methods for manufacturing improvement ieor 130 prof ...courses.ieor.berkeley.edu/ieor130/130...

Semiconductor Manufacturing

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IEOR 130 Review

Methods forManufacturing Improvement

Prof. Robert C. LeachmanUniversity of California

at Berkeley

November, 2018


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IEOR 130• Purpose of course: instill cross-disciplinary,

industrial engineering perspective and skills in future engineers, managers or researchers for technology-intensive manufacturing

• Course grade: Max { F, 0.67F + 0.33M} – M & F exam scores converted to letter grades on a curve

• Final exam: Tuesday, Dec. 11, 3-6pm– Final exam covers entire course

– Open notes, calculators, laptops (but no internet)


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TopicsWhat matters in high-tech manufacturing:• Process control – We need a stable manufacturing process. We

need to consistently make good product.

• Yield analysis – We need to identify root causes of quality losses and eliminate them.

• Equipment efficiency – We need to achieve good return on very expensive equipment assets. We need to understand capacity and plan investments wisely.

• On-time delivery – We need to promise delivery dates we can achieve, and we need to achieve them.

• Speed (AKA cycle time) – For competitive reasons and economic reasons, we need manufacturing to be fast.


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Technical Topics and Relationshipto Other IEOR Courses

• Statistical Process Control (IEOR 165), Process Controllability and Six Sigma Analysis

• Statistical Yield Analysis• Maintenance Scheduling Under Uncertainty (renewal

models, IEOR 172)• Equipment Efficiency Measurement • Production Planning (IEOR 150) and Delivery Quotation• Factory Floor Scheduling (IEOR 150) and Management of

Work-in-Process• Economics of Speed (Continuous-time discounting of

cash flows, E120)• Cycle Time Analysis (Queuing analysis, IEOR 173 & 151)• Capacity Planning


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Statistical Process Control

• Basic idea: Sort out abnormal variation from normal variation. Stop process when abnormal variation detected, thereby mitigating losses. Find root cause and fix.

• Trade-off for choosing parameters: Cost of Type I errors (false alarms) and measurement cost vs. Cost of Type II errors (missed excursions)

• Different charts for different types of parameters of quality:

– X-bar and R charts for a real-valued parameter– P and Z charts for a binary parameter– C chart for a countable parameter


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• For a real-valued parameter of quality, we apply X-bar and R charts

– Control limits of X-bar chart at– Control limits of R-chart at

• For a binary parameter of quality, we apply P or Z charts

– In a P chart we plot the fraction defective– Control limits of a P chart at – In a Z chart we plot the normalized fraction defective:

– Control limits of a Z chart at

n/3σµ ±σ243 where and dRRdRd =

nppp /)1(3 −±

.)1(

npp

ppZ−−

=

3±


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• For a countable parameter of quality, we apply the C chart

– If the average no. of defects is > 20, we can set control limit at

- If the average no. of defects is < 20, we need to look up Poisson distribution probabilities to set the control limit

cc 3+


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Deming’s PDCA Cycle

• Plan – Identify important parameters of product or process quality and establish spec limits, establish out-of-control action procedures (OCAPs) and train

• Do – Set up control charts for the important parameters

• Check – Run SPC• Act – When OOC signal is received, perform OCAP.

Find root cause for process variation and mitigate.


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FMEA

• Failure Mode and Effects Analysis (FMEA)• Identify the possible failure modes of a product or

process• Estimate likelihood, detectability and consequences

of the failure mode• Design tests or inspections to detect failure mode

and prove failure mode does not exist before passing product downstream

• Design measures that mitigate consequences if and when failure mode is revealed


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Six Sigma• Quality is measured by comparing the mean and

standard deviation of the process parameter to specification limits LSL, USL for the parameter

• Cp = Process controllability = (USL – LSL)/6σ– If Cp > 1.5, process is reasonably controllable

• Cpk = Process performance index = Min { (USL – µ)/3σ, (µ – LSL)/3σ }

– If Cpk > 1.5, process performance is good

• Note that in the case of only an upper specification limit, and if exceeding the spec limit is the only failure mechanism, then

