimated failure rates. The numerical experiments demonstrate that compared to the state-of-the-art algorithm, the proposed method can achieve around $10\times $ runtime reduction without surrendering any accuracy. [ABSTRACT FROM AUTHOR]

Parametric yield estimation over multiple process corners plays an important role in robust circuit design. In this article, we propose a novel Bayesian inference method based on Bernoulli distribution (BI-BD) to efficiently estimate the multicorner yields for binary output circuit. The key idea is to encode the circuit performance correlation among different corners as our prior knowledge. Consequently, after combining a few simulation samples, the yield estimation over all corners can be calibrated via Bayesian inference based on iterative reweighted least squares (IRLS) and expectation maximization (EM). A circuit example demonstrates that the proposed BI-BD method can achieve up to 2.0 × cost reduction over the conventional Monte Carlo method without surrendering any accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a graph-constrained sparse performance modeling method is proposed for analog circuit optimization. It builds sparse polynomial models constrained by an acyclic graph. These models can be used to solve analog optimization problems within local design spaces by using convex semidefinite programming relaxation both efficiently and robustly. Our numerical examples demonstrate that the proposed modeling and optimization method can quickly and accurately converge to a superior solution for analog circuits while the conventional method fails to work. [ABSTRACT FROM AUTHOR]

In this paper, a Bayesian optimization approach is proposed for yield optimization of analog and SRAM circuits. Gaussian process (GP) regression is employed to predict the yield over the design space with uncertainty information. An expected improvement acquisition function is constructed over the model and guides the optimization with a utility-based strategy. These techniques, as a whole, can significantly reduce the number of expensive yield estimations during the optimization procedure. Furthermore, the GP model encodes the observation uncertainties of noise-corrupted objectives, which enables an adaptive control over yield estimations. By ensuring high estimation accuracies for promising designs while tolerating higher variabilities for low-yield ones, the proposed method can significantly cut down the average computational cost of yield estimations without surrendering the accuracy of the final result. Experimental results show that, compared with the state-of-the-art yield optimization approaches, the proposed method can significantly reduce the number of circuit simulations without compromising optimization efficacy. [ABSTRACT FROM AUTHOR]

Interlayer liquid cooling network has been considered as one of the effective cooling mechanisms for heat dissipation in three dimensional integrated circuits (3D ICs). In this paper, an optimization approach is proposed for 3D IC interlayer cooling network design with consideration of cooling energy minimization and thermal constraints. First, a channel patterning technique is proposed which adopts straight-channel patterns and corner-barrier patterns to efficiently reduce the temperature of hotspots in the chip. Second, an iterative channel pruning process is proposed for cooling network optimization that reduces the temperature gradient and cooling energy. Furthermore, algebraic multigrid-preconditioned generalized conjugate residual solver is applied for thermal simulation in this optimization process to achieve better computational efficiency. Experimental results have shown that the proposed optimization approach can produce optimal interlayer cooling networks with 11.3%–61.3% cooling energy savings and 49.3%–59.4% pumping pressure savings in comparison with the first place winner of 2015 computer-aided design contest at International Conference on Computer-Aided Design. [ABSTRACT FROM AUTHOR]

Automated analog circuit design is promising for increasing the design productivity and narrowing the time-to-market, but is facing the bottleneck of tremendous design complexity. In this paper, a simulation-based optimization approach named smart-multiple starting point (MSP) is proposed for analog circuit synthesis. The proposed smart-MSP is based on the framework of MSP optimization, which is shown to be much more efficient than other global optimization methods like simulated annealing, genetic algorithm, particle swarm optimization, etc. Efficient techniques including heuristic-biased starting point selection, sparse regression and probabilistic TABU are developed in smart-MSP and make the algorithm quite smart in a way that the overall optimization process is self-adaptive by learning from the previous local searches and can efficiently produce optimal results to approximate the global optimum. Experiments have demonstrated that the proposed smart-MSP is 2.6-12.5\times faster than the original MSP method, and is 1.3-2100\times faster than other state-of-the-art methods. [ABSTRACT FROM PUBLISHER]

A distance metric of patterns is crucial to hotspot cluster analysis and classification. In this paper, we propose an improved tangent space (ITS)-based distance metric for hotspot cluster analysis and classification. The proposed distance metric is an important extension of the well-developed tangent space method in computer vision. It can handle patterns containing multiple polygons, while the traditional tangent space method can only deal with patterns with a single polygon. It inherits most of the advantages of the traditional tangent space method, e.g., it is easy to compute and is tolerant with small variations or shifts of the shapes. The ITS-based distance metric is a more reliable and accurate metric for hotspot cluster analysis and classification. We also propose a hierarchical density-based clustering method for hotspot clustering. It is more suitable for arbitrary shaped clusters. [ABSTRACT FROM AUTHOR]

