Parametric Sensitivity Analysis Identify in a big mass

Parametric Sensitivity Analysis Identify in a big mass of data the significant predictors of the Probe wafer yield by using JMP scripting

Parametric Sensitivity Analysis Gianpaolo Polsinelli, Felice Russo LFoundry s. r. l Italy a Smic Company Abstract In a Silicon-Fab several electrical and functional measurements are collected for each single silicon wafer. So it is very important to identify in a big mass of data which variables are really modulating the wafer yield the most important key performance indicator. Usually a scatter plot with a linear regression fit is used for that. Anyway this technique works well only if distributions are normal, in absence of outliers and data noisy. All those factors can obscure the true’s relationship between yield loss and in line issues. Objective To determine how different values of a predictor variable impact the wafer yield. Identify the right candidates by using Parametric Sensitivity Analysis (PSA) algorithm. JMP Script to automate the entire process.

Parametric Sensitivity Analysis Gianpaolo Polsinelli, Felice Russo LFoundry s. r. l Italy a Smic Company Methodology The PSA technique is used when data are very noisy and contain confounding effects. The response distribution is divided in N different balanced groups and a label is assigned to all database rows. For each group the predictors mean and/or median is calculated. Predictor 1 by Group ( A correlation is visible) Response by Group Grp 6 Grp 1 Gr 2 Gr 3 Gr 4 Gr 5 Predictor 2 by Group (NO correlation is visible ) Gr 6 The linear fit R 2 is then calculated using mean and/or median of groups instead of raw data points. Besides R 2 value the P-Val is evaluated too. A table with predictors ranked by a decreasing R 2 value is generated. Scatter plot for Yield vs. Predictor 1 Scatter plot for Yield vs. Predictor 2

Parametric Sensitivity Analysis Correlations Output ranked by R 2 Result FAB Data: Not normal distributions, long tails, fliers… Raw Data Gianpaolo Polsinelli, Felice Russo LFoundry s. r. l Italy a Smic Company ……. ….

Parametric Sensitivity Analysis Gianpaolo Polsinelli, Felice Russo LFoundry s. r. l Italy a Smic Company Input GUI Output Table Graph Builder To notice the strong improvement of R 2 value.