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

Liang Tao; Jia Xinzhang

doi:10.1088/1674-4926/33/12/125008

J. Semicond. > 2012, Volume 33 > Issue 12 > 125008

SEMICONDUCTOR INTEGRATED CIRCUITS

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

Liang Tao and Jia Xinzhang

+ Author Affiliations

DOI: 10.1088/1674-4926/33/12/125008

Abstract: 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.

Key words: yield estimation, one-sided specification, truncated normal, empirical formula

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Liang Tao, Jia Xinzhang. An empirical formula for yield estimation from singly truncated performance data of qualified semiconductor devices[J]. Journal of Semiconductors, 2012, 33(12): 125008. doi: 10.1088/1674-4926/33/12/125008

Liang T, Jia X Z. An empirical formula for yield estimation from singly truncated performance data of qualified semiconductor devices[J]. J. Semicond., 2012, 33(12): 125008. doi: 10.1088/1674-4926/33/12/125008.

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Received: 20 August 2015 Revised: 31 May 2012 Online: Published: 01 December 2012

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.

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

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