A Methodology for Predictive Failure Detection in Semiconductor Fabrication
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1 A Methodology for Predictive Failure Detection in Semiconductor Fabrication Peter Scheibelhofer (TU Graz) Dietmar Gleispach, Günter Hayderer (austriamicrosystems AG) Peter Scheibelhofer (TU Graz) Page 1/16
2 Agenda Overview austriamicrosystems Statistics in semiconductor fabrication Classification and Regression Trees (CART) & Random Forests methodology Case studies Peter Scheibelhofer (TU Graz) Page 2/16
3 austriamicrosystems AG I Design and fabrication of analog integrated circuits I Power Management, sensors, mobile infotainment I worldwide customers I 100k+ fabricated wafers per year Peter Scheibelhofer (TU Graz) Page 3/16
4 Why use statistics in semiconductor fabrication? Peter Scheibelhofer (TU Graz) Page 4/16
5 Concepts State of the art: Statistical Process Control (SPC) Fault Detection and Classification (FDC) Advanced: Predictive Maintenance (PdM) Virtual Metrology (VM) Peter Scheibelhofer (TU Graz) Page 5/16
6 Requirements for statistical methods Handle multivariate classification and regression problems Identification of important machine parameters Analysis of complex data situations, often unknown interaction structure Reliable prediction Peter Scheibelhofer (TU Graz) Page 6/16
7 Requirements for statistical methods Handle multivariate classification and regression problems Identification of important machine parameters Analysis of complex data situations, often unknown interaction structure Reliable prediction Classification and Regression Trees Peter Scheibelhofer (TU Graz) Page 6/16
8 Classification And Regression Trees (CART) binary recursive partitioning of given data Peter Scheibelhofer (TU Graz) Page 7/16
9 CART - Approach Split response at predictor thresholds resulting partitions as pure as possible Impurity: I (A) = Φ(P(Y = 1 A)) Minimize Class-Impurity (binary) / squared error (continuous) binary: [ ( )] max I (A) P(A L ) I (A L )+P(A R ) I (A R ) continuous: ] max x [SE (SE 1, x + SE 2, x ) Peter Scheibelhofer (TU Graz) Page 8/16
![squared error (continuous) binary: [ ( )] max I (A) P(A L ) I (A L )+P(A R ) I (A R )](/docs-images/42/12635882/images/page_9.jpg "continuous: ] max x [SE (SE 1, x + SE 2, x ) Peter Scheibelhofer (TU Graz) 09-09-2011")
10 CART - Advantages Intuitive and interpretable overview of data Suitable for complex data situations with interactions Important parameters recognizable Robust with respect to outliers Prediction of new observations possible Modeling in R with packages rpart and party Peter Scheibelhofer (TU Graz) Page 9/16
11 Random Forests Averages over many (> 500) different CART-models Lower variance No overfitting In R with randomforest package Peter Scheibelhofer (TU Graz) Page 10/16
12 Random Forests Randomization draw data with replacement from original data (bootstrap samples) random feature selection for every split Test error estimation with remaining data (out-of-bag error) Variable Importance: Aggregating change in out-of-bag error Change in error after random value shuffling Peter Scheibelhofer (TU Graz) Page 11/16
13 Methodology for building models Peter Scheibelhofer (TU Graz) Page 12/16
14 Case Study 1: Virtual Film Thickness Measurement Thickness of metal film measured using test wafers (target 800nm) Material and time consuming Goal: Replace measurement with estimation based on process data RF model allows accurate prediction R 2 75%, RMSE 7nm high potential for cost reduction Peter Scheibelhofer (TU Graz) Page 13/16
15 Case Study 2: Prediction of Implanter Maintenance Implanting: impinge ions under wafer surface Part of ion source: filament Part breaks approximately every 5-14 days Goal: Prediction of filament breakdown moment Peter Scheibelhofer (TU Graz) Page 14/16
16 Case Study 2: Prediction of Implanter Maintenance Model for continuous time-to-event response (in h) Prediction accuracy of +/ 12 hours (test error) Model allows condition based maintenance Peter Scheibelhofer (TU Graz) Page 15/16
17 Summary CART-based models suitable for high-dimensional data analysis, classification and regression problems Used statistical method allows Real time monitoring of production tools save qualification material and maintenace costs Increase throughput Tree-based methods combined with multidimensional methods (Hotelling T 2, PCA, cluster analysis,...) suitable for practical modelling Peter Scheibelhofer (TU Graz) Page 16/16
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