A Yield Aware Sampling Strategy for Tool Capacity Optimization

Muhammad Kashif Shahzad123, Thomas Chaillou1, Stéphane Hubac1, Ali Siadat2 and Michel Tollenaere31STMicroelectronics, 850 Rue Jean Monnet. 38926 Crolles, France

2LCFC Arts et Métiers Paris Tech, 4 rue Augustin Fresnel 57078Metz, France3G-SCOP; ENSGI - INP Grenoble 46 Avenue Félix Viallet 38000 Grenoble, France

Abstract— The product quality in semiconductor manufac-turing is ensured with 100% inspection at each process step;hence inspection tools quickly run out of capacities resultingin the production cycle delays. To best utilize the productionand inspection capacities, existing sampling (static, dynamicand smart) strategies are based on the risk and delays.These strategies, however do not guarantee a reliable lotsample that represents a likely yield loss and there is ahigh risk of moving a bad production lot to next productionsteps. We present a 3-step yield aware sampling strategy tooptimize inspection capacities based on the likely yield losswith the predictive state (PSM) and alarm (PAM) modelsas: (i) classify potentially suspected lots, (ii) cluster and/orpopulate suspected lots in the priority queues and (iii) applylast in first out (LIFO) to optimize capacities. This strategyis implemented with two heuristics. We also present a datamodel with ASCM (Alarm and State Control Management)tool for the multi source data extraction, alignment andpre-processing to support the validation of [PSM, PAM]predictive models.

Keywords: sampling strategy, tool capacity optimization, yieldprediction

1. IntroductionThe SI has revolutionized our daily lives with electronic

chips that can be found in almost all the equipments aroundus and follows the slogan smaller, faster and cheaper drivenby Moore’s law [1]. It postulates that the number of transis-tors shall double in every 18 to 24 months at reduced costand power. Since then the SI has kept its pace as per Moore’slaw by continuously investing in R&D for the new technolo-gies. New equipments are being manufactured to support andkeep up with the emerging demands and the pace definedby the Moore’s law. The equipments are highly expensive;hence decisions to purchase new production equipments arebased on the business strategy and estimated ROI (returnon investment). The metrology/inspection tools carry fixedcosts and often phase out or need changes to cope up with thenew emerging technologies; hence efforts are made to usethe capacity optimization strategies to balance the inspectionload instead of purchasing new inspection tools.

An electronic product (chip) undergoes the most complexmanufacturing process with approximately 200 operations,

1100 steps and 8 weeks of processing. The sequences ofoperations to manufacture an electronic chip (transistorsand interconnections between transistors) are classified asthe FEOL (front-end-of-line) and BEOL (back-end-of-line)processes. The transistor acts like an on/off switch andit is a basic building block in the chip manufacturing.The interconnections are the wire networks that connectthese transistors to form an electronic circuit. To ensure theproduct quality, measurement (metrology/inspection) stepsare added within the manufacturing flow almost after everymanufacturing step. Here we make decisions based on theparametric yield to either scrap or move the wafer to the nextstep with an objective to stop bad products consuming ex-pensive resources and production capacities while ensuringthe product quality. We know that the inspection tools havelimited capacities; hence optimal capacity utilization inahigh product mix is a key for success. There are some criticalsteps as well where the delay due to inspection capacitylimitation might have a strong impact on the next productionstep, so these priority products must be inspected beforeother products in the queue. Till now the proposed inspectioncapacity optimization strategies (static, dynamic and smartsampling) are based on the risk, delays and tool capacities,however these strategies do not guarantee a reliable lotsample that represent a likely yield loss.

Let us start with an introduction to a generic productionprocess (Fig.1) where lots are processed and controlled atproduction and inspection tools respectively to avoid badlots moving to the next steps. The inspection capacities arealways less than the production capacities and to balancethe difference we have static, dynamic and smart samplingstrategies. It can be viewed as a blind strategy with a highrisk of skipping bad lots to the next steps whereas in ourstrategy we empower the control with PSM and PAM modelsto filter good and bad lots followed by capacity optimization.We argue that for a given product yield e.g. 85% the focusmust be on finding and controlling the 15% bad productsthan inspecting 100% product using blind inspection strate-gies that do not differentiate between bad/good products. Inthis paper we present a yield aware sampling methodologythat identify the potential inspection lots as good, bad orsuspected and then only bad or suspected lots are potentiallyinspected while skipping the good lots to move to the nextproduction steps. Inspection waiting queues are established

