ABSTRACT

This paper describes some problems and investigations encountered when implementing new resource scheduling policies in a large semiconductor manufacturing facility (FAB). The FAB described here uses a product release policy based on customer orders and a work-in-progress (WIP) chart. The scheduling of resource tools is done on a first in, first out (FIFO) basis on high speed tools and due date first (DDF) at bottleneck tools, except for high priority LOTS, called MAXI’s. Minimum Inventory Variability Scheduling Policies (MIVP®) [10] were introduced in February 1996. The development of a simulation model representing the FAB and a partial implementation of MIVP® were completed over the period from May, 1996, through January, 1997.

This presentation describes briefly the theory behind MIVP®. A heuristic explanation of the minimum inventory variability for resource scheduling policies is given here.

Finally a large semiconductor manufacturing facility is discussed in generic terms, including (sanitized) data collection. The results of the baseline output and historical data are compared to MIVP®.

1 THEORY

1.1 Little’s Law

Little’s law in queueing theory [6] states that:

where is inventory, is the mean arrival rate of products for processing, is the total cycle time, namely the processing time plus waiting time involved. As a result, we have that for a fixed input or output, cycle time is proportional to the total system inventory.

We let be the average service (processing) rate and the server utilization (loading intensity), then

since products are fed in no faster than the processing rate.

1.2 Kingman’s Formula

To account for random variations in arrival and

processing times, let denote the coefficient of variation of the inter-arrival times and let denote the coefficient of variation of the service times . We define

We say that describes the total systems variability. Assume that the inter-arrival times and service times are independent identically distributed (iid) random variables and the two streams are independent of each other. Assume that there is one server, so we consider GI/GI/1 queue [8] (general independent service times, and 1 server).

Kingman’s formula [7] states that

Hence, if is near 1, the inventory is very sensitive to variability. For fixed system variability , the inventory decreases as decreases.

So reducing inventory without improving the system can be detrimental. We focus here on decreasing variability to reduce cycle time. At any given machine group, the order to service the items in the queue affects the variability of the output stream, especially so for semiconductor fabrication processes because of resource sharing caused by reentrant flows. These items may create larger or smaller variability in inter arrival times.

When in Kingman’s formula, we obtain the theoretical cycle time. In this case, the minimum inventory achieved is . From Little's Law, the minimum cycle time in this case is . But this is not possible for systems with . Let denote a stream of inter-arrival times from an upstream machine and let denote the stream of the service times for these arrivals. Let the inter-arrival times and the service times be independent of each other. Let us schedule the upstream machine. Since the arrival times and service times are independent, the best we could hope to achieve through scheduling is to minimize variability for the inter-arrival times, i.e., set to and so to minimize .

So the task is to minimize the variability of the inter-departure time of the upstream machine through proper scheduling of the queue. We introduce the correlation between the inter-arrival time and the service time of the downstream machines, we get better results: if the random variables and are correlated such that , where >1 is a constant, , and ..., [4], [5], [9], [10], [11].

Hence, for a system with uncertainty, we could achieve the same minimum inventory as the deterministic system - the theoretical best!

Minimum Inventory Variability Scheduling Policies (MIVP®) is based on exactly this realization. It introduces maximum correlation between inter arrival times and service times to reduce the man-made scheduling variability.

1.3 Minimum Inventory Variability Scheduling Policies (MIVP®)

With this policy, the dynamic inventories shown in Figure 1., will keep close to the long-term historical average inventory (the profile) in a stable factory. This leads to reduction of the scheduling variability, reduction in total inventory, and reduction in mean cycle time. The result of the MIVP® is line balancing to reduce WIP variability. Large queues in front of a particular process will cause irregularity in the process flow, i.e., an unbalanced line. Some stations are overloaded and some are starved. The mean cycle time will rise due to starvation even though the total system inventory stays approximately the same [1], [2], [4], [5], [9], [10], [11]. MIVP® can reduce the line imbalance by pulling WIP into the queues having lower inventory as shown in Figure 1.

