물리적 설계 자동화에서 표준셀 합성 및 최적화와 설계 품질 예측 방법론

학위논문(박사) -- 서울대학교대학원 : 공과대학 전기·정보공학부, 2023. 2. 김태환.In the physical design of chip implementation, designing high-quality standard cell layout and accurately predicting post-route DRV (design rule violation) at an early stage is an important problem, especially in advanced technology nodes. This dissertation presents two methodologies that can contribute to improving the design quality and design turnaround time of physical design flow. Firstly, we propose an integrated approach to the two problems of transistor folding and placement in standard cell layout synthesis. Precisely, we propose a globally optimal algorithm of search tree based design space exploration, devising a set of effective speeding up techniques as well as dynamic programming based fast cost computation. In addition, our algorithm incorporates the minimum oxide diffusion jog constraint, which closely relies on both of transistor folding and placement. Through experiments with the transistor netlists and design rules in advanced node, our proposed method is able to synthesize fully routable cell layouts of minimal size within a very fast time for each netlist, outperforming the cell layout quality in the manual design. Secondly, we propose a novel ML based DRC hotspot prediction technique, which is able to accurately capture the combined impact of pin accessibility and routing congestion on DRC hotspots. Precisely, we devise a graph, called pin proximity graph, that effectively models the spatial information on cell I/O pins and the information on pin-to-pin disturbance relation. Then, we propose a new ML model, which tightly combines GNN (graph neural network) and U-net in a way that GNN is used to embed pin accessibility information abstracted from our pin proximity graph while U-net is used to extract routing congestion information from grid-based features. Through experiments with a set of benchmark designs using advanced node, our model outperforms the existing ML models on all benchmark designs within the fast inference time in comparison with that of the state-of-the-art techniques.칩 구현의 물리적 설계 단계에서, 높은 성능의 표준 셀 설계와 배선 연결 이후 조기에 설계 규칙 위반을 정확히 예측하는 것은 최신 공정에서 특히 중요한 문제이다. 본 논문에서는 물리적 설계에서의 설계 품질과 총 설계 시간 향상을 달성할 수 있는 두 가지 방법론을 제안한다. 먼저, 본 논문에서는 표준 셀 레이아웃 합성에서 트랜지스터 폴딩과 배치를 종합적으로 진행할 수 있는 방법론을 논한다. 구체적으로 탐색 트리 기반의 최적화 알고리즘과 동적 프로그래밍 기반 빠른 비용 계산 방법과 여러 속도 개선 기법을 제안한다. 여기에 더해, 최신 공정에서 트랜지스터 폴딩과 배치로 인해 발생할 수 있는 최소 산화물 확산 영역 설계 규칙을 고려하였다. 최신 공정에 대한 표준 셀 합성 실험 결과, 본 논문에서 제안한 방법이 설계 전문가가 수동으로 설계한 것 대비 높은 성능을 보이고, 설계 시간도 매우 짧음을 보인다. 두번째로, 본 논문에서는 셀 배치 단계에서 핀 접근성과 연결 혼잡으로 인한 영향을 종합적으로 고려할 수 있는 머신 러닝 기반 설계 규칙 위반 구역 예측 방법론을 제안한다. 먼저 표준 셀의 입/출력 핀의 물리적 정보와 핀과 핀 사이 방해 관계를 효과적으로 표현할 수 있는 핀 근접 그래프를 제안하고, 그래프 신경망과 유넷 신경망을 효과적으로 결합한 새로운 형태의 머신 러닝 모델을 제안한다. 이 모델에서 그래프 신경망은 핀 근접 그래프로부터 핀 접근성 정보를 추출하고, 유넷 신경망은 격자 기반 특징으로부터 연결 혼잡 정보를 추출한다. 실험 결과 본 논문에서 제안한 방법은 이전 연구들 대비 더 빠른 예측 시간에 더 높은 예측 성능을 달성함을 보인다.1 Introduction 1 1.1 Standard Cell Layout Synthesis 1 1.2 Machine Learning for Electronic Design Automation 6 1.3 Prediction of Design Rule Violation 8 1.4 Contributions of This Dissertation 11 2 Standard Cell Layout Synthesis of Advanced Nodes with Simultaneous Transistor Folding and Placement 14 2.1 Motivations 14 2.2 Algorithm for Standard Cell Layout Synthesis 16 2.2.1 Problem Definition 16 2.2.2 Overall Flow 18 2.2.3 Step 1: Generation of Folding Shapes 18 2.2.4 Step 2: Search-tree Based Design Space Exploration 20 2.2.5 Speeding up Techniques 23 2.2.6 In-cell Routability Estimation 28 2.2.7 Step 3: In-cell Routing 30 2.2.8 Step 4: Splitting Folding Shapes 35 2.2.9 Step 5: Relaxing Minimum-area Constraints 37 2.3 Experimental Results 38 2.3.1 Comparison with ASAP 7nm Cell Layouts 40 2.3.2 Effectiveness of Dynamic Folding 42 2.3.3 Effectiveness of Speeding Up Techniques 43 2.3.4 Impact of Splitting Folding Shape 48 2.3.5 Runtime Analysis According to Area Relaxation 51 2.3.6 Comparison with Previous Works 52 3 Pin Accessibility and Routing Congestion Aware DRC Hotspot Prediction using Graph Neural Network and U-Net 54 3.1 Preliminary 54 3.1.1 Graph Neural Network 54 3.1.2 Fully Convolutional Network 56 3.2 Proposed Prediction Methodology 57 3.2.1 Overall Flow 57 3.2.2 Pin Proximity Graph 58 3.2.3 Grid-based Features 61 3.2.4 Overall Architecture of PGNN 64 3.2.5 GNN Architecture in PGNN 64 3.2.6 U-net Architecture in PGNN 66 3.2.7 Final Prediction in PGNN 66 3.3 Experimental Results 68 3.3.1 Experimental Setup 68 3.3.2 Analysis on PGNN Performance 71 3.3.3 Comparison with Previous Works 72 3.3.4 Adaptation to Real-world Designs 81 3.3.5 Handling Data Imbalance Problem in Regression Model 86 4 Conclusions 92 4.1 Chapter 2 92 4.2 Chapter 3 93박