Fig. 1: Generic production process with existing sampling strategies.

and a second level optimization based on LIFO is applied tofurther save the inspection capacities as (i) inspections lotsare clustered based on the product type and process recipeand (ii) if a potential lot results in a bad lot than all lotsin the same cluster manufactured before the inspected lotsare scarped. The success of this approach depends on theaccuracy of learning and classification algorithm for PSMand PAM models. We propose two heuristics, first for thePSM and PAM models and second to cluster the suspectedlots and applying queue optimization. A tuning parameter isalso provided at the discretion of the user to control the PSMand PAM prediction confidence levels. In order to supportthe strategy we have also proposed a data model and ASCMtool for data extraction, alignment and pre-processing tosupport PSM and PAM model validations.

We have divided this paper in 4 sections. Section-1provides a brief introduction to the semiconductor industry,problem context and the proposed methodology. Section-2 presents the literature review on the existing samplingstrategies proposed and being used for capacity optimization.The proposed approach, heuristic algorithms, data modeland ASCM tool are presented in the section-3. Finally weconclude this paper with discussion and future perspectivesin sections 4 and 5.

2. Literature reviewChip manufacturing has become a complex but expensive

production process resulting in process control challengesto find the lots with yield issues before they consume theexpensive production resources. Limited inspection toolscapacities has a strong impact on the production cycle times,hence an efficient sampling and control strategy is requiredto optimize the capacities and economic benefits. We havedivided our research in two distinct areas as (i) we shallpresent a historical brief review on the interaction of productquality and process that lead to the emergence of SPC (sta-tistical process control) and process control plans to ensureproduct quality and (ii) sampling approaches to optimizethe inspection tools capacities and dynamic adaption of theprocess control plans.

The measurement tools are categorized as metrology andinspection tools. The metrology tool physically measures the

geometric features and the product follows the SPC basedcontrol plan that either scraps the wafer or moves it tonext production step. The inspections tools are used to findthe defects on the surface of wafer right after the criticalproduction steps to mark the bad chips on the circuit. Itis important to understand from where the idea of controland product quality emerged or evolved and what are thelatest contributions? The design of an economical controlfor a production process has always been an interestingresearch area that was initiated by [2] that lack robust resultsand require a balance between controls and their costs. [3]proposed a control plan with the concept of skipping bydecreasing control frequency as compared to a 100% in-spection plan. [4] presented that sampling size and frequencyas two levels of controls are the better solution to quicklyidentify the issues while minimizing the cost of errors. [5]introduced the concept of SPC in the semiconductor industrythat served as the basis for an updated control plan. Manyapproaches have been proposed for an adaptive control as(i) sampling strategy based on the number of wafers passedon metrology tools [6], (ii) updating control plan basedon process excursions [7] and (iii) updating control planbased on risk encountered during productions. [8] ,[9] havedesigned a buffer for control machines taking into accountthe quality and cycle time expectations and it is the latestcontribution in research regarding control plans.

Now we move to the second part of the literature wherewe shall present the inspection capacity allocation (referredas scheduling) problem in semiconductor industry. Existingstrategies are classified as static and dynamic where staticsampling [10] selects the same numbers of lots but dynamicsampling [6] select the number of lots for inspection, basedon the overall production. Smart sampling is a new approachthat sample lots by taking into account the risk associatedwith production tools, inspection tools capacities and delaysto dynamically minimize the wafers at risk [11], [12]. It isa better approach than the static and dynamic strategies. Inthis strategy, if a lot in the waiting queue is controlled anditpasses the inspection step then all lots in the waiting queues,processed before this lot are removed with a belief that theyare also good lots. But none of them provide an evidence fora likely yield loss against sampled lots resulting in skipping

the suspected lots to move to the next process steps. We needa yield aware strategy to classify good, bad and suspectedlots to reduce the inspection load significantly followed byan optimization strategy that exploit the production resourcesagainst limiting inspection tools capacities.

