Date of Submission

11-10-2025

Date of Award

8-21-2026

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science

Department

Advance Computing and Microelectronics Unit (ACMU-Kolkata)

Supervisor

Sur-Kolay, Susmita

Abstract (Summary of the Work)

Integrated Circuit (IC) technology has progressed significantly over the last six decades, culminating in billions of transistors on a chip. The widely used 193 nm immersion lithography process exceeds modern feature sizes, leading to layout pattern distortions and electrical violations. Mitigation techniques such as Multiple Patterning and Optical Proximity Correction become ineffective below 45 nm, prompting the development of several Next-Generation Lithography (NGL) methods such as Extreme Ultraviolet Lithography (EUVL), Multiple Electron Beam Lithography (MEBL). MEBL employs thousands to millions of e-beams in parallel to overcome throughput limitations. A 2D layout is partitioned into vertical stripes by stitch-lines (SLs), each written by a distinct beam. Beam deflections near SLs cause distortions in the stitch-unfriendly region within a distance of ϵ of an SL. Minimizing these distortions during routing is critical. As routing is NP-hard in conventional lithography, the additional constraints of MEBL pose greater challenges, motivating this thesis to develop enhanced routing strategies for MEBL in VLSI physical design automation. This thesis first addresses the reduction of stitch-induced distortions during global routing. A stitch-avoiding global routing framework that integrates stitch-lines into the routing process is designed. It combines net-shifting strategies with stitch -constrained Integer Linear Programming (ILP) and maze routing to achieve a significant reduction in stitch-line violations compared to earlier approaches. For further reductions, a dedicated full-routing framework by introducing a stitch-avoiding detailed router is designed, which classifies nets by characteristics and applies a multi-stage routing strategy. Layer assignment is integrated within detailed routing, while segment-to-track assignment is formulated as a maximum weighted independent set problem on a segment conflict graph, with weights derived from stitch-line proximity. Combining the stitch-avoiding global and detailed routers yields substantial improvement over conventional routing flows. Beyond lithography-specific routing, the backbone of global routing is a Rectilinear Steiner Minimum Tree (RSMT), which connects a set of n pins of a net on a 2D plane, augmented with Steiner points, with minimum total wirelength under the Manhattan metric. An optimal RSMT construction is NP-hard, existing methods either achieve optimality with exponential/sub-exponential complexity, or produce approximate solutions by using heuristics or reinforcement learning. Here, a machine learning approach for finding an RSMT of a net is proposed, followed by another ML method for the construction of RSMTs of multiple nets concurrently. The input for RSMT construction is the Hanan grid of the pin locations, which can be represented as an image. Supervised training of a Conditional Generative Adversarial Network (cGAN) with data from an existing exponential-time optimal RSMT method enables the generator to produce valid RSMTs with minimal wirelength. To the best of our knowledge, this is the first application of image-to-image translation for RSMT construction, achieving notable improvements in wirelength and runtime over heuristic and RL-based methods. For concurrent RSMT construction, individual Hanan grids of multiple nets are merged into a combined grid graph with node and edge labels for each net. An ILP-based formulation is used to generate group-wise edge-overlap-minimized combined RSMT that acts as the ground truth for our proposed hybrid Graph Neural Network (GNN) model. Experiments show a significant reduction in runtime, group-wise edge-overlap, and wirelength compared to multiple baseline methods. To the best of our knowledge, this is the first successful attempt for the concurrent construction of RSMTs of multiple nets using a hybrid GNN model. Thus, this thesis advances routing for MEBL and efficient RSMT construction for global routing to improve the performance of modern ICs.

Control Number

TH699

DOI

http://164.52.219.250/items/3f09f640-e84d-42e6-8be8-8a6327a0991a

DSpace Identifier

http://hdl.handle.net/10263/7952

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