A Timing Yield Model for SRAM Cells at Sub/Near-Threshold Voltages Based on a Compact Drain Current Model

Abstract

Sub/near-threshold static random-access memory (SRAM) design is crucial for addressing the memory bottleneck in power-constrained applications. However, the high integration density and reliability under process variations demand an accurate estimation of extremely small failure probabilities. To capture such a “rare event” in memory circuits, the time and storage overhead of conventional simulations based on the Monte Carlo (MC) analysis cannot be tolerated. On the other hand, classic analytical methods predicting failure probabilities from a physical expression become inaccurate in the sub/near-threshold voltage domain due to the hypothetical distribution or the oversimplified drain current ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{ds}$ </tex-math></inline-formula> ) model for nanoscale devices. This work first proposes a simple but efficient empirical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{ds}$ </tex-math></inline-formula> model to describe the drain-induced barrier lowering (DIBL) effect. Based on that, the probability density functions of the interest metrics in SRAM are derived. Two analytical models are then put forward to evaluate SRAM dynamic stabilities, including the access time failure and the write failure. The proposed models can be extended easily to different types of SRAM with different read/write-assist circuits. The models are validated against MC simulations across different operating voltages and temperatures. The average relative errors at 0.5-V <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm{ DD}}$ </tex-math></inline-formula> are only 8.8% for the access-time failure model and 10.4% for the write failure model. The size of the required sample data set is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$43.6\times $ </tex-math></inline-formula> smaller than that of the state-of-the-art method.