{ } { } { } )3(3 Prob3 Prob Prob 1pkpkpk CCZCXUSLXY −Φ=<=+<=<= σµ


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Yield Analysis

• When the primary failure mechanism is defects, and the defects are not significantly clustered, the simple Poisson model may be applied:

• Even if defects are clustered, the Poisson model is useful for estimating the change in yield resulting from a reduction in the fatal defect density:

AYDeY AD /) (ln , −== −

YeeY DADDANew

∆∆−− == )(


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Yield Analysis• For estimating yield of a new device, compound defect

density models are useful when defects are clustered and/or die sizes are large. The general form is:

• The most general defect model is the negative binomial:

• The cluster parameter is estimated as

∫∞ −=

0)( dDDfeY AD

α

α

−

+=

ADY 1

( )λσλα−

= 2

2

dieper defects ofnumber theof deviation standard and mean theare and where σλ


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Yield Analysis• A more general yield model allows for both baseline

random defect and systematic losses. Systematic losses have a spatial and/or temporal signature, whereas baseline random defects have no spatial or temporal signature.

• Using wafer maps, we can estimate YR by applying the binomial model. We consider only wafers free from excursion losses and die sites free from systematic losses.

• If there are m wafers in the stack and n good die sites, and the maximum yield is observed at l of the n sites,

0ADSRS eYYYY −==


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Yield Analysis

mYYnlYY RRR /)1()/1(Max 1 −−Φ=− −

formula. quadratic theusing for solved bemay which RY

. and from deduced bemay turn,In YYY RS


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Yield Analysis

• Best practice: (1) Establish Yr, Ys from top-down wafer-map analysis. (2) Determine yield losses bottom-up from specific systematic mechanisms, and compare total specific losses to the top-down Ys to ascertain if there are systematic losses yet to be explained.


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PM Scheduling• If preventive maintenance restores an equipment to like-

new condition, then we can apply renewal theory to optimize the PM frequency

• A renewal cycle is the duration between events when the equipment is made like-new

• The objective function is (expected costs or benefits during a cycle) / (expected length of a cycle)

• Let pk be the probability the equipment fails in the kth period after maintenance. If t is the target elapsed time before performing a PM, then the expected length of a cycle is

∑∑∞

+==

+++11

)()(tk

k

t

kk pMTTPMtMTTRkp


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PM Scheduling

• If the lengths of MTTR and MTTPM are small compared to the length of a period, this simplifies to

• The numerator is constructed by adding up the expected costs or down time or output during a cycle

• The objective function can be computed for various values of t to find the best value of t

• Potential objectives: Cost rate, availability, output rate

∑∑∞

+==

+11 tk

k

t

kk ptkp


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Equipment Efficiency• OEE = S/T, the “should-take” time for the good

output of the equipment divided by the actual elapsed time

• OEE = A * U/A * RE * QE where A is availability, U/A is the utilization of availability, RE is the rate efficiency and QE is the quality efficiency

• The determination of OEE depends on defining ThPTs (theoretical process times, AKA theoretical takt times) for each recipe performed by the equipment

– This is the minimum time to complete the recipe for a machine in perfect working order

– RE is computed by applying ThPTs to the wafers actually processed of each recipe and comparing the should-take time to the time actual required to complete the wafers


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TPM• Total Productive Manufacturing• Factory staff should not just execute production,

they should inspect and correct production equipment

– Fix minor flaws before they become major problems– Factory staff should be part of the engineering organization

• Elevate knowledge and role of all employees in maintaining equipment health

– Establish inspection procedures and deterioration limits– Train

• Move to predictive maintenance


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Equipment Capacity

• EPT = effective process time, the actual average time to perform a recipe considering rework, speed loss, etc.

• CRE = capacity rate efficiency, computed like RE except using EPT’s instead of ThPT’s

• Umax = the maximum utilization for an equipment that we allow (considering the cycle time consequences)

• CEE = capacity equipment efficiency = A * Umax/A * CRE

• Capacity of equipment = CEE * (# of machines) * length of period


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Equipment Capacity

• Note that capacity is expressed in terms of processing hours per period.

