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Statistical Process Control Implementation in Semiconductor Manufacturing Tzu-Cheng Lin 林資程 Advanced Control Program/ IIPD/ R&D Taiwan Semiconductor Manufacturing Company, Ltd [email protected], [email protected] March 26, 2010 NCTS Industrial Statistics Research Group Seminar Page 1 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Agenda: This presentation will cover the following topics: 1. MVA application: Advanced Bi-Variate Semiconductor Process Control Chart. 2. MVA application: Yield2Equipment Events Mining. 3. PLS application: Virtual Metrology of Deep Trench Chain. 4. Time series application: KSI-Based to Predict Tool Maintenance. 5. Survival application: Advanced Queue-Time to Yield Monitoring System. 6. SPC chart application: Smart Process Capability Trend Monitoring System. NCTS Industrial Statistics Research Group Seminar Page 2 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Case(1): MVA application Advanced Bi-Variate Semiconductor Process Control Chart. NCTS Industrial Statistics Research Group Seminar Page 3 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Advanced Bi-Variate Semiconductor Process Control Chart Motivation: Process Variation = (Process Metrology Value) + (Tool Healthy Quality) + (Metrology Tool Calibration) SPC monitoring system FDC monitoring system MSA calibration scheme As you know, In Line Process Control is a great important task on semiconductor manufacturing. We usually use the SPC system to monitor the process measurement data, and use the FDC system to monitor the tool healthy index. Although engineers via theses two regular systems, they could check the process is stable or not ?? BUT it is time consuming for engineers, …….. Innovative idea !! If we could build up the Bi-Variate Process Control Chart which based on the relationships between In-Line metrology data and FDC tool parameter monitoring data, and provide the Ellipse Control Region to real time tell engineers what’s current status for the latest process capability is stable or not?? In this way, it will give a big hand for engineers not only to monitor the SPC chart , but also to monitor the FDC chart at the same time. SPC NCTS Industrial Statistics Research Group Seminar Page 4 of 56 FDC Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Advanced Bi-Variate Semiconductor Process Control Chart Innovative idea profile: Remarks: (1) Process_A FDC Summary Value (Y) (3) (5) (6) (4) (7) (X,Y ) (9) 9 (8) 8 (10) In-Line Metrology Value (X) NCTS Industrial Statistics Research Group Seminar (1) The box is showing the process information on this chart. (2) X-axis is the In-Line metrology value (X). (3) Y-axis is the FDC summary value (Y). (4) The light-gray area is the Ellipse Control Region with 1 sigma. (5) The mid-gray area is the Ellipse Control Region with 2 sigma. (6) The dark-gray area is the Ellipse Control Region with 3 sigma. (7) The red point is contributed from (X,Y) and draw it on this specific control chart. (8) When the point is out of 3 sigma area, it’ll give a ‘x’ symbol to represent the OOC case. (9) When the point is OOC, it’ll also provide the Wafer_ID nearby it. (10) The ‘green’, ‘yellow’, and ’red’ light will point out the degree of stability on this process. (2) Page 5 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Full-Line Bi-Variate Semiconductor Process Control Chart It can integrate semiconductor full-line process & tool information into one system, and to be a kind of real time control tool for modern 12” iFab. Via this advanced process control chart, we’d be more easily to check the process status. NCTS Industrial Statistics Research Group Seminar Page 6 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Case study ALD NOLA Depth is a new process for new generation. So, we’re going to use this “Advanced Bi-Variate Semiconductor Process Control Chart” to monitor this critical process: 1) In-line metrology value: Depth (nm). 