Scheduling Analysis of Cluster Tools with Buffer/Process Modules

Transcription

1 Schedulng Analyss of Cluster Tools wth Buffer/Process Modules Jngang Y Dept. of Mech. Eng. Texas A&M Unversty College Staton, TX jgy@tamu.edu Shengwe Dng Dept. of IEOR Unversty of Calforna Berkeley, CA dngsw@cal.berkeley.edu Dezhen Song Dept. of Computer Scence Texas A&M Unversty College Staton, TX dzsong@cs.tamu.edu Mke Tao Zhang AzFSM Industral Eng. Intel Corporaton Chandler, AZ mke.zhang@ntel.com Abstract Modelng and schedulng of cluster tools are crtcal to mprovng the productvty and to enhancng the desgn of wafer processng flows and equpment for semconductor manufacturng. In ths paper, we ext the decomposton methods n [1] for mult-cluster tools wth buffer/process modules (Ms). The computaton of the lower-bound cycle tme (fundamental perod) s presented. Optmalty condtons and robot schedules that realze such lower-bound values are then provded usng pull and swap strateges for sngle-blade and double-blade robots, respectvely. The mpact of Ms on throughput and robot schedules s studed. It s found that such an mpact deps on the M processng tme and the cycle tmes of the decomposed clusters on both sdes of Ms. A chemcal vapor deposton (CVD) tool s used as an example of mult-cluster tools to llustrate the proposed method, analyss, and algorthms. The numercal and expermental results demonstrate the effectveness and effcency of the algorthms. I. INTRODUCTION Cluster tools are wdely used as semconductor manufacturng equpment. In general, a cluster tool conssts of three types of modules (Fg. 1): cassette modules (CM) store the unprocessed and processed wafers, process modules (PM) execute semconductor manufacturng processes, such as chemcal vapor deposton (CVD), and transfer modules (TM), whch are robot manpulators, move wafers among process modules and between process and cassette modules. Durng a semconductor manufacturng process, wafers are transported by robots from the cassette module, sequentally go through varous process modules, and then return to the cassette module. We consder an nter-connected M-cluster tool shown n Fg. 2. A buffer module B between C and C +1 (Fg. 2) s called a buffer/process module (M) f t also functons. The use of Ms can make a cluster tool more compact and save the tool footprnt and cost. The exstence of Ms could, however, affect the throughput and the robot schedule because ts dual role as a process module could ntroduce a sgnfcant complexty n the analyss. We dscuss robot schedulng of a mult-cluster tool wth Ms. Our goal s to fnd an optmal schedule that mnmzes cycle tme and, therefore, maxmzes throughput. For cluster tools, robot movement and wafer processng sequences repeat cyclcally at steady state. Lke most of the as a process module wth processng tme Process module P 1 Cassette module Fg. 1. P 2 P 3 C 1 C 2 Transfer module R A schematc of a cluster tool. lteratures, we consder the cycle tme for a one-wafer acton sequence as the optmzaton objectve. A one-wafer acton sequence s defned as a sequence of robot actons whch pck and place each module exactly once [2]. In [3], [4], analytcal models of steady-state throughput are dscussed for a cluster tool equpped wth sngle-blade and double-blade robots. A sngle-blade robot can usually hold only one wafer at a tme whle a double-blade robot has two ndepent arms and, therefore, can hold two wafers at a tme. For a sngle-blade robot, Perknson et al. [3] propose a pull (or so-called downhll) optmal schedule strategy for the robot movng sequence. For a double-blade robot, Venkatesh et al. [4] propose one optmal schedule by a swap acton. Dawande et al. [2] summarze the sequencng and schedulng n robotc cells, whch s smlar to cluster tools. Gesmar et al. [5] ext the result n [6] and dscuss the throughput and schedulng analyss of a robotc cell wth a sngle-grpper robot and parallel statons. Dng et al. [7] ext the network model n [8] for a general study of a mult-cluster tool. Recently, Gesmar et al. [9] dscussed a robotc cell wth three sngle-grpper robots for semconductor manufacturng. In [7], an ntegrated event graph and network model s used to fnd all optmal schedules for a mult-cluster tool. In [10] P 4

