# IEOR 130 Methods of Manufacturing Improvement Practice Examination Problems Part I of Course Prof. Leachman Fall, 2017

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1 IEOR 130 Methods of Manufacturing Improvement Practice Examination Problems Part I of Course Prof. Leachman Fall, The thickness of a film deposited on wafers at a particular process step is subject to statistical process control. The upper specification limit for the film thickness is 50 angstroms and the lower specification limit is 20 angstroms, i.e., wafers with film thickness more than 50 angstroms or less than 20 angstroms deposited on them are scrapped. At present, the process has considerable variability, with mean film thickness equal to 25 angstroms and standard deviation equal to 5 angstroms. (a) What kind of control chart(s) should be used to track this parameter? (b) What is the process performance index for this step? (c) Assume the only yield loss mechanism at this process step is out-of-spec film thickness. What is the yield of this process step? (d) To raise the yield of this step to 95%, what value for the process performance index must be achieved? 2. A production process is subject to defects. If the number of defects on a production unit exceeds USL, the unit is scrapped. The yield of the process averages Assume the only yield loss mechanisms are the defects. (a) What kind of control chart is most appropriate for this process? (b) Estimate the process performance index. (c) The upper control limit of the control chart is 100. Estimate USL. 3. The thickness of a film deposited on wafers at a particular process step is subject to statistical process control. The thickness is measured at five points on one wafer per lot. The upper control limit is 132 angstroms and the lower control limit is 96 angstroms. (a) What kind of control chart should be used to track this parameter? Assume in the following questions that this kind of chart is in use. 1

2 (b) What are the mean and standard deviation of the film thickness? (c) Assume the yield loss due to out-of-spec film thickness is 1 percent and assume all of this loss is from wafers whose film thickness exceeded the upper specification limit. What is the equivalent process performance index? (d) What is USL for this film thickness? 4. For a product with 300 gross die per wafer, stacked wafer maps of yield by die site have been studied. Considering only wafers believed to be free of yield excursions, the best observed yield is 90%. The average die yield for the product is 80%. (a) Determine baseline random and systemic mechanisms-limited yields for the product. (b) The die size is 0.5 square centimeters. What defect density is equivalent to the baseline random yield? (c) If the defect density in (b) were cut in half, what would be the improvement in average die yield for the product? (d) The following systematic yield-loss mechanisms have been identified: Mechanism Fraction of wafers Fraction of die loss on such wafers Edge losses Missing photo patterns (excluding edge die) Poly etch bridging (excluding edge die) Metal II particle excursions (excluding edge die) Metal I particle excursions (excluding edge die) Assume the last four mechanisms can be overlapping, i.e., the same die might experience poly etch bridging, missing photo patterns, and/or particle excursions. Edge die are excluded when figuring average losses from the other mechanisms, i.e., the above figures for the last four mechanisms express losses in addition to edge losses. How much systematic yield loss remains to be explained? 2

3 5. A simple manufacturing technology has three process steps. Each step is subjected to statistical process control procedures. The process capability and process performance indices are as follows: Step Cp Cpk (a) Assume the only yield loss mechanisms are violations of the specification limits at the three steps. What is the overall yield of the manufacturing technology? (b) Now suppose that in addition there is a yield loss mechanism of random defects. There is no inspection for such defects until testing after production is completed. Further, suppose the overall yield for a device with area equal to 0.5 sq cm fabricated using this manufacturing technology is 87.5%. What is the defect density equivalent to the random defect yield loss? 6. A simple manufacturing process consists of a sequence of four steps: Step Cpk Cp (a) Which step is in most urgent need of process improvement? If the process was well-centered at each step, which step would be in most urgent need of improvement? (b) Considering only the yield loss mechanisms underlying these process performance indices, estimate the yield of the manufacturing process. (c) The engineering department is considering several projects to reduce process variability as follows: Step 1 new / Required engineering hours

