Co-optimizing placement with congestion is integral to achieving high-quality designs. This paper presents GOALPlace, a learning-based approach to improving placement congestion by controlling cell density. It efficiently learns from an EDA tool's post-route optimized results and uses an empirical Bayes technique to adapt the target to a specific placer's solutions, effectively beginning with the end in mind. Our method enhances correlation with the tool's router and timing-opt engine, while solving placement globally without expensive incremental congestion estimation and mitigation methods. A statistical analysis with hierarchical netlist clustering establishes the importance of density and the potential for an adequate cell density target across placements. Our experiments show that our method, when integrated into an academic GPU-accelerated global placer, consistently produces macro and standard cell placements that match or exceed the quality of commercial tools. Our empirical Bayes methodology also shows a substantial quality improvement over leading academic mixed-size placers, achieving up to 10× fewer design rule check (DRC) violations, a 5% decrease in wirelength, and a 30% and 60% reduction in worst and total negative slack (WNS/TNS).

Modern VLSI design flows necessitate fast and high-quality global routers. In this paper, we introduce DGR, a differentiable global router capable of concurrent optimization for hundreds of thousands of nets 1. Our innovation lies in the development of a routing Directed Acyclic Graph (DAG) forest to represent the 2D pattern routing space for all nets, enabling coordinated selection of Steiner trees and 2-pin routing paths from a global perspective. For efficient search within the DAG forest, we relax the discrete search space to be continuous and develop a differentiable solver accelerated by deep learning toolkits on GPUs. Experimental results demonstrate that DGR substantially mitigates routing overflow while concurrently reducing total wirelengths from 0.95% to 4.08% and via numbers from 1.28% to 2.54% in congested testcases compared to state-of-the-art academic global routers. Additionally, DGR exhibits favorable scalability in both runtime and memory with respect to the number of nets.

Buffering is a prevalent interconnect optimization technique to help timing closure and is often performed after placement. A common buffering approach is to construct a Steiner tree and then buffers are inserted on the tree based on Ginneken-Lillis style algorithm. Such an approach is difficult to scale with large nets. Our work attempts to solve this problem with a generative machine-learning (ML) approach without Steiner tree construction. Our approach can extract and reuse knowledge from high quality samples and therefore has significantly improved scalability. A generative ML framework, BufFormer, is proposed to construct abstract tree topology while simultaneously determining buffer sizes & locations. A baseline method, FLUTE-based Steiner tree construction followed by Ginneken-Lillis style buffer insertion, is implemented to generate training samples. After training, BufFormer can produce solutions for unseen nets highly comparable to baseline results with a correlation coefficient 0.977 in terms of buffer area and 0.934 for driver-sink delays. On average, BufFormer-generated tree achieves similar delays with slightly larger buffer area. And up to 160X speedup can be achieved for large nets when running on a GPU over the baseline on a single CPU thread.

Chip-level clock tree synthesis (CCTS) is a key problem that arises in complex system-on-a-chip designs. A key requirement of CCTS is to balance the clock-trees belonging to different IPs such that the entire tree has a small skew across all process corners. Achieving this is difficult because the clock trees in different IPs might be vastly different in terms of their clock structures and cell/interconnect delays. The chip-level clock tree is expected to compensate for these differences and achieve good skews across all corners. Also, CCTS is expected to reduce clock divergence between IPs that have critical timing paths between them. Reducing clock divergence reduces the maximum possible clock skew in the critical paths between the IPs and thus improves yield. This paper proposes effective CCTS algorithms to simultaneously reduce multicorner skew and clock divergence. Experimental results on several test-cases indicate that our methods achieve 30% reduction in the clock divergence with significantly improved multicorner skew variance, at the cost of 2% increase in buffer area and 1% increase in wirelength.

