用空间采样与机器学习提升芯片测试覆盖率,降低成本。
Optimizing FPGA and Wafer Test Coverage with Spatial Sampling and Machine Learning
- 提出SDE算法,剔除空间邻近点,使采样更均匀。
- 在真实数据上,预测误差降低13%以上,最高达16.5%。
- 适合半导体测试优化、工业数据建模人员参考。
在半导体制造中,测试成本居高不下,尤其在晶圆和FPGA测试阶段。为减少测试数量同时保持预测精度,本研究对比了随机采样、分层采样和k-means聚类采样三种基础策略,并提出改进方法。基于真实工业生产数据,引入两种混合策略:分层+短距离消除(S-SDE)与k-means+短距离消除(K-SDE)。核心是短距离消除(SDE)算法,通过剔除空间邻近的候选点,提升训练数据在物理域上的分布均匀性。通过参数扫描(alpha, beta)∈{0,1,2,3,4}且不全为零,确定最优组合为(2,2),后续实验均采用此配置。在高斯过程回归框架下评估性能,结果表明:在晶圆测试中,K-SDE相比k-means提升16.26%,FPGA测试中提升13.07%;在分层采样基础上,S-SDE在晶圆测试中提升16.49%,FPGA测试中提升8.84%。
原文摘要 · Abstract (English)
In semiconductor manufacturing, testing costs remain significantly high, especially during wafer and FPGA testing. To reduce the number of required tests while maintaining predictive accuracy, this study investigates three baseline sampling strategies: Random Sampling, Stratified Sampling, and k-means Clustering Sampling. To further enhance these methods, this study proposes a novel algorithm that improves the sampling quality of each approach. This research is conducted using real industrial production data from wafer-level tests and silicon measurements from various FPGAs. This study introduces two hybrid strategies: Stratified with Short Distance Elimination (S-SDE) and k-means with Short Distance Elimination (K-SDE). Their performance is evaluated within the framework of Gaussian Process Regression (GPR) for predicting wafer and FPGA test data. At the core of our proposed approach is the Short Distance Elimination (SDE) algorithm, which excludes spatially proximate candidate points during sampling, thereby ensuring a more uniform distribution of training data across the physical domain. A parameter sweep was conducted over the (alpha, beta) thresholds, where alpha and beta are in the range {0, 1, 2, 3, 4} and not both zero, to identify the optimal combination that minimizes RMSD. Experimental results on a randomly selected wafer file reveal that (alpha, beta) equal (2, 2) yields the lowest RMSD. Accordingly, all subsequent experiments adopt this parameter configuration. The results demonstrate that the proposed SDE-based strategies enhance predictive accuracy: K-SDE improves upon k-means sampling by 16.26 percent (wafer) and 13.07 percent (FPGA), while S-SDE improves upon stratified sampling by 16.49 percent (wafer) and 8.84 percent (FPGA).
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