A discussion on SRAM forward/inverse problem analyses for RTN long-tail distributions

This paper discusses, for the first time, how the statistical SRAM design analyses should be changed when: (1) the shift-amount of the time-dependent (TD) voltage margin variations (MV) after the screening test will become larger than that before and (2) the shapes of the MV distribution will change from the Gaussian to the complex mixtures of Gamma distributions. We discuss on the SRAM TD-MV analyses with not only the forward problem but also the inverse problem, i.e., deconvolution analyses. The proposed algorithm for the deconvolution to circumvent the issues caused by high-pass filtering behavior is discussed. Based on the proposed convolution /deconvolution design analyses, it has been shown for the first time that: (1) detecting the truncating point of the distributions of TD-MV by the screening test and (2) predicting the required the MV-shift-amount by the assisted circuit schemes to avoid the out of specs in the market during the life-time, etc, has become enabled based on the target specification.