Importance sampling Monte Carlo simulations for accurate estimation of SRAM yield

Abstract

Abstract-Variability is an important aspect of SRAM cell design. Failure probabilities of P fail ≤10-10 have to be estimated through statistical simulations. Accurate statistical techniques such as Importance Sampling Monte Carlo simulations are essential to accurately and efficiently estimate such low failure probabilities. This paper shows that a simple form of Importance Sampling is sufficient for simulating P fail ≤10 -10 for the SRAM parameters Static Noise Margin, Write Margin and Read Current. For the SNM, a new simple technique is proposed that allows extrapolating the SNM distribution based on a limited number of trials. For SRAM total leakage currents, it suffices to take the averages into account for designing SRAM cells and modules. A guideline is proposed to ensure bitline leakage currents do not compromise SRAM functionality.

A yield centric statistical design method for optimization of the SRAM active column

“…As simulating an entire distribution requires simulation of very small probabilities, these simulations cannot be done with standard MC, as this would require too many MC trials. Using Importance Sampling (IS) MC [1], these small probabilities can be simulated and this technique is therefore applied using 50k trials, which is not a high number for estimation of probabilities in the range of 10 -7 . The distribution for ∆V SAo is normal and standard MC simulations (20k trials) can be used to estimate mean and standard deviation and to construct extrapolated distributions.…”

“…With technology scaling, an increasing amount of memory per SoC and the drive for low power and low voltage systems, SRAM variability and how to deal with variability in designs have rightfully received a large amount of attention. A lot of recent effort has been put into dealing with the impact of mismatch on SRAM cell parameters like static noise margin (SNM) [1]- [3]. However, the impact of mismatch does not stop at the memory cell level.…”

Fast Time-Domain Simulation for Reliable Fault Detection

“…Importance Sampling is a technique that provides sufficiently accurate results and is relatively easy to implement [12], [13], [18]. Using this, a speed-up of several orders can be achieved when compared to regular Monte Carlo methods [1], [5]. And, more important, we were able to optimise the SRAM active column, while guaranteeing that the failure probability remained below 10…”

Importance Sampling for Determining SRAM Yield and Optimization with Statistical Constraint

“…The threshold voltages V t of the six transistors in an SRAM cell are the most important parameters causing variations of the characteristic quantities of an SRAM cell [2] like Static Noise Margin (SNM) and Read Current (I read ). In [2,6] Importance Sampling (IS) was used to accurately and efficiently estimate low failure probabilities for SNM and I read .…”

“…In [2,6] Importance Sampling (IS) was used to accurately and efficiently estimate low failure probabilities for SNM and I read . SNM = min(SNM h , SNM l ) is a measure for the read stability of the cell.…”