From the above literature, it is evident that the inspectioncapacity allocation problem is linked with the process controlplans in the semiconductor industry. If we commit mistakeslike skipping the bad lots to the next production steps as theexisting approaches do not provide any evidence of likelyyield loss then the consequences are evident in terms ofcustomer dissatisfaction and costs. We argue that our focusshould be on the identification of the bad or suspected lotswhile moving the good lots to the next steps. It shall notonly increase the inspection capacities but shall also addresscritical step implications where the max time between twosteps is fixed. Our proposed yield aware 3-step strategyuses the predictions made by the PSM and PAM models.Based on the predictive output combinations lots are eitheradded to the priority inspection queues or moved to the nextproduction steps followed by the capacity optimization.

3. Proposed approachThe proposed 3-step yield aware inspection strategy is

presented in Fig.2. In our scenario, equipments are composedof 1...n modules in the parent child relationship. Thesemodules are further classified as critical/non-critical andshared/non-shared elements. All the modules are character-ized by meters, alarms and states which are recorded inthe databases during the production operations. The alarmsare generated at the module level, however based on thesealarms the automation system changes the states of thechild and parent modules. The changes in the states of thechild modules serve as the basis for change in the stateof parent modules. It represents the equipment health andsuch information can accurately predict a likely yield lossin the production induced due to unpredictable equipmentbehavior. The meter data triggers the preventive maintenanceoperations; however the module level meter data shall beincluded in the future to compute the weighted probabilitiesto weight the state and alarm level predictions. The alarmsand states data represents the status of the production processand equipment health respectively; hence we use them tolearn predictive alarm [PAM] and state [PSM] models.

In the proposed methodology we have used only thestates and alarms data; however the module level meter datashall be included in the future to compute the weightedprobabilities to refine the state and alarm level predictions.The first step in the inspection strategy is to classify thegood, bad and/or suspected lots. In this step we start withthe exploitation of the historical equipment states, alarmsand SPC (statistical process control) data from the process,maintenance and alarms databases to build predictive state[PSM] and alarm [PAM] models. These models [PSM, PAM]

are then used to classify the new production lots as goodand/or bad lots and generate four possible outputs: (i) [good,good], (ii) [good, bad], (iii) [bad, good] and (iv) [bad, bad].The good production lots [good, good] are moved to the nextproduction steps without metrology and bad lots [bad, bad]undergoes the 100% inspection and their results are used toupdate the prediction [PAM] and [PSM] models.

The suspected lots [good, bad] or [bad, good] are clustered(2nd step) based on the equipment, product and recipe. Itfollows by a priority queue allocation algorithms (3rd step)that enter the suspected lot clusters into priority queuesfor further optimization based on LIFO (last in first out)principal. It states that if a suspected lot defies the predictionupon measurement then all the lots in the same clustershall be subjected to 100% inspection otherwise the clustermembers shall be skipped. The predictive state and alarmmodels [PSM, PAM] are updated with the feedback againstall coherent and incoherent predictions as good and/or badexamples. It provides us an intelligent way to reliably sampleonly bad or potentially suspected lots followed by priorityqueuing and optimization for the economic benefits.

The step-1 where we learn the predictive [PSM, PAM]models and classify the new production lots as good, bad orsuspected lots, is implemented with a heuristic algorithm aspresented in section 3.1. The step-2 and step-3 are presentedwith a flow chart in section 3.2 that corresponds to theclustering and priority queue optimization.

3.1 Heuristic algorithm for predictive modelsThe alarms and states data collected from the equipment

is not trivial to be used with the existing classificationand pattern sequence learning algorithms; hence we haveproposed a heuristic algorithm to predict the given waferWj as a good or bad. The time required for a productionoperation vary from 30 minutes to 4 hours and duringoperation a series of set of equipment states and alarms aregenerated. It is evident that data collected is a matrix ofsets of alarms and states. Our proposed algorithm is simpleand is based on probabilistic likely hood with the previousinspections. We start with the presentation of the variablesused in the algorithm as under:

The T[Ei] is a tuning parameter and is defined by theuser to tight the prediction and it is used to optimize theinspection capacities utilization, if required. For example,if user set its value to 50%, it means that computed likelyhood shall be compared with this target prior to [good, bad]predictions. It is also important to note that the historicaldata shall be used to populate alarms and states matrixesfor all equipments; however a confusion matrix [C] shallcomprise of duplicated states and alarms sets found in bothgood and bad matrixes.

Proposed algorithm for the prediction of [PSM, PAM]model is as under. We start with the learning by computinggood, bad and confusion matrixes of alarms and states

Fig. 2: 3-step methodology with predictive state (PSM) and alarm (PAM) models.

