Statistical analysis of temperature dependence of worst case static random access memory data retention voltage using extreme value theory

Abstract

The extreme value theory was adopted to analyze the temperature dependence of the worst case data retention voltage (DRV) in static random access memory (SRAM). It was found that the measured worst case DRV of bulk and fully depleted silicon-on-thin-buried-oxide (SOTB) SRAM follow a Gumbel distribution. By extrapolating the fitted Gumbel distribution, the worst DRV of large capacity SRAM at high temperature was estimated. It was also found that the temperature dependence of the worst case DRV in bulk SRAM diminishes as the capacity increases while that in SOTB SRAM is almost unchanged.

Estimation of minimum operating voltage in fully depleted SOI SRAM cells using gamma distribution

“…The Kolmogorov-Smirnov (K-S) test is used for the model verification. 28) The K-S test results show that the gamma distribution cannot be rejected at a 95% significance level, while the log-normal distribution is rejected.…”

“…Previous researches have shown that extreme values of V min follow the Gumbel distribution. 15,[26][27][28] Here, the 32 kb cells are divided into 128 blocks, each block containing 256 cells. The maximum V min values of each block are extracted and fitted with a straight line using the least-squares method There will be no eyes in the butterfly curve when V DD is lower than V min .…”

“…Being a special case in the three-parameter GENG distribution, the gamma distribution has only two parameters, but it does not necessarily have worse fitting accuracy, since more model parameters might lead to overfitting problems. 28) Therefore, the GENG and gamma distribution models need to be compared. Figure 9 shows their model quantiles against the measured empirical quantiles.…”