1

Abstract —Based on a simulated Non Volatile Memory fab,

we employ data-mining to Identify and quantify the apparent

causes of work in process bubbles along the process. The

chosen bubble formalization methods proved able to detect the

phenomenon and enabled its occurrence frequency to be

forecasted. In the chosen environment, bubbles seem to be

highly correlated with the utilization patterns of the process

segment considered.

Index Terms—Production management, semiconductors,

work-in-process, congestion.

I. INTRODUCTION

his paper addresses the issue of fab line robustness

regarding acute Work-In-Process (WIP) congestion

over a short process segment. This phenomenon, termed

“bubbles” in the fab jargon, is known to be one of the main

sources of variability in the process flow and to drain a

substantial portion of the operation workforce focus and

energy. Its impact has so far not been measured and even

the meaning of the term “bubble” differs slightly from place

to place. Most practitioners agree that a “WIP bubble,” or

“bubble” for short, is an acute WIP congestion at a certain

segment of the line, but such a definition does not provide a

quantification scale that would allow tackling the issue in a

somewhat rational way (see Cunningham et al. [2],

McGlynn et al. [13], Potti et al. [8] or Bilgin et al. [16]).

Only very recently has the bubble phenomenon been

studied in its own right (See Hirade et. al, [14]). In an

earlier article (Hassoun et. al, [10]), we formally defined the

concept of WIP bubble, formulated the means of bubble

identification, and measured the impact of bubbles on the

line.

In the present work we aimed to identify the

characteristics of the line that most influence the occurrence

of bubbles. In order to reach a certain level of generality as

well as to have control over plant running conditions, we

preferred to generate data via simulation and not to base our

analysis on actual data from a fab. Our industrial partners

had a special interest in flash or Non Volatile Memory

(NVM) factories, and so the “SEMATECH dataset one”

model, which represents such a fab, was chosen. We

generated a large number of variations of this model, thus

creating different characteristics for each of the processing

steps under each scenario. The frequency of the appearance

of bubbles was measured in the different pre-defined

process segments, and we correlated this frequency with the

segment characteristics. Data mining tools have recently

proven their ability to extract important information from

large amounts of data typically generated by today’s high-

tech manufacturing environment (see Gardner et al. [9] or

Kusiak [11]). We employed some of these data mining

techniques to establish a prediction model for bubble

frequency.

In the following sections, we restate our formalization of

the bubble concept, provide the technical details of our

experimentation framework, and present the results both in

terms of the forecasting capabilities of the models and of

the most important prediction variables for the appearance

of bubbles. A similar analysis in a real plant would allow

for accurate predictions of the tendency of certain segments

in the line to undergo bubbles and may be helpful in

improving existing fabs and in designing production lines

that are less prone to develop WIP bubbles.

Hunting Down the Bubble Makers in Fabs

M. Hassoun, G. Rabinowitz

T

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II. BUBBLE DEFINITION AND PRINCIPLES OF IDENTIFICATION

For reader convenience, we briefly review the means of

formal bubble identification as provided in Hassoun et al.

[10]. We have based our bubble identification mechanism

on two basic principles: First, the capacity of a segment to

recover from a bubble (also called its “burst capacity”, see

Arazy et. al, [17]) determines a certain WIP threshold that

delimitates between normal operation and WIP congestion.

Second, the capacity of any segment that includes a

bottleneck is limited by the capacity of the bottleneck. The

cumulative WIP level in such a segment is an indication of

the segment’s capacity. We thus divided the process into

segments, each of which included one bottleneck, and

monitored their cumulative WIP. Then, we built an

Exponentially Weighted Moving Average (EWMA) control

chart for the daily WIP level and defined any extrusion

from the upper limit of the chart as a “Local Bubble Event”

(LBE), meaning that the congestion is measured only in a

defined segment. A bubble, in its traditional meaning, is

thus the appearance of several LBEs in consecutive

operation segments along the process.

For the sake of clarity, we recall that the smoothed

central line value is given by:

1ˆ)1(ˆ ttt WWW (1)

The smoothened standard deviation is given by:

1ˆ)1(ˆ ttt SSS (2)

Therefore, the Upper Control Limit for the WIP in the

segment is given by:

ttt SZWUCL ˆˆ (3)

where tW is the average WIP level at period t (we used

weeks), and is the exponential factor, St is the standard

deviation in the WIP values at t, and is the smoothing

factor. Z is the chart range.

An example of the control chart for one of the segments

is shown in Figure 1. Days with average WIPs exceeding

the chart upper bounds (areas circled in the figure) are

considered LBEs.

0

5

10

15

20

25

30

35

0 100 200 300 400 500 600 700 800

LotsLBEs

Days

Figure 1 EWMA control chart for WIP in a segment

Although the above definition (proposed in Hassoun et

al. 9]) is clear and rational, its implementation is far from

trivial, and for the current work, we needed to alter it

slightly for several reasons. In most fabs, identifying the

bottlenecks and consequently defining the line segments is

a complex task. First, the assumptions necessary for the

computation, a priori, of the workload on the stations

implies inaccuracies. The planned machine rate and

availability of the tools are only estimations, and their

realization over a defined period can differ from their

predicted values. Second, the steep changes in the

semiconductor markets are reflected at the fab level by

frequent changes in the product mix. Each product mix

stresses the fab capacity differently and both workload and

bottlenecks are subsequently redistributed. To cope with

these issues, we changed the LBE definition slightly by

allowing for more than one bottleneck in each segment.

Line segmentation can then follow management needs and

rationale. Any segmentation is legitimate as long as each

segment includes enough heavily loaded operations, thus

insuring that under a broad range of scenarios, it includes at

least one tool that behaved, a posteriori, as a bottleneck.

This revision of the former definition of the LBE is minor

as the WIP distribution remains representative of the

segment capabilities.

III. EXPERIMENTATION FRAMEWORK

The purpose of the experiments was to generate a large

number of different situations in the fab and to explore

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these situations through data mining. In this section, we

describe the simulated fab that we used, the bubble

identification mechanism, and the structure of the output

data obtained from the experiment.

A. Sematech Dataset 1 NVM fab characteristics

The simulated fab “SEMATECH dataset one” is one of 6

standard models aimed at mimicking real fab behavior that

have been broadly used as research benchmarks (see

Palmeri et al. [18], Hunter et al. [6], Iwata et al. [19], or Dai

et al. [4]). Plant structure and operation are described in

great detail, and numerous characteristics of the true fab

level of complexity are expressed. The models are available

at: ftp://ftp.eas.asu.edu/pub/centers/masmlab/.

The NVM fab model is characterized by two high-

volume products produced on 68 toolsets (i.e., group of

identical tools). The total number of tools in the plant is

211. Product 1 and product 2 require 210 and 245

processing steps, respectively, to be completed. The

operations are characterized by, among other properties,

processing batch definitions (e.g., wafer, lot, lot batch), post

process cooling times, and sequence dependant setups for

two implant tools.

Rework and in-line scrap are also modeled, at both the

wafer and the lot levels (some lots are fully

reworked/scrapped, others are partially reworked/scrapped).