2) Equipment FDC parameters: Var1-Var25. Trial data looks like… 3) 34 raw data sets. ALDA102 - PM4 1.25 LCL 1.2 ALDA102-PM4 Depth (nm) 1.15 1.1 Target 1.05 1 UCL 0.95 0.9 0 5 10 15 20 25 30 35 Run# NCTS Industrial Statistics Research Group Seminar Page 7 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(1): Select Key Steps and Parameters Due to for ALDA equipment has so many tool parameters, we need the engineers/ vendors to provide the key process steps (some critical steps in the recipe) and parameters where measurements have significant effect on product quality. Process step Variables Identify the key steps and variables. ：the key parameter in corresponding step. NCTS Industrial Statistics Research Group Seminar Page 8 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(2): T-Score Transformation TOOL: ALDA102/PM4 ChamberPressure PumpingPressure MFC1 GasLineHeater1Temp StageHeaterInTemp StageHeaterOutTemp Source1HeaterTemp Source2HeaterTemp ThrottleValveHeaterTemp PumpingLineHeaterTemp ChamberWallHeaterTemp ChamberBottomHeaterTe mp SHInletHeaterTemp VATValveHeaterTemp Source1_Outlet_Pressure ………. ……… ….. … .. . NCTS Industrial Statistics Research Group Seminar Matrix [34X25] ….. *Huge data reduce to only ONE index: T 2 f ( x1 , xn ) *FDC Summary Value: T 2 ( x x )S 1 ( x x ) Based on each wafer, we’d provide the one index- FDC summary value, which could represents all tool parameters healthy status. Page 9 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(3): Ellipse Control Region Ellipse Equations: An ellipse centered at the point (h,k) and having its major axis parallel to the x-axis may be specified by the equation This ellipse can be expressed parametrically as where t may be restricted to the interval So, we based on the historical raw data (w/ good wafers), to set up the Ellipse control region, and use the Confident-Interval concept to calculate the 1 to 3 sigma alarm region to be the SPC-like, Bi-Variate process control chart. NCTS Industrial Statistics Research Group Seminar Page 10 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(4): Simulation for NOLA Depth process These four points are in warning control region. (4) (3) The 1 to 3 sigma Ellipse control region. (2) These two points are OOC!! (1) Bi-Variate Semiconductor Process ControlStatistics Chart: NCTS Industrial Research Seminar SPC+FDCGroup information. Page 11 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Conclusions From the simulation testing, it seems that our innovative proposal Advanced Bi-Variate Semiconductor Process Control Chart can monitor the semiconductor process variation successfully. Advanced Bi-Variate Semiconductor Process Control Chart approach not only can be used to monitor the Process Information (SPC Chart) , but also to monitor the Tool Information (FDC Chart) at the same time. The degree of process capability (like Traffic Lights) for specific critical process also can be known via this novel Bi-Variate process control chart. In this way, the engineers could control process more easily and efficiently. NCTS Industrial Statistics Research Group Seminar Page 12 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Case(2): MVA application Yield2Equipment Events Mining. NCTS Industrial Statistics Research Group Seminar Page 13 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Yield2Equipment Events Mining Novel Idea: Tool-A MVA T-Score PM PM ‧‧‧‧‧‧‧‧ ‧‧ ‧‧‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧‧ ‧‧‧‧‧‧ ‧‧ T-Score ‧‧‧‧ ‧‧ ‧ ‧ ‧ ‧‧‧‧ ‧ ‧ Trend Up YB Yield Trend Down time/date Another way to point out the abnormal tool !! NCTS Industrial Statistics Research Group Seminar T ( x x )S 1 ( x x ) T-Score is an index to represent all tool parameters status. If the T-Score is larger than specific limit we can say that this data point is significant different from the normal condition. During this PM cycle, the Yield and T-Score have high correlation and T-Score is bigger than normal condition. In this way, we can induce that this may occur some critical issues in this specific time period. Page 14 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Invention Program Flowchart Variable & Key Step selection •Key Step: certain time period •Variable: critical recipe/ process parameters Data transformation to T-Score •MVA Principal Component Analysis •MVA T-Score calculation •MSPC Hotelling T2 control limit set up [0, UCL] Correlation analysis between Yield & Tool Events •Yield & T-score trend up/down monitoring •Pearson Correlation Analysis •Highlight the HIGH correlation PM Cycle to conduct Yield2Equipment Events Mining Root Cause Analysis •Identify suspected ill-parameters NCTS Industrial Statistics Research Group Seminar Page 15 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(1): Select Key Steps and Parameters Due to for each equipment has so many tool parameters, we need the engineers/ vendors to provide the key process steps (some critical steps in the recipe) and parameters where measurements have significant effect on product quality. Process step Variables Identify the key steps and variables. ：the key parameter in corresponding step. NCTS Industrial Statistics Research Group Seminar Page 16 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(2): T-Score Transformation TOOL: ALDA102 / PM5 ChamberPressure PumpingPressure MFC1 GasLineHeater1Temp StageHeaterInTemp StageHeaterOutTemp Source1HeaterTemp Source2HeaterTemp ThrottleValveHeaterTemp PumpingLineHeaterTemp ChamberWallHeaterTemp ChamberBottomHeaterTemp SHInletHeaterTemp VATValveHeaterTemp Source1_Outlet_Pressure ………. ……… ….. … .. . NCTS Industrial Statistics Research Group Seminar *Huge data reduce to ONLY one index T 2 f ( x1 , xn ) *T2 Score T 2 ( x x )S 1 ( x x ) Page 17 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(3): Correlation Analysis In this step, we’ll conduct the Pearson’s linear correlation analysis to find out the most important PM Cycle in this process and it will be our Highlight issues. Pearson linear correlation analysis equation n r ( xi x )( yi y ) i 1 n ( xi x ) 2 i 1 n (y i 1 i y)2 Tool-A ‧ ‧‧‧‧ ‧‧‧‧PM ‧‧‧‧ ‧‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧ ‧‧ ‧ ‧ ‧ ‧ ‧ ‧ T-Score ‧ ‧‧ ‧ ‧ ‧ YB Yield time/date Correlation Analysis Table NCTS Industrial Statistics Research Group Seminar It has high significant correlation !! And then we can put more emphasized eyes on this PM Cycle!! Page 18 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(4): RCA-Root Causes Analysis T1 Chart Root Cause Analysis via Multi-Variate Analysis T 2 f ( x1 , xn ) PCA Index Raw Data NCTS Industrial Statistics Research Group Seminar Highlight the suspected issued parameter based on MVA Index!! Page 19 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Conclusions From the simulation results, it seems that our proposal Yield2Equip Events Mining module can monitor PM Events on Yield effects obviously. The Yield2Equip Events Mining approach not only can be used to monitor PM performance, but also it is useful to do RCA tasks when the T-Score and Yield have HIGH correlation relationship. NCTS Industrial Statistics Research Group Seminar Page 20 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Case(3): PLS application Virtual Metrology of Deep Trench Chain. NCTS Industrial Statistics Research Group Seminar Page 21 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Virtual metrology of deep trench chain 1.5 days • DT Chain Process Flow: As you know, the deep trench control is more critical for process engineers. Due to the process time between DTMO Etch to DT Etch is about 1.5 days, during this time period no one can be aware of the quality of DT final CD. If we could set up the virtual metrology model according to DT Litho CD, DT PHMO CD, and DTMO CD to predict DT final CD. It will be more helpful to assist in on-line process control. Innovative idea !! NCTS Industrial Statistics Research Group Seminar DT DT DT Litho PHMO MO CD CD CD Page 22 of 56 predicted y f ( x1 , x2 , x3 ) DT ETCH CD Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Methodology introducedPLS modeling overview NCTS Industrial Statistics Research Group Seminar Page 23 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Methodology introducedPLS modeling geometric interpretation NCTS Industrial Statistics Research Group Seminar Page 24 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Simulation(1)Predicted DT final CD via PLS/LSE Tool: D90 OXEC103-chamber A RMSE Error Rate PLSR 0.0017766 1.211% LSER 0.0023455 1.618% Formula: (1) RMSE 1 n (Y Yˆ ) 2 n i 1 n (2) Error - Rate ( i 1 Y Yˆ Y n ) *From the chart, it seems that we could get the better DTME predicted CD via PLS modeling technical. NCTS Industrial Statistics Research Group Seminar Page 25 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Simulation(2)SPC for virtual metrology of DT final CD Tool: T90 OXEC107-chamber A It can correctly catch the process alarm message !! Summary: 1) PLS model predicts the virtual metrology values by the pre-process metrology data. 2) At the same time, SPC scheme will monitor the prediction value of metrology parameter. 