1 Optimal Preventive Maintenance Scheduling in ...ramirejs/publications/Ramirez_Ref_9.pdf · Optimal Preventive Maintenance Scheduling in Semiconductor Manufacturing ... In semiconductor

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Optimal Preventive Maintenance Scheduling in

Semiconductor Manufacturing Systems:

Software Tool & Simulation Case Studies

José A. Ramírez-Hernández, Member, IEEE, Jason Crabtree, Xiaodong Yao,

Member, IEEE, Emmanuel Fernandez, Senior Member, IEEE, Michael C. Fu,

Fellow, IEEE, Mani Janakiram, Steven I. Marcus, Fellow, IEEE, Matilda

O’Connor, and Nipa Patel

Abstract

This paper presents the architecture and implementation of PMOST, a Preventive Maintenance Opti-

mization Software Tool, based on algorithms for the optimal scheduling of preventive maintenance (PM)

tasks in semiconductor manufacturing operations. We also present results from four complex simulation

case studies, based on real industrial data and employing full fab models, to illustrate the use, data

needs and outcomes produced by PMOST. These results demonstrate significant improvements in tool

production and consolidation of PM tasks. We give a description of the different software modules that

compose PMOST, to provide guidelines as well as a template for other implementations of the PM

optimization algorithms utilized by PMOST.

This work was partially supported by a grant from the Semiconductor Research Corporation (SRC) and International Sematech(ISMT), within the Factory Operations Research Center (FORCe), Task NJ 877.001.

José A. Ramírez-Hernández, and Emmanuel Fernandez are affiliated with the Department of Electrical and ComputerEngineering, University of Cincinnati, OH 45221-0030, USA (e-mails: [email protected]; [email protected];address: 822 Rhodes Hall, University of Cincinnati, PO Box 210030, Cincinnati, Ohio 45221-0030.

Jason Crabtree is with Integral Analytics Inc., Cincinnati, OH, (e-mail: [email protected]).

Xiaodong Yao is with SAS Institute, Inc., (e-mail: [email protected]).

Michael C. Fu and Steven I. Marcus are with the Institute for Systems Research, University of Maryland, College Park, MD20742, USA, emails: {mfu; marcus}@isr.umd.edu.

Mani Janakiram is with Intel Corp., Chandler, AZ, USA Email: [email protected].

Matilda O’Connor was with Advanced Micro Devices Inc, Austin, TX 78741, USA.

Nipa Patel is with Advanced Micro Devices Inc, Austin, TX 78741, USA (e-mail: [email protected]; address: 5204 E.Ben White Blvd. M/S 563, Austin, TX 78741; phone: 512-602-9441; fax: 512-602-0360).

November 30, 2009 DRAFT

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I. INTRODUCTION

In semiconductor manufacturing systems, Preventive Maintenance (PM) is performed by tak-

ing off-line a specific tool to apply a prescribed maintenance task. PM increases the overall

operational reliability while decreasing unanticipated (expensive) down-time from tool failures.

The importance of the PM operations in the semiconductor industry is clearly illustrated by

the large costs of the tools utilized in the fabrication process. For instance, a new fab using

technology for 300 mm wafers can cost in excess of $3 billion [1], [2]. PM properly applied

is a necessity in the fab to maintain and improve productivity, and to justify enormous capital

investments of this industry. In addition, PM operations are usually based on heuristic methods,

e.g., cumulative experience obtained by the engineers from the fab operations. The application

of optimization methods in this problem is a topic that has received significant attention recently

[3], [4], [5].

The objectives of this paper are as follows. First, to present the architecture and implemen-

tation of a software tool called Preventive Maintenance Optimization Software Tool (PMOST),

based on the PM scheduling optimization algorithm for semiconductor manufacturing operations

proposed in [3], [4], [5]. This software tool receives operational data and baseline PM schedules

to generate an optimized PM schedule. Second, to present the architecture and implementation

of PMOST, in order to provide guidelines and a template, as well as experimental data, that

can help in the adoption of these by others, and also perhaps serve as the basis for generic

third-party commercial tools. Third, to present a set of four complex simulation case studies,

based on real industrial data and using full fab models, to illustrate the use, data needs and

outcomes produced by PMOST. Both the PM optimization algorithms reported in [3], [4], [5]

and PMOST are the result of research supported by the Semiconductor Research Corporation

(SRC) and International Sematech (ISMT) within the “Factory Operations Research Center”

(FORCe) program. The project was justified by the fact that neither algorithms nor software

tools for PM scheduling optimization in semiconductor manufacturing operations were available

previous to this research.

The case studies presented in this paper consisted of simulations of four different tool groups

in photolithography, metal deposition, and thin films processes on which the impact of optimized

PM schedules, obtained with PMOST, versus heuristic and baseline PM schedules was evaluated.


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The simulation experiments were performed in two fabs from different semiconductor companies.

For the experiments, the companies allowed the utilization of industrial data as well as the full

factory simulation models. Moreover, the simulations were conducted under the strict supervision

of the personnel in charge of factory simulations, and according to the simulation practices

utilized by each company.

We also studied the problem of incorporating non-calendar based PM schedules into the PM

scheduling optimization. As a result, a conversion algorithm [6], [7] was designed to provide

estimates of the equivalent calendar-time PM schedules for PM tasks defined under other non-

calendar time units, e.g., number of wafers processed or processing-time elapsed since last PM

task. The algorithm reported in [6], [7] utilizes as input the projections of the Work-In-Process

(WIP) and the system’s parameters (e.g., tool throughput rate, number of chambers), and then

yields estimates of the dates for which the corresponding tool could receive a prescribed non-

calendar time type of PM task. In addition to the fact that calendar-time PM schedules are easy to

use and to implement, in terms of the optimization algorithm given in [3], [4], [5], calendar-time

schedules are preferred because the search space for the optimization problem may be smaller

when compared to the use of other units used to describe the PM schedules. Specific details

of the conversion algorithm are provided in [6], [7]. Moreover, in [7] an overview of how the

calendar-time PM schedules generated by the conversion algorithm are incorporated in the PM

optimization with PMOST is presented, as well as a case study with real industrial data that

demonstrates the accuracy of the conversion algorithm.