4 Rank the projects in order of decreasing return per expended engineering hour. 7. Two factories A and B make the same product in three manufacturing steps. Each step has an upper specification limit but no lower specification limit. Data on the process performance index (Cpk) for each of the steps at each factory is as follows: Step Fab A Fab B Suppose the only yield loss mechanisms are from exceeding the upper spec limits. Further, suppose yield losses at each step are independent. Assume there is 100% inspection after each step, and bad units are discarded before processing by the next step. (a) Explain why, for any of the steps above, the yield of the step may be well-estimated as Prob{Z < 3*Cpk} where Z is ~ N(0,1). (b) Estimate the overall yield at each factory. Which factory is doing better? (c) Suppose the first step involves a countable parameter of quality, and suppose USL for this step is 100. What is the upper control limit of an SPC chart for the first step in Fab A? (d) Suppose we could utilize the best step from each fab to make the product. How much better would the yield be? 8. The engineering management of a fabrication line is considering three projects to improve the process stability of certain manufacturing steps. (Stability in this case means the standard deviation of the process quality parameter for the step would be reduced.) Information about the current performance, estimated engineering effort and predicted performance of the steps after process improvement is as follows: Step Cpk new Required_engineering_man_hours (a) Estimate the percentage product cost reduction for each project and if all three projects are completed. State any assumptions you need to make. 4

5 (b) If the fab could only do one of the projects, which one should be done? If it could only do two, which ones should it do? Justify your answers. 9. The management of a factory is trying to sort out how much yield loss is coming from a stationary baseline distribution of defects vs. how much is coming from defect excursions and other systematic mechanisms of yield loss. A stacked wafer map is analyzed including only wafers believed to not be involved in any defect excursions. The best-yielding die site on the wafer map has a 65% yield. The number of 0.5 sq-cm dice printed on the wafer is 450. The average die yield over all wafers (including those involved in excursions) is 35%. (a) Calculate the baseline defect-limited yield and the underlying baseline defect density. (b) Management is considering an upgrade of the air flow system costing \$1.5 million. Engineering tests have been performed that indicate that this upgrade can be expected to cut baseline particle contamination on the wafers by 20%. However, particle excursions do not seem to be abated by the improved air flow. Estimate the improvement in baseline defect-limited yield and in the overall die yield if this upgrade is undertaken. (c) Management also is considering investment in a \$1.5 million inspection system enabling increased process monitoring so that excursions can be detected earlier and thereby reduce yield losses. Engineering analysis and experiments indicate that total systematic and excursion yield losses could be cut 20% by this investment. Assuming the air flow system is NOT upgraded, what overall die yield would result from implementation of this inspection system? If only \$1.5 million is available to spend, which is a better expenditure for improving yield the air flow system upgrade, or the new inspection system? 10. A product with 400 die per wafer has an average die yield of 61% and a die area of 0.5 cm 2. The best die yield observed near the center of a wafer map is 82%. (This wafer map was made from wafers in lots not subject to excursions.) (a) Estimate the stationary random yield (when systematic losses are not present), and estimate the systematic mechanisms limited yield. (b) Determine the Poisson defect density equivalent to the stationary random yield. (c) The following systematic mechanisms have been identified: 5

6 Mechanism Fraction of wafers Fraction die loss Total yield loss Wafer edge losses Missing photo patterns (counting only losses not overlapping the edge losses) Particle excursions (counting all die containing fatal defects, including those die experiencing missing photo patterns and those die in the edge losses) How much systematic yield loss is occurring from mechanisms not listed above? (d) The following contributors to the baseline stationary random yield have been identified: Layer Defect density Fraction fatal (defects per cm 2 ) Metal Metal Poly What amount of fatal defect density is occurring that is not observed by the above three inspections? How much yield loss does that account for? 11. A product with 400 die per wafer has an average die yield of 62% and a die area of 0.5 cm 2. The best die yield observed near the center of the wafer map is 82%. (a) In-line inspections have been implemented at the Metal 1, Metal 2 and Poly layers, and the observed defects have been correlated with the wafer maps of die yield to estimate the fraction of observed defects that are fatal. The following results were obtained: Layer Defect density Fraction fatal (defects per cm 2 ) Metal Metal Poly What amount of fatal defect density is occurring that is not observed by the above three inspections? How much yield loss does that account for? (b) The following systematic yield loss mechanisms have been identified: Mechanism Fraction of wafers Fraction die loss Total yield loss Wafer edge loss