3) It will also give alarms to engineers when the prediction value is out of the specification. → So, via this virtual scheme, we could ensure that the process is within specification. NCTS Industrial Statistics Research Group Seminar Page 26 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Conclusions • • • Virtual Metrology of deep trench chain. DT Chain Healthy Index set up. Early alarm/detection system. Process grouping for following process. Improve throughputs for critical process. Improve line stability. NCTS Industrial Statistics Research Group Seminar Page 27 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Appendix NCTS Industrial Statistics Research Group Seminar Page 28 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab page.1 Partial least squares regression (PLSR) • Abstract: When the number of X is large compared to the number of observations, the multiple linear regression is no longer feasible ( because of multicolinearity). In order to solve the problem, several approaches have been developed. One is principal component regression (PCR) and the other is Partial least squares regression (PLSR) • Goal: To solve multicolinearity problem To reduce data dimension To predict Y from X and to describe their common structure To get important X variables • Difference between PLSR and PCR: PLSR finds components from X that are also relevant for Y NCTS Industrial Statistics Research Group Seminar Page 29 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab page.2 Basic concept 11 12 ... 1n 1 Cov( X ) 1 , w s.t. w T 1 w R1 n1 n 2 nn 0 (w is the eigen vect or of 1 , R1 is the eigenv value of 1 ) 11 12 ... 1n 1 Cov(Y ) 2 , c s.t. c T 2 c R2 n1 n 2 nn 0 (c is the eigenvecto r of 2 , R2 is the eigenv value of 2 ) 0... 0... 0 0 0 n 0 n t = Xw Cov(t) = Cov(Xw) = wTCov(X)w = 1 u = Yc Cov(u) = Cov(Yc) = cTCov(X)c = 2 To find two sets of weights w and c in order to create (respectively) a linear combination of the columns of X and Y such that their covariance is maximum!! NCTS Industrial Statistics Research Group Seminar Page 30 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab page.3 Nonlinear Iterative Partial Least Squares Algorithm (NIPALS) X TP E T a t j 1 Y UQ F T Y UQ F pTj E T is score matrix qTj F The columns of T are the latent vectors a u j 1 T j j a u j qTj F (U TB) P is loading matrix j 1 j=0, E0=Xn×m , F0=Yn×p , uj=any column of Y matrix, t = Xw, u = Yc (1) w j E Tj 1.u j E Tj 1.u j (2) t j E j 1.w j (3) c j FjT1.t j FjT1.t j (4) u j Fj 1.c j ( . (5) p j E Tj 1.t j t Tj .t j (6) p j ,new p j ,old p j ,old (10) j j 1, to j min(m, n) E j E j 1 t j pTj u Tj t j (7) t j ,new t j ,old . p j ,old Fj Fj 1 b t c , b j (8) w j ,new w j ,old . p j ,old When E is a null matrix then stop T j j j t Tj t j is Euclidean norm or 2-norm) NCTS Industrial Statistics Research Group Seminar Page 31 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Case(4): Time series application KSI-Based to Predict Tool Maintenance. NCTS Industrial Statistics Research Group Seminar Page 32 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab KSI-Based to Predict Tool Maintenance Due to the tool maintenance schedule is usually arranged by date, wafer run counts, RF hours, and for the furnace process it will also consider the equipment sidewall film thickness, but all of them are not sensitive to catch tool real status which need to conduct PM or not?. However, we all know that correct trend monitoring via tool signals can be used to determine approaching timing for preventive maintenance. In this way, our innovative idea can be described as following: Idea of invention: PM Once this KSI is greater than a pre-scribed limit (threshold). PM KSI Threshold Time Call for engineers & Call for tool maintenance !! KSI: Key Sensitive Index. NCTS Industrial Statistics Research Group Seminar Page 33 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Invention Program Flowchart Variable & Key Step selection Correlation analysis Time series model NCTS Industrial Statistics Research Group Seminar •Key Step: certain time period •Variable: critical recipe/ process parameters •Correlation: the quantity of variables •Screen out key parameter & key step •Extract out the signal characteristics •Time series models fit the trend of variables •Auto-correlation: the q of MA model •Partial Auto-correlation: the p of AR model •Defined Time Series ARIMA(p,d,q) model •KSI would decide when to call tool maintenance Page 34 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(1): Select key steps and parameters Due to for each equipment has so many tool parameters, we need the