SRAM Model Expression Generation via Vertex Simulation Allocation
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Solution Overview
Problem
Current SRAM design optimization techniques face challenges in reducing the number of simulations required, especially when dealing with a large number of parameters, as the search space becomes too broad, and existing methods do not utilize the unique characteristics of SRAM effectively.
Innovation Solution
A method for generating model expressions by allocating initial simulation times to objective functions based on weight values at designated vertexes of a quadrilateral plane, determining the influence on yield, and adjusting simulation times accordingly to optimize approximation accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the number of parameters is increased to dozens of parameters for comprehensive SRAM design optimization, then the design coverage and completeness are improved, but the search space becomes broad and the number of simulation times increases making it impossible to obtain an optimum solution within a reasonable period of time
Solution Approach 1:
The patent segments the design parameter space by identifying and focusing on vertex parameters of a quadrilateral that define the search space boundaries. Instead of uniformly optimizing all dozens of parameters, the method segments the problem into vertex parameter optimization and interior point evaluation, reducing the number of parameters requiring intensive simulation to a manageable subset.
Solution Approach 2:
The patent performs preliminary action by first determining the vertex parameters and establishing the quadrilateral search space before conducting simulations. The vertex parameters are optimized first to define the boundaries, and only then are interior points evaluated. This preliminary structuring of the search space reduces the overall simulation burden compared to exhaustive search methods.
2Measurement precision
If the number of simulation times is increased to achieve high accuracy in model expressions, then the approximation accuracy is improved, but the processing time and computational cost increase
Solution Approach 1:
The patent applies local quality by allocating different numbers of simulation times to different regions of the parameter space. Vertex parameters, which have greater influence on the yield model expression, are allocated more simulation times for higher accuracy, while interior points receive fewer simulation times. This non-uniform allocation optimizes the overall model accuracy while reducing total computational cost compared to uniform high-accuracy simulation across all points.
Solution Approach 2:
The patent implements feedback by evaluating the approximation accuracy of model expressions after simulations and using this information to determine whether additional simulations are required. The system calculates evaluation indicators for each model expression and compares them against thresholds, automatically deciding whether to perform more simulations or proceed with the current model, thus avoiding unnecessary simulations and optimizing the balance between accuracy and efficiency.
3Adaptability or versatility
If conventional Monte Carlo method is used to analyze circuit characteristics, then the general analysis capability is maintained, but the SRAM-specific characteristics are not utilized resulting in insufficient reduction of simulation times
Solution Approach 1:
The patent changes the parameter representation by transforming circuit parameters into a geometric quadrilateral structure with vertex parameters. Instead of using traditional Monte Carlo sampling of individual parameters, the method changes to optimizing vertex parameters that define a quadrilateral in the parameter space. This parameter transformation leverages SRAM's specific characteristics where yield is determined by corner cases, enabling more efficient optimization tailored to SRAM while maintaining adaptability to different SRAM configurations.
Data Source
AI summary
When model expressions of objective functions are generated at vertexes of a quadrilateral on a plane concerning P and N channels of transistors in SRAM, the initial number of times of simulation is allocated to each objective function at each designated vertex according to weight values set based on relationships presumed among the objective functions at each designated vertex. For each objective function at each designated vertex, first simulation is executed the allocated number of times. Furthermore, a model expression is generated from the first simulation result, and an evaluation indicator of an approximation accuracy of the model expression is calculated. Then, for each model expression, it is determined whether the corresponding model expression has influence on the yield, and based on the evaluation indicator of the corresponding model expression and presence or absence of the influence, it is determined whether additional simulation is required for the corresponding objective function.