Figure 1. WIP CHART [4], [5], [9], [10]

2 HEURISTICS

2.1 1-Step Ahead MIVP® policy

Choose the items in the queue according to the following priorities:

Priority I: Operation such that

Priority II: Operation such that

and

Priority III: Operation such that

Priority IV: Operation such that

and

These are decision rules: If ..., then, else where is the historical average. If two items tie with the same priority, use FIFO or DDF or some other (pre-defined) allocation rule.

For example, four process steps require the service of Machine A (Figure 1.). Which one do we choose? Machine A, serving these four process steps, is the feeder machine to the next machine in the process flow called a bleeder machine. Applying the priority rules from a 1-Step Ahead MIVS Policy we look down stream to the next queue in the process flow for each job requiring Machine A and select the job that will feed the bleeder machine leaving its instantaneous queue length below its historical average, . In our example, then we would choose process step 35, then 10, then 26 and finally 18 using the priority matrix shown in Figure 2. This example shows four queues in contention for service of Machine A, but in reality you can have many more with a reentrant line producing multiple products.

Figure 2. The Priority Matrix for Machine A

in Figure 1. CHART [4], [5], [9], [10]

2.2 K-Step Ahead MIVP® policy

Choose the items in a queue for service according to the following priorities:

Priority I: Operation such that and

Priority II: Operation such that and

Otherwise, choose FIFO or DDF or some other pre-determined allocation rule.

Based on this rule, if the instantaneous inventory is larger than its average at operation for Machine A, the operation , etc., will be the one with its largest current inventory sum below average in the next K steps.

2.3 K-Step Ahead and J-Step Back MIVP® policy

Choose operation k_i in the queue such that:

Otherwise, choose FIFO or DDF or some other pre-determined allocation rule.

Here we choose the next processing step for Machine A to be the operation k_i, which includes its J-predecessor steps as well as the K-steps that follow, that will have the largest current inventory sum below average for the next K-steps ahead and including J-steps back. This could easily include the total number of process steps for the entire line.

A machine may be shared by different operations within a single process flow as well as operations from different processes in a manufacturing line that contains multiple products. In this case, the same algorithms still apply, except that the indexing is more complicated.

3 SEMICONDUCTOR FAB MODEL

3.1 Model Definitions and Requirements

MIVP® is motivated by the need to meet delivery schedules, reduce product cycle times, increase product yield, increase product through-put, optimize utilization of equipment resources, increase confidence for on-time delivery schedules, and increase profits. Companies use schedules and release policies that can be implemented on the factory floor, and that agree with common sense. Therefore, we use stochastic discrete event modeling and simulation to test some simple heuristic rules. These simple rules rely on common sense and can be easily implemented by operators on a factory floor. MIVP® uses these rules for resource scheduling and product release. The control of process resource scheduling is refereed to as inner loop control, and the release of raw material into the factory, is referred to as outer loop control [13]. We will discuss resource scheduling in the remainder of this paper. MIVSRP product release policies will be discussed elsewhere.

A reduction in the number of control variables is required to effectively use what tools are available and to approach optimality within time constraints available on a factory floor. A global approach, from a raw wafer through shipping the completed product, is required to understand all the complexities involved in scheduling and release policies. Complications are the reentrant nature of certain critical resources, variations in recipes for processing due to multiple products, and the random nature of machine failure and repair introduce a higher level of complexity, and the number of variables is large. A possible reduction in the number of

key variables used to optimally control the inner and outer loops should follow from analysis of a comprehensive simulation model that has been validated in factories using historical data. An excellent discussion on the use of a reduced set of variables to maximize decisions is presented in Ho [3].