Parametric yield estimation is a critical task for design and validation of analog and mixed-signal (AMS) circuits. However, the computational cost for yield estimation based on Monte Carlo (MC) analysis is often prohibitively high, especially when multiple circuit performances and/or environmental corners (e.g., voltage and temperature corners) are considered. In this paper, a novel statistical method named correlation-aided yield estimation (C-YES) is proposed to reduce the computational cost for parametric yield estimation. Our proposed approach exploits the fact that multiple circuit performances over different environmental corners are often correlated. Hence, we can accurately predict the performance value at one corner from the simulation results for other performances and/or corners. Based upon this observation, instead of running a large number of MC simulations to cover all performances and corners, an efficient algorithm is developed to select a small set of the most “informative” simulations that should be performed for yield estimation. Our numerical experiments show that for parametric yield estimation with multiple circuit performances and environmental corners, C-YES achieves 6.5– 9.3 \boldsymbol \times runtime speedups over other conventional methods. [ABSTRACT FROM PUBLISHER]

Efficient performance modeling is an extremely important task for yield analysis and design optimization of analog circuits. In this paper, a novel regression modeling method based on hierarchical shrinkage priors is proposed to construct hybrid performance models with both high accuracy and low computational cost. In particular, the user-defined model templates derived from design equations and the general-purpose orthogonal polynomials are combined together to set up a hybrid dictionary. Next, in order to avoid over-shrinking large model coefficients, a novel regression method based on hierarchical shrinkage priors and variational Bayesian inference is adopted for model fitting. A rail-to-rail operational amplifier example demonstrates that the proposed method achieves up to 40% error reduction over other state-of-the-art approaches without increasing the modeling cost. [ABSTRACT FROM PUBLISHER]

As the feature size keeps scaling down and the circuit complexity increases rapidly, a more advanced hybrid lithography, which combines multiple patterning and electron-beam lithography (EBL), is promising to further enhance the pattern resolution. In this paper, we formulate the layout decomposition problem for this hybrid lithography as a minimum vertex deletion K -partition problem, where K is the number of masks in multiple patterning. Stitch minimization and EBL throughput are considered uniformly by adding a virtual vertex between two feature vertices for each stitch candidate during the conflict graph construction phase. For K = 2 , we propose a primal-dual (PD) method for solving the underlying minimum odd-cycle cover problem efficiently. In addition, a chain decomposition algorithm is employed for removing all “noncyclable” edges. Furthermore, we investigate two versions of the PD method, one with planarization and one without. For K > 2 , we propose a random-initialized local search method that iteratively applies the PD solver. Experimental results show that compared with a two-stage method, our proposed methods reduce the EBL usage by 65.5% with double patterning and 38.7% with triple patterning on average for the benchmarks. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a novel spatial variation modeling method based on hidden Markov tree (HMT) for nanoscale integrated circuits, which could efficiently improve the accuracy of full-wafer/chip spatial variations recovery at extremely low measurement cost. Applying this method, HMT is introduced to set up a statistical model for coefficients after exploring the underlying correlated representation of the spatial variation in the frequency domain. Accordingly, two key inherent properties of the modeling coefficients, i.e., correlations and sparse presentations in the frequency domain, can be captured exactly and the modeling accuracy can be improved evidently. Then, maximum-a-posteriori estimation is applied to formulate the original problem as a convex optimization that could be solved efficiently and robustly. Numerical results based on industrial data demonstrate that the proposed method can achieve superior accuracy over other existing approaches including orthogonal matching pursuit, l 1 -norm regularization, and reweighted l 1 -norm regularization. [ABSTRACT FROM AUTHOR]

Efficiently optimizing large-scale, complex analog systems requires to know the performance tradeoffs for various analog circuit blocks. In this paper, we propose a radically new approach for analog performance tradeoff modeling. Our key idea is to broadly search the rich design knowledge from the Internet, and then mathematically encode the knowledge as high-dimensional performance tradeoff curves that are referred to as Pareto fronts in the literature. Toward this goal, several novel numerical algorithms, such as sparse regression and semi-infinite programming, are developed in order to construct the high-dimensional Pareto front model while guaranteeing its monotonicity. Our numerical examples demonstrate that the proposed modeling technique can accurately capture the high-dimensional Pareto fronts for large-scale analog systems (e.g., analog-to-digital converter) while most traditional methods are limited to low-dimensional Pareto front modeling of small circuit blocks without considering layout parasitics and manufacturing nonidealities. [ABSTRACT FROM PUBLISHER]