The organization of this paper is as follows: Section II presents an overview of the optimal

PM scheduling framework utilized by PMOST. This is followed by a description of PMOST

in section III that describes the data utilized by the software tool and how optimization results

are provided. An overview of the simulation studies and the corresponding optimization and

simulation results are given in section IV and V, respectively. Finally, conclusions are presented

in section VI.

II. OVERVIEW OF PM SCHEDULING OPTIMIZATION

PMOST is based on the modeling framework for optimization of PM schedules given in [3],

[4], [5]. This framework is described as a two-level hierarchical model [3], with a Markov

Decision Process (MDP) [4] at the higher level and a Mixed Integer Programming (MIP)


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formulation [3], [4], [5] at the lower level, as depicted in Fig. 1 below.

Upper MDP

Lower MIPWIP

PM Schedule

PM Policy

Objective

Constraints

Demand Pattern

Failure Dynamics

Figure 1. Two-level hierarchical framework for PM planning and scheduling (adapted from [3], [4], [5]).

The long-term PM planning policies are produced by the MDP, which employs “the available

information in a way that provides a trade-off between immediate and future benefits and costs,

and that utilizes the fact that observations will be available in the future" [8]. In the lower

level, a MIP formulation [3], [4], [5] generates the optimized PM schedules according to an

optimization objective, projections of the Work-In-Process (WIP), and these are subjected to

several constraints. It is this PM scheduling optimization algorithm that is implemented by

PMOST, and the PM planning policy, or frequency for performing the different PM tasks, is

obtained from the baseline, or nominal, schedule employed in daily fab operations. This frequency

is determined by the semiconductor fab operations, and based on recommendations from the

tool’s manufacturer.

Next we present some notation and details on the optimization models and algorithmic solu-

tions, presented previously in [3], [4], [5], which are utilized in PMOST.

As presented in [3], [4], [5], the objectives utilized for the lower level MIP model are as

follows:

MIP Objective 1

max

Tp∑t=1

M∑i=1

(bi · Vi(t)− cI

i · Ii(t)−ρi∑

l=1

cli · al

i(t)

), (1)


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MIP Objective 2

max

Tp∑t=1

M∑i=1

(b′i ·Xi(t)−

ρi∑

l=1

cli · al

i(t)

), (2)

where, using the same notation as in [3], [4], [5], Tp represents the number of time units or

periods in the PM scheduling horizon, M is the number of tools (or tool chambers), Vi(t) is

availability of tool i in period t, bi is the profit coefficient for availability of tool i, Ii(t) is the

workload level (i.e., WIP) for tool i in period t, cIi is the cost coefficient for inventory in tool i,

ρi is the number of PM tasks on tool i, ali(t) is a binary decision variable (1: do PM, 0: don’t

do PM) for PM task l on tool i in period t, and cli is the cost of performing PM task l on tool

i. Moreover, in MIP Objective 2 the quantity Xi(t) represents the wafer throughput of tool i in

period t and b′i is the profit coefficient for throughput on tool i. The above MIP objectives (1)

and (2) would be optimized under constraints such as inventory levels, availability of resources

(e.g., maintenance technicians per period), tools availability and throughput. Notice that each

objective aims to maximize two different performance indices in a tool group. In MIP Objective

1 the goal is to maximize the availability of tools while minimizing inventory and PM task costs.

For MIP Objective 2, the goal corresponds to maximize the tool throughput while minimizing

the PM costs.

The PM scheduling optimization considers a scheduling horizon where PM tasks are specified

by "PM windows" and are delimited by a warning, due and late date, or by the amount of units

completed (e.g., wafers, kilowatt-hours), see Fig. 2.


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Time (day)

Tool

Tool 1

Tool 2

Tool 3

…

Schedul ing Horizon Present

… Warning Due Late

Figure 2. Calendar-time based PM windows.

Thus, the range of time or units completed, as indicated by a PM window, represents the

interval of time or production when a PM task can be applied. The warning represents the

earliest moment when a PM should be conducted, and the due and late dates are the suggested

and latest time to perform a PM task, respectively. The optimization algorithm assigns the

occurrence of these tasks within the associated PM windows. Thus, PM tasks have a nominal

frequency to be performed; for example, every 30 days or every 15000 wafers since the last

PM task was completed. The frequency is determined by the semiconductor fab operations and

based on recommendations from the tool’s manufacturer.

The optimization increases tool throughput and availability by determining due dates of PM

tasks, within the scheduling horizon, e.g., by avoiding periods of high incoming WIP, and

by consolidating PM tasks. Consolidating PM tasks involves scheduling PM tasks to occur

synchronously, if those tasks can be performed concurrently on the tool, thus reducing the total

time to complete all the tasks and increasing overall tool availability. When a consolidation is

obtained, PM tasks with the longest repair time are selected. Scheduling PM tasks by avoiding

periods of high incoming WIP helps ensure that the tools are not down for maintenance during

times when these are most needed.

In the next section, we present a description of the software tool PMOST, which implements

the PM scheduling optimization algorithm.


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III. PREVENTIVE MAINTENANCE OPTIMAL SCHEDULING TOOL (PMOST)

Different operational data from the process is required to formulate the MIP problem (e.g.,

estimated WIP, tool parameters, scheduling horizon). The optimization algorithm [3], [4], [5] was

originally designed to use PM tasks based on calendar-time schedules because of ease of use of

data in this format and dimensionality of the MIP. When non-calendar based PM schedules are

considered (e.g., processing-time based PM tasks), these need to be converted into calendar-time

format by using, e.g., the conversion algorithm in [6], [7].