We use a stochastic discrete-event simulation modeling (here in after referred to as the FAB Model) to test and compare the ability of new policies to improve existing scheduling and release policies. The FAB Model must accurately represent the factory as a production system. It must include the production mix, the production flows, the production recipes and processing times, the equipment maintenance database, and labor. This level of detail is required if FAB management is to have confidence in decisions being supported partly by our FAB Model. An employee database is utilized when determining labor requirements, but is not necessary when comparing release and scheduling policies. Correct staffing is important and does affect cycle time and production, but for our FAB Model and comparison, staffing is assumed to be equal and therefore it is not accounted for in the FAB Model when changing the scheduling policies from FIFO and DDF to MIVP®.

The FAB Model compares a validated baseline simulation model using FIFO and DDF with one using new MIVP® resource polices that reduce man-made variability’s of scheduling resources in the FAB. The development of the baseline FAB Model is a long and tedious process, but if done with care and attention to detail for future updates, it will serve as a flexible tool in management decision making for a long time. Changes occur on a daily basis, such as new product introductions, new production flows, process changes reducing process steps, device shrinks changing process times on critical machines, and product elimination just to mention a few. A FAB model must account for these changes to adequately represent daily activities. Changes, additions and deletions must be easy to implement.

In our project the MIV policies were reviewed using previous research results and experience in two other FABs. Extend® Software was used because of its visual icon based libraries that represent scenarios on the factory floor. The objective was to reduce cycle time to a set goal of 29 days on average and 32 days with 95% confidence, prior to the end of the 3rd quarter. The 1-Step Ahead and 1-Step Back policy was implemented on the factory floor using the WIP Chart and Priority Matrix. The MAXI priority schedules were maintained because of commitments to certain customers, but the FIFO and DDF were changed to incorporate the 1-Step Ahead and 1-Step Back priority scheduler for resources. This was particularly useful when there were some major failures of critical equipment. The production line was slowed down in front of these failures and speeded up in front of other resources. When the equipment came back on line the reverse was done for an amount of time equal to the time that the equipment was down, thus maintaining a balanced line. The

following examples show that a new methodology could help improve the cycle time.

3.2 SEMATECH Model Statistics

The SEMATECH dataset included two non-volatile memory products with two different process flows, 210 steps for product A and 245 steps for product B. There are 85 machine groups (266 total machines) with historical mean-time-before-failure (MTBF) and mean-time-to-repair (MTTR) data. There are 16,000 wafer starts per month with arrivals calculated on a constant distribution. The actual raw process time for product A was 313.4 hours and 358.6 hours for product B. The start rate for product A was 380 wafers per day and 190.48 wafers per day for product B. The LOT size was 48 wafers. R. Weidmeyer, graduate student thesis [11] using the discrete event simulation software package Extend™, generated these comparative results. A second and third comparison is being completed now by V. Palmiri (K-Step Ahead Policy) and T. Torsina (K-Step Ahead and J-Step Back Policy), masters student thesis defense, using AutoMOD®/AutoSched® from AutoSimulations, Inc. and ManSim® from Tycin Systems, Inc., also with positive preliminary results.

We are continuing this research to compare algorithms and off-the-shelf industry supported discrete event simulation software packages.

3.3 ExtendÒ SEMATECH Simulation Results

The ExtendÒ Model simulated 30,000 hours of continuous manufacturing with data collected every 500 hours. The first 2,500 hours of data was eliminated due to ramp up of the model. The goal was to establish a baseline model and collect data using FIFO resource scheduling with a constant release policy, and then compare this baseline data with data collected using the MIV policy of 1-Step Ahead. Work-in-progress and Cycle time data were the two important sets of data that we are interested in.

