SRAM Yield Estimation via Perturbation Vectors
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Solution Overview
Problem
Conventional SRAM yield estimation methods require a large number of samplings and are inefficient due to linear approximation, especially in low-voltage environments where non-linear characteristics of SRAM metrics are not accurately considered, leading to increased simulation time and errors.
Innovation Solution
A method that generates perturbation vectors based on DC voltage conditions for assist and normal operations, using piecewise-linear approximation to minimize errors caused by non-linear characteristics, and selects the minimum margin for yield estimation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Monte-carlo simulation is used for yield estimation, then yield estimation can be performed, but a large number of samplings is required which sharply increases simulation time
Solution Approach 1:
The simulation process is segmented into two distinct phases: an assist operation phase with DC voltage conditions, and a normal operation phase with AC simulation. This segmentation allows the complex simulation to be broken down into manageable sections, each optimized for specific purposes, thereby reducing overall simulation time while maintaining accuracy.
Solution Approach 2:
The perturbation vector is calculated in advance during the assist operation phase based on DC voltage conditions before the actual AC simulation begins. This preliminary calculation of the perturbation vector prepares the system for the subsequent yield estimation, avoiding the need for extensive sampling during the main simulation and thus reducing simulation time.
2Ease of manufacture
If linear approximation is used for yield estimation, then calculation is simplified, but non-linear characteristics of SRAM metrics in low-voltage environments are not accurately considered leading to errors
Solution Approach 1:
The perturbation vector is dynamically adjusted based on the voltage conditions applied during different operation phases. Instead of using a fixed linear approximation, the system adapts the perturbation characteristics to match the actual non-linear behavior of the SRAM under different voltage conditions, thereby maintaining accuracy while managing calculation complexity.
Solution Approach 2:
The voltage parameters are changed between the assist operation phase (DC conditions) and the normal operation phase (AC conditions). By varying these parameters and calculating perturbation vectors appropriate for each phase, the system captures non-linear characteristics that would be missed by a single linear approximation, improving accuracy without excessive computational burden.
3Reliability
If assist operations are performed in low-voltage environment, then SRAM performance is improved by widening operation margin, but perturbation vector must be modified depending on applied voltage which increases complexity
Solution Approach 1:
The simulation employs periodic action by alternating between assist operation phase and normal operation phase. During the assist phase, DC voltage conditions are applied and perturbation vectors are calculated; then AC simulation is performed. This periodic structure allows the system to handle the complexity of voltage-dependent perturbation vectors in a systematic, manageable sequence rather than continuously.
Solution Approach 2:
The perturbation vector acts as an intermediary that bridges the assist operation phase and the normal operation phase. It is calculated during the assist phase based on DC conditions and then used to guide the AC simulation in the normal phase. This intermediary structure allows the system to account for voltage-dependent effects without requiring direct, complex modifications during the main simulation.
Data Source
AI summary
A method for SRAM yield estimation includes: generating a first perturbation vector depending on a DC voltage input condition for an assist operation section of a SRAM which is an estimation target; calculating a first margin on the basis of the first perturbation vector; performing an AC simulation during the assist operation section depending on the DC voltage input condition; generating a second perturbation vector depending on a DC voltage input condition for a normal operation section which is set when the AC simulation is ended; calculating a second margin on the basis of the second perturbation vector; and selecting a minimum margin from among the first margin and the second margin and estimating a yield of the SRAM on the basis of the selected margin.