7 Missing photo patterns (excluding the edge loss) Particle excursions How much systematic yield loss is the result of mechanisms yet to be discovered? 12. In a large stacked wafer map of wafers printed with 1,000 die, the die site with the maximum observed yield has a yield equal to 85%. (a) Estimate the baseline defect-limited yield. (b) Suppose fatal baseline defect density is reduced by 0.05 per sq cm. Suppose the die size is 0.5 sq cm. Predict the new maximum observed yield. (c) The following systematic yield loss mechanisms have been identified: Mechanism Fraction of lots Fraction of wafers Fraction of die lost affected affected per lot affected per wafer affected Edge loss Particle excursions Poisoned vias (Note: These mechanisms are not mutually exclusive, i.e., multiple failure mechanisms may be present in the same die.) 13. A product with 400 die per wafer has an average die yield of 65% and a die area of 0.5 cm 2. The best die yield observed near the center of a wafer map is 85%. (This wafer map was made from wafers in lots not subject to excursions.) (a) Estimate the stationary random yield (when systematic losses are not present), and estimate the systematic mechanisms limited yield. (b) Determine the Poisson defect density equivalent to the stationary random yield. (c) Clustering of the random defects has been studied. It has been found that mean number of defects per die is 0.8 and the variance in the number of defects per die is 1.2. Revise the estimate of the random defect density accordingly. 7

8 (d) In-line inspections have been implemented at the Metal 1, Metal 2 and Poly layers, and the observed defects have been correlated with the wafer maps of die yield to estimate the fraction of observed defects that are fatal. The following results were obtained: Layer Defect density Fraction fatal (defects per cm 2 ) Metal Metal Poly What amount of fatal defect density is occurring that is not observed by the above three inspections? How much yield loss does that account for? 14. Rework is sometimes required at photolithography steps. Statistics on rework in recent shifts are as follows: Shift # # of wafers # of wafers processed reworked (a) During which shifts was photo rework in statistical control? (b) The photo engineer has determined that an adjustment to the photo machine can reduce rework. The adjustment requires 60 minutes to perform. The process time per lot is 30 minutes. The photo engineer has collected statistics on rework and has found that the probability of rework grows as a function of the number of lots processed since last adjustment. The probability of no rework on the n th lot processed after an adjustment is P(n) = n-1. Consider the following potential frequencies for adjustment: Once every 10 lots, once every 20 lots, once every 30 lots, once every 40 lots, or once every 50 lots. Which frequency maximizes photo capacity? Explain. 15. A wet bench consists of a series of tanks served by a robot arm. Two production lots (50 wafers total) form one batch that travels down the bench. The batch is dunked in each tank by the robot arm. One of the tanks contains sulfuric acid that strips an undesired film off the wafers. With repeated use, the acid bath contains more and more residue from previously stripped wafers, and there is increasing probability that the film on the wafers in the next batch may be inadequately stripped. An inspection step carried out after the wet bench step would detect this, in which case the batch must be re-worked. At some point the acid bath must be dumped and re- 8

9 poured with fresh acid; this involves one hour of down time to the wet bench as well as the expenses for new sulfuric acid and disposing of the old acid. The process time in the sulfuric acid tank is 30 minutes per batch, whether for a first-time batch or a re-worked batch. The wet etch engineer estimates the probability that rework is required is a linear function of bath usage: P(n) = 0.05*n, where n is the number of first-time batches processed since the acid bath was re-poured and P(n) is the probability that the n th batch must be re-worked. You may assume that with probability one a batch that is reworked will be successfully stripped of the undesired film on the second pass through the tank, and that reworking does not cause the acid bath to deteriorate. (a) Suppose our objective is maximum wet-bench capacity. What frequency of re-pour is best? (By frequency, we mean how many batches between re-pours of the sulfuric acid bath.) (b) Now suppose our objective is minimum cycle time. Assume the following data for the wet bench: m=1, ca = 1, ce = 1, the wet bench receives 250 lots per week (i.e., 125 batches per week, excluding rework), and the only down time is for re-pouring the acid bath. Now what frequency of re-pour is best? (Hint: You can calculate the availability and average rework rate as functions of the re-pour frequency. And be sure to include rework in utilization.) (c) Now suppose our objective is maximum profit. What factors should be taken into account to decide the best frequency of re-pour? What other data would you request in order to make this determination? 16. The overlay alignment of the exposure machine used in a particular manufacturing technology is difficult to control. After re-calibration of the machine, the first lot processed has zero probability of mis-alignment. The second lot processed has probability 0.02 of misalignment. The third lot has probability 0.02(2) = 0.04 of mis-alignment, the fourth lot has probability has probability 0.02(3) = 0.06, and so on. Each lot that is mis-aligned must be re-worked. Re-worked lots are manually aligned on the machine, so there is zero chance of mis-aligning a rework lot. Processing one lot through the machine takes 1 hour. It takes another 1 hour to process the lot through the machine if rework is required. To re-calibrate the machine takes 8 hours, during which time processing can not be performed. The exposure machine is the bottleneck of the manufacturing process. (a) Starting with a just-calibrated machine, assuming a continuous supply of work-in-process, and assuming no further re-calibration of the machine, provide a formula for the expected duration for the exposure machine to complete processing of n lots, including any required rework of those lots. You do not need to simplify the expression. 9