• Capacity analysis compares the workload on equipment (computed using EPT’s and average line yields) resulting from proposed wafer starts and work-in-process to the allowed capacity of the equipment

• To maintain cycle time performance and on-time delivery, we limit wafer starts so that the workload on any equipment does not exceed its allowed capacity in any period.


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On-Time Delivery

• To achieve on-time delivery, quotes for delivery dates should be calculated based on the on-hand inventories, the production plan and previously-made customer commitments. The cumulative product availability is calculated as

where St is the cumulative product supply and Ot is the cumulative commitments up until time t.• Let Rt denote the cumulative amount requested for a

delivery quote until time t. Then the cumulative quote is

{ } .,,2,1,,,1,| TtTttOSMinAt =+=−= τττ

{ } .,,2,1,, TtRAMinQ ttt ==


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On-Time Delivery

• If the delivery quote is accepted by the customer and converted into a purchase order, the cumulative availability is updated as

• The (cumulative) order board is updated as

{ } .,,2,1,,,1,| TtTttQAMinAt =+=−← τττ

.,,2,1, TtQOO ttt =+←


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Production Planning

• A production planning cycle consists of the following four phases:

– Definition and prioritization of demands for each product– Requirements planning– Capacitated loading– Calculation of product availability

• If the product structure is simple, MRP logic may be applied to perform requirements planning. If there are alternative source products or processes, a linear programming formulation is required.

– Minimize discounted production cost to meet orders– Maximize discounted cash flow for generating availability in response to

demand forecasts


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Production Planning

• Linear programming models may be developed for capacitated loading calculations assuming rate-based production starts.

• Capacity constraints with non-integer time lags may be formulated to properly constrain new wafer starts considering the total workload from performance of all process steps on both new starts and work-in-process.

• Priority classes of demands may be properly accommodated by optimizing a series of linear programs calculated on the same matrix. The programs are linked by bounds placed on the backorder variables:

11 −− −+≤ rt

rt

rt

rt DDBOBO


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Production Planning

• Build-to-order products may be accommodated by placing upper bounds on the period one production start variables in the LPs for forecast classes. The bounds are equal to the optimal values for production starts in the LP for the last non-forecast class.


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Economics of Speed

• If product prices are declining fast, manufacturing speed has great economic value.

• The total lifetime revenue is calculated as:

• In the case of constant yield Y and wafer volume W, the revenue gain from a reduction in cycle time ∆CT is:

[ ]∫ +−=H tCTt dttYtWePR

0

)(0 )()(α

( ) .11 0

−−=∆

−−∆

α

ααα

HCTCT eeWYPeR


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Economics of Speed• In the case of a yield learning curve, constant wafer

volume and constant cycle time, the lifetime revenue is calculated as:

• The yield learning parameter b can be computed as

where YLF (yield learning factor) is the fraction of yield learning completed halfway through the ramp time RT.

( )( )

+

−−

−

−

−+

−

+

− +−−

−

−−−+−

− bee

eYY

eYYeeeWYP

RTbRT

bRTF

RT

F

HRTCTVT

FVT αααα

αααααα 11

1

11

0

0

−

−= 11ln

5.01

YLFRTb


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Queuing Analysis

• The entitlement cycle time of a product-step is expressed as ECT = QT + PT/A + (SCT – PT) where

and

• ECT can be reduced by increasing m, increasing A,or by reducing PT, u, MTTR or σTTR

−

+=

−+

APT

umucecaQT

m

)1(2

1)1(222

−++=

PTMTTRAAcrcce )1()1( 22

02


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Queuing Analysis• For batch tools (e.g., diffusion furnaces), the queuing

entities are the batch types rather than the product-steps (because lots from multiple product-steps can be part of the same batch).

• We apply queuing analysis to estimate the queue time for a batch type, then append an additional term BT for the average time waiting for a batch to be accumulated:

• Here, b is the batch size and S is the arrival rate of lots belonging to the batch type.

SbBT2

1−=


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Queuing Analysis• For setup tools (e.g., ion implanters), the queuing entities

are the setup types rather than the product-steps (because lots from multiple product-steps share a setup).