2 C 1 C 1 C C +1 C M 01 C 11 C 12 B Cassette modules Fg. 2. A schematc of an nter-connected M-cluster tool. and [11], several rule- or prorty-based heurstc schedulng methods of robot actons of mult-cluster tools have been dscussed. However, there are few analyses and comparson studes of those heurstc methods n terms of optmalty. Ths paper exts the robot schedulng results n Y et al. [1] for mult-cluster tools. The man goal of ths study s to analytcally nvestgate the throughput and robot schedulng of mult-cluster tools wth Ms. The remander of ths paper s organzed as follows. We present and ext the robot schedulng results for a snglecluster tool n secton II. In secton III, we present algorthms to compute the lower-bound of the mnmal cycle tme and dscuss the optmalty condtons and optmal robot schedules. In secton IV, we analyze the buffer/process modules (Ms). An example of throughput analyss and robot schedulng s nvestgated for a CVD tool n secton V. Fnally, we summarze wth concludng remarks. II. CLUSTER TOOL CONFIGURATIONS AND SINGLE-CLUSTER SCHEDULING A. Cluster tool confguraton For the M-cluster tool shown n Fg. 2, we assume that robot R, =1,,M, takes the same amount of tme T to pck and place a wafer and that robot transfer tme T and PM processng tme t j are determnstc. We also consder the assumptons that (1) all wafers follow the dentcal vst flow V, (2) cassette modules always have wafers/spaces, (3) each robot R s ether sngle-bladed or double-bladed, (4) buffer module B (or M) has ether one- or two-wafer capacty, and (5) each cluster must connect to at least one, but at most two other clusters, and these clusters cannot form a loop nterconnecton. We also call cluster C a transfer cluster f (1) R s a sngleblade robot, (2) there s no process module n C, and (3) both sde buffer modules (or M) have one-wafer capactes. Due to the fact that there s not enough wafer storage space to flexbly move wafers, we wll handle transfer clusters slghtly dfferent. For the cyclc producton pattern n whch wafers are drven by a fxed sequence of robot actons, we can only consder the sequencng and tmng of robot actons. We can denote the robot schedule π as a doublet of ts actons ACT and ther relatve startng tmes ST n one cycle: π=act, ST, =1, 2,,m,andm s the total number of robot actons. We defne the optmal schedules as the set of any repeated onewafer cycle under whch the throughput of the cluster tool s maxmzed. It s observed that f an optmal schedule π o maxmzes the throughput μ, t must mnmze the cycle tme T (π). In ths paper, we adopt the termnology fundamental perod, denoted as FP n the lterature, for the mnmal onewafer cycle tme [1], [3], [4], namely, FP = mn T (π). π B. Sngle-cluster tool optmal schedule 1) Maxmal cassette watng tme strategy: A sngle-cluster tool could be runnng n two possble regons: process-bound and transfer-bound regons. For a sngle-blade robot, the robot pull strategy s optmal and for double-blade robot, the swap strategy s optmal [3], [4]. Consderng a N-PM cluster tool, denote the maxmum and mnmum processng tme as t max and t mn, respectvely, t max = max 1 j N t j, t mn = mn 1 j N t j. If we consder the cassette module functons as a process module P 0 wth zero processng tme,.e. t 0 =0, then we can calculate the fundamental perod FP as [1] FP =2rT + max 1 j N t j,t 0, 2(N +1 r)t, (1) where r =1f R s double-blade and r =2f sngle-blade. When the sngle-cluster robot schedulng s appled to a mult-cluster tool, t s mportant to analyze the robot dle tme at the nter-connected buffer modules. We need to ndeed consder how to allocate the robot dle tme (or watng tme) at the cassette modules. We defne the robot cassette watng tme, t R, as the tme lag of robot R between the moments when fnshng the acton pck an unprocessed wafer from nput cassette and startng the subsequent acton place a processed wafer nto output cassette. It s noted that the pull and swap robot strateges for a sngle-cluster tool are maxmal cassette watng tme strateges. We can also fnd alternatve pull and swap strateges to mnmze the robot cassette watng tme.