Clock mesh networks are well known for their variation tolerance. But their usage is limited to high-end designs due to the significantly high resource requirements compared to clock trees and the lack of automatic mesh synthesis tools. Most existing works on clock mesh networks either deal with semi-custom design or perform optimizations on a given clock mesh. However, the problem of obtaining a good initial clock mesh has not been addressed. Also, the problem of achieving a smooth tradeoff between variation tolerance and resource requirements has not been addressed adequately. In this paper, we present our MeshWorks framework, the first comprehensive automated framework for planning, synthesis, and optimization of clock mesh networks that addresses the above issues. Experimental results suggest that our algorithms can achieve an additional reduction of 31% in buffer area, 21% in wirelength, and 23% in power, compared to the best previous work, with similar worst case maximum frequency. We also demonstrate the effectiveness of our framework under several practical issues such as blockages, multiple clocks, uneven load distribution, and electromigration violations.

NBTI (Negative Bias Temperature Instability) has emerged as the dominant PMOS device failure mechanism for sub-100 nm VLSI designs. There is little research to quantify its impact on skew of clock trees. This paper demonstrates a mathematical framework to compute the impact of NBTI on gating-enabled clock tree considering their workload dependent temperature variation. Circuit design techniques are proposed to deal with NBTI induced clock skew by achieving balance in NBTI degradation of clock devices. Our technique achieves up-to 70% reduction in clock skew degradation with miniscule (<0.1%) power and area penalty.

A leaf-level clock mesh is known to be very tolerant to variations (Restle et al., 2001). However, its use is limited to a few high-end designs because of the high power/resource requirements and lack of automatic mesh synthesis tools. Most existing works on clock mesh (Restle et al., 2001) either deal with semi-custom design or perform optimizations on a given clock mesh. However, the problem of obtaining a good initial clock mesh has not been addressed. Similarly, the problem of achieving a smooth tradeoff between skew and power/resources has not been addressed adequately. In this work, we present MeshWorks, the first comprehensive automated framework for planning, synthesis and optimization of clock mesh networks with the objective of addressing the above issues. Experimental results suggest that our algorithms can achieve an additional reduction of 26% in buffer area, 19% in wirelength and 18% in power, compared to the recent work of Venkataraman et al., (2006) with similar worst case maximum frequency under variation.

A key problem that arises in System-on-a-Chip (SOC) designs of today is the Chip-level Clock Tree Synthesis (CCTS). CCTS is done by merging all the clock trees belonging to different IPs per chip specifications. A primary requirement of CCTS is to balance the sub-clock-trees belonging to different IPs such that the entire tree has a small skew across all process corners. This helps in timing closure across all the design corners. Another important requirement of CCTS is to reduce clock divergence between IPs that have critical timing paths between them, thereby reducing maximum possible clock skew in the critical paths and thus improves yield. In this work, we propose effective CCTS algorithms to simultaneously reduce multi-corner skew and clock divergence. To the best of our knowledge, this is the first work that attempts to solve this practically important problem. Experimental results on several testcases indicate that our methods achieve 10%-31%(20% on average) clock divergence reduction and between 16--64ps skew reduction (1.6%-6.4% of cycle time for a 1GHz clock) with less than 0.5% increase in buffer area/wirelength compared to existing CTS algorithms.

Clock network synthesis is a key step in the ultra deep sub-micron (UDSM) VLSI Designs. Most existing clock network synthesis algorithms are designed for nominal operating condition, which are insufficient to address the growing problem of process, voltage and temperature (PVT) fluctuations. Link based clock networks have been suggested as a possible way of reducing skew variability [1-3]. However, [1,2] deal with only unbuffered clock networks, making them impractical. In [3], the problem of constructing a link based buffered clock network has been addressed . But [3] requires special kind of tunable buffers, which might consume more area/power and might not be available for all designs. Also, [3] uses SPICE for tuning the locations of internal nodes and buffer delays, thereby making it slow even for clock networks with a few hundred sinks. In this paper, we propose a unified algorithm for synthesizing a variation tolerant, balanced buffered clock network with cross links. Our approach can make use of ordinary buffers and does not require SPICE for clock network synthesis. SPICE based Monte Carlo simulations show that our methodology results in a buffered clock network with 50% reduction in skew variability with minimal increase in wire-length, buffer area and CPU time.