The release rate of the 48 wafer lots is constant—about one

lot every 3 hours for Product 1 and one lot every 6 hours for

Product 2—leading to a total of 4,000 wafers per week. For

loading and unloading lots on machines, assisting during

either part or all the process, and transporting lots from

machine to machine, 83 human operators of 28 types are

required. Based on these characteristics, this model proved

to be unstable, and the CT and WIP continued to grow with

time. We therefore adjusted the model in two ways: We set

the release rate at 90% of the SEMATECH definition

(3,600 wafers per week) and increased the head count of

operator number 7 (which appeared to be fully utilized,

even under the new, lower release rate) from 1 to 2. Under

these new conditions, the model showed converging,

steady-state behavior while still operating close to full

utilization (any increase in the release rate would

destabilize it).

B. Bubble analysis in the Sematech NVM fab

We applied the LBE analysis scheme to the NVM fab

first by dividing the process route into segments

corresponding to re-entrance loops, and each segment

ended with the litho operation “Develop”. This resulted in

fifteen and seventeen segments for products 1 and 2,

respectively. The average number of operations in a

segment was approximately fifteen for each product. The

first segment of each product differed slightly: it had about

half the number of operations exhibited by the other

segments and it included no bottleneck. (The way a tool is

identified as a bottleneck is presented later on.)

We then tuned the EWMA chart coefficients to

effectively discriminate extreme congestion from regular

variability in WIP. The exponential factors for both the

control chart central line and its smoothened standard

deviation was set at 0.2. The control range Z was set at a

value of 2. One of the charts was already presented in

Figure 1.

Finally, we chose a target variable suitable to the planned

analysis. Hassoun et al. [10] have evaluated the impact of

bubbles from the viewpoint of lots by counting the number

of LBEs each lot suffered. Here, however, we evaluated

bubble occurrence at the segment. We decided to measure

the number of days the segment suffered an LBE, denoting

this metric as the Local Bubble Event Count (LBEC).

Another possibility would have been to count the number of

LBEs appearing in the measured period, but since this

metric would not reflect the duration of the bubbles, we

abandoned this option.

C. The data structure

The experiment generates a single observation for each

segment under each scenario. The structure of the

observation data is described here. Each segment’s

characteristics were constructed from its operation

variables. Some of the operation variables describe the

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operation in itself; others are related to the toolset on which

the operation is processed. The operation variables

comprise parameters that are set prior to the simulation run

(e.g., distance from last bottleneck, next operation of the

same product on the station, etc.) and performance

measures that result from the simulation run. Most

performance measures are variables related to the toolset

that runs the operation (Availability, utilization, mean and

standard deviation of the number of down times, etc.). One

remarkable exception is the standard deviation of lot Inter-

Arrival Time to the operation. Note that the average of the

Inter-Arrival Time to the operation is an atrophied

performance measure that differs from the release rate only

due to small amounts of rework and lots scrap. We

therefore did not use it as a descriptor but merely as a

normalization value for the Process Time.

One of the most important variables is what is called the

“Load” on a station. It represents the expected portion of

the station capacity needed to actually process the required

product mix and is calculated following formulae used in

the industry. We used this metric to define any station

having a load above 90% as a bottleneck.

We processed the operation vectors for constructing the

segment’s characteristic vector. The variables describing

the segment are presented in Table 1 below. Some of the

variables are obvious metrics and describe the segment

directly (availability, number of BNs, etc.). Others quantify

the interactions between two subsequent operations. The

segment characteristic vector consists of 30 variables,

including the LBEC in the analyzed period. Each

simulation run yields 32 (15 and 17 of products 1 and 2,

respectively) observations of 30 fields.

Table 1 Segment descriptors

Descriptor Variables Remarks

Length Segment length Number of steps in

segment

Position Measured in steps distance of the first

operation of the

segment from the start

of the line

Load and BN

operations

Number of BN's, minimum

number of tools in a BN station,

min distance between

consecutive BN's, max load in

layer

BN defined as tools

loaded above 90%

Special regime

operations

Number of setup operations and

batch operations in the layer.

Maximum batch size in the

layers batch operations.

Availability average, standard deviation,

minimum, max gap between

two consecutive operations

stdv is measured among

the averages of the layer

operations availability

Utilization Weighted average, stdv of avg,

overall stdv, minimum,

maximum, max gap between

consecutive operations.

Number of tool

breakages

Weighted average, stdv of avg,

overall stdv, maximum, max gap

between consecutive operations.

Inter-Arrival Time stdv

Raw Process

time / IAT ratio

minimum, maximum Raw ratio. May yield

values higher than 1

Normalized

Process time /

IAT ratio

minimum, maximum normalized by the

number of tools and

batch size. Values are

in the 0-1 range

D. Design of Experiment

After setting the simulation framework and its data

processing infrastructure, we had to decide on the most

suitable experiment for achieving our goal. We needed to

generate a large number of scenarios that were

characterized by fairly high stress levels on fab capacity

and that were sufficiently different from one another. On

the other hand, we took the decision, a priori, to discard any

data coming from a simulation run that would not stabilize.

We wanted to maintain the highest possible level of control

and reduce the chances of creating an exploding WIP

situation. With these two contradictory ideas in mind, we

decided to create two hundred experiments by randomly

altering the basic settings supplied by SEMATECH (after

our changes as described earlier) on two levels. First, we

changed the product mix for each experiment. The original

figures were 2400 wafers per week and 1200 wafers per

week for products 1 and 2, respectively. For each

experiment, the release rate of product 1 was randomly

chosen from a uniform distribution between 2000 and 2600.

The product 2 release rate was then set accordingly to give

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a total, combined release rate for both products of 3600

wafers per week. In parallel, because we wanted to act on

each station individually, we altered the stations’

availability definitions in two ways: for half the scenarios,

we multiplied both the MTBF (Mean Time Between

Failures) and the MTTR (Mean Time To Repair) of each

station by the same random factor taken from a uniform

distribution in a range of [0.5; 2]. In these scenarios, the

resulting availabilities were not changed and we acted only

on the variance of the availability. In the remaining

scenarios, the machines’ availability was changed. The

MTBF was set at the original value and the MTTR was

multiplied by a factor chosen randomly from a uniform

distribution. The factor distribution ranges were [0.7; 1.05]

for bottleneck and [0.8; 1.2] for non-bottleneck stations.

At this stage, we conducted a single simulation run for

each of the 200 scenarios and examined their stabilizations.

We found that 39 of them diverged, and therefore, we

discarded their data. Then, in each of the stable scenarios,

we discarded segments with no bottlenecks (7% of

instances). The remaining usable data comprised a list of

4765 observation vectors.

IV. DATA MINING AND RESULTS

Using data mining methods to explore the database and

find emergent bubble phenomena, we addressed two main

questions about the occurrence of LBEs:

1. Can the chosen segment descriptors predict LBEC?

2. Which segment descriptors are more influential in terms

of the LBEC?

A. Understanding the data

Below we present a few characteristics of the data, which

are, in our view, essential to understand the following

sections.