3 2) Mnmal cassette watng tme strategy: We can consder schedulng robot R to wat as long as possble at the process module wth the mnmal processng tme. We denote the robot watng tme at the PM wth the mnmum processng tme as t PM dle.letδt = tmax t mn. Then the maxmal robot watng tme at the module wth the mnmum processng tme s t PM dle = mnδt, t dle. We propose the followng mnmal cassette watng tme pull and swap strateges that mnmze t R by allocatng most of t dle to the process module wth mnmal processng tme: (1) Robot R s acton sequence follows the maxmal cassette watng tme pull and swap strateges, respectvely. (2) Sngle-blade robot R wats t PM dle before movng an unprocessed wafer nto the PM wth processng tme t mn. (3) Double-blade robot R places a processed wafer nto the cassette rght after t pcks an unprocessed wafer from the cassette. Usng ether the mnmal cassette watng tme pull strategy (for sngle-blade robot) or the swap strategy (for doubleblade robot), we can show that the fundamental perod FP (1) can be mantaned unchanged whle the robot cassette watng tme t R mn s mnmzed as 0 f r =1 t R mn = maxt mn 2(N 1)T,0 +2T f r =2. Wthout confuson, we wll abuse the notaton t R to denote t R mn n the rest of the paper unless explctly ndcated. It s common that there may exst several dentcally parallel PMs that perform exactly the same functonalty. We consder a sngle cluster tool C wth N process steps. We denote l as the number of parallel modules for process P, = 1,,N.Defne the least common multple (LCM) of l as λ =LCM(l 1,,l N ). We can ext the results n [5] and re-wrte Eq. (1) as FP =2rT + t +2r(1 l )T max 1 N l (2),t 0, 2(N +1 r)t.(3) III. OPTIMAL SCHEDULING OF MULTI-CLUSTER TOOLS A. Computaton of the lower-bound fundamental perod In [1], a decomposton method to decouple the nterconnecton among clusters s presented to analyze the steadystate performance and robot schedulng results. The key of the decomposton approach s to decouple the lnk between clusters. As shown n Fg. 2, for C, we know that wafers flow n or out of the cluster through ether buffer modules or cassette modules. C exchanges wafers wth C 1 through B 1, >1. B 1 plays dual roles: for C, B 1 acts lke a fcttous cassette module; for C 1, on the other hand, t acts lke a fcttous process module. We can consder decouplng a mult-cluster tool nto a set of ndepently runnng sngle-cluster tools by treatng buffer modules as ether fcttous cassette modules or fcttous process modules. We can then fnd the mnmal fundamental perod FP d 1 for each C. After we obtan the set FP d, =1,, M, we can dentfy the lower-bound value as the largest FP d, whch wll determne FP for the entre system. Assume that a decoupled C has N 0 PMs and denote the fcttous process module as the (N +1)th PM, denoted by P(N. We assume that P +1) (N +1) has a fcttous processng tme t d (N and the fcttous cassette module +1) C has a wafer supply tme t d 0. From Eq. (1), we can obtan FPd as follows. 4T d (N + +1) td 0 f C s a transfer cluster FP d = 2r T md otherwse, where t md = max t j,t d 1 j N (N +1),td 0, 2(N +2 r )T. Fcttous cassette C s supply tme td 0 can be consdered as the mnmum loadng delay tme of R 1 [1] 2r 1 t d T 1 S 1 =1 0 = (5) maxt 1 (2r 1)T, 0 S 1 =2. The value of t d (N +1) deps on the mnmal loadng tme delay at P(N +1). Smlarly, we can calculate td (N as +1) t d (N = 2r+1 T +1 R +1 S =1 +1) (6) maxt +1 (2r 1)T, 0 S =2. B. Optmalty condtons of the lower-bound fundamental perod The lower-bound fundamental perod FP computed n the prevous secton mght not be realzed due to the fact that we use a mnmal tme nteracton between adjacent clusters n the computatons. Therefore, t