In this paper, we propose an efficient oscillation-diminishing cubic Hermite spline interpolation method for the table-based transistor model approximation. We use the cubic Hermite spline interpolation to ensure the continuity of the derivatives. Oscillation-diminishing techniques are proposed to reduce the oscillations (bumps) of interpolations such that both convergence and accuracy are significantly improved. Further, the oscillation-diminishing schemes do not rely on any real derivatives. Therefore, the proposed method can be used to build table models from measured data of the physical devices, where the real derivatives are not always available. In the proposed method, an adaptive approach is employed to generate the nonuniform interpolation grids such that the interpolation accuracy is guaranteed and the memory requirement is minimized. We also propose a novel combined exponential extrapolation method for off-state (leakage) current, which exactly follows the exponential-decay characteristic of that current. Test simulations on several classic industrial analog and mixed-signal circuits show that the proposed method can achieve high accuracy with lower computational cost compared with existing table-based model approximation methods. [ABSTRACT FROM PUBLISHER]

Transient analysis of large-scale power delivery network (PDN) is a critical task to ensure the functional correctness and desired performance of today’s integrated circuits (ICs), especially if significant transient noises are induced by clock and/or power gating due to the utilization of extensive power management. In this paper, we propose an efficient algorithm for PDN transient analysis based on sparse approximation. The key idea is to exploit the fact that the transient response caused by clock/power gating is often localized and the voltages at many other “inactive” nodes are almost unchanged, thereby rendering a unique sparse structure. By taking advantage of the underlying sparsity of the solution structure, a modified conjugate gradient algorithm is developed and tuned to efficiently solve the PDN analysis problem with low computational cost. Our numerical experiments based on standard benchmarks demonstrate that the proposed transient analysis with sparse approximation offers up to $2.2\times $ runtime speedup over other traditional methods, while simultaneously achieving similar accuracy. [ABSTRACT FROM PUBLISHER]

To reduce chip-scale topography variation in chemical mechanical polishing process, dummy fill is widely used to improve the layout density uniformity. Previous researches formulated the density-driven dummy fill problem as a standard linear program (LP). However, solving the huge linear program formed by real-life designs is very expensive and has become the hurdle in deploying the technology. Even though there exist efficient heuristics, their performance cannot be guaranteed. Furthermore, dummy fill can also change the interconnect coupling capacitance which might lead to a significant influence on circuit delay, crosstalk, and power consumption. In this paper, we develop a dummy fill algorithm that can be applied to solve both the traditional density-driven problem and the problem considering fill-induced coupling capacitance impact. The proposed algorithm is both efficient and with provably good performance, which is based on a fully polynomial time approximation scheme by Fleischer for covering LP problems. Moreover, based on the approximation algorithm, we also propose a new greedy iterative algorithm to achieve high quality solutions more efficiently than previous Monte Carlo based heuristic methods. Final experimental results demonstrate the effectiveness and efficiency of our algorithms. [ABSTRACT FROM PUBLISHER]

With increasing process variation, binning has become an important technique to improve the values of fabricated chips, especially in high performance microprocessors where transparent latches are widely used. In this paper, we formulate and solve the binning optimization problem that decides the bin boundaries and their testing order to maximize the profit (considering the test cost) for a transparently-latched circuit. The problem is decomposed into four sub-problems. First, to compute the clock period distribution of the transparently-latched circuit, a sample-based statistical static timing analysis (SSTA) approach is developed which is based on the generalized stochastic collocation method with the sparse grid technique. The minimal clock period on each sample point is found by solving a minimal cycle ratio problem in the constraint graph. Second, a greedy method is proposed to maximize profit considering both the sales revenue and the test cost by iteratively assigning each boundary to its optimal position. Third, an optimal algorithm of O(n\log n) runtime is used to generate the optimal testing order to minimize the test cost, based on alphabetic tree. Last, a simple approach is presented to decide the optimal number of bins, which helps to complete the whole binning scheme with maximal profit. Experiments on all the ISCAS'89 sequential benchmarks with 65 nm technology show 10.68% profit improvement in average. Some comparisons with other methods suggest the advantage of our method. The results also demonstrate that the proposed SSTA method achieves an error of 0.70% and speedup of 110 X in average compared with the Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

Computational complexity has been the primary challenge of many very large scale integration computer-aided design (CAD) applications. The emerging multicore and many-core microprocessors have the potential to offer scalable performance improvements. How to explore the multicore resources to speed up CAD applications is thus a natural question but also a huge challenge for CAD researchers. This paper proposes a methodology to explore concurrency via nondeterministic transactional models, and to program them on multicore processors for CAD applications. Various run-time scheduling implementations on multicore shared-memory machines are discussed and the most efficient one is identified. The proposed methodology is applied to the min-cost flow problem which has been identified as the key problem in many design optimizations, from wire-length optimization in detailed placement to timing-constrained voltage assignment. A concurrent algorithm for min-cost flow has been developed based on the methodology. Experiments on voltage island generation in floorplanning have demonstrated its efficiency and scalable speedup over different numbers of cores. [ABSTRACT FROM PUBLISHER]