The data inputs and outputs for the optimization algorithm are illustrated in Fig. 3 below.

As presented, the algorithm receives as data inputs a set of tools, an initial PM schedule, a

scheduling horizon, projected incoming WIP, cost parameters and constraints, as well as the

available resources. As data outputs, it generates the optimized schedule, the estimated tool

availability and the estimated WIP when the optimized PM schedule is utilized.

PM Optimization Scheduling

Model/algorithm

A set of toolsInitial schedule (PM tasks)

Scheduling horizonProjected Incoming WIP

Cost Parameters andconstraints

Available resources

Optimized ScheduleEstimated AvailabilityEstimated WIP

Figure 3. Data inputs and outputs for the PM optimization algorithm.

The Preventive Maintenance Optimal Scheduling Tool (PMOST) is a comprehensive software

tool designed to implement the PM scheduling optimization model presented in [3], [4], [5];

see also [9]. This software tool was developed as a joint effort of the Systems Modeling &

Information Technology Laboratory (SMITLab) at the University of Cincinnati, and the Institute

for Systems Research at the University of Maryland.

In the same way as the optimization algorithm [3], [4], [5], PMOST accepts a set of input

parameters and data related to the PM optimization process, e.g., scheduling horizon, number

of available resources for the PM tasks, cost coefficients related to the PM tasks (see Fig. 3),

via data files and user input. The data files consist of both static and dynamic data. Static data

is information that does not generally change from run to run of the optimization, e.g., mean

duration of a PM task. This data is generally entered manually into text files. Dynamic data


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is information that changes from run to run of the optimization, e.g., upcoming due date of a

PM task. Thus, PMOST’s static data files include information of the tool family, PM tasks per

tool, and a file with a mapping of the effective throughput of tools with multiple chambers.

The dynamic data files include data of the initial or baseline PM schedule for the tool group,

the projected WIP levels per tool at each period in the scheduling horizon, and the number of

technicians available per period in the scheduling horizon. Regarding the length of the periods

for the scheduling horizon, it is a common practice in the industry to utilize scheduling horizons

of one or two weeks, with periods of one day or one shift, i.e., half day. Also, data projections of

WIP levels at each tool can be obtained from scheduling tools such as the Real-Time Dispatcher

[10]. Moreover, the collection of the dynamic data could be automated by linking the necessary

input files to the different fab information systems, e.g., Manufacturing Execution System (MES)

[10], Enterprise Resource Planning (ERP).

PMOST assembles the input data into a Mathematical Programming System (MPS) file [11],

[12], which contains the objective function, constraints, and all input data. The MPS file format,

created by IBM in the 1960s, is a standard for defining linear programming (LP) problems, and

is widely accepted by commercial LP solvers [13]. Although PMOST does not need a Modeling

Description Language (MDL) [14], [13] to model the optimization process and generate the

corresponding MPS file, modifications on future versions of PMOST may include interfaces

with MDL software, e.g., AMPL [15] and ILOG Optimization Programming Language (OPL)

[16].

Currently, PMOST has the ability to work directly with any commercial mathematical program-

ming solvers that accept command line executions. Solvers that have been successfully utilized

with PMOST include IBM Optimization Solution Library (OSL) [17] and ILOG CPLEX [18].

For instance, PMOST is able to generate a call to IBM’s OSL, transferring the MPS file and

processing the output results from the solver. The parsed solution from the IBM’s OSL can be

easily read and displayed, or used to create a PM order file for simulation purposes, e.g., in

AutoSched AP [19], [20].

The core of PMOST was written in C [21], which allows portability across different platforms

or operating systems. For the current version of PMOST, we also developed a User Interface

(UI) in C++ [22] which works under Microsoft Windows platforms. Fig. 4 below depicts the

flow diagram of PMOST with the different processes that are executed by this software tool. As


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illustrated in the figure, the program “pmost_ui.exe,” which corresponds to the UI application,

includes the process utilized to gather information manually from the user, such as the scheduling

horizon, tool family information, and number of technicians. The UI application is also utilized to

manually start the PM optimization process. Also, the application “conv2cal.exe” implements the

conversion algorithm reported in [6], [7] for the conversion of non-calendar time PM schedules,

e.g., wafer-based PM tasks. Within the user interface is the core application, “pmost.exe,” which

uses as input the data collected by reading the static and dynamic information contained in

multiple data files. The core application then generates the corresponding MPS file that is passed

to the LP/MIP solver to generate the PM optimization. Once the solver finds a feasible solution

according to the input data provided, then the solution is properly parsed into a calendar-time

format that can be used by the fab simulation model, or for direct use in the PM operations. In

the work described here, the simulation models utilized were those in use at the industrial sites,

which were implemented utilizing commercial software, e.g., AutoSched AP [19], [20].


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START User input

ReadInput Data

-Tool data files-PM data files-PM schedule-Estimated WIP data files-Conversion of PM Schedule

to calendar-time format (conv2cal.exe)

WriteMPS file

LP/MIPSOLVER

ParseSolution

MPS file

Output: PM Orders

PM Optimal Scheduling Tool (PMOST)

-Scheduling horizon-Tools family-Number of Technicians

Solution file

Solution file in calendar-time format

Fab Simulation

Baseline PM Schedule

pmost_ui.exe

pmost.exe

Figure 4. PMOST flow diagram.

The current version available for PMOST is version G2.0. Several screenshots from the user

interface of this version are found below. Fig. 5 shows a screenshot of a Tool/PM data file open

for editing. This file contains the general parameters for the tool group.


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Figure 5. PMOST user interface screenshot, tool/PM data file.

Fig. 6 shows a screenshot that illustrates the progress of the optimization process during a

run. After a successful optimization run, the user can open and view the optimal PM schedule

in a text file.

Figure 6. PMOST user interface screenshot, progress of optimization process during a run.