Table 1: Description of variables

Notations and Variables Description[G,B,C]: G→Good, B→Bad, C→Confusion

[Ei,Wj ]: Ei → Equipment(i), Wj → Wafer(j)

M[A,S,Ei,Wi.9]

[G,B,C]: Matrix for alarms and states historical data for

equipment Ei

M[A,S,Ei,Wi.9]

[G,B,C](∑n

j=1[aj , sj ]): Matrix for [G,B,C] alarms and states for allequipments and wafers

M∑n

j=1[aj , sj ]Ei

Wj : Matrix for alarms and states sequence for equip-ment Ei and wafer Wj

LS[G,B,C](∑n

j=1[aj , sj ]Ei

Wj ): Local support for each set of alarms and statesin the Matrix for equipment Ei and wafer Wj

GS[A,S,Ei,Wj ]

[G,B,C]: Global support for alarms and states for equip-

ment Ei and wafer Wj

T[Ei]: Target defined by the user for equipment Ei tobe used for model predictions

sequence sets for all equipments as shown in step-1. It shallbe used during the computation of the local support. InStep-2, we compute the local support for each set of alarmsand states sequence for a given wafer Wj by countingthe similar set of alarms or states sequences in [G,B,C]matrixes. This count is divided by the respective countof sequences in [G,B,C] matrixes to get the local supportvalues for each sequence of alarms and states in waferWj . Further we compute global support for the wafer Wj

by multiplying the local supports computed for each setof alarms and states sequence against [G,B,C] matrixeswith the sum of computed local supports. The results aresummed at [G,B,C] level for the prediction by comparingit against the T[Ei] in step-4. If the global support issmaller than the T[Ei] then the benefit of doubt is given tothe prediction by adding the global support for [C]. Saidalgorithm for [PSM, PAM] models is presented as under:

Step-1:Compute M[A,S,Ei]

[G,B,C]for states and alarms data for each equipment Ei

M[A,S,Ei]

[G,B,C]= M[A,S,Ei,Wi.9]

[G,B,C](∑n

j=1[aj, sj ]) (1)

Step-2:Compute local support for each set of alarms or states sequences forgiven wafer Wi and equipment Ei

LS[G,B,C](M∑n

j=1[aj, sj ]Ei

Wj ) = Count(M∑n

j=1[aj , sj ]Ei

Wj ==

M[A,S,Ei,Wi.9]

[G,B,C][∑n

j=1[aj, sj ]])/Count(M[A,S,Ei,Wi.9]

[G,B,C]

[∑n

j=1[aj , sj ]]) (2)

Step-3: Compute global support for a given equipment Ei and wafer Wj

GS[A,S,Ei,Wj ]

[G,B,C]= Sum(Sum(LS[G,B,C]

∑nj=1[aj , sj ]

Ei

Wj ) *

LS[G,B,C][M∑n

j=1[aj , sj ]Ei

Wj ]) (3)

Step-4:Predict [PSM,PAM] output for the given Wafer Wj

If (GS[A,S,Ei,Wj ]

[G])≥T[Ei] =⇒ Good

eleseif (GS[A,S,Ei,Wj ]

[G]≤T[Ei] AND (GS[A,S,Ei,Wj ]

[G]+

GS[A,S,Ei,Wj ]

[C])) =⇒ Good

elseIf (GS[A,S,Ei,Wj ]

[B])≥T[Ei] =⇒ Bad

eleseif (GS[A,S,Ei,Wj ]

[B]≤T[Ei] AND (GS[A,S,Ei,Wj ]

[B]+

GS[A,S,Ei,Wj ]

[C])) =⇒ Bad (4)

To demonstrate the said algorithm we present a simpleexample with [G,B,C] matrixes for alarms data as under(Fig.3):

Fig. 3: Example [G,B,C] matrixes for alarms data.

Computed results against the potential lotWj for predic-tion are detailed as under and as per computed global supportthis production lot with 54% likely hood is predicted as a

good lot (Fig.4).

Fig. 4: Local and global supports for [PAM] prediction.

