Constructing Control Process for Wafer Defects Using Data Mining Technique

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1 The Fourth nternatonal Conference on Electronc Busness (CEB004) / Bejng 5 Constructng Control ocess for Wafer Defects Usng Data Mnng Technque Leeng Tong Hsngyn Lee Chfeng Huang Changke Ln Chenhu Yang Department of ndustral Engneerng and Management Natonal Chao Tung Unversty Hsnchu Taan Chna ltong@cc.nctu.edu.t {chaba.em89 frogman.em89changke.em89mmosa.em90g}@nctu.edu.t ABSTRACT The afer defects nfluence the yeld of a afer. The ntegrated crcuts (C) manufacturers usually use a Posson dstrbuton based c-chart to montor the lot-to-lot afer defects. As the afer sze ncreases defects on afer tend to cluster. When the c-chart s used the clustered defects frequently cause erroneous results. The man objectve of ths study s to develop a herarchcal adaptve control process to montor the clustered defects effectvely and detect the afer-to-afer varaton and lot-to-lot varaton smultaneously usng data mnng technque. Keyords: afer defects c-chart defect clusterng adaptve control chart data mnng.. NTRODUCTON The C fabrcaton has been the most popular ndustry n recent decades. The key compettve ablty of C products s the afer yeld. The afer yeld s defned by the percentage of the chp thout defects on a afer. To enhance the afer yeld most C manufacturers employ a Posson dstrbuton based defect control chart (c-chart) to montor the afer defects. The c-chart s proved to be effectve hen afer sze s small (e.g. four or sx nches afers). As the afer sze has been enlarged to telve-nch the manufacturng process becomes very complcated. Consequently the clusterng phenomenon of the defects becomes ncreasngly apparent. Ths phenomenon ll affect the accuracy of the c-chart. When the conventonal c-chart s used to montor the large-sze afers the clustered defects frequently cause erroneous results. That s the c-chart may cause too many false alarms. Ths s because c-chart requres that the occurrence of a defect n any locaton s ndependent of the occurrence of defects n other locatons. The C manufacturng process s composed of hundreds of steps. At each step many possble factors may affect the qualty of a afer. There are three types of afer varatons: thn-afer varaton afer-to-afervarataon and lot to-lot varaton. The c-chart can only detect the lot-to-lot varaton under the condton that the defects are scattered randomly on a afer and there s no afer-to-afer varaton. Besdes the cost of samplng afers from a lot becomes expensve for large-sze afers. An adaptve control chart may be utlzed to reduce the samplng cost. Therefore the man objectve of ths study s to develop a complete adaptve detectng procedure of afer defects hch concerns both multple varatons and clusterng phenomenon. Usng the proposed procedure the afer defects can be controled effcently th lo samplng cost.. DOCUMENTATON DSCUSSON. Clusterng analyss [4] Cluster analyss s a popular data mnng technque used for combnng observatons nto groups or clusters such that each cluster s homogeneous th respect to certan characterstcs and observatons of one cluster should be dfferent from the observatons of other clusters. n herarchcal cluster analyss clusters are formed herarchcally such that the number of clusters at each step s n- n- n- and so on. A number of dfferent algorthms for herarchcal clusterng ere developed. These algorthms dffered manly th respect to ho dstances beteen to clusters are computed. The Eucldean dstance for p varables s a common formula used for computng the dstance beteen to observatons. The dstance s utlzed as a measure of smlarty n cluster analyss.. Three-step herarchcal control process n the C manufacturng process there are three types of afer varatons: thn-afer varaton afer-to-afer varaton and lot to-lot varaton may cause the yeld loss. Wells and Smth [5] clamed that the three varatons must be under control to assure the qualty of a afer and they proposed a step-by-step control process as follos: () Determne the unformty of a afer. Calculate the non-unformty ( ) of each afer: = V and V = 00σˆ / X ( ) Where σˆand X represents the estmated standard devaton and mean. () Dra X R control chart usng the values of to determne hether the non-unformty of each afer s under control.