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The screenshot in Fig. 7 shows a solution file that contains the optimal PM schedule from

the optimization run. The optimal PM schedule is given alongside the initial PM schedule.

Figure 7. PMOST user interface screenshot, optimal PM schedule file.

In the next section we present an overview of the simulation studies, including the general

conditions for the simulation experiments, as well as additional terminology utilized in the

subsequent sections. Each case study described in the following sections utilized PMOST,

together with IBM’s OSL or CPLEX, to obtain the optimized PM schedules.

IV. SIMULATION STUDIES OVERVIEW

Four simulation case studies were performed for three relevant semiconductor manufacturing

operations: photolithography, metal deposition, and thin films. In previous work presented in

[3], [5], another simulation case study is provided for which a group of 11 tools in a thin films

operation was considered. That case study also considered the optimization objectives given in

(1) and (2), and the results reported in [3], [5], demonstrated an increase of tool throughput of

up to 13.9%. In this paper we present results from simulation experiments conducted in two

fabs, each from a different semiconductor companies. Moreover, the metal deposition and thin

films operations case studies presented here included both calendar-time and wafer-based PM


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tasks. Similarly to the study reported in [3], [5], the results presented in this paper indicate that

a maximum increase of 14.2% was observed in tool throughput for the thin films operations.

All the case studies presented in this section were conducted utilizing industrial data and the

corresponding full factory simulation models, including modeling of unscheduled tool down-

times due to failures, from the two fabs that participated in the study. The simulation experiments

were performed under strict supervision of the personnel in charge of factory simulations at each

company, and by following the simulation practices utilized at each fab. In addition, the different

data required for modeling and the optimization process was collected in meetings with personnel

in each fab, from technicians to tool/process managers.

It is important to mention that the types of simulation case studies described in this section

are difficult to perform. These experiments are costly, in terms of the time invested by qualified

personnel in charge of factory simulation, the need that they be conducted over a limited time

period, the experiments involve very sensitive data related to the simulation model, and the

complexity of the corresponding implementation of the experiments. Therefore, in this section

we present as much information as possible from our on-site research at the fabs and companies

that participated in the study. As indicated earlier, these simulation case studies were done in

two different industrial settings. Therefore, the two sets of simulation studies conducted differ

in terms of the factory simulation model utilized, and some simulation parameters, e.g., number

of replications, simulation lengths, warm-up periods which were done as per common practices

utilized by the different industrial groups. Unfortunately, not all the numerical results presented

in this paper are given in the same format because of the difficulties mentioned above and

because of the different simulation practices utilized at each fab.

In the case of the photolithography process, two different groups of tracker/stepper tools were

selected. These tools are utilized to expose wafers with the circuit patterns, which are later

etched into the wafers. Steppers are good candidates for optimization because of their high cost,

and these are common bottlenecks in the manufacturing process. Increasing the throughput of

a set of steppers through optimization can alleviate the bottleneck condition and possibly allow

a fab to reduce equipment costs by obtaining the same productivity from a smaller amount of

tools. Tracks are responsible for preparing the wafers for the steppers. This preparation involves

coating the wafers with photoresist and spinning them to evenly distribute it. The tracks were

considered in the simulation studies because these are physically connected to the steppers, and


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thus PM activities performed on them affect the operation of the steppers.

The tools in the thin films and metal deposition processes are utilized to deposit thin layers

of material on the wafers (e.g., metallic layers, silicon oxide). As with the tracker/steppers,

these tools are good candidates for optimization because they are common constraints (e.g.,

bottlenecks) in the fab.

The four simulation case studies are organized as follows:

• Case I: considered a PM schedule with only calendar-time based PM tasks in a tracker/stepper

tool group for a photolithography process.

• Case II: this case included a PM schedule with only calendar-time based PM tasks and was

performed on a second tracker/stepper tool group for a photolithography process.

• Case III: utilized PM schedules with only wafer-based PM tasks on a set of metal deposition

tools.

• Case IV: applied a PM schedule of both calendar and wafer-based PM tasks for a thin films

tool group.

From the previous list notice that although the case studies I and II utilized the same type

of tools and process, we preferred to differentiate these because each case was conducted in a

different fab, and thus under significant data and simulation settings differences. The pair of case

studies {I, III}, and {II, IV} were performed in different industrial settings. Therefore, these two

sets of experiments differ in terms of the factory simulation model utilized and the simulation

experiments parameters, e.g., number of replications, simulation lengths, warm-up periods, etc.,

as per common practices utilized by the different industrial groups.

The simulations were performed by using actual fab simulation models built in AutoSched

AP [19], [20]. For each of the four case studies, two schedules were simulated for multiple

replications: one generated by applying a heuristic or baseline PM schedule employed by the

fab, and the other obtained through the PM optimization algorithm. Performance was compared

between the optimized and non-optimized schedules.

Through the next sections, we use the following terminology for PM schedules:

• Baseline: is defined as the nominal PM schedule that contains the raw PM due dates based

on PM frequencies. These frequencies are suggested by the tool manufacturers and fab

operations. The baseline schedules can be specified in calendar-time, wafer, or processing

time formats.


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• Initial: is a strictly calendar-time version of the baseline schedule, where all non-calendar

PM tasks (e.g., wafer-based) have been converted to equivalent calendar-based PM tasks.

The initial PM schedule is the input schedule for PMOST.

• Heuristic: is defined as a PM schedule generated and implemented by fab engineers. In

general, this type of schedule is created manually from a baseline schedule.

• Optimal schedule: is obtained from the PM scheduling optimization algorithm implemented

in PMOST.

The following are common conditions considered in the four case studies:

• The semiconductor fab operated 24 hours a day, seven days of the week.

• The statistics of interest collected from the simulation studies were: percentage of tool

availability, tool utilization, and tool throughput (production).

• Actual heuristic PM schedules were obtained by collecting historical operational data from

the fab information systems. The data include the baseline PM schedules for the scheduling

horizon that were based on the assigned frequencies for each PM task.

