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Analytical Heterogeneous Die-to-Die 3D Placement with Macros

Yuxuan Zhao, Peiyu Liao, Siting Liu, Jiaxi Jiang, Yibo Lin, Bei Yu

TL;DR

The paper introduces an analytical framework for 3D mixed-size placement in heterogeneous F2F bonded 3D ICs, coupling a dedicated density model with a bistratal wirelength formulation and a novel 3D preconditioner to handle macros and standard cells in a 3D space. A MILP-based macro-rotation assignment and GPU-accelerated implementation enable fast convergence and high-quality results, demonstrated by a 5.9% quality-score improvement over the ICCAD 2023 first place with 4.0x speedup, and further validation on modern RISC-V designs showing substantial wirelength reductions and large runtime gains. The flow combines 3D mixed-size global placement, macro-rotation optimization, multi-die 2D placement, and legalization/detailed placement, with adaptive 3D density accumulation and a 3D prefix-sum technique to efficiently handle macro density. Overall, the approach advances efficient, scalable placement for heterogeneous 3D ICs by explicitly modeling die-to-die interfaces, HBTs, and macro interactions in a GPU-accelerated, optimization-driven pipeline.

Abstract

This paper presents an innovative approach to 3D mixed-size placement in heterogeneous face-to-face (F2F) bonded 3D ICs. We propose an analytical framework that utilizes a dedicated density model and a bistratal wirelength model, effectively handling macros and standard cells in a 3D solution space. A novel 3D preconditioner is developed to resolve the topological and physical gap between macros and standard cells. Additionally, we propose a mixed-integer linear programming (MILP) formulation for macro rotation to optimize wirelength. Our framework is implemented with full-scale GPU acceleration, leveraging an adaptive 3D density accumulation algorithm and an incremental wirelength gradient algorithm. Experimental results on ICCAD 2023 contest benchmarks demonstrate that our framework can achieve 5.9% quality score improvement compared to the first-place winner with 4.0x runtime speedup. Additional experiments on modern RISC-V designs further validate the generalizability and superiority of our framework.

Analytical Heterogeneous Die-to-Die 3D Placement with Macros

TL;DR

The paper introduces an analytical framework for 3D mixed-size placement in heterogeneous F2F bonded 3D ICs, coupling a dedicated density model with a bistratal wirelength formulation and a novel 3D preconditioner to handle macros and standard cells in a 3D space. A MILP-based macro-rotation assignment and GPU-accelerated implementation enable fast convergence and high-quality results, demonstrated by a 5.9% quality-score improvement over the ICCAD 2023 first place with 4.0x speedup, and further validation on modern RISC-V designs showing substantial wirelength reductions and large runtime gains. The flow combines 3D mixed-size global placement, macro-rotation optimization, multi-die 2D placement, and legalization/detailed placement, with adaptive 3D density accumulation and a 3D prefix-sum technique to efficiently handle macro density. Overall, the approach advances efficient, scalable placement for heterogeneous 3D ICs by explicitly modeling die-to-die interfaces, HBTs, and macro interactions in a GPU-accelerated, optimization-driven pipeline.

Abstract

This paper presents an innovative approach to 3D mixed-size placement in heterogeneous face-to-face (F2F) bonded 3D ICs. We propose an analytical framework that utilizes a dedicated density model and a bistratal wirelength model, effectively handling macros and standard cells in a 3D solution space. A novel 3D preconditioner is developed to resolve the topological and physical gap between macros and standard cells. Additionally, we propose a mixed-integer linear programming (MILP) formulation for macro rotation to optimize wirelength. Our framework is implemented with full-scale GPU acceleration, leveraging an adaptive 3D density accumulation algorithm and an incremental wirelength gradient algorithm. Experimental results on ICCAD 2023 contest benchmarks demonstrate that our framework can achieve 5.9% quality score improvement compared to the first-place winner with 4.0x runtime speedup. Additional experiments on modern RISC-V designs further validate the generalizability and superiority of our framework.
Paper Structure (12 sections, 28 equations, 5 figures, 1 table)

This paper contains 12 sections, 28 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. 3D Analytical Global Placement
  4. Problem Formulation
  5. Proposed 3D Placement Framework
  6. 3D Mixed-Size Global Placement
  7. MILP Macro Rotation Assignment
  8. Multi-Die 2D Global Placement
  9. Legalization
  10. Detailed Placement
  11. Density and Wirelength Algorithms
  12. Adaptive 3D Density Accumulation

Figures (5)

  • Figure 1: D2D wirelength of a net is the sum of the wirelength of the top net and bottom net. HBTs are on the top-most layer for both dies. Pins connected by a net are in the same color.
  • Figure 2: The overall 3D mixed-size placement flow.
  • Figure 3: Our density model and wirelength model consider instance partitioning explicitly for accurate modeling of heterogeneous technology nodes. The instance attributes are updated dynamically in the global placement stage. The macro size transition is smoothed for stable density optimization.
  • Figure 4: Illustration of die-to-die HPWL wirelength in $x$-axis, the $y$-axis is similar. \ref{['subfig:hpwl-example-a']} The 3D HPWL is inconsistent with the D2D HPWL. The $x$-axis D2D HPWL is larger than the $x$-axis HPWL of the entire bounding box. \ref{['subfig:hpwl-example-b']} With the planar locations fixed, changing the pin partition can significantly reduce the $x$-axis D2D HPWL in some cases.
  • Figure 5: The optimal region $B_{t_e}$ is the region bounded by the median values of the top net box $B_{e}^{+}$ and bottom net box $B_{e}^{-}$. HBT $t_e$ placed outside $B_{t_e}$ will introduce extra wirelength. \ref{['subfig:optimal-region-a']} If $B_{e}^{+}$ and $B_{e}^{-}$ overlap in $x$-axis, the minimal $x$-axis D2D HPWL is $p_{e^{+}}(\bm{x})+p_{e^{-}}(\bm{x})$. \ref{['subfig:optimal-region-b']} If $B_{e}^{+}$ and $B_{e}^{-}$ have no overlap in $x$-axis, the minimal $x$-axis D2D HPWL is $p_{e}(\bm{x})$.

Theorems & Definitions (2)

  • Definition 1: 3D HPWL
  • Definition 2: D2D HPWL