Increasingly significant variational effects present a great challenge for delivering desired clock skew reliably. Nontree clock network has been recognized as a promising approach to overcome the variation problem. Existing nontree clock routing methods are restricted to a few simple or regular structures, and often consume excessive amounts of wirelength. This paper suggests to construct a low-cost nontree clock network by inserting crosslinks in a given clock tree. The effects of the link insertion on clock skew variability are analyzed. Based on the analysis, this paper proposes two link insertion schemes that can quickly convert a clock tree to a nontree with significantly lower skew variability and very limited wirelength increase. In these schemes, the complicated nontree delay computation is circumvented. Further, they can be applied to the recently popular nonzero skew routing easily. The effectiveness of the proposed techniques has been validated through SPICE-based Monte Carlo simulations.

Under modern very large-scale integrated technology, process variations greatly affect circuit performance, especially clock skew, which is very timing sensitive. Unwanted skew due to process variation forms a bottleneck, preventing further improvement on clock frequency. Impact from intrachip interconnect variation is becoming remarkable and is difficult to be modeled efficiently due to its distributive nature. Through wire shaping analysis, the authors establish an analytical bound for the unwanted skew due to wire width variation, which is a nonnegligible factor among interconnect variations. Experimental results on benchmark circuits show that this bound is safer, tighter, and computationally faster than similar existing approach.

Clock skew is becoming increasingly difficult to control due to variations. Link based non-tree clock distribution is a cost-effective technique for reducing clock skew variations. However, previous works based on this technique were limited to unbuffered clock networks and neglected spatial correlations in the experimental validation. In this work, we overcome these shortcomings and make the link based non-tree approach feasible for realistic designs. The short circuit risk and multi-driver delay issues in buffered non-tree clock networks are investigated. Our approach is validated with SPICE based Monte Carlo simulations, considering spatial correlations among variations. The experimental results show that our approach can reduce the maximal skew by 47%, improve the skew yield from 15% to 73% on average with a decrease on the total wire and buffer capacitance.

In the nanometer VLSI technology, the variation effects like manufacturing variation, power supply noise, temperature etc. become very significant. As one of the most vital nets in any synchronous VLSI chip, the Clock Distribution Network (CDN) is especially sensitive to these variations. Recently proposed link-based non-tree [1] addresses this problem by constructing a non-tree that is significantly more tolerant to variations when compared to a clock tree. Although the two algorithms proposed in [1] are effective in reducing the skew variability, they have a few drawbacks including high complexity, lengthy links and uneven link distribution across the clock network. In this paper, we propose two new algorithms that can overcome these disadvantages. The effectiveness of the proposed algorithms has been validated using HSPICE based Monte Carlo simulations. Experimental results show that the new algorithms are able to achieve the same or better skew reduction with an average of 5% wire length increase when compared to the 15% wire length increase of the existing algorithms in [1]. Moreover, the new algorithms scale extremely well to big clock networks, i.e., the bigger the clock network, the less overall link cost (less than 2% for the biggest benchmark we have).

Increasingly significant variational effects present a great challenge for delivering desired clock skew reliably. Non-tree clock network has been recognized as a promising approach to overcome the variation problem. Existing non-tree clock routing methods are restricted to a few simple or regular structures, and often consume excessive amount of wire-length. In this paper, we suggest to construct a low cost non-tree clock network by inserting cross links in a given clock tree. The effects of the link insertion on clock skew variability are analyzed. Based on the analysis, we propose two link insertion schemes that can quickly convert a clock tree to a non-tree with significantly lower skew variability and very limited wirelength increase. In these schemes, the complicated non-tree delay computation is circumvented. Further, they can be applied to the recently popular non-zero skew routing easily. Experimental results on benchmark circuits show that this approach can achieve significant skew variability reduction with less than 2 increase of wirelength.