MODELING TOOL FAILURES IN SEMICONDUCTOR FAB SIMULATION. Oliver Rose. Institute of Computer Science University of Würzburg Würzburg, 97074, GERMANY.

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1 Poceedings of the 004 Winte Simulation Confeence.G. Ingalls M. D. ossetti J. S. Smith and B.. Petes eds. MODELING TOOL FILUES IN SEMICONDUCTO FB SIMULTION Olive Institute of Compute Science Univesity of Wüzbug Wüzbug GEMNY. BSTCT In this eseach we investigate how well Weibull Gamma and special bimodal distibution ae suited as an altenative to the exponential distibution appoach in the stochastic modeling of machine downtimes and times between failues. We also discuss the question whethe sampling shop-floo data should not only include fist ode statistics but also measues that allow to monito and model the vaiability of the equipment and pocesses and even the coect distibution of the data. INTODUCTION typical semiconducto manufactuing facility contains up to 000 vaious machines and tools. Besides the complexity of handling this vast amount of equipment thee ae seveal othe factos that make poduction planning and contol in this envionment paticulaly difficult. (Cf. (Schömig and Fowle 000) and (Uzsoy et al. 99) fo a thoough summay of these factos and shopfloo contol poblems in semiconducto manufactuing.) Unpedictable machine downtimes ae believed to be the main souce of uncetainty in the semiconducto manufactuing pocess. Obviously downtimes ae a sevee poblem since poduction capacity is lost and the flow of mateial is disupted. The eliability of semiconducto manufactuing equipment is unusual fom a numbe of standpoints. Despite of all effots to tune and calibate machines to an optimum pefomance they ae still subject to andom failues. The failue of equipment o pocesses is often not a had failue in the sense that something obviously beaks o goes wong; but athe a soft failue in which the equipment begins to poduce out of the toleance egion. Fo this eason the equipment usually completes a lot o batch pio to being taken out of sevice fo epai which often involves moe tuning calibation and test athe than component eplacement. Since some wafe fabication tools such as ion implantes may be down 30-40% of the time the impact of peiods of unavailability on poduction contol as well as oveall poductivity is temendous. Hence appopiate modeling of equipment and pocess failues is a must to deive meaningful output pefomance measues. The SEMI E0 and E58 standads povide a famewok fo sampling machine-level data in the semiconducto industy. Downtime is a peiod of time duing which the equipment is not in a condition to pefom its intended function. This peiod does not include any potion of time whee the equipment o the entie facility ae not scheduled to pefom fabication. Geneally it is distinguished between scheduled and unscheduled downtimes. scheduled downtime occus when the equipment is not available to pefom its intended function due to planned events such as peventive maintenance poduction test change of consumables and machine setup fo unning a diffeent pocess. ll of these pocedues ae clealy sepaable and planned in thei espective pocess. lso included ae test un times fo the equied subsequent equalification and e-appoval. Waiting times esulting fom delays in the pocess ae also included. Unscheduled downtimes ae peiods of time duing which the equipment is not in a condition to pefom its intended function due to an unplanned event. Examples ae: technical failues unplanned measues to secue opeation unplanned shut down of supply infastuctue. These events inteupt equipment opeation. In esolving these inteuptions (Inteupts) they ae distinguished as follows based on tig and pesonnel equiements: n assist is an unplanned inteuption that occus duing an equipment cycle if all thee of the following conditions apply: () The inteupted equipment cycle is esumed though extenal intevention (e.g. by an opeato) () thee is no eplacement of a pat othe than specified consumables (3) thee is no futhe vaiation fom specifications of equipment opeation. n assist usually lasts not longe than utes. failue howeve is any unplanned inteuption o vaiance fom the specifications of equipment opeation othe than assist. MODELING EQUIPMENT DOWNTIMES Obtaining the aveages of uptimes and downtimes ae sufficient when these time peiods ae assumed to be exponentially distibuted. This is the pevalent assumption in eli-

