一种由合格品的单侧截尾性能数据估计半导体元器件成品率的经验公式

本文研究了仅根据合格样品的性能测试数据估计半导体元器件成品率的问题。基于成品率与过程能力指数的关系构造了一种经验公式，当合格样品的性能数据服从单侧截尾正态分布时，可由样本均值和标准差直接计算成品率。首先，比较了四种常用正态性检验法的功效，结果表明在识别单侧截尾正态样本时Shapiro–Wilk检验功效最高。其次，使用蒙特卡洛仿真法比较了极大似然法和经验公式的估计精度，结果表明在利用单侧截尾正态样本估计成品率时，该经验公式利用极其简单的运算就可取得与极大似然法几乎完全相同的精度。此外当满足一定的条件时，该公式亦可用于双侧截尾正态样本的成品率估计。使用文献中的数据以及芯片实测数据估计成品率,验证了该方法的有效性。

An empirical formula for yield estimation from singly truncated performance data of qualified semiconductor devices

The problem of yield estimation merely from performance test data of qualified semiconductor devices is studied. An empirical formula is presented to calculate the yield directly by the sample mean and standard deviation of singly truncated normal samples based on the theoretical relation between process capability indices and the yield. Firstly, we compare four commonly used normality tests under different conditions, and simulation results show that the Shapiro-Wilk test is the most powerful test in recognizing singly truncated normal samples. Secondly, the maximum likelihood estimation method and the empirical formula are compared by Monte Carlo simulation. The results show that the simple empirical formulas can achieve almost the same accuracy as the maximum likelihood estimation method but with a much lower amount of calculations when estimating yield from singly truncated normal samples. In addition, the empirical formula can also be used for doubly truncated normal samples when some specific conditions are met. Practical examples of yield estimation from academic and IC test data are given to verify the effectiveness of the proposed method.