The next subsections describe the specific conditions considered in each case. Case I and II

are presented together because of the similarity of their conditions, while case III and IV are

described independently.

A. Case studies I and II: Optimal scheduling of calendar-time PM tasks on photolithography

process tools

Case I and II considered stepper and track tools in a photolithography process. In both cases,

the PM activities were strictly calendar-based, thus no conversions were needed to feed the PM

tasks into the optimization algorithm (i.e., the PM optimization works in calendar time only).

The simulation studies were conducted under the following conditions:

Case I conditions

• The scheduling horizon considered was 8 days.

• PM tasks were only calendar-time based. A total of 12 single-chambered tools were con-

sidered in the simulation study, of which only eight tools had their PM windows in the

scheduling horizon.

• PM tasks were performed with different frequencies since the last PM (e.g., every week,

month), from 7 to 90 days.


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• A baseline PM schedule, in calendar-time format, was obtained from the fab information

systems, e.g., Manufacturing Execution System (MES), in-house customized systems. It was

directly used as an initial schedule by PMOST.

• Estimated incoming WIP, from the fab’s lot scheduling system, e.g, Real-Time Dispatcher

(RTD) [10], was specified in hours of processing-time.

Case II conditions

• The scheduling horizon was one week (7 days).

• The simulation study involved 25 steppers and 25 tracks, e.g., each stepper and track

combination modeled as a single tool. Of these tools, 13 had PM tasks due within the

scheduling horizon.

• The baseline PM schedule was in calendar-format; thus it was utilized as an initial schedule

by PMOST.

• Additional data, such as a WIP snapshot for the fab at the beginning of the week and the

wafer starts for the week, were gathered to ensure an accurate simulation.

For case II, a WIP snapshot was used to initialize the fab at the beginning of the scheduling

horizon. The snapshot indicated the amount of WIP at each tool and processing step at the horizon

start. The wafer starts data indicated the amount of new wafers started during the scheduling

horizon. Coupled with the WIP snapshot, this data enabled the simulation to accurately reflect

the WIP conditions in the fab.

In particular, for case II, since each stepper and track combination was modeled as a single

tool, PM activities were scheduled on the whole tool as opposed to being scheduled on the tool’s

chambers. However, since each stepper and track were physically linked together, taking one tool

down for maintenance disabled the other tool. Thus, the steppers and tracks were each considered

chambers of a two-chambered tool. Treating each stepper-track combination as a two-chambered

tool allowed the optimization algorithm to take advantage of potential PM consolidations, where

if a PM task was scheduled on one chamber, then a second PM task could be scheduled to

occur concurrently on the second chamber. In contrast, the tools in case I were considered as

single-chambered.

In general, by scheduling PM tasks to occur concurrently, the total time to complete the tasks

may be reduced. That is, by consolidating several PM tasks for a tool, the number of times


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that the tool needs to be taken down is reduced as compared with the case in which the PM

operations are not performed concurrently. The immediate benefit from PM consolidations is

then an increase in tool availability. That is, consolidating PM tasks helps to minimize the total

maintenance time that a tool experiences, which in turn, helps to maximize both tool availability

and throughput.

B. Case study III: Optimal scheduling of wafer-based PM tasks on metal deposition tools

The third case study focused on scheduling strictly wafer-based PM tasks on a group of tools

for a metal deposition process. To optimally schedule wafer-based PM tasks, the conversion

algorithm in [6] was applied to obtain an equivalent baseline PM schedule in calendar-time

format. This was used as an initial PM schedule in PMOST.

The simulation study considered the following conditions:

• The scheduling horizon was 8 days.

• Four different wafer-based PM tasks were considered.

• Although a total of 29 tools were included in the simulation study, only five tools had their

PM windows in the scheduling horizon. These five tools were then considered for the PM

optimization process.

• The due amounts of wafers required to perform each PM task were in the order of thousands

of wafers.

• Estimated incoming WIP, from the fab’s lot scheduling system, e.g, Real-Time Dispatcher

(RTD) [10], was given in hours of processing time.

In addition to comparing the performance of optimized and non-optimized PM schedules, a

related goal was also to utilize this case study to validate the integration of non-calendar based PM

schedules into the PM optimization process. Moreover, the accuracy of the conversion algorithm

was evaluated by comparing historical data against the estimated calendar-time PM schedules. In

general, a satisfactory performance was obtained as it is reported in [7]. However, an important

conclusion from this experience is that accurate projections or estimates of the incoming WIP are

required to improve the accuracy of the equivalent calendar-time PM schedules. For instance, in

the evaluations of the conversion algorithm reported in [7], it was observed that the accuracy in

the estimations is affected by projected WIP levels that are far from the PM window targets, i.e.,

warning, due, and late dates. In practice, the engineers in charge of the factory simulations at the


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fabs prefer to utilize WIP projections of no more than two weeks for the scheduling horizons. In

doing so, the goal is to provide accurate simulations that are then utilized in different planning

of operations in the fab, including PM. Moreover, accurate estimates of the incoming WIP will

directly affect the PM optimization process. For instance, MIP Objective (1) depends directly

on the projected incoming WIP; therefore, the solution obtained by solving the MIP will reflect

the operational conditions assumed by using the WIP projections.

C. Case Study IV: Optimal scheduling of mixed-type PM tasks on thin films tools

The fourth simulation study was performed on a group of thin films tools, which are responsible

for depositing a layer of dielectric material ("glass") on wafers.

The simulation study was conducted under the following conditions:

• The scheduling horizon was 22 days.

• The simulation study involved 28 thin films tools. Of these tools, 16 had PM tasks due

within the scheduling horizon.

• The thin films tools employed both calendar and wafer-based PM tasks.