2 6 The Fourth nternatonal Conference on Electronc Busness (CEB004) / Bejng () Determne the lot-to-lot varaton. () Calculate the average run value of every lot. () Dra X MR chart to determne hether the lot-to-lot varaton s under control. (4) Calculate the total varatons of the process / σ ˆ ( ˆ ˆ ˆ TOTAL = σ R + σ W + σ L ) ( ) The estmated thn afer varaton can be calculated usng the average non-unformty of every lot. The formula s gven as follos: σ ˆL = ( X )( X ) 00 ( ) Moreover the afer-to-afer varaton can also obtaned usng the average range of every lot. The formula s gven as follos : σ ˆW = R d ( 4) Fnally the estmated lot-to-lot varaton can be obtaned usng the average movng-range of every lot. The formula s gven as follos : σ ˆ = MR R d ( 5) The control process proposed by Wells and Smth has to drabacks: t can only detect the large shft of the process that s t s not senstve to the small shft; t can only be used n the quanttatve qualty characters.. Adaptve control chart Adaptve control chart s a specal knd of qualty control tool n hch the sample sze and the samplng nterval are changeable. t utlzes the prevous sample data as a bass to fluctuate the samplng szes and samplng ntervals. When sample ponts are near out of control a strcter samplng scheme (e.g. larger sample sze and shorter samplng perod) s adopted to detect the out-of control stuaton effcently. When sample ponts are near the target value a looser samplng scheme (e.g. smaller sample sze and longer samplng perod) s adopted to save the samplng cost. n order to determne hen to adopt the strct normal or loose samplng scheme the upper and loer arnng lmts must be constructed thn the upper and loer control lmts. f a sample pont falls thn the arnng lmts a loose samplng scheme s utlzed. f a sample pont falls beteen the arnng lmts and the control lmts a strct samplng scheme should be utlzed. The basc model of an adaptve control chart s depcted n Fg...4 X adaptve control chart [] The assumptons and parameters of desgnng a X adaptve control chart can be descrbed as follos: () Assumptons () The observatons follo a Normal Fgure. Adaptve control chart dstrbuton. () Suppose the sample sze and the samplng nterval of the tradtonal control chart are n and t 0 0 respectvely. A samplng scheme of n (small sample sze) and h (long sample nterval) or n (large sample sze) and h (short samplng nterval) s determned for an adaptve control chart. When the process s n control the sample sze and samplng nterval of an adaptve control chart should be the same as a tradtonal X control chart. That s E [ n( ) ] = n 0 ( 6) E [ t( ) ] = t 0 ( 7) () Desgn of parameters () Let be the zone thn the arnng lmts be the zone beteen the control lmts and arnng lmts and be the zone thn the control lmts. The loer and upper boundares of and are defned as follos: = (8) UCL) = ( (9) = ( ) (0) () From the assumpton () the follong equaton can be obtaned: n Z = n Z + n Z () ( ) ( ) ( ) 0 Because Z follos a standard normal dstrbuton the follong results can be obtaned: ( Z ) = φ ( ) ( Z ) = ( φ( UCL) φ( ) ) ( Z ) = φ ( UCL) ()