Figure 2 plots the LBEC distribution evolution along the

processes for each of the two products. The box-and-

whiskers graphs clearly display the extreme points, the

quartiles (box boundaries), and the median (thick bar in the

box) for each segment.

0

20

40

60

80

100

120

140

160

Segments

LB

EC

02 03 04 1514131211100908070605

Product 1

0

20

40

60

80

100

120

140

160

Segments

LB

EC

02 03 04 1514131211100908070605 1716

Product 2

Figure 2 LBEC distribution along the process for the

two products

First, we remark that there are almost no cases of either

null or very low LBECs, meaning that all segments have

suffered at least a certain number of days in LBE.

Additionally, product 1 seems to have suffered more LBEs

than product 2. This is due to the Lowest Buffer Ahead

(LBA) scheduling scheme that systematically gives priority

to the operations with the Lowest Buffer Ahead, thus

conferring an advantage on the lower-volume product

between the two. We chose LBA as being a simplified but

reasonable representation of the dynamic scheduling

methods often found in fabs. Partial experiments run under

different scheduling patterns have shown that the choice of

a scheduling scheme has a non-negligible influence on

LBEC, an issue we left for future studies. In addition to its

different behavior between the two products, the LBEC

tends to increase with the segment’s position along the

process. This tendency is also evident in the prediction

models presented in the next section.

6

To address the dimensionality of the data, we performed

a Principal Component Analysis. This procedure identified

five components in the output data. Hence, we expected the

number of variables in use for prediction to be many fewer

than the original 29 variables.

B. Data-mining methodology

As already stated, the purpose of this research was

twofold: First, to study and improve our ability to predict

bubbles (or their quantitative definition, LBEC), based on

the chosen set of variables. Second, and perhaps more

important, to draw some insightful conclusions concerning

the main prediction attributes. Numerous statistical methods

may be considered, but as is discussed below, certain data

mining methods, e.g. decision trees (See Han et al. [5]), are

more applicable to our problem.

We denote an “observation tuple” as the vector of the

observed LBEC and its corresponding attributes, which will

be used as independent explanatory variables. Although the

LBEC is an integer, we preferred predicting it via a

classification model that classifies the tuples into groups

(ranges of LBEC values) rather than predicting their

individual LBEC values. Although this technique causes us

to lose both the numeric order of the LBEC values and the

internal LBEC variability within each class, classification

models were chosen over prediction models for two

reasons. First, in contrast to the various regression methods,

they do not require any assumption regarding model

structure. Second, they allow us to control the LBEC ranges

and thus to obtain more meaningful results.

The more commonly used classification models are

Decision Trees, Neural Networks, Bayesian Classifiers, and

Rule based classifiers (see Han et al. [5]). The decision tree

classifiers have the advantage of being easy to generate and

parameterize, and they enable a clear reading of their

internal logic. We therefore adopted them as our models of

choice. To generate decision tree classifiers, we used one of

the two major algorithms in the industry, namely the C5

procedure (see Quinlan [7]). Decision trees in general and

the C5 procedure in particular have demonstrated their

robustness and subsequent abilities in analyzing the large

and complex data sets usually generated in the

manufacturing environment (see Ozturk et al. [1] or Yeh et

al. [15]). It is important to emphasize that, while we

preferred the described method, alternative techniques

could have been used.

In this section, we analyze some different procedures for

building prediction models and then evaluate the models’

performances. We identify the best procedure (the one

yielding the best models), and address the level of

performance it achieved. In the next section, we apply the

best procedure, build the prediction model, and study its

characteristics.

In our quest for the best procedure, models were

systematically built and trained on a training subset of the

dataset (70% of all the tuples), and the quality of their

predictions was then evaluated on a test subset (the

remaining 30% of the instances). We evaluated each model-

generating procedure on ten random partitions of the data

into training and test sets to limit the risk of a biased

separation between the sets. Although we employed a

classification model, our performance measure was based

on the square of the prediction errors and is described

herein.

For all means related to computing variance, the

predicted LBEC of each instance is the average LBEC for

the predicted category of that tuple. The prediction error for

one instance, error(i), was defined as the gap between the

actual LBEC score of the tuple and the predicted LBEC.

Thus, the proportion of variance explained by the model

can be derived as follows:

2

1

( ) 1

1 ( )

n

i

error i n

Explained VarianceVariance test set

(4)

where n is the number of observations in the test set, i is

observation index in the test set, and Variance(test set) is

the variance of LBEC in the test set.

Since we chose to use classification models for the

LBEC, first we had to partition the data into meaningful

classes with respect to this metric. The LBEC is a new

7

measure, for which no user defined levels are available.

Thus, we were free to define the LBEC partition levels

according to our requirements. This partition must not only

make sense, it must also allow for efficient classification

models to be built. Therefore, after a short phase of

parameterization of the C5 algorithm (mostly based on the

industry rules of thumb), we conducted a trial and error

process intended to find a partition of LBEC levels that

would lead to high prediction performance.

Initially, we tried to part the data into equally populated

groups (Binning) according to LBEC values. This method

is the simplest, but it yielded relatively poor predictions,

with only about 30% (or lower) of the variance explained

by the model, no matter the number of bins that were

chosen. Next we used a centroid-based clustering

technique, the K-means method (See MacQueen [3]).

Basically, this method creates a user-defined number of

clusters such that the distance between each tuple and the

centroid of its corresponding cluster (computed on certain

attributes, in our case only LBEC) is minimized. We tested

this method with different numbers of clusters. For the

cases of 2, 3, and 4 clusters, Table 2 presents the average,

minimum, and maximum of the explained variance ratio

from ten trials. We also tried models that are based on more

than four clusters, but one of the clusters was invariably too

small to be detected (terminal tree nodes were restricted to

at least 1.5% of the training population).

Table 2 Proportion of variance explained by models

2 clusters 3 clusters 4 clusters

Average 42% 54% 56%

Maximum 48% 59% 60%

Minimum 36% 49% 51%

In our case, the results in Table 2 show that the option of

four clusters yields the highest performance in terms of

explained variance. Incidentally, considering the

complexity of the environment studied and the elusive

nature of the phenomenon we wish to predict, we found the

level of performance of the prediction models to be

satisfactory. We thus adopted the following steps as our

chosen procedure to create a prediction model for LBEC:

1. Discretize the LBEC into four clusters using the

K-means algorithm.

2. Build a prediction tree using the C5 algorithm, with

the clusters as targets.

C. Model, rules, and descriptors for LBEC

After choosing an efficient workflow, we had to

determine which segment descriptors were “bubble

makers.” We applied the workflow to the entire set of data

to get the best possible model and analyzed model structure

through its classification rules. In the first phase of the

chosen workflow, the K-means algorithm generated four

clusters, which are presented relative to the LBEC

distribution (Figure 3).

