Fast Monte Carlo Simulations For Timing Variation Analysis

Process variations and device mismatches profoundly affect the latest ultra-small geometrical processes. Complexity creates additional factors that impact device manufacturing variability, which in turn impact overall yield. Monte Carlo (MC) simulations use repeated random sampling to relate process variations to circuit performance and functionality, thus determining how they impact yield. However, for comprehensive design space exploration, design teams need to do a vast number of MC simulations to reach the necessary confidence level.

With billions of elements on a chip, process variations, and device mismatches, can we afford to run billions of statistical simulations and spend so much time on verification?

The turnaround time and computing resources for running millions or even billions of simulations are impractical; hence, there is a strong need to improve throughput while still meeting the statistical accuracy requirements. Broadcom achieved good results and meaningful productivity gains leveraging Cadence Spectre FMC Analysis. In addition, Spectre simulation’s multiple-processor mode further improved the runtimes without losing accuracy. This blog discusses the accuracy and performance improvements achieved by Broadcom by using Spectre FMC and is an excerpt from the CadenceLIVE Silicon Valley 2024 presentation delivered by the Broadcom team.

Why it is difficult to capture process variations?

Semiconductor foundries accurately capture device-level variations by developing statistical models. This has enabled variation-aware design techniques to minimize the likelihood of integrated circuit (IC) failures due to random variations. MC simulations utilize these statistical models to identify the worst-case scenarios and ensure the desired yield. However, these simulations demand extensive computing resources and time, particularly for design blocks frequently used on the chip and have a low failure requirement, such as standard cells, memory bit cells, and analog IP like ADCs, DACs, PLLs, and bandgaps.

Despite advancements in simulation tools and access to large-scale computing resources like multiple cores and cloud computing, performing computationally intensive MC simulations remains impractical and often impossible. This is particularly true for high-sigma MC analysis, where over a billion simulations may be required to achieve a high yield—for instance, 2.5 billion samples to confirm six-sigma.

The semiconductor industry requires EDA tools to accurately estimate yields and identify worst-case scenarios with fewer simulations and less time. Advanced EDA solutions with state-of-the-art simulation capabilities are essential for quick, precise, high-sigma MC analysis.

To overcome the challenges mentioned above, Cadence developed Spectre FMC Analysis as part of the Spectre Simulation Platform for high-performance SPICE-accurate circuit simulation.

It uses AI-enhanced techniques to:

• Estimate the yield early and faster without compromising statistical accuracy
• Find the statistical outliers and worst-case samples
• Extract useful statistical information with far fewer simulations than brute force Monte Carlo

What motivated Broadcom to adopt Spectre FMC Analysis?

Broadcom required a solution that could accurately measure and validate variation models while being cost-effective and seamlessly integrating with existing flows. Additionally, scalability to meet both current and future design demands was crucial. Broadcom’s collaboration with Cadence has led to their adoption of the Spectre FMC Analysis into their timing-related accuracy and analysis project. Benefits to Broadcom’s adoption include:

• High accuracy at high sigma
• Capability of making use of the existing license pool
• Command line interface (CLI) friendly
• Ease of integration with the existing flows and netlists
• Distributed processing
• Easy to scale
• Variation accuracy certification

Case study: Non-Gaussian distribution

To investigate the accuracy and performance of Spectre FMC, the Broadcom team presented a case with a long tail that is not strictly a Gaussian distribution.

They found out that Spectre FMC handles a challenging distribution like this. Performance data comparing brute force MC with Spectre FMC were exceptionally motivating.

Without Spectre FMC Analysis, processing required 12 hours per job with a total run time of approximately 245 months of CPU time and 1000 Spectre licenses. With Spectre FMC, each job takes around 0.2 hours on average using 300 Spectre licenses, reducing the total CPU time to 14 months. Spectre FMC Analysis enabled Broadcom to complete the project in about a month, demonstrating significant performance improvements.

Benefits

Spectre FMC has improved accuracy and performance substantially while integrating seamlessly with Broadcom’s existing flow. Broadcom achieved an improvement of approximately 60X per CPU per job when operating under the appropriate licensing conditions. Even with a reduced number of licenses, the benefits remain substantial, achieving an ~18X enhancement in performance. Broadcom mentioned that the key advantages of using Spectre FMC are its precise accuracy and a significantly reduced runtime. Ensuring an adequate pool of licenses is crucial. Additionally, the ease of command line usage and scalability make it well-suited for efficiently exploring the entire design space.