Evaluating Production Yields of TFT-LCD Manufacturing Processes

Transcription

1 Evaluating Production Yields of TFT-LCD Manufacturing Processes A presentation to the Institute of Industrial Engineering, National Taiwan University Oct. 7 th, 2009 Chen-ju Lin Department of Industrial Engineering & Management Yuan Ze University, Taiwan

2 Outline Introduction Capability index S pk Process selection procedure Application: TFT-LCD Conclusions 2

3 Introduction and motivation Compare two manufacturing processes with very low fraction of defectives Select the process with the higher yield A two-phase testing hypotheses based on S pk 3

4 Thin-film transistor type liquid-crystal display, TFT-LCD Fundamental photonic of LC Applications: cell phones, PDAs, notebook computers, and monitors * Picture from Chi Mei Optoelectronics 4

5 Thin-film transistor type liquid-crystal display, TFT-LCD Structure: * Picture from Chi Mei Optoelectronics 5

6 Process capability indices Measure the capability of meeting product characteristic requirement preset by the product designers or the process engineers C p, C PU, C PL, C pk, C pm, C pmk, and S pk (Kane, Chan et al., Pearn et al., and Boyles) 6

7 Yield index S pk 1 1 USL 1 LSL S pk Yield = Pr(LSL<X<USL) = 2Φ(3S pk )-1 S pk value NCPPM* *NCPPM: fractions of nonconformities in parts per million 7

8 Statistical inference on Sˆpk ˆ USL x 1 x LSL Spk 3 2 s 2 s 1 By Taylor expansion ˆ W Spk S pk 6 n 3S where W W~N(0, a 2 + b 2 ) 8 pk 2 2 n S USL USL LSL LSL n X USL LSL 1 USL USL LSL LSL a 2 USL LSL b

9 Process selection procedure Selection procedure: Phase I: Selecting process with higher production yield Phase II: Magnitude outperformed measurement Sample size requirement 9

10 Phase I: Selecting process with higher production yield Hypothesis testing H 0 : S pk2 /S pk1 1 H 1 : S pk2 /S pk1 > 1 Decision rule: If R S ˆ ˆ pk 2 / Spk 1 > c 0, process 2 has higher yield than process 1 Otherwise, process 2 may not be superior Type I error: Pr R c H : S S, n, n, and S C 0 0 pk 2 pk1 1 2 pk1 10

11 Distribution of R 2 N Spk2, s 2 ˆ pk2 / pk1 ~ 2 N Spk1, s 1 R S ˆ S where a b s1 2 36n 3S 1 pk1 a 11 b s2 2 36n 3S 2 pk2 a , 1, 2 i Cpi C ai Cpi C ai CpiCai CpiCai i 2 b 3C 2 C 3 C C, i 1, 2 By convolution f R (r)= i pi ai pi ai s2 s 1r 2 s2spk1 s 1Spk 2r S pk1 Spk2r s2spk1 s1spk 2r 1 S pk1 S pk2 exp s1 s2 s 2 s 1r 2 s1 s2 2 2 s 2Spk1 s1spk 2r 2 1 s1 s s 1 s2 s 2 s1r s2 s 1r where < r < S pk1 S pk2 exp s1 s2

12 Results Critical points at α = 0.05 n 30 c n 90 c n 150 c

13 Phase II: Magnitude outperformed measurement Due to high cost of process replacement, the factory would consider changing to the new process only if the new process s capability significantly outperforms the existing process s capability by a magnitude of h > 0. 13

14 Phase II: Magnitude outperformed measurement Hypothesis testing H 0 : S pk2 S pk1 + h H 1 : S pk2 > S pk1 + h (h>0) Decision rule: If R Sˆ / Sˆ > c 0, pk 2 pk 1 the capability of process 2 outperforms the capability of process 1 by h Pr R c H : S S h, n, n, and S C 0 0 pk2 pk1 1 2 pk1 14

15 Results: Critical values for rejecting S pk2 S pk1 + h at α=0.05 (S pk1, S pk2 ) n (1.00, 1.10) (1.00, 1.20) (1.00, 1.30) (1.00, 1.40) (1.00, 1.50)

16 Results: Critical values for rejecting S pk2 S pk1 + h at α=0.05 (S pk1, S pk2 ) n (1.33, 1.43) (1.33, 1.53) (1.33, 1.63) (1.33, 1.73) (1.33, 1.83)

17 Power analysis (at α=0.05) 1 Power function for S pk1 = 1 power n=30 n= n=100 n=150 n= S pk2 17

18 Required sample size Sample size required for testing H 0 : S pk2 S pk1 versus H 1 : S pk2 > S pk1. Power Power S pk1 S pk S pk1 S pk

19 Application in TFT-LCD industry Spec: Target thickness = 0.70mm USL = 0.77mm and LSL = 0.63mm the minimal requirement for S pk = 1 Sample: size = 100 /each process x1 = , x2= , s 1 = , s 2 = , S S = , = , ˆpk1 ˆpk2 thus R =

20 Analysis Step 1 Since R = > 1.180, we therefore conclude that the Process II is superior to Process I with a 95% confidence level Step 2 Process II has a manufacturing production yield that is significantly higher than that of the Process I by a magnitude of 0.35 S pk S pk h c Decision Reject H 0 Reject H 0 Reject H 0 Do not Reject H 0 20

21 Conclusions Consider the process selection problem for two two-sided processes Present an exact analytical approach to solve the problem The proposed approach is effective for in-plant applications 21

22 References 1. V. E. Kane. Process capability indices. Journal of Quality Technology 1986; 18 (1): L. K. Chan, S. W. Cheng, F. A. Spiring. A new measure of process capability: Cpm. Journal of Quality Technology 1988; 20 (3): W. L. Pearn, S. Kotz, N. L. Johnson. Distributional and inferential properties of process capability indices. Journal of Quality Technology 1992; 24 (4): R. A. Boyles. Process capability with asymmetric tolerances. Communication in Statistics: Simulation and Computation 1994; 23 (3): W. L. Pearn, K. S. Chen. Multi-process performance analysis: a case study. Quality Engineering 1997; 10 (1): W. L. Pearn, M. H. Shu. Manufacturing capability control for multiple power distribution switch processes based on modified Cpk MPPAC. Microelectronics Reliability 2003; 43 (6): D. R. Bothe. A capability study for an entire product. ASQC Quality Congress Transactions 1997; 46: W. L. Pearn, C. W. Wu. An effective decision making method for product acceptance. OMEGA, International Journal of Management Science 2007; 35 (1): W. L. Pearn, S. Kotz. Encyclopedia and handbook of process capability indices. World Scientific: Singapore, J. C. Lee, H. N. Hung, W. L. Pearn, T. L. Kueng. On the distribution of the estimated process yield index Spk. Quality and Reliability Engineering International 2002; 18 (2): W. L. Pearn, G. H. Lin, K. H. Wang. Normal approximation to the distribution of the estimated yield index Spk. Quality and Quantity 2004; 38 (1): Chen-ju Lin, W. L. Pearn. Process selection for higher production yield based on capability index Spk. to appear in Quality and Reliability Engineering International. 22

23 Q&A Thank you. 23