Ecole Nationale Supérieure des Mines de Saint-Etienne Generalized Moving Variance and Decompositions Ariane FERREIRA Associate Professor 2 nd ISSPC July 13th, 2011 Rio de Janeiro

Statistical Control Charts for Generalized Moving Variances 2 Outline  Introduction  What’s VARIATION?  Problems and Motivation 1  Temporal Moving Variance/Covariance  Temporal Moving Variance  Temporal Moving Covariance  Performance  Example of Application 2  Generalized Moving Variance (GMV)  Distribution-based Concept: GMV  GMV Decomposition  Methodology for GMV calculation 3  Case Study of Semiconductor manufacturing  CVD equipment: linkage detection  EWMA control chart 4  Perspectives 5

Statistical Control Charts for Generalized Moving Variances Introduction: What is variation ? 3 a change or slight difference in a level, amount, or quantity …… Variance  a measure of the amount of variation within the values of data ……… s 2 (A) = 0.85 s 2 (B) = S 2S 2 nini S 2S 2 nini ;

Statistical Control Charts for Generalized Moving Variances Introduction: Data described by the Profiles In real world, you’ll always have data like: 4 Pattern-induced Variation Systematic Variation Random Variation =+ =+ Identify Systematic Pattern? Measure Random Noise? Variation Analysis Total Variation =+

Statistical Control Charts for Generalized Moving Variances Introduction: Practical Method for Random Variation Analysis 5 There can be hundreds or thousands of data profiles……… Profile analysis by windows Window

Statistical Control Charts for Generalized Moving Variances 6 Introduction: Problems and Motivation Difficulties pattern-dependent profiles non-stationary data distributions Model-based methodologies are commonly practiced. Costly, time-consuming Chen and Blue 2009  data itself should speak much more before domain knowledge is involved. Concept of Moving Variance Generalized Moving Variance proportional to the volume of data distributed in the multi- dimensional variable space and can be used to measure the dispersion of profiles A. Chen and J. Blue, “Recipe-independent Indicator for Tool Health Diagnosis and Predictive Maintenance,” IEEE Transactions on Semiconductor Manufacturing, pp , 22, 4, November, 2009

Statistical Control Charts for Generalized Moving Variances Temporal Moving Variance (p=2) 7 Profiles name : Status Variable IDentification (SVID) Moving Windows of size p (<n) Chen and Blue, 2009

Statistical Control Charts for Generalized Moving Variances Temporal Moving Covariance (p=2) 8 Profiles name : Status Variable IDentification (SVID) Moving Windows of size p (<n) Chen and Blue, 2009

Statistical Control Charts for Generalized Moving Variances Performance of Temporal Moving Variance/Covariance 9

Statistical Control Charts for Generalized Moving Variances Example of Application Semiconductor manufacturing Voltage Pressure Temperature T=1, 2, 3, ………………………………, 100 Measurement Tool Process Tool SVID 1 SVID 2 SVID 3 10

Statistical Control Charts for Generalized Moving Variances ………………… What Do Engineers Do? Voltage Pressure Temperature wafer 1 wafer 2 …… wafer n 10~50 SVID’s in a process ………………… More than 2 summarized statistics a SVID More than 300 Process Tools 11

Statistical Control Charts for Generalized Moving Variances Distribution-based Concept: Generalized Variance 12 Voltage Pressure Temperature Voltage Pressure Generalized Variance Size of Distribution wafer 1 Chen and Blue, 2009 SVID 1 SVID 2 SVID 3

Statistical Control Charts for Generalized Moving Variances 13 PM1 PM2 PM3.... PM cycle.... step 1step Moving Variance/Covariance Matrix Generalized Moving Variance wafer 1 Generation of Generalized Moving Variance Chen and Blue, 2009

Statistical Control Charts for Generalized Moving Variances Example of GMV Monitoring PM1 PM2PM3 EWMA Control Limit.... Equipment Condition Generalized Moving Variance 14

Statistical Control Charts for Generalized Moving Variances Generalized Moving Variance decomposition 15 Moving variance/covariance matrix S Matrix S’ only considers moving variance: Set all the moving covariances on the off- diagonal to zeroes. Matrix S’’ consider the moving covariance only: the influence of moving variance within S, i.e., the effect of S’, should be removed. Only relationships among SVIDs Only SVIDs variability

Statistical Control Charts for Generalized Moving Variances Summary of generalized moving variance decomposition 16 Property from Chen and Blue, 2009 Moving Generalized Variance decomposition

Statistical Control Charts for Generalized Moving Variances Equipment Condition SVID VariabilitySVID Interrelation Property : det(S) = det(S’)det(S’’) Property : det(S) = det(S’)det(S’’) Equipment Condition SVID Variability SVID Interrelation 17

Statistical Control Charts for Generalized Moving Variances Methodology for GMV calculation 18

Statistical Control Charts for Generalized Moving Variances SVIDs profile Data quantitative SVIDs profile data Process steps: 9~12 Engineering Knowledgment: Main SVIDs Case Study of Semiconductor Manufacturing Diffusion: CVD Equipment MSP18-3: Linkage Detection

Statistical Control Charts for Generalized Moving Variances Case Study of Semiconductor Manufacturing 20 Diffusion: CVD Equipment MSP18-3: Linkage Detection Analysis Done Calculate the Generalized Moving Variance for all process steps. nothing obvious found. Calculate the Generalized Moving Variance for Step9~12. abnormal pattern shown on 3 rd of December similar pattern in SVID interrelation Check all the interrelations for Step9~12. Check all the temporal profiles for Step9~12.

Statistical Control Charts for Generalized Moving Variances 21 3 rd of December Generalized Moving Variance on Step9~12

Statistical Control Charts for Generalized Moving Variances Decomposition of GMV  SVID Variability 22

Statistical Control Charts for Generalized Moving Variances Decomposition of GMV  SVID Interrelation 23 Similar pattern as shown in Generalized Moving Variance

Statistical Control Charts for Generalized Moving Variances SVID Interrelations Check Investigate all the “moving covariances” between throttle step (8) and other SVID’s. The moving variances become less fluctuant after 3/12/2010. AFC current flow (1) AFC current flow 22 CVD BacksPressure 08 The level of moving covariance drops down a little after 3/12/2010. AFC current flow 20 AFC current flow 23 The level of moving covariance rises up a little after 3/12/2010. AFC current flow 21 forward pwr (8) 24

Statistical Control Charts for Generalized Moving Variances Wafer FDC Analyser Prototype Demonstration 25

Statistical Control Charts for Generalized Moving Variances Perspectives 26 To develop the statistical design for GMV and Decompositions 1.Advanced Parametric Control Chart 2.Non Parametric Advanced and Innovating Control Charts

Statistical Control Charts for Generalized Moving Variances Appendix SVID Interrelations screen shots 27

Statistical Control Charts for Generalized Moving Variances Jakey Blue 28

Statistical Control Charts for Generalized Moving Variances Jakey Blue 29

Statistical Control Charts for Generalized Moving Variances Jakey Blue 30

Statistical Control Charts for Generalized Moving Variances Jakey Blue 31

Statistical Control Charts for Generalized Moving Variances Jakey Blue 32

Statistical Control Charts for Generalized Moving Variances Jakey Blue 33

Statistical Control Charts for Generalized Moving Variances Jakey Blue 34