Scheduling Dedicated
0 likes226 views
The document discusses scheduling dedicated lithography equipment in semiconductor manufacturing facilities. It describes how lithography accounts for a significant portion of cycle times and how matching restrictions require spreading production across multiple routes. An integer programming model and goal programming approach are used to schedule fab starts across machines and days to minimize overloads while balancing workloads and linearizing start rates. Implementing this IP-based scheduler reduced average photo wait times by 1.5 days, providing revenue gains given the economic value of cycle time reductions.
Scheduling Dedicated
- 1. Scheduling Dedicated Lithography Equipment Dr. Robert C. Leachman Dept. of Indus Eng & Oper Res U C Berkeley Dr. Vincent Lin Leachman & Associates LLC Dr. Paolo Palezzato Cypress Semiconductor, Inc.
- 2. What’s happening in semiconductors Moore’s Law : the number of transistors quadruples every four years Rock’s Law : the cost of a fab doubles every four years Result 1 : equipment pushed to technological limits, more process instability, more scheduling complexity Result 2 : fewer advanced fabs and fewer fab operators, fabless/foundry partnerships Result 3: fabless firms do naïve planning, foundry must do real planning and scheduling and do it fast
- 3. Semiconductor supply chain (Develop process technology – 1 year) Wafer fabrication – 6 weeks Test chips on wafer – 1 week (Ship overseas – 0.5 week) Packaging and final test – 1 week (Ship overseas – 0.5 week)
- 7. The economic value of cycle time in the supply chain Let P i (t ) denote the sales price of device i at time t . P i ( t ) = P 0 i exp(- t ), where P 0 i is the current price. Let W i ( t ) denote the wafer starts, Y i ( t ) the yield, CT i ( t ) the manufacturing cycle time, and H i the remaining product life. Then the remaining lifetime revenue is
- 8. Lithography Lithography represents the greatest capital expense in an advanced fab Strategies to stretch machine capabilities: each manufacturing lot must be processed using the same lens (machine) at 3-10 “critical layers” at other layers, the lot may only be processed by one or several machines that have been “matched” to the critical machine Lithography accounts for ~25-40% of the wait-time portion of fab cycle time e.g., 20 mask layers, 6-8 hours avg. wait time per layer
- 9. Lithography Example small litho dept: 3 scanners (S1, S2, S3), 3 DUV steppers (D1, D2, D3), 5 I Line steppers (I1, I2, I3, I4, I5) Example alternative photo routes for a high-volume device: Layers Route 1 Route 2 Route 3 1 and 3 I1 I3 I4 4, 5 and 7 I1 or I2 I3 or I4 I4 or I5 2, 6, 8-12 and 13 S1 S2 S3 14, 15 and 16 D1 D2 S2 17 I1 – I5 I1 – I5 I1 – I5
- 10. Lithography Despite the matching restrictions, the photo process occasionally fails and requires engineering effort to restore stability As a risk-mitigation strategy, it is desirable to spread the production of a given device across several photo routes
- 11. Lithography capacity Capacity for new starts depends on the device mix Capacity for new starts each week depends on the WIP status Photo wait times are sensitive to the allocation of the planned weekly starts to photo routes and to days of week
- 12. Rest of fab In contrast, capacity of the other process areas in the the fab is expressable by technology (i.e., all lots of all devices in same technology have same set of qualified machines, same process times, etc.) To control wait times in the rest of the fab, linear production rates by technology are desired
- 13. Planning and scheduling architecture – fabless firm Use commercial LP-based tools such as i2, Adexa, MIMI, Avere, etc. Plan starts requests - Obtain estimates of cycle times and yields from foundry periodically, obtain WIP snapshot on-line Incorporate start commits from foundry as if it is additional WIP Quote delivery dates based on WIP-out projections
- 14. Sophisticated planning and scheduling architecture - foundry LP-based planning system to analyze weekly wafer start requests and/or die out requests Dynamic capacity analysis of workloads from WIP and new production Rigorously analyze lithography and other capacities IP-based fab starts scheduling system to allocate the accepted starts to machines and to days of week
- 15. Fab starts scheduling problem Given: time-varying machine capacities, qualified photo routes, process times, total manufacturing lots to be started this week, WIP snapshot, estimated cycle times and yields Variables: what day of week and what photo route on which to start each manufacturing lot Multiple objectives: balance workloads of photo machines, linearize starts rates by technology, spread out device starts across photo routes
- 16. Integer programming model Constraints: Workload on machine i on day t = workload from WIP arriving on day t and workload from allocated starts arriving on day t Overload of ( i , t -1) + workload of ( i , t ) <= capacity( i , t ) + overload( i , t ) Other accounting constraints and variables (e.g., define total overload by machine type)
- 17. Goal programming approach First, we minimize 10 different objectives independently: Max overload of any photo machine on any day Total of daily overloads on scanners Total of daily overloads on DUV steppers Total of daily overloads on I Line steppers Max total workload on any scanner Max total workload on any DUV stepper Max total workload on any I Line stepper Max starts on any day of technology 1 Max starts on any day of technology 2 Sum over devices of max starts of device i on a single route
- 18. Goal programming approach Afterwards, we solve for an objective to minimize the weighted deviation from optimality of each of the 10 goals Try to simultaneously minimize overloads, equalize workloads, linearize starts by technology, and minimize risk of too many lots of same device assigned to same route
- 19. Implementation and results Fab switched from manual scheduling of fab starts to the IP-based fab starts scheduler Application is fully automated, takes about 40 mins to run using CPLEX (5K constraints, 1.5K integer vars, 11 IPs) IP’s are solved to first integer solution within 1-2% of optimality Six weeks later, the average photo wait time per lot at the fab had declined by 1.5 days for both major technologies in production, while fab start volume was slightly increased
- 20. What is 1.5 days reduction worth? For the case-study fab’s current technology and product portfolio, The revenue gains will be even larger for future technologies
- 21. Summary Industry trends have increased the value of cycle time compression in the supply chain Optimization in the semiconductor industry is now being employed at the supply chain level, at the foundry planning level, and, starting with this application, at the scheduling level