engineers/ vendors to provide the key process steps (some critical steps in the recipe) and parameters which measurements have significant effects on product quality. Process step Variables Identify the key steps and variables. ：the key parameter in corresponding step. NCTS Industrial Statistics Research Group Seminar Page 35 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(2): Extract out KSV from tool signals The KSV (Key Sensitive Process Variables), may not be the measurements itself in corresponding key step. However, we can transform the original tool signals into some statistic quantity, such as slop, area, maxima and minima…,etc., which can really represent the characteristics of tool status. Tool signals How to extract out the useful tool signal information ?? 1. Time Length 2. Mean 3. Stdev 4. Median 5. Max 6. Min 7. Area 8. Quantile………………. NCTS Industrial Statistics Research Group Seminar Page 36 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(3): Correlation analysis In this step, we’ll conduct the Pearson’s linear correlation analysis to find out the most important KSV in this process and it will be our Time Series Modeling variable. Correlation Analysis Table Pearson linear correlation analysis equation n r ( x x )( y i 1 i n i n y) (x x) ( y 2 i 1 i i 1 2 y ) i It has high significant correlation !! And then we can use it to be modeling item. NCTS Industrial Statistics Research Group Seminar Page 37 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(4): Fitted the Time Series model to get KSI According to the previous study, we can realize that (Step_4)+(Variable_3)+(Stdev) is the KSV in this process, and correct trend monitoring can be used to determine appropriate timing for preventive maintenance. Trend chart for Variable_3 － Stdev 10 Fitted Time Series Model Model: ARIMA(1,1,2) Variable 3__Stdev 5 A(q )y (t ) C (q )e(t ), (1 q 1 ) A(q ) 1 0.873q 1 0 C (q ) 1 0.657 q 1 0.358q 2 How to fit this Time Series model ?? -5 0 50 100 150 200 NCTS Industrial Statistics Research Group Seminar 250 Wafer# 300 350 400 450 500 Page 38 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(5): Compute KSI & Simulation ARIMA(1,1,2) predicted model Time Series Model can catch the tool KSV decayed trend. 10 Variable 3__Stdev 5 In this work, the KSI (Key Sensitive Index) based approach is proposed for process trend monitoring. 0 -5 0 50 100 150 200 250 Wafer# 300 350 400 450 500 10 10 PM PM PM KSI Index KSI-Based 0 -5 Threshold 5 Variable 3__Stdev 5 PM 0 0 200 400 600 800 1000 1200 1400 1600 1800 Wafer# -5 KSI 0 200 400 KSI KSI 600 800 1000 1200 1400 1600 1800 Wafer# Based-on KSI and Threshold limit we can predict when to do Preventive Maintenance !! NCTS Industrial Statistics Research Group Seminar Page 39 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Conclusions From the simulation results, it seems that our proposal KSI can catch the tool decayed trend, and when the KSI is greater than users defined threshold, then we can suggest engineers to do PM jobs. The KSI-Based to Predict Tool Maintenance approach not only can be used for Furnace and Etch tools to assist engineers in when to call for Preventive Maintenance, but also it is useful to do process trend monitoring in FDC system. NCTS Industrial Statistics Research Group Seminar Page 40 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Case(5): Survival application Advanced Queue-Time to Yield Monitoring System. NCTS Industrial Statistics Research Group Seminar Page 41 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Survival Function BasedAdvanced Q-Time2Yield Morning System Motivation: Queue Time Definition: Q-Time = [t2 - t1] Process A end time (t1) Process A Process B start time (t2) Process B … For chemical processes, they usually put the criteria for Q-Time control to avoid excursions. If the Q-Time longer than the specific specification, we can induce that this may occur some critical issues in this specific time period. As you know, Q-Time Process Control is a great important task on semiconductor manufacturing. In Fabs, the following processes are also involved in Q-Time issues: 1. DT ME → Change FOUP (Q-Time < 3hrs) HSG Depo → HSG Recess (Q-Time < 10hrs) 3. RC1a → Poly1b (Q-Time < 6hrs) …,and so on. 2. Nowadays, we usually set the Q time < k hours monitoring scheme to control these critical processes. If we could build up the Survival Function Model which based on the relationships