-0.0005

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 10 20 30 40 50 60 70 80 90 100

LBEC

Fre

qu

en

cy

Cluster 1 Cluster 3 Cluster 4Cluster 2

Figure 3 Clusters and LBEC distribution for total

population

The top part of Table 3 presents the LBEC statistics for

each cluster, and the lower part lists the distribution of

instances among the clusters for each segment along the

line. For example, based on the number of LBEC it

generated, segment number 03 of product 1 was classified

in cluster 1 in 52% of the experiments, in cluster 2 in 46%

of the instances, and in cluster 3 in 3% of the instances.

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Table 3 LBE instance distribution among the clusters

Cluster 1 Cluster 2 Cluster 3 Cluster 4

Average LBEC 24.7 35.6 50.6 74.8

Standard deviation LBEC 3.8 3.5 5.2 11.8

Minimum LBEC 10.0 31.0 44.0 63.0

Maximum LBEC 30.0 43.0 62.0 168.0

Population 2434 1479 636 216

Population fraction 51% 31% 13% 5%

02 87% 13%

03 52% 45% 3%

04 75% 24% 1%

05 4% 18% 37% 41%

06 63% 37%

07 38% 48% 14%

08 31% 51% 18%

09 65% 34% 1%

10 17% 42% 34% 7%

11 16% 34% 43% 7%

12 19% 50% 29% 2%

13 3% 17% 39% 41%

14 9% 37% 46% 8%

15 16% 58% 26%

Total for Product 1 33.7% 33.3% 23.4% 9.7%

02 20% 55% 25%

03 100%

04 78% 22%

05 98% 2%

06 91% 9%

07 97% 3%

08 32% 47% 19% 1%

09 80% 20%

10 85% 15%

11 68% 32%

12 50% 49% 1%

13 57% 39% 4%

14 64% 36%

15 41% 54% 5%

16 79% 20% 1%

17 20% 61% 19%

Total for Product 2 66.2% 29.1% 4.6% 0.1%

Seg

men

ts / P

rod

uct

1S

eg

men

ts / P

rod

uct

2

Table 3 prompts the following observations:

The K-means algorithm built clusters based on

LBEC density, which is skewed toward a high

LBEC (see Figure 3). The first cluster represents

about half the total population, while the fourth

cluster, which has the highest LBEC and shows

the highest LBEC variability, is the smallest, with

less than 5% of the population.

The distribution of the data among the clusters

follows the patterns that we emphasized in the

descriptive statistics phase. Product 1 was affected

more by LBEs than product 2, and there was a

general shift toward higher LBECs in later phases

of the process.

For most segments, the LBECs were spread among

several clusters. Also, all clusters were populated

by situations generated by more than one segment,

which is indicative of successful experimental

design in terms of the ability of the specific

simulation scenarios to generate different LBECs

from the same operation segment.

In the second phase of the chosen workflow, the C5

algorithm was applied to all data, with the clusters as a

target. The resulting decision tree has 8 levels and includes

19 branching nodes. Because of its complexity, it cannot be

fully presented here, and we include some of its

characteristics in Table 4. In this table, we also address the

importance of each parameter in the tree, based on the

cumulative sum of squared errors (SSE) explained by each

split. To illustrate our evaluation method, let’s assume that

somewhere in the tree a condition based on explanatory

variable y splits the instance population A into populations

B and C. We define the Split Gain (SG) as the reduction in

variance associated with this condition. A formal

expression of SG is given by:

)()( SSCSSBSSAySG (5)

where SSA, SSB, and SSC are the internal SSEs of the

corresponding populations. The higher the Split Gain, the

more efficiently the related condition will reduce the

variance in the population, and thus, the greater the

contribution the condition will make to the model. We then

sum the SG(y)s of each variable y over the different

branching nodes that used y for the split condition. We

present the Total Split Gain (TSG) for each variable as a

fraction of the general population variance, and then as a

fraction of all TSGs in the tree.

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Table 4 Decision tree variable characteristics

instances Influence% of total

variance

% of total

TSG

1Max Normalized

Process/IA Time ratio2 + 21.4% 36.6%

2 Util overall stdv 7 + 13.0% 22.3%

3 Length 2 +/- 8.0% 13.7%

4 Avail avg 2 - 6.0% 10.4%

5Min Normalized

Process/IA Time ratio2 + 3.9% 6.6%

6Max Raw Process/ IA

time ratio1 + 3.5% 6.0%

7 # of batch oper 1 - 1.6% 2.8%

8 Position 1 + 0.9% 1.5%

9Maximum load in

layer1 + 0.1% 0.1%

Total 19 58% 100%

Variable

Some more details for the descriptors (only briefly

addressed in section III ) in Table 4 are presented below:

Predictors 1 and 5 are based on the normalized ratio of

Process Time to Inter-Arrival Time, and they are

calculated at the operation level as follows:

Batch size ProcessTimeNorm Ratio

Inter ArrivalTime Number of Tools

(6)

This normalized ratio has been calculated for each of the

operations in the segment. Predictor 1 is the maximum

over the segment of this metric, and predictor 5 is its

minimum.

Predictor 6 is the maximum over all operations in the

segment of the raw ratio of Process Time to Inter-

Arrival time:

ProcessTimeRaw Ratio

Inter ArrivalTime (7)

While the normalized ratio is clearly an estimate of the

utilization, the raw ratio is merely intended to provide

additional insight into the lot flow properties through the

operation.

Predictor 2: the overall standard deviation of the

utilization among the operations in the segment is given

by:

2[ ( )]i i

i

i

i

stdv Util Tool n

Util overall STDVn

(8)

in which ( )iUtil Tool and in represent, respectively, the

utilization and the number of tools in the toolset on which

operation i is processed.

Predictor 4 is the average, over the segment, of the

average availabilities of the toolsets used in the segment.

The variables that were used in the model represent a

broad range of descriptor types (highlighted in Table 1).

The direction of the influence of each parameter in the

model is marked in Table 4 by either a “+” or a “-” sign for

positive or negative correlations with LBEC, respectively.

We found that although some variables are present at

several branching nodes, their correlation is always of the

same sign. The only exception is “length” which

participates in a contradictory manner in two of the tree’s

branching nodes. We believe that such a self-contradiction

at a certain point of the tree is the result of idiosyncrasies of

the SEMATECH dataset, and as such, it can be disregarded.

Additionally, we can verify that no correlation direction is

counterintuitive. All variables except “length” show a

higher LBEC when their values are stressing the

manufacturing operation (i.e., high utilization variability or

high maximum ratio of the process time to the inter-arrival

time).

To summarize the data shown in Table 4, we can assess

that the main predictors of LBEC seem to be highly related

to the utilization schemes (predictors 1, 2, and 5 cumulate

about 65% of the total TSG). The segment length, the

maximum raw process time/inter-arrival time ratio, and the

average availability over the segments are also important in

the decision tree. The position and the maximum load in the

segment, although participating in the tree, seem to allow

only for a marginal improvement in the split efficiency We

remark that all predictors are either perfectly known a-priori

(e.g. “length”) or are calculated based on performance

measures that are usually estimated or even modeled in fabs

10

as a matter of ongoing manufacturing monitoring (e.g.

Availability or Utilization. see Rose [12] for an example).

