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Semiconductor Yield @ 28nm HKMG!

Semiconductor Yield @ 28nm HKMG!
by Daniel Nenni on 08-28-2011 at 4:00 pm

Whether you use a gate-first or gate-last High-k Metal Gate implementation, yield will be your #1 concern at 28nm, which makes variation analysis and verification a big challenge. One of the consulting projects I have been working on with the foundries and top fabless semiconductor companies is High-Sigma Monte Carlo (HSMC) verification technologies. It has been a bumpy two years certainly, but the results make for a good blog so I expect this one will be well read.

GLOBALFOUNDRIES Selects Solido Variation Designer for High-SigmaMonte Carlo
and PVT Design in its AMS Reference Flow

“We are pleased to work with Solido to include variation analysis and design methodology in our AMS Reference Flow,” said Richard Trihy, director of design enablement, at GLOBALFOUNDRIES. “SolidoVariation Designer together with GLOBALFOUNDRIES models makes it possible to perform high-sigma design for high-yield applications.”

Solido HSMC is a fast, accurate, scalable, and verifiable technology that can be used both to improve feedback within the design loop, as well as for comprehensive verification of yield critical high-sigma designs.

Since billions of standard Monte Carlo (MC) simulations would be required for six sigma verification, most yield sensitive semiconductor designers use a small number of MC runs and extrapolate the results. Others manually construct analytical models relating process variation to performance and yield. Unfortunately, both approaches are time consuming and untrustworthy at 28nm HKMG.

Here are some of the results I have seen during recent evaluations and production use of Solido HSMC:


  • 4,700,000x faster than Monte Carlo for 6-sigma analysis
  • 16,666,667x fewer simulations than Monte Carlo for 6-sigma analysis
  • Completed in approximately 1 day, well within production timelines


  • Properly determined performance at 6-sigma, with an error probability of less than 1e-12
  • Used actual Monte Carlo samples to calculate results
  • Provided high-sigma corners to use for design debug


  • Scaled to 6-sigma (5 billion Monte Carlo samples)
  • Scaled to more than 50 process variables


  • Error probability was reported by the tool
  • Results used actual Monte Carlo samples – not based on mathematical estimates

Mohamed Abu-Rahma of Qualcomm did a presentation at #48DAC last June in San Diego. A video of his presentation can be seen HERE. Mohamed used Solido HSMC and Synopsys HSPICE for six sigma memory design verification.

Other approaches to six-sigma simulation include:

  • Quasi Monte Carlo (QMC)
  • Direct Model-based
  • Worst-Case Distance (WCD)
  • Rejection Model-Based (Statistical Blockade)
  • Control Variate Model-Based (CV)
  • Markov Chain Monte Carlo (MCMC)
  • Importance Sampling (IS)

None of which were successful at 28nm due to excessive simulation times and the inability to correlate with silicon. Especially the Worst-Case Distance approach, which is currently being peddled by an EDA vendor who’s name I will not mention. They claim it correlates to silicon but it does not! Not even close! But I digress…..

Being from Virage Logic and working with Solido the last two years, this blog is based on my personal experience. If you have hard data that suggests otherwise let me know and I will post it.

I would love to describe in detail how Solido solved this very difficult problem. Unfortunately I’m under multiple NDA’s with the penalty of death and dismemberment (not necessarily in that order). You can download a Solido white paper on high-sigma Monte Carlo verification HERE. There is another Solido white paper that goes into greater detail of how they solved this problem but it requires an NDA. You can also get a Webex HSMC briefing by contacting Solido directly HERE. I observed one just last week and it was quite good, I highly recommend it!

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