2 ability and simulation modeling when using simple models. Pevious expeiments (Schömig 999) wee concened with exploing the effect of the distibution of down events. The esults poved the coupting influence of vaiability that is caused by equipment unavailability and also showed the shotcogs of classical static capacity calculations the expeiments concening the type of the downtime distibution howeve found no significant diffeence even when the system eaches a high load. Hence it was concluded that in this case the actual distibution of downtimes play only a o ole in the pefomance of the fab. Futhe expeimentation in the context of an investigation concening how simplifying assumptions in the stochastic modeling pocess fo closed fom queuing-type fomulae affect the deived output pefomance measues as well as ecent publications (Leemis 00) gave eason to evisit the poblem of finding an appopiate distibution fo modeling the poductive time between equipment failues and the time to epai. In (Schömig and 003) we discussed the poblems of finding the paametes fo a Weibull failue model fom eal fab data. In addition we povided some fist esults on the effects of diffeent failue models on cycle times fo a vaiety of fab models. We concluded that not only the mean and vaiance of the failue data plays an impotant ole but also the shape of the distibution. 3 BIMODL FILUE MODEL Because of seveal pactitiones comments on ou afoementioned pape we investigated bimodal TTF (Time To Failue) and TT (Time To epai) distibutions fo ou factoy models. The pincipal motivation is that eal factoy tool failue measuement histogams ae also bimodal in a lot of cases. This is due to the fact that thee ae a lot of shot outages that happen fequently and a few long failues that occu aely. Due to the lack of eal fab data we developed a simple model fo this type of machine failues whee we can use given aveages fo the TT and TTF and thei coefficients of vaiation (CoV) whee the CoV is defined as the standad deviation divided by the mean. The two CoVs ae assumed to be the same fo TT and TTF. Fo simplicity we constuct ou bimodal distibutions fom two symmetic tiangula distibutions of type tia ( mode max ) = tia (( ) mm ( + ) m) whee 0 < <. The mean of this tiangula distibution is m its vaiance is and its CoV is. m In the fist pat of model desciption we outline the computation of the individual aveage values fo TTF and TT of the two tiangula distibutions. In the second pat we detee the span/ange of the tiangula distibutions to adapt the CoV of the bimodal distibutions. In the following we intoduce the notation of the paametes used: Input paametes: veage TT and aveage TTF F taget CoV C. Output paametes: veage TTs and aveage TTFs f and f span of the tiangula distibutions. In the sequel subscipt will be used fo the shot/fequent failues and fo the long/ae ones. To compute 5 output paametes fom 3 input paametes we need to intoduce an additional assumption: Both the shot/fequent and the long/ae failues lead to the same outage pecentages a and a which ae equal to half the outage pecentage induced by the input paametes a = a = ( ) whee a = a = and = + F + f + f In addition we need to elate one of output paametes to one of the input paametes. In ou case we choose fom the inteval ;. Smalle values of lead to lage CoVs and lage values to smalle CoVs of the esulting bimodal distibution. fte some algeba we end up with + f = = + f + f + =. ( + f) ( ) and Based on these 4 aveage values the pobability α that a shot/fequent outage is computed esults in α and analogously + f = + f + + f + f α =. + f + + f

3 The vaiance of the bimodal distibution fo the TT geneated fom the two tiangula distibutions is deived as + ( α + α ). This leads to a imum CoV of the combination of tiangula distibutions of C α + α = fo = 0 and a maximum CoV of C 7 α + α = max fo =. Hence has to be selected appopiately to povide an adequate ange of CoV values [ C ; C max ] to choose fom. Note that afte a value fo is deteed all othe vaiables apat fom can be computed. bitay CoV values fom [ 0; [ can be geneated. Fo = we obtain 0 Cmax. C = and leads to Given a taget CoV C [ C ; C ] max distibution paamete is computed by ( C + ) α + α =. fo the bimodal In summay the two steps to detee the paametes of the tiangula distibutions ae to find a value fo that povides the appopiate inteval [ C ; C max ] and then to fine-tune the CoV by computing with the above fomula. ll dependent paametes ae given explicitly. Thus no numeical poblems ae expected fo the above fomulae. 4 SIMULTION EXPEIMENTS s test models we used the MIMC (Measuement and Impovement of Mnufactuing Capacities) test bed datasets Dataset was not used because the simulation package epoted poblems in the dataset. Fo futhe details on the datasets and thei download: see < The simulation uns wee caied out with Factoy Exploe.8 fom WWK. We simulated 7 yeas of fab opeation with poduct mixes as given. The fist two yeas wee consideed as wam-up phase and not taken into account fo the statistics. We checked the length of the initial tansient both by the cycle time ove lot exit time chats and the Schuben test. If thee was an indication of initial bias poblems the wam-up phase was inceased appopiately. The measuement inteval was 5 yeas in all cases. s pefomance measues we consideed the aveage and the 95%-quantile of the cycle times of all lots. We simulated factoy loads fom 70% to 98% of the bottleneck tool goup capacity. s dispatching ules we used Fist In Fist Out (FIFO) and Citical atio (C) with a taget flow facto of 4.0. In the oiginal fab models all Time To Failue (TTF) and Time To epai (TT) distibutions wee set to exponential. This leads to a coefficient of vaiation of fo TTF and TT. In ou expeiments we eplaced the given exponential distibutions by Gamma and Weibull distibutions o ou new bimodal failue model with the same mean values but diffeent Coefficients of Vaiation. The following Gamma and Weibull distibutions wee consideed: CoV = 0.5: less vaiation than exponential distibution Gamma distibution: shape paamete α = 4 Weibull distibution: shape paamete α =.035 CoV =.0: exponential distibution CoV =.0: moe vaiation than exponential distibution Gamma distibution: shape paamete α = 0.5 Weibull distibution: shape paamete α = Fo the bimodal model we had to eplace each of the oiginal unimodal exponential distibutions by two tiangula distibutions unning in paallel. Hee it is impotant that the simulato does not ignoe down events that happen duing an ongoing down phase of a tool. If this happens the simulato has to polong the cuent downtime by the amount of the new downtime. In Table and 3 we list the aveage cycle times of all lots fo all fab models unde a load of 98%. The cycle times ae given as multiples of the lots aw pocessing times. The tables contain both the FIFO and the C esults. The 95%-quantiles ae not given because they show essentially the same behavio as the aveage cycle time esults. s expected the cycle times incease when the CoV values of the TTF and TT distibutions incease. Fo the low CoV values the cycle time esults match. Fo the high CoV values howeve the shape of the distibutions mattes. Whethe Gamma Weibull o bimodal models lead to highe cycle times depends on the fab model. In all cases the esults fo the Exponential distibution ae between the low and the high CoV esults.