s natural to ask what are the optmalty condtons under whch the computed FP s feasble, and how can an optmal robot schedule under these condtons be found. We have the followng results 2. Proposton 1: For an M-cluster tool, the computed fundamental perod FP n the prevous secton s feasble f for each cluster C k, k>1, the mnmal robot cassette watng tme t R k satsfes the followng condton FP 2rk 1 t R T k 1 2T k f S k 1 =1 k (7) 2FP 2r k 1 T k 1 2T k f S k 1 =2. C. Robot schedulng The followng s a no watng schedule that has been mplemented to acheve FP: once the wafer has been placed nto the process module, the process can start rght away. For such a schedule, each process startng tme s completely depent on the robot acton startng tme. For robot R and decoupled C, we denote ts schedule as π. After a proper tmng shft of π s startng tme by the nter-connecton relatonshps, they can be ftted nto a mult-cluster schedule π wth fundamental perod FP. Algorthm 1 descrbes an algorthm to fnd optmal robot schedule. 1 We use the superscrpt * to denote the varables assocated wth fcttous modules. 2 Due to the page lmt, we neglect all propostons proofs n ths paper. (4)

4 Algorthm 1: A no-wat optmal robot schedule. Input : Cluster tool confguraton, wafer flow V, and fundamental perod FP m Output: Schedule π for V for =1to M do Obtan the decomposed schedule π = ACT j,stj by swap strategy (f r =1) or the mnmal cassette watng tme pull strategy (f r =2). Intalze system schedule as π π 1. for =2to M do Search for ACT s 1 π 1 that pcks wafers from B 1 / 1.MarkACT s 1 startng tme as ST s 1. T shft ST s 1 2T. for j =1to L do Update ST j π π + π. STj + T shft. IV. BUFFER/PROCESS MODULES (MS) We consder that there s a M k between C k and C k+1,1 k M 2, (Fg. 3). k has ether a one- or twowafer capacty. We denote the ncomng M (wafer flow from C k to C k+1 )as and the outgong M (wafer flow from C k+1 to C k )as, respectvely. If k has a one-wafer capacty, S k =1,then and share the same physcal buffer devce. If k has a two-wafer capacty, S k =2, and are ndepent buffer devces. For presentaton smplcty, we use Fg. 3 to represent both cases. Let and be the processng tme of and, respectvely. C k ACT I C k+1 ACT O R k R k+1 ACT O ACT I robot cassette watng tme for the decoupled cluster C k.we can frst compute the fundamental perod by the decomposton algorthm n secton III assumng that there were no M wthn the cluster tool, namely = =0. We denote such a calculaton as FP 0. Depng on the M wafer capacty and processng tmes and, we can obtan the followng results. Proposton 2: For an M-cluster tool wth a M k between clusters C k and C k+1, the fundamental perod FP of the cluster tool can be calculated as If S k =1 FP = If S k =2 FP0 f FP 0 FP = FP 0 2Tk s T k B + T k B +2T k s, otherwse. (8) f ) max,t + T s k f ) +t +T B k 4 =1 6 =5, f (t,t ) T 7, 2 + Tk s (9) where T 1 -T 7 are defned as Eqs. (17a)-(17g) on the next page (and graphcally shown n the -t plane n Fg. 4). Moreover, the pull strategy for sngle-blade robots and the swap strategy for double-blade robots can be used to acheve FP calculated above. FP 0 T s k T B k FP 0 T s k O + =2(FP 0 Tk s ) Tk B FP 0 T s k T B k = T B k FP0 T s k T T Fg. 4. S k =2. FP calculaton for dfferenm process tmes and f Fg. 3. A combned buffer/process module (M) wth a two-wafer capacty. We defne the followng notatons Tk s = T k + T k+1, Tk B = t R k+1 T k,andtt k =2(r k 1)T k, where t R k s the mnmal The M analyss can be ntegrated nto the fundamental perod computaton algorthms dscussed n the prevous secton. Suppose there exst Q Ms wthn the M-cluster tool, where Q M 1, and we denote the M ndexng set

