针对小样本晶圆制造数据，构建了可预测光电晶体管增益的分层不确定性模型。
Forward and Inverse Virtual Metrology for Phototransistor Gain: A Hierarchical, Uncertainty-Aware Approach for Small Production Datasets
- 基于多层级数据质量评估，建立分层建模框架以捕捉工艺差异
- 发现约一半增益方差来自批次间而非批次内，限制了仅靠配方预测的精度
- 提供正向预测与反向搜索功能，适合半导体工艺优化人员使用
硅双极性光电晶体管工艺流程的定制、优化与稳定需数月洁净室时间才能完成器件测量，因此在生产前基于工艺参数预测器件增益的模型具有远超其准确度的价值。本文基于真实制造历史数据，研究了13至14次工艺运行的单一器件，处于小样本、分层结构的特殊场景，不同于常规虚拟量测的大规模数据环境。通过分解器件增益的方差，发现约一半方差存在于工艺批次之间而非批次内部，因此仅依赖工艺配方的预测存在本质上限。基于此，本文提出一种相对且具备不确定性感知能力的正向增益预测模型，一种可返回目标增益对应工艺配方的逆向搜索方法，并构建了面向制造中嵌套物理实体（批、片、晶粒）的多级数据质量评估体系，包含显式的跨层级关联评分。所用归一化数据集与分析代码已公开，确保完全可复现。
原文摘要 · Abstract (English)
The customization, optimization and stabilization of the process flow of a silicon bipolar phototransistor commits months of cleanroom time before a finished device can be measured, so a model that predicts device gain from process parameters before a run has value out of proportion to its accuracy. We study this problem on a real fabrication history, thirteen to fourteen process runs of a single device: a small-sample, hierarchically structured setting unlike the large-corpus regime of conventional virtual metrology. Decomposing the variance of device gain, we find that roughly half of it lies between process runs rather than within them, so recipe-only prediction is bounded by construction. Building on these findings we provide a forward gain predictor with a relative, uncertainty-aware signal, an inverse search that returns recipes for a target gain, and, as the foundation for all of it, a multi-level data-quality assessment tailored to the nested physical entities of fabrication (batch, wafer, die) with an explicit cross-level linkage score. The normalized dataset and analysis code are released for full reproducibility.
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