On the Throughput of Clustered Photolithography Tools:

Transcription

1 On the hroughput of lustered Photolthography ools: Wafer Advancement and Intrnsc Equpment Loss Maruth Kumar Mutnur James R. Morrson, Ph.D. September 23, 2007

2 Presentaton Outlne Motvaton Model : Synchronous photolthography model System Descrpton me between lot completons wth dverse lot populatons me between lot completons wth same class of lots Model 2: Asynchronous photolthography model System Descrpton Wafer completon tmes wth a sngle class of lots Intrnsc equpment loss: Retcle change (as a pause n the bottleneck module) oncludng remarks 2

3 Motvaton Goal: One generc model for all classes of seral processng cluster tools Abstract models useful for clustered photolthography tools Movement of ndvdual wafers can be analyzed Module level rather than conventonal tool level approach ontrbuton to flow lne lterature Hgh fdelty models wth drect applcaton to fabrcator smulaton A new class of falures setup dependent upon state of system Smplfed recursons for system evoluton 3

4 Synchronous Photolthography Model: System Descrpton m m 2 m 3 m 4 m 5 m 6 m 7 W wafers/lot Robot m 8 M modules m 5 m 4 m 3 m 2 m m 0 m 9 Lots may have dfferent determnstc process tmes n a module Wafers can only advance at the same nstant as all others n the tool ther movement s synchronzed Process tme n module m j for famly F lots s D F j May be 0 to model a buffer (only useful for module falure analyss) Let k() denote the number of empty modules n advance of lot l 4

5 Synchronous Photolthography Model: Wafer Advancement Rate of wafer advance s dctated by the maxmum module tme for all occuped modules m m 2 m 3 m 4 m 5 m 6 m 7 m 8 m 9 m 0 m m 2 m 3 m 4 m 4 For lot l wth famly F(), defne the effectve module process tme as F p, q { r: r p max qrm } he slowest possble effectve process tme s F max j D or F j D F r 5

6 Synchronous Photolthography Model: Lot ompleton for Dverse Lot Populatons here are two famles of lots me between the departure of the prevous lot and departure of lot l may be calculated as: M F ( ) j, M jm k ( ) ( W k ( ) j M M F ( ) 0, j j2k ( ) ) max( F ( ) F ( ) 0, j, F ( ) ) j k ( ), M me for frst wafer to reach last module me for last wafer to ext frst module me untl frst wafer of lot l + enters tool me untl last wafer exts the tool Here, for notatonal smplcty, we assume that at most two lots can be on the tool at any nstant 6

7 Synchronous Photolthography Model: Lot ompleton for Unform Lot Populaton Lots are of same famly me between the departure of the prevous lot and departure of lot l may be calculated as: M jm k ( ) ( W k ( ) j M M j, M 0, j ) j k ( ), j j2k ( ) me for frst wafer to reach last module me for last wafer to ext frst module me untl frst wafer of lot l + enters tool me untl last wafer exts the tool Here, for notatonal smplcty, we assume that at most two lots can be on the tool at any nstant 7

8 Synchronous Photolthography Model: Example 900 me between lot completons, Parameters: M= and W=0 Process mes D D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 0 D Famly F Famly F me between lot completons, No. of Empty Modules, K =K + 8

9 Asynchronous Photolthography Model: System Descrpton Assume that all wafers n the tool advance at ther own rate so long as there are module locatons avalable to do so Process tme n module m j for all lots s D j May be 0 to model a buffer Only one class of lots (can readly model many classes but requres full smulaton approach) m m 2 m 3 m 4 m 5 m 6 m 7 W wafers/lot m 8 M modules m 5 m 4 m 3 m 2 m m 0 m 9 Lots are of same class, but may have dfferent sze 9

10 Asynchronous Photolthography Model: Parameters m m 2 m 3 m 4 m 5 m 6 m 7 W wafers/lot m 8 M modules m 5 m 4 m 3 m 2 m m 0 m 9 Lots are of same class, but may have dfferent sze Number of modules n the cluster: M Includes buffers Process tme for a wafer n module m: D m Largest (bottleneck) process tme: Number of wafers per lot W Denote the -th lot: l Arrval tme of lot l : a an easly generalze to depend upon the lot 0