5 T 1 = T 2 = T 3 = T 4 = T 5 = T 6 = T 7 = ) k FP 0 Tk s Tk B,=1, 2, (17a) ) FP 0 Tk s Tk B, and FP 0 Tk s Tk B FP 0 Tk s, (17b) ) FP 0 Tk s Tk B, and FP 0 Tk s Tk B FP 0 Tk s, (17c) ) + FP 0 Tk s Tk B k FP 0 Tk s,=1, 2, and + 2(FP 0 Tk s ) Tk B,(17d) ) > FP 0 Tk s, and Tk B, (17e) ) > FP 0 Tk s, and Tk B, (17f) ) + + > 2(FP 0 Tk s ) Tk B, and <Tk B. (17g) as Q. We can calculate the fundamental perod of the cluster tool wth Ms based on Proposton 2. Algorthm 2 descrbes such a modfed fundamental perod calculaton. C 11 P 1 11 P 1 12 P 2 11 P P 21 Algorthm 2: FP calculaton of a cluster tool wth Ms. Input : Cluster tool confguraton and wafer flow V Output: Fundamental perod FP for V Calculate FP 0 assumng j =0, Q,j=1, 2 for Qdo Calculate FP for each M usng Eqs. (8) or (9). FP max FP. Q P22 1 P22 2 C 2 P C 12 Transfer module P 2 22 For robot schedulng wth Ms, t s proper to schedule n the way such tha process s rght before acton R k pckng wafer from starts,and process starts rght rght after acton R k placng wafer nto s. Then n Algorthm 1, we can modfy the calculaton T shft ST s 1 2T ( 1)2. V. EXPERIMENTAL EXAMPLES In ths secton, we demonstrate how to apply the proposed methodology to semconductor manufacturng practce and show one example that has been used at Intel Corporaton. Thn flm tools are wdely used n semconductor manufacturng to depost metals onto a slcon wafer surface usng ether chemcal vapor deposton (CVD), physcal vapor deposton (PVD), sputter, etc. Fg. 5 shows a layout of an ALD/CVD cluster tool. Ths s a two-cluster tool. The servce cluster C 1 ncludes a double-blade robot, cassettes C 11 and C 12, and four process modules (chambers): parallel process modules P11 and P12, =1, 2. The processng cluster C 2 ncludes a double-blade robot and three process modules (chambers) wth P22 1 and P22 2 are parallel modules. 11 and 12 are Ms. All processng wafers follow the vst route (the splt arrows ndcate the flow at parallel PMs) The CVD cluster tool can be decomposed nto two sngle clusters, C 1 and C 2, as shown n Fg. 5. We can drectly P P 1 11 Cassette module C 11 C 12 Process module P 1 12 P 2 12 Fg. 5. P 2 11 C 1 A schematc layout of a CVD cluster tool. TABLE I PROCESS AND TRANSFER TIME (IN SEC.) OF THE CVD CLUSTER TOOL T 1 T 2 t 11 t t 21 t apply the decomposton technque dscussed n secton III

6 to ths two-cluster tool. We have to use Eq. (3) for parallel process modules n both clusters C 1 and C 2.ForC 1 and C 2, the redundant level s l 11 = l 12 = 2, and from Eqs. (3)- (4), we have FP d 1 = sec. FP d 2 = sec. We can calculate the FP 0 of the two-cluster CVD cluster tool as FP 0 = maxfp d 1, FP d 2 = sec. For Ms 11 and 12,wefnd that max 11, 12 + T 1 + T 2 =90< FP 0 = sec. (18) Therefore, by Eq. (9), Ms 11 and 12 do not have any mpact on the entre cluster tool throughput. Therefore, the fundamental perod for the cluster tool s FP = FP 0 = sec.. (19) From Proposton 1, we know that the computed FP for the CVD cluster tool s achevable. To llustrate the optmal schedule, we label all robot actons as n Table II. Followng Algorthm 1, we compute the robot schedules 3 as shown n Table II, whch comples wth the calculated FP. Wefurther use an event-graph/network based method [7] to verfy the optmal schedulng for the CVD cluster tool. The smulaton gves the same results. The producton at one Intel Corporaton fab acheved a throughput of 28.6 wafers per hour (125.8 sec. cycle tme per wafer) at the steady state. The producton results further valdate the analytcal and smulaton studes. VI. CONCLUSION In ths paper, we exted a decomposton method to analyze the steady-state throughput and robot schedulng of