On another level of interest, we recall that our Principal

Components Analysis led to five components. We correlate

this fact with the Cumulative TSG of the model, which

approaches 90% of total TSG for the five most important

variables. These results indicate that five reasonably

independent variables from the proposed set should be

enough to predict the segment LBEC.

V. CONCLUSIONS

The present research is an effort to study and provide

information that may help reduce the WIP bubble

phenomenon. A strong linkage between Cycle Time and

bubbles was shown in our previous paper (Hassoun et al.

[10]). Here, we present a methodology for identifying the

characteristics with the most influence on the occurrence of

bubbles and for designing a prediction model to detect the

tendency of a process route segment to undergo bubbles. In

so doing, we expect to allow both the practitioner and the

researcher to tackle the issue of cycle time control by better

managing WIP flow variability.

While applying our methods to a benchmark simulated

NVM fab, we showed that the long-term tendency of a

carefully defined operation segment to undergo WIP bubble

events is predictable. By showing that a fair level of

correlation exists between the process segment

characteristics and the LBEC, we assessed the pertinence of

the LBE analysis scheme as formerly defined in Hassoun et

al. [10]. We also showed that the most influential

characteristics in terms of bubble occurrence in the chosen

NVM fab model relate to the utilization profile of the

segment (See table 4 for a list of these predictors). All of

these predictors are computed based on fundamental

parameters and performance measures that are either fully

known a priori or that can be estimated by models.

To the practitioner, the methodology presented offers some

important insights into several real-life scenarios: When

tailored to a specific fab, the prediction model will be able

to forecast the impact on bubble occurrence of different

“what-if” scenarios. By highlighting the rules and

conditions that influence Bubbles, this problem can be

rationally tackled by influencing specific variables of the

line. Moreover, we believe that extended use of this

methodology on a broad range of fabs will elicit a few

general rules or highly influential variables. This kind of

insight will enable planned fabs to be evaluated for their

potential to generate WIP bubbles even before they are

built. As a byproduct of our analysis, we propose that

practitioners begin calculating and gathering new metrics

(including, of course, LBEC) with potential significance in

WIP flow variability and in other fields of line evaluation.

ACKNOWLEDGEMENTS

We gratefully acknowledge the partial support we received

from the Intel Corporation to conduct this study.

11

REFERENCES

[1] A. Ozturk, S. Kayahgil, N. E. Ozdemirel. “Manufacturing lead

time estimation using data mining”. European Journal of

Operational research. Vol 173, pp 683-700, 2006

[2] C. Cunningham, R. Babikian, “A80-a new perspective on

predictable factory performance”. IEEE/SEMI Advanced

Semiconductor Manufacturing Conference and Workshop, pp

71-76, Sep 1998.

[3] J. B. MacQueen. “Some methods for classification and analysis

of multivariate observation” Proceedings of the 5th Berkeley

Symposium on mathematical statistics and probability, pp 281-

297, 1967.

[4] J. G. Dai and Steven Neuroth, “DPPS scheduling policies in

semiconductor wafer fabs,” In G. T. Mackulak, J.W. Fowler

and A. Schomig, editors, Proceedings of the International

Conference on Modeling and Analysis of Semiconductor

Manufacturing, (194-199), Tempe, Arizona, 2002

[5] J. Han, M. Kamber. Data Mining, concepts and techniques.

Second edition. San Francisco: Morgan Kaufman Publishers,

2006, Chapter 6.

[6] J. Hunter, D. Delp, D. Collins and J. Si (2002). “Understanding

a Semiconductor Process Using a Full-Scale Model”. IEEE

Transactions on Semiconductor manufacturing, Vol. 15, No. 2.

[7] J. R. Quinlan. C4.5: Programs for machine learning. Morgan

Kauffman Publishers,1993.

[8] K. Potti, A. Gupta, “ASAP applications of simulation modeling

in a wafers fab”, Proceedings of the 2002 Winter Simulation

Conference. Pp 1846-1848, 2002.

[9] M. Gardner, J Bieker. “Data mining solves tough

semiconductor manufacturing problems”. Proceedings of the

sixth ACM SIGKDD international conference on Knowledge

discovery and data mining, pp 376-383, 2000.

[10] M. Hassoun, G. Rabinowitz, S. Lachs, “Identification and Cost

Estimation of WIP Bubbles in a Fab”. IEEE Transactions on

Semiconductors Manufacturing, Vol. 21, No. 2, May 2008.

[11] M. Kusiak. “Rough set theory: a data mining tool for

semiconductor manufacturing”. IEEE transactions on

electronics packaging manufacturing. Vol 24, No.1, 2001.

[12] O. Rose. “modeling tool failures in semiconductor fab

simulation”. Proceedings of the 2004 winter simulation

conference. pp 1910-1994, 2004.

[13] P. McGlynn, M. O’Dea, “How to get predictable throughput

times in a multiple product environment”, IEEE International

Symposium on Semiconductor Manufacturing,pp 27-30, 1997.

[14] R. Hirade, R Raymond, H. Okano, “Sensitivity analysis on

causal events of WIP bubbles by a log-driven simulator,

Proceedings of the 2007Winter Simulation Conference, pp

1747-1754, 2007

[15] RL. Yeh, C. Liu, BC Shia, YT Cheng, YF Huwang. “Imputing

manufacturing material in data mining”. Journal of intelligent

manufacturing. Vol 19, No. 1, pp 109-118, 2007.

[16] S. Bilgin, M. Nishimura, “ Implementation of a WIP modeling

system at LSI logic”, IEEE International Symposium on

Semiconductor Manufacturing, pp 293- 296, Oct 2003.

[17] U. Arazy, Y De-Russo, “A framework for fab agility and 25

ways to be agile”, Proceedings of the ninth international

symposium on semiconductor manufacturing (ISSM), pp 213-

216, 2000

[18] V. Palmeri, and D. W. Collins . An Analysis of the “K-Step

Ahead” Minimum Inventory Variability Policy® Using

SEMATECH Semiconductor Manufacturing Data in a

Discrete-Event Simulation Model. Proceedings of IEEE 6th

International Conference on Emerging Technologies and

Factory Automation , Los Angeles, 1997.

[19] Y. Iwata, , K.Taji and H.Tamura . “Multi-objective capacity

planning for agile semiconductor manufacturing”. Production

Planning and Control. Vol. 14 No. 3, pp. 244-254, 2003

Michael Hassoun is a PhD student in the Industrial

Engineering and Management Department at Ben

Gurion University of the Negev, Israel. He earned

his MSc from the same department and his BSc in

Mechanical Engineering from the Technion, Israel

He worked during the years 2000-2001 at Intel fab8

as a functional area industrial engineer. His PhD

research interest is in the bubble phenomenon in fabs.

Gad Rabinowitz is an Associate Professor in the

Industrial Engineering and Management

Department at Ben Gurion University of the

Negev, Israel. His research interests focus on the

theory and practice of operation and scheduling of

production and logistics systems and the modeling

of quality engineering and management issues. He

received his BSc and MSc from Ben Gurion

University, and his PhD in Operations Research from Case Western

Reserve University.