11 Asynchronous Photolthography Model: Wafer Advancement he evoluton equatons for the system may be wrtten Let x j (w) denote the entry tme of wafer w to module m j, At the frst module: w a, x w x max w 2, For the ntermedate modules (2 w M-): x For the last module: x j M w x w D, x w max j j j w max x w D, x w M M M D M

12 Asynchronous Photolthography Model: owards ompleton me he completon tme of lot l s dctated by two possbltes: ase : Lot l arrves early enough so that ts wafers begn to ext mmedately after those of lot l - W One wafer exts every unts of tme ase : Lot l arrves so late that t does not run nto lot l - n front of t M a D W j j Remanng wafers ext every unts of tme Frst wafer exts 2

13 Asynchronous Photolthography Model: ompleton tme he completon () tme of lot l obeys the followng recurson: a e D, max W wth ntal condton (for an empty tool) a e D W where W Number of wafers n a lot a e Arrval tme of lot to the system,, M Number of modules n the track D m D Processng tme of a wafer n module D, max, DM D, M m Proof: Start wth the max-plus algebra representaton of the evoluton equatons and employ an nducton wthn an nducton 3

14 Asynchronous Photolthography Model: Example Example: M = 5, W = 3, = 50 sec Process me 5 Module Module Module Module Module L enters system at tme a = 0 L exts system at tme c = 40 L2 enters system at tme a2 = 85 L2 exts system at tme c2 = 230 W 0 80 (3 )30 40 a e D 2 a e D, W max 85 80,40 30 max 2 max 65, No tme lost on the bottleneck! (2)(30) 4

15 Asynchronous Photolthography Model: Example 2 Example: M = 5, W = 3, = 50 sec Process me 5 Module Module Module Module Module L enters system at tme a = 0 L exts system at tme c = 40 L2 enters system at tme a2 = 00 L2 exts system at tme c2 = 240 W 0 80 (3 )30 40 a e D 2 a e D, W max 00 80,40 30 max 2 max 80, seconds lost on the bottleneck! (2)(30) 5

16 Asynchronous Photolthography Model: One class of Intrnsc Equpment Loss If the bottleneck module fals (pauses), a recurson for the completon tme of lots may be found me of the r-th pause: Duraton of the r-th pause: t R (r) d R (r) he frst lot whch may be delayed by the pause has the smallest lot ndex satsfyng M max a e D, c W D t r j B j R ompleton tme of the lot had there been no pause me after extng the bottleneck Departure tme from the bottleneck f no pause 6

17 Asynchronous Photolthography Model: ompleton tme wth Loss Adjust the completon tme of the frst possbly delayed lot (otherwse use the standard recurson) 0 max 0, g where g 0 a e D, c W max mn d R r, t r d r R R W M D jb j Orgnal completon tme of the lot f Delay ncurred an be used to model retcle change events 7

18 Asynchronous Photolthography Model: Example wth Loss Example: M = 5, W = 3, = 50 sec, t R (r)=95, d R (r)=5 Proces s me 5 Module Module R R R Module Module Module ## ## ## ## ## ## Retcle hange at tme t R (r) = 0 L enters system at tme a = 0 L exts system at tme c = 55 L2 enters system at tme a2 = 00 L2 exts system at tme c2 = 245 f g 2 a mn dr f max e D W r, t r d rw D f mn 5,75 R 0, g 40 max 0, (3 )30 40 R M jb a e D, W max 00 80,55 30 max 2 max 80, j Retcle change 5 (2)(30) 8

19 oncludng Remarks Synchronous model Realstc manufacturng system sngle robot transfers the wafers K can be used to model ntrnsc equpment losses such as omplete tool falure Late lot arrval Setup change Asynchronous model Ideal manufacturng system wth effcent wafer transport system Future work Synchronous model of generc arrvals, retcle change and setup change Asynchronous model wth setup tmes ompare performance between models wth real data Incorporate nto fab smulaton Recommend operatonal desgn prncples 9