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半導體產業常用的統計方法
大綱 ,[object Object],[object Object],[object Object]
基本統計量 ,[object Object],[object Object],[object Object],[object Object]
統計方法 ,[object Object],[object Object],[object Object],[object Object]
Design house ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
可用的統計方法 ,[object Object],[object Object],[object Object]
統計上的問題 ,[object Object]
Correlation Coefficient
Regerssion Residual standard error: 6.297 on 201 degrees of freedom Multiple R-Squared: 0.4439,  Adjusted R-squared: 0.3111  F-statistic: 3.343 on 48 and 201 DF,  p-value: 1.455e-09   Improve the model?
Testing Hypothesis  ,[object Object],[object Object],[object Object]
Result:
Display Graphics ,[object Object],[object Object]
Fab 廠資料來源 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Fab 廠的挑戰 ,[object Object],[object Object],[object Object]
Fab 廠常用的統計方法 Statistical Method Purpose Distribution  Basic material for statistical tests. Used to characterize a population based upon a sample . Hypothesis testing Decide whether data under investigation indicates that elements of concern are the “same” or “different.” Experimental design and analysis of variance Determine significance of factors and models; Decompose observed variation into constituent elements. Categorical modeling Use when result or response is discrete (such as “very rough,” “ rough,” or “smooth”). Understand relationships, determine process margin, and optimize process. Statistical process control Determine if system is operating as expected. Regression Yield modeling. Yield impact Duane S. Boning, Jerry Stefani and Stephanie W. Butler: Statistical Methods for Semiconductor manufacturing
Yield maintenance  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Statistical Process Control Normal, +- 3 sigma ~ 99.7
Yield drop ,[object Object],[object Object],[object Object]
Group comparison ,[object Object],[object Object],[object Object],[object Object],[object Object]
PM ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Yield enhancement ,[object Object],[object Object],[object Object]
Process improvement ,[object Object],[object Object]
Key parameters  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Yield impact model ,[object Object],[object Object],[object Object]
Yield impact model ,[object Object],[object Object],[object Object],[object Object]
Yield Prediction ,[object Object],[object Object],[object Object]
Wafer Yield -- Poisson Model ,[object Object],[object Object],Assumption: n defects randomly distribute in wafer with N chips The probability of one chip contains k defects m=n/N,  K=0    Chip pass D = m/A  Yield = Pass chip number/N
Wafer Yield -- Other models ,[object Object],[object Object],f(D) is the defect density distribution Murphy model density formulation triangular Exponential Seeds
Daily/Weekly/Monthly Yield ,[object Object],[object Object],[object Object]
Next product Yield ,[object Object],[object Object],Time Yield Pilot Rump Mass production Phase out
Summary of “basic statistical method”  ,[object Object],[object Object],[object Object],[object Object],[object Object]
新的挑戰  --  進階分析的方法 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Advanced topic -- testing ,[object Object],[object Object]
Display  – violin plot
Display -- Correlogram
Pattern classify  ,[object Object],[object Object],[object Object],[object Object],Ref: pattern recognition
Pattern Classify ,[object Object],[object Object],[object Object],[object Object]
Clustering  分群 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Single Tool  ,[object Object],[object Object]
Golden Path P1 P2 P3 E1 E2 T1 T2 3*2*2 = 12 combination for 3 steps   Whole combination? Partition method Golden wafer/golden lot tracking
Parameters >> observations ,[object Object],[object Object]
Advanced Process Control ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Reference: ,[object Object],[object Object]

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統計在半導體產業的應用 -- Basic Statistic Methods

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  • 9. Regerssion Residual standard error: 6.297 on 201 degrees of freedom Multiple R-Squared: 0.4439, Adjusted R-squared: 0.3111 F-statistic: 3.343 on 48 and 201 DF, p-value: 1.455e-09  Improve the model?
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  • 15. Fab 廠常用的統計方法 Statistical Method Purpose Distribution Basic material for statistical tests. Used to characterize a population based upon a sample . Hypothesis testing Decide whether data under investigation indicates that elements of concern are the “same” or “different.” Experimental design and analysis of variance Determine significance of factors and models; Decompose observed variation into constituent elements. Categorical modeling Use when result or response is discrete (such as “very rough,” “ rough,” or “smooth”). Understand relationships, determine process margin, and optimize process. Statistical process control Determine if system is operating as expected. Regression Yield modeling. Yield impact Duane S. Boning, Jerry Stefani and Stephanie W. Butler: Statistical Methods for Semiconductor manufacturing
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  • 17. Statistical Process Control Normal, +- 3 sigma ~ 99.7
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  • 40. Golden Path P1 P2 P3 E1 E2 T1 T2 3*2*2 = 12 combination for 3 steps  Whole combination? Partition method Golden wafer/golden lot tracking
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Notas del editor

  1. N defects uniformly distribute in wafer with m chips, probability of chip contain defect n/m chip area A Pr{n/m; K=k}=[exp(-n/m)][(n/m)^k]/(k!) k=0, Y=exp(-n/m)