Simulation Sample Generation Using Adaptive Sampling Regions
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Solution Overview
Problem
Current semiconductor device design and manufacturing processes require extensive simulation to ensure specifications are met, leading to increased simulation time and cost due to the generation of a large number of random samples, which can compromise accuracy and efficiency.
Innovation Solution
The method involves generating simulation samples with constraints, focusing on a sampling region where failures are most likely to occur, using a bin division scheme and score determination to identify low-probability check points, thereby concentrating samples in areas where specification violations are likely, reducing the number of samples needed while maintaining accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a large number of random samples are generated for simulation, then the accuracy of specification verification is improved, but the simulation time and cost increase significantly
Solution Approach 1:
The sample space is segmented into multiple regions based on probability density, with different sampling strategies applied to each region. Critical regions with high failure probability receive concentrated sampling, while safe regions use minimal sampling, thus reducing total simulation time while maintaining verification accuracy.
Solution Approach 2:
Different sampling densities are applied to different regions of the sample space. Regions with higher failure probability (critical regions) receive higher sampling density, while regions with lower failure probability receive lower sampling density, optimizing the trade-off between accuracy and simulation time.
2Reliability
If a large number of random samples are generated for simulation, then the coverage of sample space is improved, but the simulation cost increases
Solution Approach 1:
The sample space is pre-analyzed to identify critical regions with high failure probability before conducting the main simulation. This preliminary action allows the simulation to focus resources on critical areas, achieving comprehensive coverage with fewer samples and reduced cost.
Solution Approach 2:
Instead of uniformly sampling the entire sample space, the method creates multiple copies of critical regions through stratified sampling, concentrating computational resources on areas that contribute most to verification accuracy, thereby reducing overall simulation cost.
3Ease of operation
If samples are generated uniformly across the entire sample space, then the distribution of samples is simple, but the accuracy in critical regions is insufficient
Solution Approach 1:
The sampling strategy transitions from static uniform distribution to dynamic adaptive distribution. The sampling density automatically adjusts based on the local failure probability characteristics of different regions, concentrating samples in critical areas while maintaining operational feasibility through algorithmic automation.
Data Source
AI summary
A method includes determining a sampling region in a sample space, generating samples in the sampling region without generating samples outside the sampling region, and simulating a performance of a device using the generated samples as input data. The sample space is defined by a plurality of variables associated with the device. Values of the plurality of variables in the sampling region having lower probabilities to meet a specification of the device than values of the plurality of variables outside the sampling region. The method is performed at least partially by at least one processor.