Extreme Value Theory: Application to Memory Statistics

Device variability is increasingly important in memory design, and a fundamental question is how much design margin is enough to ensure high quality and robust operation without overconstraining performance. For example, it is very unlikely that the “worst” bit cell is associated with the “worst” sense amplifier, making an absolute “worst-case” margin method overly conservative, but this assertion needs to be formalized and tested. Standard statistical techniques tend to be of limited use for this type of analysis, for two primary reasons: First, worst-case values by definition involve the tails of distributions, where data is limited and normal approximations can be poor. Second, the worst-case function itself does not lend itself to simple computation (the worst case of a sum is not the sum of worst cases, for example). These concepts are elaborated later in this chapter.