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 Objective 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. 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. Gr 1 Gr 2 Gr 3 Gr 4 Gr 5 Gr 6 The linear fit R2 is then calculated using mean and/or median of groups instead of raw data points. Besides R2 value the P-Val is evaluated too. A table with predictors ranked by a decreasing R2 value is generated. Grp 6 Grp1 Scatter plot for Yield vs. Predictor1 Scatter plot for Yield vs. Predictor2 Predictor1 by Group ( A correlation is visible) Predictor2 by Group (NO correlation is visible ) Response by Group

Parametric Sensitivity Analysis Gianpaolo Polsinelli, Felice Russo LFoundry s.r.l Italy a Smic Company Raw Data Result Correlations FAB Data: Not normal distributions, long tails, fliers… Density function estimation box: Hyperlink to page 4 Modes filtering box: Hyperlink to page4 Picture Table “Result”: Hyperlink to page 5 …….…. …….…. …….…. Parametric Sensitivity Analysis Output ranked by R2

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 R2 value.