1

Identification and Cost Estimation of WIP Bubbles in a Fab

M. Hassoun, G. Rabinowitz and S. Lachs

Abstract —We quantify the impact of work in process (WIP)

bubbles on a semiconductor fab. As a preliminary step we formalize the concept of WIP bubbles by decomposing them into local events of relatively acute and temporary WIP congestion. The local bubble is empirically identified and its impact on local waiting time distribution is assessed. We then estimate its marginal impact on the overall line waiting time and cost. Finally, a novel visualization tool for the bubble's progression is proposed.

Index Terms—Production management, semiconductors, work-in-process, congestion.

I. INTRODUCTION hew

operational difficulties associated with inflated ork-in-process (WIP) along the complex, highly re-

entrant process used in the semiconductor industry represent one of the major roadblocks to the smooth operation of fabs. The cycle time of lots going through a congested fab is tightly correlated with WIP levels by Little's law [6]. Thus, a reduction in cycle time is frequently obtained through an improvement in WIP management. For example, Leachman et al. [14] proposed an integrative WIP management tool based on the allocation of overall waiting time to bottleneck operations exclusively. By doing so, they prioritized these operations in terms of WIP buffers and reduced the odds of bottleneck starvation. Sadjadi et al. [4] reported the successful implementation of a cycle time reduction plan based mainly on an improved WIP management policy.

Most semiconductor manufacturers agree that one of the most harmful events in WIP management is what is known as a WIP bubble or "bubble" for short (see Cunningham et al. [2], McGlynn et al. [12], Potti et al. [8] or Bilgin et al. [15]). However, bubbles remain to be studied as phenomena in their own right. The term bubble still lacks a clear definition, Shen et al. [22] and Dabbas et al. [13] use it to describe any unbalance in the WIP flow, while others (i.e. Rippenhagen et al. [1] or Bilgin et al. [15]) refer to it as a temporary acute inflation of WIP levels over a limited segment of the line, requiring unusual means for mitigation.

After a bubble has emerged at a certain stage of the production process, typically at a bottleneck station,

substantial efforts are needed to reduce the WIP. The bubbles are particularly harmful to the WIP flow and cycle time of the fab processing lines because of the re-entrant nature of the semiconductor production process (see Kumar and Kumar [16]). In such plants, the WIP progresses along a series of processing loops while using the same tools repeatedly. Each loop includes a photolithography step that is typically the fab's bottleneck. The effort spent to move a bubble through a bottleneck is therefore quite often an endless and ineffective task that inevitably congests the next bottleneck in the process (see McGlynn et. al [12]). Once formed, and despite all efforts to eliminate it or at least mitigate its negative effects, the bubble often advances along the process like a shockwave all the way to the end of the line (see Potti et al. [8]).

Manuscript received June, 2007.

While it is known that bubbles are related to some of the main causes for delays and cycle time variability, the impact of bubbles on the line and the mechanisms of bubble formation, propagation, and disappearance/elimination have not been systematically studied. Different studies refer to the causes of bubbles in a somewhat informal context, as if those causes are common knowledge. Some practitioners implicate human decisions. Bilgin et. al [15] cite the "big WIP move mentality" as one of the causes of bubbles. Robinson et. al [7] speak of the will to maximize utilization of large batch tools, thus increasing variability. Also cited are preemptive causes like unscheduled down time (see Dabbas et. al [13] or Cardarelli et. al [5]) or technological constraints (Grewal et al [10] use the example of dedication on large batch tools).

The impact of bubbles is also treated as common knowledge. Many agree that the main performance measures affected by bubbles are cycle time and cycle time variability, and consequently the service level to customers (See Cunningham et al [2] for an example). Nonetheless, scientific evidence of the causality that binds bubbles to cycle time is lacking, and the intensity of the correlation between bubbles and cycle time has not been assessed.

This paper is the first phase of a broader work aimed at studying the bubble phenomenon in a fab. We propose a methodology to quantify the impact of bubbles on cycle time (section III) and on cost (section IV). As a preliminary stage, section II develops the tools needed for bubble identification.

The proposed method is demonstrated using eight months of daily WIP data from Fab 2 of Tower Semiconductors Ltd, Migdal-Haemek, Israel.

T

2

II. BUBBLE IDENTIFICATION

A. Bubble definition and principles of identification We propose to define bubbles as excessive WIP levels in a

segment of processing steps, and the values of said excessive WIP levels cannot be restored to regular values in a reasonable amount of time. In practice, bubbles are identified with WIP levels at a line segment that are excessive compared to the segment recovery capability (what Arazy et al. [20] defined as "burst capacity"). The amount of extra WIP and the segment burst capacity, when compared, designate the time needed for recovery.

While the proposed definition expresses the common understanding of the term bubble, translating it into a method for its identification involves practical difficulties. First, the definition is based on a subjective determination of "regular WIP level" and "reasonable amount of time." Second, computing the actual recovery capability of a segment is a complex task that yields inaccurate results, which, in any case, usually become obsolete quickly in the dynamic fab environment. Thus, identifying bubbles directly from the above definition is not a viable method.

We suggest using a different logic based on WIP distribution and WIP flow through bottlenecks. Using a statistical process control approach (see Montgomery [3]), we first identify excessive WIP in a process segment as any upper excursion from the segment’s natural WIP distribution. We then define process segments such that each one contains a single bottleneck operation which, by definition, has a poor recovery capability. As shown by Rose [11], any excess WIP level at a bottleneck station typically requires long periods of recovery time to stabilize and return to the WIP baseline distribution. Therefore, any excess WIP in a segment that contains a bottleneck is a bubble according to our definition. This approach, which is based on a careful segmentation of the production process and on the WIP level analysis, bypasses the difficulties involved in computing the burst capacity of the segments.

B. Identifying local bubble events We describe the proposed methodology for identifying

bubbles and illustrate it using historical data from the main technology of Tower's Fab 2 . (This technology constitutes most of the fab's production volume.) Tower’s Fab 2 is a relatively young plant, and we identified the bottleneck steps in this plant as the lithography operations. As such, we decided to make the analysis segments correspond to the product layers (26 such layers in this case), each containing exactly one lithography operation. We define a congested segment as having undergone a "local bubble event" (LBE). What is broadly known as a bubble in fab jargon is therefore the appearance of several LBEs at subsequent times and process stages. In this work, we use this decomposition and study LBEs solely, without considering bubble propagation behavior.

We identify an LBE as the excursion of a local WIP level

from the upper control limit of an exponentially weighted moving average (EWMA) control chart for the average daily WIP level in each segment (see Montgomery [3]). Over time, frequent product mix variations change the loading on the tools. Also, other infrastructural modifications in the fab influence the capacity and burst capacity of the tools. The WIP baseline level is therefore expected to change over time, thus justifying the use of a dynamic bubble identification mechanism.

Figure 1 presents the control chart of a random layer, which we refer to as layer 01. The dots in the chart represent the daily WIP level in this layer. The central line (bold) and the control limits (light grey) are calculated based on the EWMA of weekly values for both the average and the standard deviation of the WIP in the layer. Specifically, the chart centerline at week t is defined by:

(1 ) 1W W Wt ttλ λ= + − −

where is the average WIP level at t, and tW λ is the exponential factor.