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Cell layout is a critical step in the design process of computer chips. A cell is a logic function or storage element implemented in CMOS technology by transistors connected with wires. As each cell is used many times on a chip, improvements of a single cell layout can have a large effect on the overall chip performance. In the past years increasing difficulty to manufacture small feature sizes has lead to growing complexity of design rules. Producing cell layouts which are compliant with design rules and at the same time optimized w.r.t. layout size has become a difficult task for human experts. In this thesis we present BonnCell, a cell layout generator which is able to fully automatically produce design rule compliant layouts. It is able to guarantee area minimality of its layouts for small and medium sized cells. For large cells it uses a heuristic which produces layouts with a significant area reduction compared to those created manually. The routing problem is based on the Vertex Disjoint Steiner Tree Packing Problem with a large number of additional design rules. In Chapter 4 we present the routing algorithm which is based on a mixed integer programming (MIP) formulation that guarantees compliance with all design rules. The algorithm can also handle instances in which only part of the transistors are placed to check whether this partial placement can be extended to a routable placement of all transistors. Chapter 5 contains the transistor placement algorithm. Based on a branch and bound approach, it places transistors in turn and achieves efficiency by pruning parts of the search tree which do not contain optimum solutions. One major contribution of this thesis is that BonnCell only outputs routable placements. Simply checking the routability for each full placement in the search tree is too slow in practice, therefore several speedup strategies are applied. Some cells are too large to be solved by a single call of the placement algorithm. In Chapter 7 we describe how these cells are split up into smaller subcells which are placed and routed individually and subsequently merged into a placement and routing of the original cell. Two approaches for dividing the original cell into subcells are presented, one based on estimating the subcell area and the other based on solving the Min Cut Linear Arrangement Problem. BonnCell has enabled our cooperation partner IBM to drastically improve their cell design and layout process. In particular, a team of human experts needed several weeks to find a layout for their largest cell, consisting of 128 transistors. BonnCell processed this cell without manual intervention in 3 days and its layout uses 15% less area than the layout found by the human experts

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