Question

SRAM Assist Techniques for Operation in a Wide Voltage Range in 28-nm CMOS. show the some simulation results .

Answer 1

Sram Assist techniques:

1.)Important sampling:

Monte Carlo simulations can be used to measure the effect of variability, but an unfeasible number of simulations would be required to find a rare failure event. IS enables enormous speedup for Monte Carlo analysis of rare events.Under the assumption that threshold voltage deviations due to random dopant fluctuation can be modeled with a Gaussian distribution, Monte Carlo will simulate the two-device circuit with threshold probability density functions (PDF) given by Y1 and Y2, where the mean is the device’s nominal value and the σ is given by AV t/ √ W ∗ L. This enables investigation of a technology before full statistical models are available as long as an approximate σVth is known. In general, this method can be applied to any statistically modeled technology parameter. Ordinary Monte Carlo will only sample failure events with the very small probability shown by region 1 . For IS, the mean of Y1 and Y2 is changed to create a new PDF, labeled Yˆ1 and Yˆ2, so Monte Carlo samples failure events with the probability given by region 2 . To determine how often these failures would occur without the artificial shift, these samples are unbiased

2.)Variable-Radius Most Probable Failure Point Search:

Finding the optimal sampling distribution is complex for a multi-dimensional design space. For quick convergence, the set of mean shifts must be the multi-dimensional most-probable failure point (MPFP), which is the point closest in distance to the origin. This paper uses a method that performs uniform sampling of a variable-radius n-dimensional sphere around point

3.)analysing results:

The MPFP approach will not only determine failure probability, it will also determine the relative strengths of particular devices that cause failure, and therefore explains why a cell fails. For example, consider the MPFP that this algorithm found for writeability failure determination at 0.8 V.The intuitive explanation of this MPFP is that if Monte Carlo was run for a very long time, most failures will have devices with thresholds shifted by around these amounts. Assuming device models are correct, real silicon cells would also fail for similar device characteristics. σ is around 25 mV, so the MPFP has a right PG with a threshold that is about 140 mV larger than normal.

4.)verification:

These results closely match Monte Carlo simulation, as shown in Fig. 3. Note that this IS implementation assumes that the only source of variation is the Vth variation, yet can be seen to track full MC well. BER smaller than 10−4 causes an excessive MC runtime. Other studies have shown that IS matches MC for longer simulations.