3 The Fourth nternatonal Conference on Electronc Busness (CEB004) / Bejng 7 Usng () and () the arnng lmts can be rertten as follos: φ ( UCL)[ n0 ] ( n ) + n = 0 φ () For a gven samplng nterval a formula derved from () and () s gven as follos: t Z = t Z + t Z (4) ( ) ( ) ( ) 0 can then be rertten as follos: φ ( UCL)[ t0 t ] + t t0 ( t t ) = φ (5) After obtanng fx any three of the four parameters n n t and t the last parameter can be calculated usng () and (5). For example fxng the values of n n and t t b and c can be obtaned by settng ()=(5): b t t = ( n ) n b t c 0 c ( t0 t )( n ) φ( UCL) ( n ) ( UCL) + ( n ) = c = φ n. 0. CONSTRUCT A HERARCHCAL CONTROL PROCESS FOR CLUSTERED DEFECTS Ths study utlzes the clusterng analyss to adjust the number of defects on a afer hen the cluster phenomenon s detected. By dong so the defect clusters are dstrbuted randomly on a afer and the type error of the c-chart can then be reduced. The unformty of a afer s calculated and the adaptve control chart s employed to detect the afer-to-afer and lot-to-lot varatons. The proposed procedure for detectng the clustered defect s descrbed n the follong: Step : Obtan the afer map usng KLA 0 afer nspecton system. Cluster analyss s utlzed to combne the clustered defects. Treat all defects n a cluster as one defect and the locaton of ths defect s the locaton of the cluster s center. Recalculate the number of defects on each afer Use a goodness of ft test to check hether the adjusted (reduced) number of defects satsfes the assumpton of a Posson dstrbuton. f t does go to Step ; otherse repeat Step. Step : Determne hether the afer-to-afer varaton s n control. 0 Calculate the value of usng the adjusted number of defects on a afer. Transfer the values of to satsfy the normalty assumpton. The X R chart and X MR chart are constructed to detect the afer-to-afer varaton. Step: Determne hether the lot-to-lot varaton s n control. The proposed adaptve U control chart s developed based on the X control chart. n montorng C manufacturng process the afers are usually sampled from every lot. The samplng nterval s treated as a fxed constant (e.g. a lot). Therefore only the sample sze needs to be changed accordng to the prevous samplng result. The process of usng U control chart to montor the lot-to-lot varaton s descrbed as follos:. Standardze the sample data. Because µ and σ are unknon they are estmated usng the hstorcal data.. The transformaton formula s : u µ u u (6) Z = σ n u n here u s the mean number of defects on each afer and the varance s the same as the mean snce the number of adjusted defects on a afer follos a Posson dstrbuton.. Contract dfferent samplng schemes (strct and loose) for dfferent sample sze n and n.. Determne the control lmts and the arnng lmts of the U control chart. The control lmts are ± snce the sample data s standardzed. The arnng lmts can be obtaned usng the follong formula: φ ( UCL)[ n0 ] ( n ) + n = 0 φ (7) 4. Plot the sample ponts on the U control chart. f a sample pont falls outsde of the control lmts the process s sad to be out of control.. f a sample pont falls beteen the control lmts and the arnng lmts n s adopted as the next sample sze. f a sample pont falls thn the arnng lmts n ll be used as the next sample sze. 5. Return to Step to perform the next samplng. 4. CASE STUDY Ths secton presents a case study to demonstrate the effectveness of the proposed approach. The requred data n ths case study are obtaned from an C manufacturng company n Taan. When the afer goes through the process of :Metal Etch the

4 8 The Fourth nternatonal Conference on Electronc Busness (CEB004) / Bejng coordnates of the afer s defects are collected usng a KLA 0 afer nspecton system hch s a standard nspecton tool utlzng the laser scan technque. Follo the steps descrbed n Secton the result of each step s gven as follos. Step There are forty lots of afers and each lot has tenty-fve afers. To afers the ffth and the tenty-ffth afers of every lot ere selected. The coordnates of defects and the number of defects are obtaned for each afer. Wafer lot Fg. The proposed U adaptve control chart Fg.. The revsed x control chart Fg..4. The tradtonal c-chart Fg.. The revsed MR control chart Step: The X R chart and X MR chart are constructed to detect the afer-to-afer varaton. The results are shon n Fg and. No afer-to-afer varatons are observed n these to charts. Step ( )[.5 ] +.5 ( ) = φ ω φ = φ = [ ] The U adaptve control chart can detect out-of control lots; hle the tradtonal c-chart only detect 5 out-of control ponts. Consequently the proposed control process can detect small shft and determne the source of varaton comng from the afer-to-afer varaton or the lot-to-lot varaton. 5. CONCLUSON As the afer sze ncreases a afer s defects are no longer randomly dstrbuted. They tend to cluster. n ths study a procedure s proposed to montor the afer defects n C manufacturng. The Clusterng Analyss s employed to adjust the number of afer defects thereby allong not only the adjusted number of defects to satsfy the assumpton of Posson dstrbuton but the conventonal c-chart to stll be used as ell. The adaptve control chart s utlzed to reduce the samplng cost. The proposed approach can reduce the false alarms caused by the clustered defects. The effectveness of the proposed approach s demonstrated through a case study. REFERENCES [] Costa F. B. Antono Jont X and R Charts th Varable Sample Sze and Samplng ntervals Journal

5 The Fourth nternatonal Conference on Electronc Busness (CEB004) / Bejng 9 of Qualty Technology Vol. No. 4 pp87-98 [] Costa F. B. Antono X Charts th Varable Parameters Journal of Qualty Technology Vol. No. PP [] abhu S. Sharad Montgomery C. Douglas and Runger C. George A Combned Adaptve Sample Sze and Samplng ntervals X Control Scheme Journal of Qualty Technology Vol. 6 No. pp [4] Sharma Subhash Appled Multvarate Technques Wley 996 [5] Wells W. Stephen and Smth D. James Makng Control Chart Work For You Semconductor