The EWMA of the weekly WIP standard deviation is calculated in a similar manner:

1(1 )t ttS S Sδ δ −= + − where St is the standard deviation of the daily WIP values during week t, and δ is the exponential factor. We initialize

W and S by using the WIP average and standard deviation

over the entire period: 0 tW W= and 0 tS S= . The upper and lower limits of the control chart are given by:

/ t tt tUCL LCL W Z Sα= ± ⋅ where Zα is the chart range and α can be modified by the

user. α represents the two-tailed probability of an excursion of the WIP level while it is in-control. is therefore the probability of wrongly identifying an LBE.

/ 2α

The EWMA control chart for the WIP level in a specific layer dynamically adapts both its center line and control limits to the recent history of the controlled variable. The level of significance (α) enables control over the severity of WIP congestion, which is considered an LBE. The smoothing factors ( δ and λ ) allow the user to determine the relative influence of historical versus recent values. A chart that over-weighs historical data (small values of δ and λ) may not adapt well to changes. In contrast, over-weighing current values would lead to over-fitting, thus reducing the ability to discover WIP level excursions.

The definition of a bubble consists of two subjective terms: the "regular value" of the WIP level and the "reasonable amount of time" needed for WIP level recovery. The first term is mainly determined by α and the second one by α, δ, and λ. To customize the chart to the specific fab that we analyzed, we asked Tower's production engineers to identify where the bubbles occurred in the fab historical data. Then we iteratively tuned the factors (α, δ, and λ) to attain the best possible match of the engineers' bubble identifications in

3

all the layers. The following values for the chart factors scored a 90% match: α = 5%, δ = 0.1 and λ = 0.1.

Fig. 1 Control Chart for average daily WIP in a specific layer Fig. 1 presents the proposed control chart of layer 01 after

the factor tuning process. We can see that this layer experienced three local bubble events during the period displayed: one during August 2004 and two slightly shorter ones during October and December of the same year. Excursions below the lower control limit are not a problem by themselves. Nonetheless, they reflect another facet of the in-line variability and may be a symptom of a blocked or congested feeder segment.

III. BUBBLE IMPACT ON CYCLE TIME

The proposed definition of an LBE is now used for quantifying the impact of bubbles on cycle time. The processing time in fabs is typically smaller in value and much lower in variability than the waiting time (see Hopp and Spearman [21]). Because we assume that bubbles have an impact solely on waiting time, we only consider that parameter. After identifying all the LBEs in each segment over time, we matched each lot with the number of LBEs it sustained during its entire production period and with its overall waiting time. For a sample of lots, we correlated the waiting time with the number of LBEs.

A. Tagging lots with local bubble events (LBEs) To count the number of LBEs encountered by a lot during

its process, each layer was analyzed separately, lots were tagged as having undergone an LBE or not, and finally the results were totaled. In each segment, a lot was marked as having been affected by an LBE if during its transit in the segment an LBE occurred that significantly increased the lot waiting time. In our effort to identify lots that were affected by the bubble, waiting time was considered to filter out high priority lots that pass through the bubble without being affected by it

Lot classification was conducted as follows: Based on the above method, we determined the starting and

ending dates of each LBE in each layer. The lots in the

samples taken from each layer were split into three groups: • Group 1: Lots that went through the layer

while it was not congested with an LBE. • Group 2: Lots that reached the layer while it

was not congested but left after the formation of an LBE.

• Group 3: Lots that reached a layer while it was congested with an LBE.

Figure 2 presents the relative frequency distributions for the waiting times of lots in the three lot groups of layer 01.

Fig. 2 Waiting time frequency by lot group, layer 01 While this classification method enables the clear and

simple differentiation of lots, to achieve a reliable analysis it requires further tuning. It is indeed quite simple to categorize a lot that was present in the layer while an LBE occurred as having suffered from a bubble. Were a “first-come, first-serve” rule a viable scheduling method in fabs, tagging lots based solely on their having undergone an LBE would be an appropriate method. In practice, due to the use of scheduling schemes based on lot prioritization, some lots run through a congested layer quickly while increasing the waiting times of other lots already waiting in the layer. To reduce the noise introduced by these high priority lots, we reconsidered the waiting times of the lots classified into Groups 2 and 3. In a first refinement step, the lots of Group 2 were reallocated either to Group 1 or Group 3 based on their average waiting times. A ratio T was determined based on the relative values of the average waiting times of the three groups:

2 1

3 1

WT WTTWT WT

−=

−

where iWT is the average waiting time of lots in the original Group i. We then reallocate the fraction T of lots from Group 2 with the longest waiting times to Group 3. The remainder of the Group 2 lots was reallocated to Group 1. It should be noted that the lower T is, the closer the waiting time distribution curves of Groups 1 and 2 and, consequently, the higher the number of lots from Group 2 that are redirected to Group 1.

In a final refinement step, a small fraction of the fastest lots

4

in Group 3, assuming these were high priority lots that did not wait significant additional amounts of time due to the occurrence of LBEs, were transferred to Group 1. In our case, the fab engineers estimated this fraction to be 5% of the lots in group 3.

Subsequent to these steps, we compiled a list of two lot populations in each layer: lots that suffered from an LBE in that layer and lots that did not. Figure 3 illustrates the results of the categorization process and presents the waiting time distribution of these two populations in layer 01. Similarly, in most of the layers, the way we tagged lots with LBEs generated two significantly different waiting time distributions for the two lot populations.

Fig. 3 Waiting time distribution in layer 01 for two lot populations, layer

01

B. The impact of LBEs on overall performance Our next step entailed quantifying the impact of the LBEs

on the cumulative waiting time of all the lots in the fab. Each lot was tagged with the number of LBEs it had experienced during its processing. This number is a measure of how heavily the lot was influenced by bubbles during its production process. Figure 4 presents the average and standard deviation of lot waiting time as a function of LBE count. The continuous line represents the cumulative percentage of lots. On the left side of the chart we highlight lots with LBE counts of up to five, about 90% of the total lot population. It is interesting to note that in this group, both the average and the standard deviation of waiting time were positively correlated with LBE count. The remaining lots that encountered the highest number of LBEs were characterized by stabilization of their waiting times, which is perhaps due to managerial efforts to expedite lots with extreme lateness.

The potential improvement in cycle time concealed within these results is enormous. In the case of Tower Semiconductor, according to the data presented in Fig. 4, a planned waiting time of about 60 days is required to achieve a 90% level of service. Should the fab reduce the number of LBEs encountered by 90% of the lots to three or fewer, the planned waiting time could be reduced by around 30% (20 days) while maintaining the same level of service. In parallel

with the reduction in average cycle time, cycle time variability is also expected to decrease significantly. Additionally, because the impact of bubbles is measured exclusively on the congested technology and at the congested segment, a certain part of the bubble impact is not measured. Therefore, we suppose that a further reduction in cycle time is possible, although not measurable. A final contribution of the proposed methodology is that it allows for the quantification of the damage, in terms of the economic costs to the fab, caused by bubbles. This is discussed in the next section.