between Q-Time and Yield decayed process, and provide the probability of risksInnovative idea !! degrees to real time tell engineers what’s the current status for yield detractor and how long could we wait for next process starting. In this way, it will give a big hand for not only Q-Time process control, but also productivity scheduling and cycle time improvement. NCTS Industrial Statistics Research Group Seminar Page 42 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Survival Function Introduction Survival analysis attempts to answer questions, such as: 1) What is the fraction of a population which will survive past a certain time? 2) What rate will they die or fail? 3) Can multiple causes of death or failure be taken into account? 4) How do particular circumstances or characteristics increase or decrease the odds of survival? Exponential Survival Function Survival Function KPIs 1) Survival function: t S (t ) Pr(T t ) 1 F (t ) 1 f (t )dt 0 2) Lifetime distribution function: How to read it ?? F (t ) Pr(T t ) 1 S (t ) If xt=2, then 3) Hazard function: Survival probability =0.2 f (t ) h(t ) S (t ) 4) MTBF/ MTTF: MTBF t f (t )dt 0 NCTS Industrial Statistics Research Group Seminar Page 43 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Invention Program Flowchart Q-Time and Yield data collecting/mapping Survival distributions selecting Model parameters fitting based on distribution Survival function KPIs calculating NCTS Industrial Statistics Research Group Seminar •Key process selecting from engineers Know-How. •Variable: critical WAT/ Yield data. •RMSE/ MME/ TMSE evaluated. •Survival model validation. •Likelihood function to fit parameters. •Kaplan-Meier estimator. •Reliability theory. •Survival function. •Lifetime distribution function. •Hazard Function. •MTTF/ MTBF. Page 44 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(1): Q-Time and Response Data Mapping From engineers Know-How, we could collect the specific Q-Time control processes, and related WAT (electrical testing data)/ Yield data. And then, we are going to conduct the Rank Correlation Analysis to find out the variables which are higher correlation between process and WAT parameters. Q-Time control process WAT Variables OP_1 OP_2 OP_3 OP_4 OP_5 Identify the sensitivity process and variable. WAT_1 WAT_2 WAT_3 WAT_4 WAT_5 WAT_6 ：the highly correlation relationship. NCTS Industrial Statistics Research Group Seminar Page 45 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(2): Survival Distribution Selecting Model identification: Probability Plots for 4 Survival distributions Four-way Probability Plot for weib ML Estimates - Complete Data Weibull Lognormal base e Weibul distribution 99 95 90 80 70 60 50 40 30 Lognormal distribution 99 95 Percent Percent For the Survival function distribution identification, we usually choose 4 popular distributions: 1) Weibul distribution 2) Lognormal distribution 3) Exponential distribution 4) Normal distribution to be the initial testing model,and based on the “Anderson-Darling value”, we could select the best fitted distribution as the Survival function. 20 10 5 3 2 1 Anderson-Darling (adj) Weibull 2.172 80 70 60 50 40 30 20 Lognormal base e 2.179 Exponential 10 2.579 5 Normal 2.219 1 10 100 100 Exponential Normal Exponential distribution 99 98 1000 Normal distribution 99 95 97 Percent 95 Percent Which one is better ?? 90 80 70 60 50 10 5 30 10 1 0 NCTS Industrial Statistics Research Group Seminar 80 70 60 50 40 30 20 100 200 300 Page 46 of 56 400 500 600 700 800 0 100 200 300 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Step(3): Model Parameters Fitting Fitted parameters to data: After identified the process decayed distribution, we need to estimate the model parameters. Currently, there are two popular methods to figure out the model parameter estimations: 1) Kaplan-Meier estimator: i (A) Mean Rank Fˆ (t(i ) ) ( ) n 1 i 0.3 ( B) Median Rank Fˆ (t(i ) ) ( ) n 0.4 2) Maximum Likelihood estimation(MLE): Find * such that L(ˆ* | x ) max{L( | x )} ˆ* is called MLE for From below CDF charts, it ‘s obviously to see that K-M estimator could estimate the survival function from life-time data as good as original distribution. 