3.2 Clustering and priority queue allocationBased on the predictions from [PSM, PAM] models (sec-

tion 3.1), we follow the 2nd and 3rd step in the proposedyield aware inspection strategy where suspected lots areclustered and added to the priority queues followed byLIFO optimization. It is presented with a simple flow chart(Fig.5). All production lots with prediction combination[PSM’Good and PAM’Good] are simply skipped whereasother lots are populated in the priority queues P1, P2 andP3 where P1>P2>P3. Lots with the combination [PSM’Badand PAM’Bad] are first clustered based on the similarity ofproduct, technology and recipe followed by the population oflast lot from each cluster in P1. If an inspected lot from theP1 validates the model prediction than its respective clustermembers are simply scrapped, otherwise each member of thecluster is inspected and the predictive [PSM, PAM] modelsare updated. In case of difference in model predictions, lotsare declared as suspected and are populated in the priorityqueues P2 [PSM’Good and PAM’Bad] and P3 [PSM’Badand PAM’Good]. The lots from P2 are sequentially in-spected; if it defies the models then all lots processed beforethe inspected lot in P2 are given the benefit of doubt andare skipped. If a lot inspected from the P3 defies the modelthen all the respective cluster members are inspected andpredictive [PSM, PAM] models are updated for coherencesand incoherencies.

It is evident from the above discussion that the [PAM]predictions have higher priority than the [PSM] predictionsbased on the two facts, (i) child modules influence the statesof their parent modules, hence prediction model developedat the module level might have a dual impact and (ii)alarms count and duration result in the change of stateof the modules. The states data is an aggregation of thealarms data at module level, hence alarms data providemore low level detailed information with no influence onthe alarms of parent modules. Based on these facts inthis proposed methodology we have given higher priorityto PAM prediction while performing information fusion ofmodules alarms and states data. The [PSM, PAM] predictionweights shall be defined in the future by including the meter

data. The meter data is very critical because the valuesof the meters initiates the preventive maintenance actionson modules. We believe that it shall play a pivotal role indefining the prediction accuracies of the PAM model. Thealarms and resulting prediction shall get more weigh whenmeter data fall within the distribution of previous preventivemaintenance actions.

Fig. 5: Flow chart for clustering and queue allocations.

3.3 Data model and ASCM tool for data ex-traction, alignment and pre-processing

The biggest challenge in building and deploying thesePAM and PSM predictive models is the multi-source dataextraction, alignment and preprocessing from SPC, mainte-nance, process and alarms data sources. To facilitate this wehave also proposed a data model (Fig.6) with the ASCM(Alarm and State Control Management) tool that allowsengineers a quick extraction and alignment of the data.

In this data model the equipments (equipment class) arecomposed of modules (module class) and every module has astate (state_history class) and alarms (module_alarms class)history. The usage meter data is also available (usagemeterclass) but in this paper we have not used this data. Theparent-child associations between modules are captured bythe parent_child_relation class. A product (product class) ismanufactured using multiple lots (lot class) but follows asingle process plan (process_plan class). The process planhas multiple operations (process_operation) and each oper-ation can have multiple steps (process_steps). The process

step undergoes different step runs (step_run class) as theproduction or metrology runs The production step runs areassociated with the equipments who have the capability(equipment_capability class) to perform the process steps.This data model is translated into a relational database whichis implemented using SQL server to support the ASCM tool.