a mult-cluster tool wth buffer/process modules for semconductor manufacturng. We frst exted the exstng snglecluster schedulng results wth robot mnmal cassette watng tme pull and swap strateges for sngle- and double-blade robots. Based on these extensons, we dscussed the lowerbound of the fundamental perod of mult-cluster tools and optmalty condtons under whch such a lower-bound cycle tme s feasble. Algorthms to compute the maxmum throughput and to schedule the robots were proposed and analyzed. The mpact of the combned buffer/process modules (Ms) on cluster tool throughput and schedulng deps on the M processng tme and decomposed cluster cycle tmes on both sdes of Ms. The proposed analytcal and computatonal approach provded an effcent systematc method to study the throughput and schedulng of mult-cluster tools. An example of a CVD cluster tool at Intel Corporaton was used to llustrate the proposed decomposton methods. REFERENCES [1] J. Y, S. Dng, and D. Song, Steady-State Throughput and Schedulng Analyss of Mult-Cluster Tools for Semconductor Manufacturng: An Decomposton Approach, n Proc. IEEE Int. Conf. Robotcs Automaton, Barcelora, Span, 2005, pp [2] M. Dawande, H. Gesmar, S. Seth, and C. Srskandarajah, Sequencng and Schedulng n Robotc Cells: Recent Developments, J. Schedulng, vol. 8, pp , The startng tme for some robot actons (e.g. ACT 1 ) n Table II are lsted twce because of the 2-wafer cycle due to the exstence of several two-parallel PMs. TABLE II ACTION LABELS FOR THE CVD CLUSTER TOOL ACT Actons Robot blade Tme (s) Start tme (s) 1 C 11 P 11 pck 1 / / C 11 P 1 11 place C 11 P 2 11 place P 1 11 P 1 12 pck P 2 11 P 2 12 pck P 1 11 P 1 12 place P 2 11 P 2 12 place P pck P pck P place P place P 21 pck 1 / / P 21 place 1 / / P 21 P 1 22 pck P 21 P 2 22 pck P 21 P 1 22 place P 21 P 2 22 place P pck P pck P place P place C 12 pck / C 12 place /136.7 [3] T. Perknson, P. McLarty, R. Gyurcsk, and R. Cavn, Sngle-Wafer Cluster Tool Performance: An Analyss of Throughput, IEEE Trans. Semconduct. Manufact., vol. 7, no. 3, pp , [4] S. Venkatesh, R. Davenport, P. Foxhoven, and J. Nulman, A Steady- State Throughput Analyss of Cluster Tools: Dual-Blade Versus Sngle- Blade Robots, IEEE Trans. Semconduct. Manufact., vol. 10, no. 4, pp , [5] N. Gesmar, M. Dawande, and C. Srskandarajah, Robotc Cells wth Parallel Machnes: Throughput Maxmzaton n Constant Travel-Tme Cells, J. Schedulng, vol. 7, pp , [6] T. Perknson, R. Gyurcsk, and P. McLarty, Sngle-Wafer Cluster Tool Performance: An Analyss of the Effects of Redundant Chambers and Revstaton Sequences on Throughput, IEEE Trans. Semconduct. Manufact., vol. 9, no. 3, pp , [7] S. Dng, J. Y, and M. T. Zhang, Mult-Cluster Tools Schedulng: an Integrated Event Graph and Network Model Approach, IEEE Trans. Semconduct. Manufact., vol. 19, no. 3, pp , [8] J. Herrmann, N. Chandrasekaran, B. Conaghan, M. Nguyen, G. Rubloff, and R. Zh, Evaluatng the Impact of Process Changes on Cluster Tool Performance, IEEE Trans. Semconduct. Manufact., vol. 13, no. 2, pp , [9] N. Gesmar, C. Srskandarajah, and N. Ramanan, Increasng Throughput for Robotc Cells wth Parallel Machnes and Multple Robots, IEEE Trans. Automat. Sc. Eng., vol. 1, no. 1, pp , [10] D. Jevtc, Method and aparatus for managng schedulng a multple cluster tool, European Patent 1,132,792 (A2), Dec., [11] D. Jevtc and S. Venkatesh, Method and aparatus for schedulng wafer processng wthn a multple chamber semconductor wafer processng tool havng a multple blade robot, U.S. Patent 6,224,638, May, [12] Y. Crama and J. van de Klundert, Cyclc Schedulng of Identcal Parts n a Robotc Cell, Opers. Res., vol. 45, no. 6, pp , 1997.