1 0.9 0.8 K-M cdf Normal cdf 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 NCTS Industrial Statistics Research Group Seminar 5 Page 47 of 56 6 7 8 9 10 11 12 13 14 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab 15 Step(4): Survival Function KPIs Calculating Survival function for Q - Time controlled process 1 Simulation Result: 0.9 We set the Q-Time controlled process belongs to Exp(Θ=12) distribution, and its Survival function is also shown here. Survival Function S(t) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10 20 30 Xt Survival KPIs: 50 60 We set Xt=10 to evaluate each KPI. 1) Survival probability: 0.4346 2) Lifetime distribution function: 3) Hazard function: 4) MTBF/ MTTF: 40 Q - Time ( hours ) 0.0362 0.0833 So, if the Lot queuing time in critical process is 10 hours, its Survival probability is 0.4346. At the same time, RTD could reference this Survival probability to dispatch FOUPs. 12 NCTS Industrial Statistics Research Group Seminar Page 48 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Conclusions From the simulation results, it seems that our innovative proposal Survival Function Based-Advanced Q-Time2Yield Morning System can estimate the Q-Time controlled process decayed behavior successfully. The Survival Function Based-Advanced Q-Time2Yield Morning System approach not only can be used to monitor queuing time between process ended to next process starting, but also give the Survival probability function for risks-degrees if wafer waited for a long time. The Cycle Time and Productivity Scheduling efficiency will also be improved, if Fab RTD System could reference this Survival probability value to work logistic dispatch. NCTS Industrial Statistics Research Group Seminar Page 49 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Case(6): SPC chart application Smart Process Capability Trend Monitoring System. NCTS Industrial Statistics Research Group Seminar Page 50 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Smart Process Capability Trend Monitoring System At present, we use the SPC (Statistical Process Control) to monitor process capability and so on. The SPC charts use Western Electric rule to monitor tools real-time alert. Western Electric rule One point out of control limit (3 Sigma) USL UCL Hold CL LCL LSL 7 points increasing or decreasing USL UCL Hold CL LCL LSL Problem: Currently, we only can find problems when a tool violates Western Electric rules. We can’t provide the prealert system when tools have potential problem. Although our Yield system provide the Cpmk index to monitor the tool health, but there are no monitoring rules like SPC in it. How: Here we will use the CUSUM (Cumulative sum control chart) method to transform the Cpmk value of tool in our Yield system. We not only provide the monitoring rules and can find the trend down situation of tools. NCTS Industrial Statistics Research Group Seminar Page 51 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Method Introduction Cusum Concept: Small trend down situation Cpmk Value Mean Cpmk limit Period/date Key Concept: The Cusum method will calculate the upper cusum value and lower cusum value which base on last cusum value. So we just need to monitor the cusum value of each period that there is trend down situation in condition periods. Method equation: upper side cusum Ci max[ 0, xi ( 0 k ) Ci1 ] lower side cusum C max[ 0, ( 0 k ) xi C ] i i 1 where C 0 C 0 0 K | 1 0 | , (if 1 0 ) 2 2 NCTS Industrial Statistics Research Group Seminar Cusum（Cumulative sum control chart） It is out of control situation, that the upper sum higher than H (decision interval) or the lower sum lower than H. Normally H 5 Page 52 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Simulation • Tool A • FAB: Cross Fab • Date range: 4/15-5/13 • Condition 4 periods • Analysis result: There is a trend down situation in periods 1-17 and periods 32-50. NCTS Industrial Statistics Research Group Seminar Page 53 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Conclusions Provided a new monitor index (CUSUM) for tools’ health and pre-alert model when tools have potential problems that engineers can handle tools’ health conveniently & prevent tools from occurring significant problems. NCTS Industrial Statistics Research Group Seminar Page 54 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Thank You. Questions & Answers… NCTS Industrial Statistics Research Group Seminar Page 55 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab Published Papers NCTS Industrial Statistics Research Group Seminar Page 56 of 56 Department of Electrical and Control Engineering, NCTU Electron Industrial Control Lab