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ATSim3D: Towards Accurate Thermal Simulator for Heterogeneous 3D-IC Systems Considering Nonlinear Leakage and Conductivity

Qipan Wang, Tianxiang Zhu, Yibo Lin, Runsheng Wang, Ru Huang

TL;DR

The paper tackles the challenge of accurate, high-resolution thermal simulation for nonlinear and heterogeneous 3D-ICs by introducing ATSim3D, a global-local framework that couples a compact global model with local finite-volume solves and employs Kirchhoff transformation to handle temperature-dependent conductivity. Through iterative updates of leakage and conductivity and parallelized local computations, ATSim3D achieves significant speedups (average around $40\times$) over rigorous solvers like COMSOL while maintaining low errors (relative $<3\%$, max $<3^\circ\mathrm{C}$) at resolutions up to $4096\times4096$. The approach demonstrates strong performance across Mono3D and TSV-based 3D-ICs, delivering a state-of-the-art high-resolution capability and enabling practical thermal-aware design for next-generation 3D integration. Overall, ATSim3D provides a scalable, multi-scale solution that effectively models nonlinear thermal effects in heterogeneous 3D-ICs with substantial efficiency gains.

Abstract

Thermal simulation plays a fundamental role in the thermal design of integrated circuits, especially 3D ICs. Current simulators require significant runtime for high-resolution simulation, and dismiss the complex nonlinear thermal effects, such as nonlinear thermal conductivity and leakage power. To address these issues, we propose ATSim3D, a thermal simulator for simulating the steady-state temperature profile of nonlinear and heterogeneous 3D IC systems. We utilize the global-local approach, combining a compact thermal model at the global level, and a finite volume method at the local level. We tackle the nonlinear effects with Kirchhoff transformation and iteration. ATSim3D enables local-level parallelization that helps achieve an average speedup of 40x compared to COMSOL, with a relative error <3% and a state-of-the-art resolution of 4096 x 4096, holding promise for enhancing thermal-aware design in 3D ICs.

ATSim3D: Towards Accurate Thermal Simulator for Heterogeneous 3D-IC Systems Considering Nonlinear Leakage and Conductivity

TL;DR

The paper tackles the challenge of accurate, high-resolution thermal simulation for nonlinear and heterogeneous 3D-ICs by introducing ATSim3D, a global-local framework that couples a compact global model with local finite-volume solves and employs Kirchhoff transformation to handle temperature-dependent conductivity. Through iterative updates of leakage and conductivity and parallelized local computations, ATSim3D achieves significant speedups (average around ) over rigorous solvers like COMSOL while maintaining low errors (relative , max ) at resolutions up to . The approach demonstrates strong performance across Mono3D and TSV-based 3D-ICs, delivering a state-of-the-art high-resolution capability and enabling practical thermal-aware design for next-generation 3D integration. Overall, ATSim3D provides a scalable, multi-scale solution that effectively models nonlinear thermal effects in heterogeneous 3D-ICs with substantial efficiency gains.

Abstract

Thermal simulation plays a fundamental role in the thermal design of integrated circuits, especially 3D ICs. Current simulators require significant runtime for high-resolution simulation, and dismiss the complex nonlinear thermal effects, such as nonlinear thermal conductivity and leakage power. To address these issues, we propose ATSim3D, a thermal simulator for simulating the steady-state temperature profile of nonlinear and heterogeneous 3D IC systems. We utilize the global-local approach, combining a compact thermal model at the global level, and a finite volume method at the local level. We tackle the nonlinear effects with Kirchhoff transformation and iteration. ATSim3D enables local-level parallelization that helps achieve an average speedup of 40x compared to COMSOL, with a relative error <3% and a state-of-the-art resolution of 4096 x 4096, holding promise for enhancing thermal-aware design in 3D ICs.
Paper Structure (21 sections, 15 equations, 6 figures, 5 tables)

This paper contains 21 sections, 15 equations, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. 3D-IC Configurations
  4. Thermal Models
  5. Nonlinear thermal PDE
  6. Previous works
  7. Problem Formulation
  8. Whole Framework
  9. Motivation
  10. Global Simulation
  11. Local Simulation
  12. Kirchhoff transformation
  13. Continuity Conditions
  14. Finite Volume Method
  15. Parallelization
  16. ...and 6 more sections

Figures (6)

  • Figure 1: Temperature difference induced by considering the (a) nonlinear thermal conductivity of Si and (b) nonlinear leakage power in a TSV-based 3D-IC (a $4\times4$ TSV array in the middle, shown by blue circles), compared to the linear case.
  • Figure 2: Cross-section of two 3D-IC structures for (a) a Mono3D-IC with 2 active layers, (b) a two-tier TSV-based 3D-IC.
  • Figure 3: The ATSim3D simulation flow, consisting of iterations between the coarse level and fine level simulation.
  • Figure 4: The hierarchical partition of the whole system. From left to right: whole package, global coarse grid, and local fine grid. The geometric dimensions and unknown variables are indicated.
  • Figure 5: The relation between the error of ATSim3D in TSV3D-IV and (a) the number of iterations, as well as (b) the global grid resolutions, with each coarse grid partitioned into $16\times16$ fine grids.
  • ...and 1 more figures

Theorems & Definitions (1)

  • proof