The following table presents our results:

Table 1. SEMATECH Model Comparisons of FIFO with MIVP® 1-Step Ahead

Product A Product B

Mean Cycle Time, FIFO 1,222.0 hrs 1,551.0 hrs

Mean Cycle Time, MIVP® 808.0 hrs 1,043.0 hrs

Raw processing Time 313.4 hrs 358.6 hrs

TQT, FIFO 908.6 hrs 1192.4 hrs

TQT, MIVP® 494.6 hrs 684.4 hrs

Reduction by MIVP® 414.0 hrs 508.0 hrs

Percentage Improvement over FIFO 46% 43%

3.4 Motorola Model Statistics

This FAB produces a total of 73 different microcontroller devices on 55 different production flows, each with processing steps ranging from 185 to 395 steps (averaging 263 steps each). Ten of these products are on the factory floor at any given time, involving 132 machine groups with a total of 485 machines. The product can reenter machine groups, such as Photo and Etch, from six to twelve times, depending on the device being fabricated. Adding to this complexity the

variability of MTBF, MTTR, including labor of 650 employees, and one can see that short interval scheduling based on knowledge of the global process is important. Therefore, the minimum number of variables is (10 technologies) times (10 average products) times (263 average steps) times (132 machine groups) equals 3.47 million variables. Add to this MTBF and MTTR for each of the 485 machines plus labor of 650 employees. The result is an intractable number of variables making discrete event simulation modeling an alternative to optimal proofs for testing new scheduling and release policies.

Let us consider minimizing the total cycle-time (from raw material to finished product) given a fixed input/output schedule. To minimize cycle time, one must reduce inventory or increase capacity according to Little’s Law, or to reduce variability. A balanced production line then is one if given a fixed input and output schedule, the mean work-in-progress does not increase over long periods of time due to randomness of machine failures and repairs.

Large queues, no matter what the cause, are referred to as bottlenecks, and days or weeks might be required to re-balance the production line. When a bottleneck occurs, it causes product to wait for service, thereby increasing its cycle time (CT). For our discussion, cycle time is defined to be the sum of the total processing time (TPT) and the total queueing time (TQT). TPT is defined as the sum of all the raw processing times for each step in a production flow and TQT is defined as the sum of all the queue waiting times for resource service for each step in a production flow. Millions of dollars can be spent on equipment to increase the capacity at a critical bottleneck resulting in reduced cycle time locally, but the overall cycle time of the product might not decrease. This local improvement approach might simply move the bottleneck to another location along the manufacturing line. Understanding that local changes to improve the service at overcrowded machines generally will not improve the total product cycle time is of utmost importance. Restarts, for example due to power failures or bomb scares are not within the domain of this research; but, we search to reduce CT by reducing the man-made variability through resource scheduling, product release policies, labor and machine utilization’s, using historical MTBF and MTTR.

3.5 FAB Model Data Collection

Data collected for the first FAB Model included all the microcontroller devices manufactured in the past two years. This included 34 shop order flows for 53 devices. These are referred to here as Product1, Product2, and Device1, Device2, etc. This FAB’s production flow was broken down into distinct operations such as Photo, Etch, Implant, Diffusion and Probe, for the different metal layers on the device and given specific code names. These operation code names Op1, Op2, etc. were broken down into individual processing steps with actual code names which then could be managed by the process engineering teams for process improvement, etc. These steps are referred to as Step1, Step2, etc. The 34 flows

having a total of 1717 operations with individual steps ranging from 2 to 15 depending on the operation giving a total of 8671 steps for all flows.

4 FAB MODEL RESULTS

In this FAB, we develop a partial implementation of a 1-Step Ahead and 1-Step Back MIV policy, on the shop floor under close supervision. When problems occurred in the FAB such as equipment failures at the bottleneck sections, the operators were programmed to look ahead and slow down the wafers that were headed for the downed machine while speeding up the wafers that were headed for the up machines. The only exceptions were the MAXI LOTs that were a very small percentage of the total LOTs being produced.

The objective to reach 29 days average was accomplished and even surpassed to 26.34 days. This represented a 29.7% reduction. The objective of 32 days with 95% confidence was achieved (31.61 days), a 32.9% reduction. Over this same period wafer starts were decreased by only 1.9%, wafers shipped increased by 2.3%, wafer yields increased by 0.15%, and wafer scrap decreased by 23%. These positive results occurred in the period from May 1996 through October 1996 (Table 2.)