Fig. 4. Waiting time average and standard deviation of lots according to

LBE count

IV. LOSS ASSESSMENT DUE TO BUBBLES

While cycle time inflation alone may be severe enough to reveal the corrupting consequences of bubbles, evaluating and presenting the damages related to bubbles on an economic scale has clear advantages. Assessing the economic effects of bubble-related damages relies on numerous data sources and is heavily dependent on human estimations; nevertheless, we found that many key players in the organization were far more receptive to economic indicators than to manufacturing metrics such as cycle time. Furthermore, such an economic assessment can also help evaluate the worthiness of potential bubble mitigation efforts.

We found the literature on costs related to cycle time in the fab to be inadequate for our needs. Nemoto et al. [9] present a cost model based on a simulation that considers only the savings related to higher yield due to a faster end-of-line feedback on quality issues. Their model is adapted mainly to ramp-up periods and disregards the costs related, for example, to supply tardiness, which in our case was recognized as the main cost factor. Murray et al. [17] employed simulation to analyze the costs of specific areas in the fab, but did not provide an integrative cost model derived from in-fab data that we could apply to our specific situation. The cost function we propose for quantifying bubble-related damage comprises three factors that are related to bubbles and were shown to be quantifiable. Various other factors, such as direct production costs and general factory expenses, were considered but were

5

not included in the bubble-related cost computation as they are not significantly influenced by either bubbles or cycle time.

The three cost factors are: 1. Manpower: The measurable manpower costs related

to bubbles are twofold. First, we considered the extra time spent in morning meetings when a bubble has developed in the fab. Second, we evaluated the additional manpower required for emergency repairs and maintenance (engineers and technicians are known to be called in for late-night maintenance on congested machines).

2. Yield: As mentioned by Cunningham et al. [18], the functional relationship between cycle time and die yield is still largely unknown, and the correlation between both parameters has not been verified. Nonetheless, our quality evaluation found a significant reduction in die yield as a function of the total waiting time in the line. Therefore, we included this factor in the cost function associated with bubbles. Figure 5 presents, from the case under study (Tower Semiconductors), the measured end-of-line die yield as a function of cycle time.

Fig. 5 Die yield vs. waiting time

3. Due date to customers: Tardiness in supplying customers is the most important cost factor considered and also the most difficult to assess. We applied an increasing slope, stepwise linear loss function for supply tardiness built by the company IE team.

We also considered the wafer scrap rate at the layer as a

potential cost-related factor as technicians working in a congested area may be more prone to commit errors and to scrap wafers. This factor, however, was not statistically confirmed, due mainly to the limited number of scraps in each layer.

Clearly, the three cost factors, which account for different sources of costs, do not overlap. Thus, the total cost function for each of the lots is the sum of these factors. Figure 6 presents the average total cost per lot versus the LBE count. The monetary units are arbitrary, and the direct production cost for one wafer is 1000 units (25000 for a lot).

Fig. 6 Estimated cost distribution by LBE count In Figure 6, the cost increases as a function of the LBE

count up to the level of five LBEs, after which it stabilizes in a pattern similar to the average waiting time in Figure 4. Here, however, the impact of the LBE count on waiting time is amplified by the increasing slope of the lateness cost function, which, in our case, emerged as the most dominant factor. Fig. 6 also shows that the additional costs inherent in bubbles often approach a scale proportionate to that of the direct production cost.

The above method for evaluating the costs related to bubbles was tailored to meet the characteristics of Tower’s Fab 2 . Another semiconductor plant with a different production line or business properties may need a different cost function. Therefore, this cost model cannot be considered a generic one. Nonetheless, factors such as manpower time and supply tardiness should be included in most bubble-related cost evaluations. Further generalizations require a wider investigation of bubble-related cost factors in a variety of fabs.

V. BUBBLE VISUALIZATION TOOL

One of the main difficulties in managing bubbles in a fab is grasping the complex progression of WIP over time. The definition and identification of LBEs provide the opportunity to tackle this issue. To that end, based on the measurements of LBEs in the EWMA control chart (Fig. 1), Figure 7 quantifies and displays the daily local WIP deviation. The vertical axis represents time (in days) and the horizontal axis reflects process progression (in layer count). The relative WIP levels are represented by shades of grey on a discrete scale: white is used for under average WIP levels, and black for levels of more than three standard deviations above average. Between these two extreme categories we consider three standard deviation zones, 0 to 1, 1 to 2, and 2 to 3, which are represented by three shades of grey, from the lightest to the heaviest tone, respectively. This chart provides a clear visualization of the bubbles’ progression along the line.

As an example, the chart shows (marked by an ellipse) the typical progression of a bubble along the process, starting close to the time origin and up to the very end of the line. The length of this WIP wave demonstrates the difficulties

6

encountered when trying to recover from a bubble. Other, less severe bubbles appear and disappear later on in the chart, mainly close to the beginning of the line. Another interesting pattern observed in this chart is the acceleration of the WIP bubbles towards the end of the line (indicated by the decreasing slope of the WIP waves progression) This phenomenon might be related to the common practice of giving higher priority to lots that are close to completion (e.g. Lu and Kumar [19]).

VI. CONCLUSIONS

In this paper we propose a formal definition for a WIP bubble, a term commonly used by fab personnel. As a first step in studying this phenomenon we defined the local bubble event (LBE). An LBE is an acute WIP congestion in a segment (that includes a bottleneck step) of the process route. We used a dynamic control chart of the daily WIP level at the segment, and identified the LBE as an excursion from the chart’s upper control limit. We then found that bubbles more than doubled the lot’s waiting time. Next, we evaluated the bubble-related economic losses and found them to be on the same order of magnitude as the total direct production costs. These results clarified for the fab managers at Tower Semiconductors the necessity of concentrating their efforts on bubble prevention and reduction. Finally, we proposed a novel visualization tool that allows one to monitor the progression of a bubble over the fab line. As such, it sharpens the production manager’s perspective on the behavior and impact of bubbles. This work establishes the foundations for a broader study of the bubble phenomenon in semiconductor fabrication plants.

Fig. 7 Bubble visualization mapping

7

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Michael Hassoun is a PhD student in the Industrial Engineering and Management Department at Ben Gurion University of the Negev, Israel. He earned his MSc from the same department and his BSc in Mechanical Engineering from the Technion, Israel He worked during the years 2000-2001 at Intel fab 8 as a functional area industrial engineer. His PhD research interest is focused on the bubble phenomenon in fabs.

Gad Rabinowitz is an Associate Professor in the Industrial Engineering and Management Department at Ben Gurion University of the Negev, Israel. His research interests focus on the theory and practice of operation and scheduling of production and logistics systems; and modeling of quality engineering and management issues. He received his B.Sc. and M.Sc. from Ben Gurion University, and his Ph.D. in Operations Research from Case Western Reserve University.

Shlomi Lachs graduated from the Industrial Engineering and Management Department at Ben Gurion University of the Negev, Israel. The present work represents his final BSc project.