A Model-Based-Random-Forest Framework for Predicting $V_{t}$ Mean and Variance Based on Parallel $I_{d}$ Measurement

To measure the variation of device $V_{t}$ requires long test for conventional wafer acceptance test (WAT) test structures. This paper presents a framework that can efficiently and effectively obtain the mean and variance of $V_{t}$ for a large number of designs under test (DUTs). The proposed framework applies the model-based random forest as its core model-fitting technique to learn a model that can predict the mean and variance of $V_{t}$ based only on the combined $I_{d}$ measured from parallel connected DUTs. The proposed framework can further minimize the total number of $I_{d}$ measurement required for prediction models while limiting their accuracy loss. The experimental results based on the SPICE simulation of a UMC 28-nm technology demonstrate that the proposed model-fitting framework can achieve a more than 99% ${R}$ -squared for predicting either $V_{t}$ mean or $V_{t}$ variance. Compared to conventional WAT test structures using binary search, our proposed framework can achieve a $120.3 \times$ speedup on overall test time for test structures with 800 DUTs.