The thin films tools were chosen because these were true parallel tools, which is what the PM

scheduling optimization is best suited for. Parallel refers to the fact that multiple chambers of

the tool can perform the same functions. This ability allows the tool to still operate, at a reduced

throughput, while a chamber is taken down for maintenance. In addition, these tools are also

common bottlenecks in the fab, because they are subject to large amounts of reentrant flow,

where a wafer comes back to the same tool type for further processing. In principle, these

tools are good candidates for the optimization. Each tool in the group was comprised of three

processing chambers along with a main transfer chamber, where a robot transfers wafers from

one processing chamber to the next, as well as initially transferring wafers from the load docks

to the first processing chamber. However, chamber-specific data was not made available to us

at the time of the study, and thus for the purpose of the PM scheduling optimization, the entire

tool was considered as one chamber.

Also included in the optimization were subfab PM activities. The term subfab refers to the

pumps and other equipment that lie beneath the floor, under the tools. These PM tasks were

included because their execution also requires that the tool be taken down for the duration of

the PM operation. The subfab was considered as an additional chamber of the tool. For the PM


19

optimization the tools had to be modeled as two-chambered tools, with the entire tool representing

the first chamber and the subfab representing the second one. This simplification reduced the

possibility of the optimization finding PM consolidations. However, as the results show, some

consolidations were made, and slight improvements in performance were then achieved.

In addition, since the optimization works in terms of calendar time, the wafer-based PM

windows needed to be converted to equivalent calendar-based PM windows. Because historical

data was being used for the simulation study, this was not a difficult task since the wafer counts

of each tool could be matched up with their corresponding calendar times. Thus, by looking at

historical production data, the wafer counts corresponding to the PM windows could be matched

up with calendar dates.

The next section presents the results from the simulation case studies.

V. OPTIMIZATION & SIMULATION RESULTS

This section presents the results from the PM scheduling optimization and simulation studies.

The results for each case study are described independently and organized by subsections. In

addition, each subsection presents a comparison between the initial and optimized PM schedules,

as well as the percentage change observed in the performance statistics for the tool group when

a baseline or a heuristic PM schedule was replaced by an optimized PM schedule.

A. Results for Case Study I: scheduling of calendar-time PM tasks on photolithography process

tools.

A comparison between the optimal and baseline PM schedules is shown in Table I. In this

table, the label STR#_PMC# represents the PM name that is associated to each pair of tools

and PM tasks. These labels are utilized instead of the actual names for proprietary reasons. For

instance, STR1_PMC1 corresponds to the PM task "PMC1" at tool "STR1".

As presented in Table I, the only PM operation that was not modified by the optimization

process is STR3_PMC2. Moreover, the optimal PM schedule indicates to not perform the PM

tasks STR5_PMC4 and STR8_PMC2 within the corresponding PM scheduling horizon.

Statistical results for this simulation study are presented in Table II. These results correspond

to average values for the entire group of twelve tools when three replications were generated

using the baseline and optimal schedules. While the first column lists the performance statistics


20

Table ICOMPARISON OF BASELINE AND OPTIMAL PM SCHEDULES FOR CASE STUDY I

PM Schedule (Day)

PM Name Baseline Optimal

STR1_PMC1 1 2

STR2_PMC1 1 2

STR3_PMC2 4 4

STR4_PMC3 1 2

STR5_PMC4 8 Do Not Perform PM

STR6_PMC2 3 4

STR7_PMC5 5 6

STR8_PMC3 7 Do Not Perform PM

considered, the second and third show the maximum and minimum percentage change for a

single tool in the group, respectively, when the baseline is replaced by an optimized PM schedule.

Similarly, the last column indicates the average change in the statistic over the entire group of

tools when the baseline is replaced by an optimized PM schedule.

Table IIPERFORMANCE RESULTS FROM CASE STUDY I: PERCENTAGE CHANGE FOR BASELINE VS. OPTIMAL PM SCHEDULE

Statistic Max.(%) Min.(%) Avg. (%)WCOMPS 96.85 -38.01 1.64

AVAIL 54.15 -34.56 1.02UTIL 53.10 -34.74 1.68

Min., Max.: minimum and maximum change in a single tool.

Avg.: average change over the entire tool group.

The first statistic in Table II corresponds to the average number of wafers completed (WCOMPS).

Results indicate that when the optimized PM schedule was applied, the group of tools produced

on average 1.64% more wafers as compared with the baseline PM schedule. Notice, however, that

the PM tasks STR5_PMC4 and STR8_PMC3, which require several hours to be completed, were

not performed under the optimized PM schedule and these were then expected to be scheduled

earlier in the next scheduling horizon.

The results also indicate that the positive change in WCOMPS is due to better PM scheduling


21

provided by the optimization algorithm rather than the non-scheduling of PM operations in the

tools STR5 and STR8. In fact, the increase in WCOMPS for the tool group under the optimal

PM schedule is due to production increases in the tools that received PM operations within the

scheduling horizon, some of them yielding an increase of up to 97% in production. Interestingly,

the results indicate that the tools STR5 and STR8 decreased their WCOMPS by about 20% under

the optimal PM schedule. Nevertheless, in other case studies presented in this paper we also

observed an increase in WCOMPS when the optimized schedule was utilized and all the PM

tasks were properly scheduled within the PM scheduling horizon.

As can be seen in Table II, by solely looking at the numbers, the percentage improvement

obtained with the optimal PM schedule is relatively small. However, even such small changes

in the tool group performance, e.g., average WCOMPS, may represent substantial increases in

marginal profits in the semiconductor manufacturing business. The results from this case study

also indicate slight but positive differences of 1.02% and 1.68% in average tool availability

(AVAIL) and average tool utilization (UTIL), respectively, by applying the optimal PM schedule.

Although the statistics for some single tools obtained a significant increase while for other tools

the statistics decreased, it was observed that the average performance of the entire tool group

was improved when the optimized PM schedule was utilized.

B. Results for Case Study II: scheduling of calendar-time PM tasks on photolithography process

tools.