10 (b) Which frequency of re-calibration will maximize the long-run output rate of the exposure machine: re-calibrate every 5 lots, every 10 lots, every 25 lots, or every 50 lots? (Hint: use your formula from part (a) to express the output rate per calibration cycle.) (c) Assuming there is no idle time and assuming 1 hour is the theoretical time to process one lot, what is the expected OEE of the machine for the frequency of re-calibration you chose in part (b)? 17. A wet etching machine processes a batch of two 25-wafer lots. The lots are dunked in an acid batch, followed by a dunk in a rinse bath. The acid tank of a wet etching machine becomes increasingly dirty with each batch processed. As a result, there is an increasing chance of particles becoming lodged in the circuitry on the wafers within each batch that cannot be rinsed off. Starting with a fresh acid bath, the process engineer estimates that the fatal defect density increases by 0.35 per sq cm after every batch processed. That is, if the fatal defect density of a batch run in a fresh acid bath is D0 per sq cm, then the fatal defect density of the next batch will be D , and that for the next batch will be D , and so on. At some point, the acid bath should be dumped and re-poured; this takes 2 hours. Suppose the process time of a batch is one hour, and suppose the die size is 0.5 sq cm. Suppose the wet etching machine is very busy, i.e., there are almost always lots waiting to be wet-etched. (a) Suppose we re-pour the acid bath after every n batches. Provide a formula to estimate the average yield of the n batches between re-pours of the acid bath. (b) Consider three alternative frequencies for re-pouring the acid bath: after every 2 batches, after every 4 batches, or after every 6 batches. Which frequency would you recommend? Explain. (c) Suppose the fab product mix changes such that this wet etching machine now has considerable idle time. Qualitatively, how should the frequency be changed, i.e., should we dump the bath more often, less often, or no change? 18. The processing cycle for a diffusion furnace consists of three phases: load, run, and unload. During the load portion of the cycle, an operator transfers wafers from incoming lots into a boat accommodating 150 wafers. If the incoming lots include less than 150 wafers, the operator inserts dummy wafers to raise the total wafers in the boat up to 150. During the run portion of the cycle, the boat is mechanically inserted into the furnace, the wafers are cooked for a specified length of time, and then the boat is mechanically withdrawn from the furnace. During the unload portion of the cycle, the operator unloads the product wafers from the boat into lots to be sent to follow-on operations, and he/she unloads the dummy wafers for re-use in subsequent furnace runs as may be required. 10

12 Parameter Theoretical Time (secs) Average Time (secs) Beam Setup Time, BSU Vent Time, VT Wafer Exchange Time, XT Pump-down time, PT Wheel Rev-up Time, RT Implant Time - step 1, IT Implant Time - step 2, IT Implant Time - step 3, IT There are two high current implant machines in the fab. For each machine, down time averages 6 hours per day and idle time averages 3 hours per day. The maximum load size per implant is 12 wafers. Assume the average load size also is 12 wafers. (a) Estimate the fab output rate. Assume line yield losses in the fab are negligible. (b) Estimate the OEE of the high current implant machines. Assume there are no quality efficiency losses for the high current implant machines. (c) The equipment vendor offers a modification to the implanters that will reduce the average beam setup time (BSU) to 60 seconds. Assuming the fab output rate is held constant, by how much will the idle time increase for each high current implanter? In this case, how will the OEE score change? (d) Now suppose high current implant is the bottleneck equipment type. Suppose the fab starts rate is raised just enough so that all of the time saved by reducing BSU is absorbed by processing more wafers per day. Now how will the OEE score change? 20. A fabrication plant includes a sophisticated etching machine purchased almost a year ago. The purchase agreement for the machine included a service contract lasting one year whereby technicians working for the machine vendor perform preventative maintenance and repairs on the machine. At present, a machine vendor s technician performs a weekly PM. The PM takes the machine down for 4 hours. When the machine breaks down, the down time averages 8 hours (including time for the technician to drive to the plant). Data on machine failures indicates that the time until failure from performance of PM is distributed as follows: Days since PM, t Fraction of breakdowns occurring on day t