5 SUMMARY

These heuristic agreements have been applied extensively in the context of real factory production by [4], [5], [9], [10], [11].

At Motorola we review MIVP® and some of its problems and successes in a large semiconductor manufacturing facility. We have demonstrated the utility of using stochastic discrete-event simulation modeling and control introduced here. Our research continues on optimal schedules and release policies to reduce man-made variations, to reduce cycle time, to increase throughput, and to balance the whole wafer production line.

This research has been supported by, College of Technology and Applied Sciences (ASU East), System Sciences and Engineering Research Center (ASU Main) and by Motorola, Inc. Mesa, AZ.

6 REFERENCES

[1] Kumar, S. and Kumar, P.R., Performance Bounds for Queueing Networks and Scheduling Policies, IEEE Transactions on Automatic Control, pages 1600-1611, Vol. 39, No. 8, Aug. 1994.

[2] Lu, Steve C. H., Ramaswamy, Deepa, and Kumar, P. R., Efficient Scheduling Policies to Reduce Mean and Variance of Cycle-Time in Semiconductor Manufacturing Plants, IEEE Transactions on Semiconductor Manufacturing, Pages 374-385, Vol. & II3, Aug. 1994.

[3] Ho, Y.C., Heuristics, Rules of Thumb, and the 80/20 Proposition, IEEE Transactions on Automatic Control, pages 1025-1027, Vol. 39, No. 5, May 1994.

[4] Li, S., Equi-Variability Graph Approach for Modeling of Manufacturing Systems, invited paper, Proceedings of the Twenty-Ninth Annual Allerton Conference, Allerton, Illinois, 1991.

[5] Li, S., Innovative Methods in Planning and Scheduling in Semiconductor Manufacturing, invited paper, Proceedings of the Semiconductor Manufacturing Technology Workshop, co-sponsored by National Taiwan University and Taiwan Industrial Technology Research Institute, Mar. 22, 1993.

[6] Little, J. D. C., A Proof of the Queueing Formula: L=lW. Operations Research, Vol. 9, 1961, pp. 383-387.

[7] Gelenbe, E. and Pujolle, G., Introduction to Queueing Networks, John Wiley & Sons Ltd., 1987.

[8] Kleinrock, Leonard, Queueing Systems, Vol. 1, John Wiley & Sons, New York, NY, 1975.

[9] Tang, (Tom) Ynn-wann, Simulation Model for Minimum Inventory Variance Policy Practiced in Semiconductor Manufacturing Plants, MT Research Project, Department of Manufacturing and Industrial Technology, Arizona State University, Aug. 1993.

[10] Li, S., Tang, T, and Collins, D.W., Minimum Inventory Variability Schedule with Applications in Semiconductor Fabrication, IEEE Transaction on Semiconductor Manufacturing, Vol. 9, No. 1, pp. 145-149, February 1996.

[11] Wiedmeyer, R. J., A Minimum Inventory Variability Policy Computer Simulation Using SEMATECH Semiconductor Manufacturing Data, Master of Technology Research Project, Department of Manufacturing and Industrial Technology, Arizona State University, Tempe, (Aug. 1996).

[12] Chen, H., Harrison, J.M., Mandelbaum, A., Van Ackere, A., Wein, L.M., Empirical Evaluation of a Queueing Network Model For Semiconductor Wafer Fabrication, Operations Research, pp. 202-215, Vol. 36, No. 2, (March-April 1988).

[13] Rivera, D. and Vargas, F., Model Predictive Control of Re-entrant Manufacturing Lines, submitted for publication in the proceedings of the 1997 American Control Conference, Albuquerque, New Mexico, June 1997.

Back to ACADZ Articles