The results of the optimization for this case are given in Table III. In this table, the optimal

PM schedule is given alongside the heuristic schedule. The first column of the table provides the

PM names, which have been also modified from the actual names. Each PM name is comprised

of the tool name (Tool#) and a chamber name (CH#). Chamber one (CH1) refers to the stepper,

and chamber 2 (CH2) refers to the track. The symbols †, 4, and ♦ indicate the dates with

consolidations of PM tasks in a tool. By consolidation we mean conducting two or more different

PM tasks in the same tool.

From Table III, notice that several PM tasks are consolidated in both the heuristic and optimal

PM schedules, e.g., PM tasks on the stepper (CH1) and track (CH2) of Tool13. The way in which

the heuristic PM schedule is presented indicates that fab engineers performed consolidations of

PM tasks as appropriate due to the physical interrelationships between the steppers and trackers


22

Table IIICOMPARISON OF INITIAL (BASELINE) AND OPTIMAL PM SCHEDULES FOR CASE STUDY II

PM Schedule (Day)

PM Name Heuristic Optimal

Tool1_CH1 2 2

Tool2_CH1 5 2

Tool8_CH1 1 3

Tool10_CH1 3 1

Tool11_CH1 1 2

Tool12_CH1 4 6

Tool13_CH1 2† 3†Tool13_CH2 2† 3†Tool14_CH1 6 3

Tool17_CH1 6 2

Tool18_CH1 34 74

Tool18_CH2 34 74

Tool19_CH1 5♦ 1♦

Tool19_CH2 5♦ 1♦

Tool20_CH1 1 2

Tool25_CH1 4 4

Tool25_CH2 4 4

† , 4, ♦: Dates with consolidated PM tasks in a tool.

described in section IV. This interdependence between steppers and trackers was also indicated

to the PM optimization algorithm as constraints. As a result, the PM optimization algorithm

preserved the PM task consolidations, while changing the dates when the tasks were scheduled.

Thus, any improvements in tool throughput made by the optimization algorithm would therefore

be left to scheduling the PM tasks around periods of high incoming WIP.

The simulation results for the tool group are given in Table IV.

Table IVPERFORMANCE RESULTS FROM CASE STUDY II: HEURISTIC VS. OPTIMAL PM SCHEDULE

Statistic Change (%)WCOMPS 0

AVAIL 0.03UTIL 0.01


23

These results show the percentage change for the total number of wafers completed (WCOMPS)

when the heuristic PM schedule was replaced by an optimized schedule. Table IV also lists

the percentage change for the average availability (AVAIL) and utilization (UTIL). The results

represent the average statistics from ten simulation replications.

The results in Table IV show very minor improvements in tool availability and tool utilization

made by the PM optimization. These gains were most likely due to scheduling the PM tasks

around periods of high incoming WIP, since the PM consolidations, made by the optimization,

were also made by fab engineers. Evidently, the fab engineers did a very good job at scheduling

PM tasks in this instance, but accomplishing this may be a very time-consuming job and highly

sensitive to the ability of the particular individual(s) performing the scheduling. Fig. 8 illustrates

a WIP profile for the tool group during the scheduling horizon, taken from the simulation results.

The figure shows that highest WIP level occurred on Day 5 and the lowest on Day 2. Referring

to the PM schedules in Table III, the PM optimization avoids scheduling PM tasks on Day 5

and schedules several tasks on Day 2.

Figure 8. Sample WIP profile for case study II optimization results.

The results of this simulation study validate the PM scheduling optimization. While the PM

optimization does not make major gains in this simulation study, it does show that it can capture

the major decision factors in the PM scheduling process and perform as well as the best heuristic

policies. An argument in favor of the use of such software tool is that it would yield optimized

schedules every time, guiding fab engineers to the best schedule and thus avoiding any potential


24

gross inefficiencies due to human error. The optimization would also be of value in efforts to

automate the PM scheduling process. Automating the PM scheduling process would not only

save time to engineers who manually generate the PM schedules, but could also lead to more

sophisticated lot scheduling in the fab.

C. Simulations results for Case Study III: scheduling of wafer-based PM tasks on metal depo-

sition tools.

In this case study an optimized schedule was obtained for wafer-based PM tasks. Table V

shows both the initial and optimal PM schedules. In the first column of Table V, the label

MDep#_PMW# identifies the PM name that is associated with the pair of tools and PM tasks.

The second and third columns list the baseline and optimal schedules, respectively. The baseline

PM schedule was estimated by using the conversion algorithm in [6].

It should be noted from Table V that consolidations of PM tasks are produced in three out

of the five tools considered in the optimization. Consolidations of PM tasks in the tools are

highlighted in bold and properly identified with the symbols †, 4, and ♦ in Table V. For instance,

before the optimization the PM tasks PMW1 and PMW2 were scheduled on different days for

the tool MDep1. After the PM scheduling optimization, these PM operations for MDep1 were

consolidated and scheduled on the same date (Day 2). Moreover, notice that for this simulation

experiment the tools considered did not have the physical constraints observed for the steppers

and trackers of case study II. Thus, in this case the PM optimization algorithm provided PM task

consolidations that both improved the overall scheduling and were not due to physical constraints

in the tools.

The statistical results from the simulation are presented in Table VI. The value of these

percentages of change in the statistics represent an average of three replications and considered

the entire tool group. In addition, the minimum and maximum change for a single tool is

indicated.

As seen in this table, the optimal PM schedule produces a positive effect in tool availability

(AVAIL); an average of 1.04% improvement was obtained. Also, the total number of wafers

completed (WCOMPS) was increased in 2.19% by utilizing the optimal schedule. Similarly,

note that some single tools obtained either substantial increases or decreases in the statistics

when the optimized PM scheduled is applied, while the percentage change over the entire tool


25

Table VCOMPARISON OF BASELINE AND OPTIMAL PM SCHEDULES FOR CASE STUDY III

PM Schedule (Day)

PM Name Baseline Optimal

MDep1_PMW1 1 2†

MDep1_PMW2 2 2†

MDep2_PMW3 3 44

MDep2_PMW1 5 44

MDep3_PMW3 5 2♦

MDep3_PMW1 3 2♦

MDep4_PMW3 4 2

MDep5_PMW3 7 5

†, 4, ♦: Dates with consolidated PM tasks in a tool.