4 The conclusions fom ou simulation study ae as follows. The CoV values of the TTF and TT distibutions have a consideable impact on the fab pefomance measues. The effect is less citical fo CoV values less than than fo CoV values lage than. The magnitude of the effects is model dependent. In geneal the effects ae stonge unde FIFO than unde C dispatch egime. In addition to the CoV the shape of the distibution also mattes. Table : veage Cycle Times fo CoV=0.5 FIFO Gamma Weibull Bimodal m...4 m m m m... m C Gamma Weibull Bimodal m m m m m m Table : veage Cycle Times fo CoV=.0 FIFO Exponential Bimodal m m3.8.8 m4.9.9 m5.9.9 m..5 m7.4.5 C Exponential Bimodal m m3.. m4.. m m.8.8 m7.4.5 Table 3: veage Cycle Times fo CoV=.0 FIFO Gamma Weibull Bimodal m m m m m m C Gamma Weibull Bimodal m m m m m m Theefoe it is questionable to use exponential distibutions fo modeling TTF and TT distibutions if the CoV value measuements fom the fab indicate that this value is not too close to. If it is lage than it is ecommended to spend some effot on finding the appopiate class of model distibutions because the shape of the distibution has a consideable influence on the quality of the esults. This does not only hold fo the cycle-time estimates but also fo the on-time delivey pefomance estimates as can be concluded fom the 95%-quantile esults. 5 CONCLUSION In ou eseach we investigated the appopiateness of nonexponential distibutions fo modeling machine time to epai (TT) and time to failue (TTF) in semiconducto wafe fabication facility models. We exaed whethe a change in the type of TT and TTF distibutions had an effect on the pefomance measues e.g. aveage cycle times of a wafe fabication facility. It tuned out that both the vaiability and the shape of the distibution used fo modeling TT and TTF had a consideable effect on the factoy pefomance estimates. Simplifying assumptions like using exponential distibutions fo that pupose will cause misleading simulation esults. CKNOWLEDGMENTS The autho would like to thank Tosten Schiele fo his valuable simulation and data analysis effots.

5 EFEENCES Leemis L. 00. Input Modeling Techniques fo Disceteevent Simulation. In Poceedings of the 00 Winte Simulation Confeence ed. B.. Petes J.S. Smith D.J. Medeios and M.W. ohe -73. Piscataway New Jesey: Institute of Electical and Electonics Enginees. Schömig On the Coupting Influence of Vaiability in Semiconducto Manufactuing. In Poceedings of the 999 Winte Simulation Confeence ed. P.. Faington H.B. Nembhad D.T. Stuock and G.W. Evans Piscataway New Jesey: Institute of Electical and Electonics Enginees. Schömig. and J.W. Fowle Modeling Semiconducto Manufactuing Opeations. In The New Simulation in Poduction and Logistics ed. K. Metins and M. abe 5-4. Belin. Schömig. and O On the Suitability of the Weibull Distibution fo the ppoximation of Machine Failues. In Poceedings of the 003 Industial Engineeing eseach Confeence. Potland Oegon. Uzsoy. C. Lee and L. Matin-Vega. 99. eview of poduction planning and scheduling models in the semiconducto industy Pat I: System chaacteistics pefomance evaluation and poduction planning. IIE Tansactions on Scheduling and Logistics 4: 47-. UTHO BIOGPHY OLIVE OSE is ssistant Pofesso in the Depatment of Compute Science at the Univesity of Wüzbug Gemany. He eceived an M.S. degee in applied mathematics and a Ph.D. degee in compute science fom the same univesity. He has a stong backgound in the modeling and pefomance evaluation of high-speed communication netwoks. Cuently his eseach focuses on the analysis of semiconducto and ca manufactuing facilities. He is a membe of IEEE SIM and SCS. His web addess is <www3.infomatik.uni-wuezbug.de/~ose>.