13 The service contract is about to expire. The machine vendor offers to renew the service contract for one year at a fixed cost of \$150,000. Alternatively, the plant could hire a local, on-call independent contractor charging \$250 per hour to perform PMs or repairs. This contractor used to work for the vendor and is very knowledgeable about the machine. It is believed that the contractor could perform high-quality maintenance work just as quickly as the vendor s staff. (a) The machine vendor is currently performing weekly PMs. Estimate the availability of the machine. (b) What frequency of PMs would you recommend to maximize machine availability? (c) Estimate the availability if the frequency of PM was changed to follow your recommendation in (b). (d) Estimate the annual costs for maintenance of the machine if the plant terminates the service contract and instead utilizes the local independent contractor following the PM frequency you calculated in (b). Would you recommend renewing the service contract? Or hiring the local contractor? 21. A wet bench consists of a series of tanks served by a robot arm. Two production lots (50 wafers total) form one batch that travels down the bench. The batch is dunked in each tank by the robot arm. Batches move along the bench one after another; the minimum spacing of the batches is the longest time spent in any one tank. One of the tanks contains sulfuric acid that strips an undesired film off the wafers. With repeated use, the acid bath accumulates more and more residue from previously stripped wafers, so there is increasing probability that the film on the wafers in the next batch may be inadequately stripped. An inspection step carried out after the wet bench step would detect this, in which case the batch must be re-worked. At some point the acid bath must be dumped and re-poured with fresh acid. The minimum time between consecutive batches run on the bench is 30 minutes, regardless of whether the batches involved are first-time batches or batches being re-worked. Once it is decided to re-pour the acid bath, no 13

14 more batches can be input to the bench until the re-pour is complete. A re-pour involves one hour of down time to the whole wet bench. The wet etch engineer estimated that the probability that rework is required is a linear function of bath usage: P(n) = 0.03*n, where n is the number of first-time batches processed since the acid bath was re-poured and P(n) is the probability that the n th batch must be re-worked. You may assume that with probability one a batch that is reworked will be successfully stripped of the undesired film on the second pass through the bench, and that rework causes negligible deterioration of the acid bath. Suppose our objective is maximum wet-bench output. Consider the following alternative frequencies for re-pouring the acid bath: Once every 4 batches, once every 8 batches, once every 12 batches, or once every 16 batches. Given an unlimited supply of WIP, which frequency of repour would achieve the highest output rate? 22. A wet etching machine processes a batch of two 25-wafer lots. The lots are dunked in an acid batch, followed by a dunk in a rinse bath. The acid tank of the wet etching machine becomes increasingly dirty with each batch processed. As a result, there is an increasing chance of particles becoming lodged in the circuitry on the wafers within each batch that cannot be rinsed off. Starting with a fresh acid bath, the process engineer estimates that the fatal defect density increases by 0.01 per sq cm after every batch processed. That is, if the fatal defect density of a batch run in a fresh acid bath is D0 per sq cm, then the fatal defect density of the next batch will be D , and that for the next batch will be D , and so on. At some point, the acid bath should be dumped and re-poured; this takes 3 hours. Suppose the process time of a batch is one hour, and suppose the die size is 0.05 sq cm. Suppose the wet etching machine is very busy, i.e., there are almost always lots waiting to be wet-etched. (a) Suppose we re-pour the acid bath after every n batches. What is the average defect density across those n batches? (b) Consider three alternative frequencies for re-pouring the acid bath: after every 50 batches, after every 100 batches, or after every 150 batches. Which frequency would you recommend? Explain. (c) Suppose the fab product mix changes such that this wet etching machine now has considerable idle time. Qualitatively, how should the frequency be changed, i.e., should we dump the bath more often or less often? 23. A vacuum process machine currently equipped with a wet pump is being modified to incorporate a dry pump. The equipment maintenance department would like to set up a preventative maintenance (PM) schedule for the dry pump. The process machine currently experiences weekly PMs, monthly PMs, bi-monthly PMs, and quarterly PMs. The maintenance 14