• We apply queuing analysis to estimate the queue time for a setup type, then append an additional term BT for the average time waiting for one’s turn within the run after a setup:

• The expression for ECT product-steps using setup type l becomes:

• Note that, with probability Ul, a lot of setup type l arrives while the machine is already set up to run type l.

lll

l stPTbBT +−

=2

1

CTl = BTl + (1 – Ul)*(QTl + PTl*bl/A) + SCTl – PTl


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Queuing Analysis• Cluster tools consist of a frame hosting multiple

chambers able to process in parallel multiple wafers from the same lot. One or more of the chambers may be down while the frame is up, resulting in lot process times that depend on how many chambers were up during processing.

• To apply queuing analysis, we use the frame availability as the server availability A, and we use the chamber availability Ac to compute weighted-average takt times:

• Here, UPH is the speed of the machine when all chambers are up, and n is the number of chambers. (If all n chambers are down, then by definition the frame is down.)

))(()1(

)1(11

1 UPHmnAA

mn

APT mn

cm

c

n

mn

c

−

=

−

−−

= ∑


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Capacity Planning• Given a desired product mix and volume, the bare-

minimum equipment set is that necessary to keep all equipment below 100% U/A. The cycle time associated with the bare-minimum equipment set would be excessive, so more equipment needs to be procured. How much?

• Starting with the bare-minimum equipment set, compute the reduction in ECT is one more machine is purchased. Do this for every machine type. Divide the reduction in ECT by the total installation cost of the machine to compute a cycle time ROI. Add the machine with the highest ROI to the equipment set.

• Continue adding machines this way until the desired ECT is reached.


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Factory Floor Scheduling• There are a number of different paradigms for scheduling

– WIP Limit paradigm (Kanban, just-in-time, negative scheduling): Bounds are placed on WIP accumulation in a step or a series of steps. Once the WIP Limit is reached, the upstream operation must cease.

– Dispatch paradigm: A priority list is maintained for the lots awaiting processing by an equipment group. Typically, priority is given to the lot most behind schedule (the least slack rule or the critical ratio rule).

– Release control paradigm: Input of new lots to the factory is regulated by constraints. These could be simple WIP Limits for the whole factory (CONWIP, taking us back to the WIP Limit paradigm), or limits expressed in bottleneck machine-hours (Workload Regulation, Starvation Avoidance, or taking us into production planning)

– IPQ-based scheduling (SLIM): End-of-shift targets are calculated for each product-step. Lots are dispatched to achieve the targets as much as possible making as few changeovers as possible.

• Most real factories use more than one of these paradigms


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IPQ-Based Scheduling• Target cycle time includes buffers for bottleneck

steps proportional to the variability in actual cycle time since the previous bottleneck step (or since fab start in the case of the first bottleneck step)

– Alternatively, the buffer could be made proportional to the difference between actual and standard cycle time

• IPQ of a product-step = (Total fab outs due up until the target cycle to fab out plus one shift) – (Total fab outs to date) – (Downstream WIP)

• Schedule score = -IPQ/(Fab out rate)• When constructing the schedule for an equipment area,

we try to complete the IPQs as much as possible while minimizing recipe changes. As much WIP is scheduled as possible.


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Suggested Spreadsheets

• Calculate simple Poisson defect density from given yield and vice-versa; calculate new yield from change in defect density

• Calculate baseline random yield from maximum observed yield on a stacked wafer map

• Calculate expected cost rate or availability as a function of PM frequency

• Compute revenue gain associated with cycle time compression from rate of price decline, volume, yield, ramp time, ramp learning rate and other parameters

– Compute ramp learning factor b from fraction YLR of learning completed at mid-point of ramp


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Suggested Spreadsheets (cont.)

• Compute QT and ECT from parameters (utilization, availability, takt time, no. of qualified machines, MTTR, σTTR, SCT, etc.)


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Course Evaluations

• Go to https://course-evaluations.berkeley.edu/berkeley/

https://course-evaluations.berkeley.edu/berkeley/

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