[Paper Review] Is Leakage Power a Linear Function of Temperature?

Hameedah Sultan, Shashank Varshney+1 more|arXiv (Cornell University)|Sep 10, 2018

Parallel Computing and Optimization Techniques6 references4 citations

TL;DR

This paper investigates whether leakage power in modern CMOS devices can be accurately modeled as a linear function of temperature. Using BSIM 4 and SPICE simulations across 28nm and 7nm technologies, it demonstrates that a linear approximation yields less than 5% error in the 40–80°C range, making it suitable for early-stage design when speed is prioritized over high accuracy.

ABSTRACT

In this work, we present a study of the leakage power modeling techniques commonly used in the architecture community. We further provide an analysis of the error in leakage power estimation using the various modeling techniques. We strongly believe that this study will help researchers determine an appropriate leakage model to use in their work, based on the desired modeling accuracy and speed.

Motivation & Objective

• To evaluate the accuracy and computational efficiency of linear leakage power models in sub-micron CMOS technologies.
• To identify the trade-off between modeling speed and accuracy in architectural leakage power estimation.
• To determine under what conditions a linear approximation of leakage power is sufficient for design-stage simulations.
• To compare various leakage modeling techniques—linear, piecewise linear, polynomial, and exponential—across different technology nodes.
• To guide researchers in selecting appropriate leakage models based on required accuracy and performance constraints.

Proposed method

• Used the simplified BSIM 4 equation to compute subthreshold leakage power as a function of temperature, with parameters calibrated to achieve 0.1W leakage at 45°C.
• Performed SPICE simulations on 28nm HVT and LVT MOSFETs and a 7nm FinFET using predictive models to validate leakage-temperature characteristics.
• Fitted linear and quadratic approximations to the BSIM-based data and computed percentage error relative to the full model.
• Evaluated computation time for linear, quadratic, and full BSIM models across temperature ranges (40–80°C, 0.1°C steps) using MATLAB.
• Reviewed and synthesized results from prior works (Liu et al., Biswas et al., Wan et al.) on linear, exponential, and higher-order polynomial leakage models.
• Implemented and benchmarked various models (linear, exponential, polynomial) to compare time complexity and error rates.

Experimental results

Research questions

• RQ1 Is leakage power approximately linear with temperature in modern sub-micron CMOS devices, particularly in the 40–80°C operating range?
• RQ2 What is the trade-off between computational speed and estimation accuracy when using linear leakage models versus more complex models?
• RQ3 How do piecewise linear, quadratic, and exponential leakage models compare in accuracy and runtime for 28nm and 7nm technologies?
• RQ4 Can a linear model with a single reference point provide sufficient accuracy for architectural-level power estimation?
• RQ5 What is the impact of using multiple expansion points in linear leakage models on estimation error and computational cost?

Key findings

• A linear leakage model introduces less than 5% error in leakage power estimation across the 40–80°C temperature range for 28nm and 7nm technologies.
• The linear model computation time is only 18.73 microseconds, a 75% reduction compared to the full BSIM 4 equation (74.18 μs).
• A quadratic model reduces error to under 1% with only a 12% increase in computation time (21.95 μs), offering a strong accuracy-efficiency trade-off.
• A piecewise linear model with three segments reduces error to less than 0.69%, as reported in prior work, while maintaining low computational overhead.
• Exponential models increase computation time by over 100% compared to linear models and are not justified by the marginal accuracy gain.
• Higher-order models (e.g., fourth-degree polynomial) increase time complexity significantly (80.04 μs) with only marginal improvements in accuracy beyond cubic models.