-EQ_ID

-Name

-Shop_Area

-Description

-State_Model_ID-EQ_Type

-Parent_Cluster

-Cluster_Type

Equipment

-State_Model_ID

-Name-Description

State_Model

1 1..*

1

1

-Module_ID-EQ_ID

-Name

-Description

-State_Model_ID

-EQ_Type

Module

1

1

-State_Model_ID-Name

-State_Name

Model_to_States

1..*

1

-EQ_Module_ID

-Name

-State_Name

-Start_Date-End_Date

-Previous_State_Name

State_History

0..*

1

0..*

1

Module_State_HistoryEQ_State_History

-Usage_Meter_ID

-Module_ID

-Meter_Name

-Units

-Meter_Value-Last_Reading

-Last_Reading_Date

-Last_PM_Value

-Next_PM_Value

UsageMeter

UsageMeter_History

1..*

1

0..*

1

0..*

1

-Critical

-Shared

Parent_Child_Relation

-Alarm_ID-Module_ID

-Location

-Alarm_Level

-Description

-System_Type-Start_Date

-End_Date

-Lot_ID

Module_Alarms

0..*

1

-Error

-Warning

Alarm_Levels

1..*

1

-Product_ID

-Process_Plan

-Soft_Version

-Product_Type

-Reticle_Set_ID-Recipe_Set_ID

Product

-Process_Plan

-Tech_Version

-Soft_Version

-Description-Technology

Process_Plan

-Process_Plan : char-Operation_Name

-Sequence

-Process_Operation_ID

Process_Operation

-Step_ID-Process_Plan

-Step_Name

-Sequence

-Recipe_ID

-PPID

Process_Steps

-Step_ID

-Step_Name

-Tech_Version

-Soft_Version-Description

-Capability

-Cluster_Type

-Step_Type

Steps

-Lot_ID

-Product_ID-Lot_Type

Lot

-EQ_ID

-Capability

-Description-PPID

-Recipe

Equipment_Capability

1..*1

0..* 1

0..*

1

1..*

1

1..*

1

1..*

1

1..*

1

1

1

Out_of_Control

-Measure_ID

-Measure_Run_ID-Process_Run_ID

-Parameter

-Eq_ID

-Lot_ID

-Wafer_ID

Measure

-Run_ID

-Step_ID

-Eq_ID

-Lot_ID-Wafer_ID

Step_Run

1..*

1 1

1

1

1

1

1

1

1

1

1

Yield

-Lot_ID-Yield

Scrap0..*

1

1

1

11

Fig. 6: Data model for extraction, alignment and processing..

A software tool is developed for the R&D engineers toextract data from SPC, maintenance and alarms databasesin VB 6.0. The extracted data from different data sourcesare populated in the database developed as per above datamodel (Fig.6). Engineers are made capable to analyze andmanage the data prior to the extraction for [PSM, PAM]model building. At present the tool is under revisions forthe online inclusion of [PAM, PSM] model synchronizationand validations. Few interfaces of the developed tools arepresented below (Fig.7). This tool provides engineers thefacility to analyze the real time state and alarm data atmodule levels for all the equipments. The states and alarmsbased pareto analysis result in the identification of insignif-icant states and alarms which are then put in quarantine tofurther improve the accurate prediction and classificationofthe [PSM, PAM] models. This tool also help the engineersto quickly identify best and worst equipments for the dataextraction to be used during the [PSM, PAM] learning step.

The first interface provides computed statistics on everyequipment being controlled and monitored for the PSM andPAM models. It provides quick information about the bestand the worst equipment where the pareto count is based oneither number of alarm counts or duration of these alarms.The equipment engineer manages the skipping of non criticalalarms which are defined and grouped at the equipment

Fig. 7: ASCM Tool for extraction, alignment and pre-processing.

type level. This configuration is updated and further usedto filter the unwanted alarms quarantined by the equipmentexperts. These alarms could easily add up the confusionmatrix if not filtered because they have no direct link eitherwith good or bad predictions. The second interface providesthe capability to exploit and analyze the alarms data at theequipment and module levels based on the pareto analysis.The third interface provide an option for the point basedalarms analysis. All these efforts are put together by theequipment engineers to update the filters list so that accurateand more complete alarms data is extracted to be used forPSM and PAM models.

4. Discussion and conclusionsExisting static, dynamic and smart sampling strategies

for inspection are focused on the tool capacity optimizationbased on risk, delay and capacity. These strategies do not

guarantee the selection of lots with a likely yield loss thatcan result in serious consequences as if the bad product lotsare skipped to the next production steps. These strategies canalso be viewed as the blind optimization strategies but riskminimization justifies its adoption in the production line.

Our methodology provides an innovative intelligent sam-pling strategy that filters the lots as good and suspected lotswhere suspected lots are further sampled to optimize theinspection tools capacities using clustering and queue allo-cation algorithm. Our contributions include (i) data modelthat provide means to extract, align and exploit historicalstates, alarms and yield data from multiple data sources, (ii)3-step data mining methodology that generates the PSM andPAM models and (iii) algorithms that perform priority queueallocation and selection of suspected lots for the inspectionor its waiver.

We conclude that multi-source information fusion for theprediction models provides an excellent inspection capacitygains in the production line. These gains are very criticalbecause they help us with additional inspection capacitiesthat can be used by the R&D teams to perform moremeasurements. It is critical because newly emerging spatialvariations that often result in increasing costs and lead times,require more measurements to model these variations.Theproduction lots have the highest priority in the productionline but unnecessary metrology results in increasing the pro-duction cycle times as well. So it is a win-win situation forboth production and R&D engineering teams. The requiredinspection/metrology capacities are spared by reducing un-necessary metrology from the production and they are usedby the R&D engineers to improve the technology. It helpsus in reducing the production cycle times as well.

