Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Cell Library Characterization for Composite Current Source Models Based on Gaussian Process Regression and Active Learning

Tao Bai, Junzhuo Zhou, Zeyuan Deng, Ting-Jung Lin, Wei Xing, Peng Cao, Lei He

TL;DR

The paper tackles the high data and simulation costs of CCS timing-model characterization by proposing a GPR-based framework augmented with Active Learning to produce uncertainty-aware current-waveform predictions across multiple PVT corners. By leveraging cross-condition correlations and an acquisition strategy, the approach significantly reduces SPICE simulations and storage while achieving high accuracy, demonstrated by an average MAE of $2.05$ ps and MAPE of $2.27\%$. The methodology, featuring a structured initialization-train-predict-until-convergence loop and variational-analysis-driven acquisitions, yields substantial gains in both speed and memory efficiency compared with commercial tools. This work enables scalable, precise CCS characterization for standard-cell libraries in advanced process nodes, with strong practical impact on design timelines and resource utilization.

Abstract

The composite current source (CCS) model has been adopted as an advanced timing model that represents the current behavior of cells for improved accuracy and better capability than traditional non-linear delay models (NLDM) to model complex dynamic effects and interactions under advanced process nodes. However, the high accuracy requirement, large amount of data and extensive simulation cost pose severe challenges to CCS characterization. To address these challenges, we introduce a novel Gaussian Process Regression(GPR) model with active learning(AL) to establish the characterization framework efficiently and accurately. Our approach significantly outperforms conventional commercial tools as well as learning based approaches by achieving an average absolute error of 2.05 ps and a relative error of 2.27% for current waveform of 57 cells under 9 process, voltage, temperature (PVT) corners with TSMC 22nm process. Additionally, our model drastically reduces the runtime to 27% and the storage by up to 19.5x compared with that required by commercial tools.

Cell Library Characterization for Composite Current Source Models Based on Gaussian Process Regression and Active Learning

TL;DR

The paper tackles the high data and simulation costs of CCS timing-model characterization by proposing a GPR-based framework augmented with Active Learning to produce uncertainty-aware current-waveform predictions across multiple PVT corners. By leveraging cross-condition correlations and an acquisition strategy, the approach significantly reduces SPICE simulations and storage while achieving high accuracy, demonstrated by an average MAE of ps and MAPE of . The methodology, featuring a structured initialization-train-predict-until-convergence loop and variational-analysis-driven acquisitions, yields substantial gains in both speed and memory efficiency compared with commercial tools. This work enables scalable, precise CCS characterization for standard-cell libraries in advanced process nodes, with strong practical impact on design timelines and resource utilization.

Abstract

The composite current source (CCS) model has been adopted as an advanced timing model that represents the current behavior of cells for improved accuracy and better capability than traditional non-linear delay models (NLDM) to model complex dynamic effects and interactions under advanced process nodes. However, the high accuracy requirement, large amount of data and extensive simulation cost pose severe challenges to CCS characterization. To address these challenges, we introduce a novel Gaussian Process Regression(GPR) model with active learning(AL) to establish the characterization framework efficiently and accurately. Our approach significantly outperforms conventional commercial tools as well as learning based approaches by achieving an average absolute error of 2.05 ps and a relative error of 2.27% for current waveform of 57 cells under 9 process, voltage, temperature (PVT) corners with TSMC 22nm process. Additionally, our model drastically reduces the runtime to 27% and the storage by up to 19.5x compared with that required by commercial tools.
Paper Structure (22 sections, 6 equations, 3 figures, 4 tables)

This paper contains 22 sections, 6 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. RELATED WORKS AND PRELIMINARIES
  3. Related Works
  4. Gaussian Process Regression
  5. Active Learning
  6. CCS Timing Model Characterization Framework
  7. Problem Formulation
  8. Overview
  9. Design of an Algorithm Using GPR with AL
  10. Initialization.
  11. Gaussian Process Model Training.
  12. Waveform Prediction by Gaussian Process Model.
  13. Uncertainty Evaluation.
  14. Termination Check.
  15. Selected Samples Update.
  16. ...and 7 more sections

Figures (3)

  • Figure 1: Overview of Proposed Standard Cell Characterization Framework for CCS Model Based on GPR and AL
  • Figure 2: Iterative Process in Waveform Estimation for INV X12 Cell at TT corner, 0.88v, 0$^{\circ}$C . (a)Current Waveform Variation. (b)Voltage Waveform Variation. (c)Acquisition Score and Selected Samples Trends.
  • Figure 3: Comparison of storage overhead for CCS model.