15 department does not want to add any more frequencies of PMs because of the long requalification time. The maintenance department is wondering to which of the existing frequencies of PMs it is best to place maintenance of the dry pump. Data received from the dry pump vendor is as follows: Weeks of service Probability of failure To add the dry pump to an existing PM involves 4 hours of incremental down time. If the dry pump fails, the unscheduled down time to repair the pump and re-qualify the process machine for service takes 12 hours. (a) From the point of view of maximizing machine availability, which of the existing PM frequencies is best for the dry pump? (b) Suppose the incremental cost of a dry pump PM is \$500, and if the dry pump fails, the cost of lost output and repair of the dry pump is \$25,000. From the point of view of cost minimization, is the same PM frequency as in (a) best? If not, which frequency is best? 24. Three photolithography scanner machines in a particular fabrication plant experience rate efficiency losses because of substandard lamp intensity. This substandard lamp intensity also generates occasional rework. The photo engineer has determined that, with weekly cleaning of the mirrors forming the optical path inside the machine, the average lamp intensity (LI) can be raised from its current average value of 700 mw/sq cm to an estimated 770 mw/sq cm. In addition, the average photo rework rate is expected to decline from 10% to an estimated 7%. However, this cleaning effort would introduce an additional 1 hour of machine down time per week. 15

16 Data concerning theoretical process times on the scanner are as follows: AT = 50 seconds XT = 35 seconds MT = 2 seconds LI = 785 mw/sq cm There is no blading required. Two products are in production, each with one photo step: Product Exposure energy (EE) No. of exposures to cover wafer A 2800 mw-sec/sq cm 500 B 2000 mw-sec/sq cm 350 Data concerning last week s operation of the scanners is as follows: Total photo department machine hours: (3 machines)(168 hours) = 504 machine-hours Total available time: = 462 machine-hours Total wafers processed by scanner machines: Product No. of wafer operations No. of wafers completed (including rework) (excluding rework) A B (a) What was the availability (A) of the photo scanner machines last week? Estimate the utilization of total time (U). Estimate the utilization of availability (U/A). (b) Estimate the overall equipment efficiency (OEE) of the photo scanner machines last week. You may assume the actual values of AT, XT and MT were equal to their theoretical values. (c) Suppose weekly cleaning of the mirrors is implemented, and suppose the production rates of A and B are kept at 300 and 250 per week, respectively. Suppose further that last week s actual availability is a good estimate of the average availability of the photo machines before cleaning of the mirrors is implemented. Estimate the values of A, U, and U/A after the change is made. Qualitatively, what do you expect would happen to cycle times? (d) Suppose instead of keeping the same production rates for products A and B, the production rates of products A and B are scaled proportionately so that U/A would have the same value as it did in part (a). Estimate the new output rates of A and B, and estimate the new OEE in that case. Qualitatively, what do you expect would happen to cycle times? Is cleaning of the mirrors a good idea? 25. A wafer fabrication plant is manufacturing a single device whose area is 0.5 sq cm and whose fatal defect density according to the Seeds Model is 0.5 per sq cm. The device has a line yield of 100%. 16

17 It has been determined that the metalization process is a source of significant particles. It is possible to reduce this contamination if a special machine clean cycle is inserted into the process recipe. This extra clean cycle will reduce particle contamination, but it will increase the metalization process time. The Process Engineering Dept. would like to know if it is beneficial to introduce this special clean cycle. There are two metallization steps in the overall process flow for the device, each performed by the same machine type. It is estimated that, without the special clean cycle, the machine deposits 0.40 particles per sq cm per wafer pass, of which 20% are fatal. If the special clean cycle is added to the process recipe of each step, it is estimated that the particles deposited per wafer pass will drop to 0.30 per sq cm. The fab inputs 21,000 wafers of the device per 30-day month, which is just equal to the capacity of the bottleneck equipment. The average process time per wafer pass of the metalization machine is currently 0.05 hours, but if the special clean cycle is introduced, this time will rise to 0.06 hours. There are five metalization machines; they average 30% down time. The metalization machines are not the current fab bottleneck, but if they were, it is estimated that their minimum idle time would be 5%. (a) Express the die yield improvement as a multiplier on the current die yield. Estimate the die yield subsequent to implementation of the special clean cycle. (b) Estimate the fab wafer throughput subsequent to implementation of the special clean cycle. (c) Estimate the % increase (or decrease) in die output if the special clean cycle is implemented. (d) Find the lower limit on the amount of particle reduction resulting from the special clean cycle in order for implementation of the special clean cycle not to reduce die output. 17

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