It is an important to identify the levels of the PAM andPSM models e.g. product, operation, recipe, equipment or agiven technology. We also need to find an optimum policyto test the accuracy of these models based on which theself correction mechanism may be controlled, however inthe proposed 3-step methodology, our self correction policyfollows the defiance from PAM and PSM predictions. Itrequires a rigorous analysis on the alarms and states data.

5. Future perspectivesWe are validating our methodology with different case

studies at the world reputed IDM (integrated device man-ufacturer) and results shall be published soon. We arealso testing our approach with the machine learning basedclassification and clustering algorithms in comparison withour heuristics. We shall improve our heuristics by adding thecapability to compute local support on the partial likely hoodwith the weighted probability assignments. We believe thatit shall improve the performance of our proposed heuristics.Further we are also working to take into account the usagemeter data associated with each module in the equipment.The weighted probabilities shall be computed based on the

usage meter to take into account the equipment status thatcan potentially impact the output of the production process.

The proposed approach improves the metrol-ogy/inspection tool capacities but makes it difficultto compute the process and machine Cpk and Cmkcapabilities. The process capability is an excellentperformance indicator to demonstrate the productionrobustness to the potential customers, however we believethat the newly emerging domain of VM (virtual metrology)shall provide sufficient metrology/inspection informationto estimate the Cpk and Cmk indictors. The VM andyield aware metrology/inspection strategy shall helpin significantly improving the capacity issues whilemaintaining the computation of the process and machine(Cpk, Cmk) indicators.

This domain is not yet exploited by the researchers atall and thats why that industrial engineers are using blindoptimization strategies to improve the capacities. The semi-conductor manufacturing domain is very complex but highlycompetitive and is characterized by the fastest change in theshortest possible time. The success of the future SI businessmodel heavily depends on their capability to improve thewaste of resources from non productive metrology/inspectionsteps. The machine learning and artificial intelligence arethe domains that must come up and take control of thesechallenges.

References[1] G.E. Moore, “Cramming more components onto integrated circuits,”

Electronics, vol. 38(8), 1965.[2] A.J. Duncan, “The economic design of X-bar charts used tomaintain

current control of a process,”Journal of the American StatisticalAssociation, vol. 51(274), pp. 228-242, 1956.

[3] J.I.S. Hsu, “A cost model for skip-lot destructive sampling,” IEEETransactions on Reliability,, 1977.

[4] M.R. Reynolds Jr, R.W. Amin, J.C. Arnold, J.A. Nachlas, “X chartswith variable sampling intervals,”Technometrics,, vol. 30(2), pp. 181-192, 1988.

[5] C.J. Spanos, “Statistical process control in semiconductor manufactur-ing, ” Microelectronic Engineering,, vol. 10(3-4), pp. 271-276, 1991.

[6] W. F. Van Raaij and T. M. M. Verhallen, “Adaptive SamplingMethod-ology for In-Line Defect Inspection,”Advanced Manufacturing Con-ference and Workshop, 2005.

[7] C. Mouli and M. Scott, “Adaptive metrology sampling techniques en-abling higher precision in variability detection and control,” Advancedsemiconductor manufacturing conference,, 2007.

[8] M. Colledani, “Integrated analysis of quality and production logis-tics performance in asynchronous manufacturing lines,”IFAC WorldCongress, 2008.

[9] M. Colledani and T. Tolio, “Performance evaluation of produc-tion systems monitored by statistical process control and off-lineinspections,” International Journal of Production Research, 2009,doi:10.1016/j.ijpe.2007.07.011.

[10] J. Lee, “Artificial Intelligence-Based Sampling Planning System forDynamic Manufacturing Process,”Expert Systems with Applications,vol. 22(2), pp. 117-133, 2002.

[11] S. Dauzere-Peres, J.-L. Rouveyrol, C. Yugma and P. Vialletelle, “ASmart Sampling Algorithm to Minimize Risk Dynamically,”AdvancedSemiconductor Manufacturing Conference, 2011.

[12] M. Sahnoun, B. Bettayeb, P. Vialletelle, A. Mili and M. Tollenaere,“Impact of Sampling on W@R and Metrology Time Delay,”IntelEuropean Research & Innovation Conference, Ireland, 2011.