Table VIPERFORMANCE RESULTS FROM CASE STUDY III: PERCENTAGE CHANGE FOR BASELINE VS. OPTIMAL PM SCHEDULE

Statistic Max.(%) Min.(%) Avg. (%)WCOMPS 14.52 -8.09 2.19

AVAIL 5.83 0 1.04UTIL 6.34 -2.65 0.75

Min., Max.: minimum and maximum change in a single tool.

Avg.: average change over the entire tool group.

group remains positive. In this case, it is clear that the consolidation of PM tasks produced a

significant positive effect in tool availability and throughput.

Two objectives were accomplished with this case study. First, it validated the PM optimization

algorithm by presenting positive improvements in the tools’ production. And second, the case

study served as proof of concept for the integration of the conversion algorithm [6], [7] for

non-calendar time schedules and the PM scheduling optimization algorithm.

D. Simulations results for Case Study IV: scheduling of mixed-type PM tasks on thin films tools.

Table VII presents the results of the optimization for this case study. In the table, the optimal

PM schedule is given alongside the heuristic schedule. The resulting PM task consolidations in

the tools are highlighted in bold in the third column and respectively marked with the symbols

†, 4, ‡, and ♦. The first column of the table provides the modified PM names. Each PM name


26

is comprised of a tool name (Tool#) and chamber name (CH#). Chamber one (CH1) refers to

the tool and chamber 2 (CH2) refers to the subfab.

The results from the simulation for the entire tool group are given in both Table VIII and

Figure 9. In Table VIII, the percentage change in the statistics represents the average from ten

simulation replications. As it can be seen in this table, both the amount of wafers completed and

the utilization of the tool group was increased about 1% by the optimal PM schedule and with

respect to the heuristic PM schedule. The availability of the tool group was also increased in

0.68%. Evidently, the fab engineers did a very good job at scheduling PM tasks in this instance

also, but again, accomplishing this may be a very time-consuming job, and highly sensitive to

the ability of the particular individual(s) performing the scheduling. Fig. 9 illustrates the ratio of

utilization to availability (U/A) for each tool obtained for this simulation case study. As depicted

in this figure, in most of the cases when an optimized PM schedule is utilized a lower value

of the ratio U/A is observed (i.e., lower level bar), indicating an increase in tool availability;

therefore, an improvement in production performance. In this case, PM consolidations made by

the optimization resulted in an average of 4.77% increase in tool availability among the four

tools that experienced consolidation, with a maximum 6% availability increase for one tool.

This simulation study showed good results. Tool availability was increased significantly for

several tools, with a maximal increase of 6%. These benefits are due mostly to the consolidation

of subfab and normal PM tasks. It is worth mentioning that simplifications were needed to specify

the tool parameters for the purpose of the PM optimization. As indicated in the overview of

this case study given in section IV, the tools studied had three processing chambers. However,

specific data for each chamber was not available. Thus, for PM optimization purposes these

three chambers were specified as one while the subfab represented the second chamber. These

necessary simplifications reduced the possibility of finding PM consolidations and thus limited

the full potential of the PM scheduling optimization algorithm.


27

Table VIICOMPARISON OF HEURISTIC AND OPTIMAL PM SCHEDULES FOR CASE STUDY IV

PM Schedule (Day)

PM Name Heuristic Optimal

Tool5_CH1 17 16

Tool6_CH1 12 10†

Tool6_CH2 5 10†

Tool7_CH2 5 3

Tool8_CH2 16 2

Tool10_CH1 9 6

Tool19_CH1 3 4

Tool20_CH1 3 1

Tool21_CH1 16 144

Tool21_CH2 6 144

Tool22_CH2 6 16

Tool31_CH2 1 8

Tool32_CH2 1 11

Tool33_CH2 17 8

Tool34_CH1 9 10‡

Tool34_CH2 17 10‡

Tool35_CH1 8 6

Tool37_CH1 2 1

Tool39_CH1 15 12♦

Tool39_CH2 8 12♦

†, 4, ‡, ♦: Dates with consolidated PM tasks in a tool.

Table VIIIPERFORMANCE RESULTS FROM CASE STUDY IV: HEURISTIC VS. OPTIMAL PM SCHEDULE

Statistic Change (%)WCOMPS 0.94

AVAIL 0.68UTIL 1.00


28

Tool ID

U/A

90%

91%

92%

93%

94%

95%

32 31 37 12 20 14 11 19 10 13 5 8 35 22 7 39 34 33 6 21

Baseline U/A

Optimal U/A

Figure 9. Tool utilization/availability (U/A) improvement using Baseline and Optimal PM schedules, case study IV.

VI. CONCLUSIONS

The architecture and implementation of the software tool PMOST, which utilizes a PM

optimization algorithm for semiconductor manufacturing operations, has been described. To

demonstrate how PMOST can be utilized in practice to improve PM operations, we presented

results from four complex simulation case studies, based on real industrial data, that were

conducted on groups of semiconductor manufacturing tools, located at two separate fabs. Results

from these simulation experiments demonstrated that the PM optimization performed as well as,

if not better than, the heuristic PM policies obtained by the fab engineers, and in Studies III

and IV it performed noticeably better than the available fab’s baseline PM schedules. Software

implementations of PM optimal scheduling algorithms as PMOST, are therefore shown to be a

valuable decision support tool, which can be used by fab engineers to aid in PM scheduling, as

well as a component in efforts to automate the PM scheduling process. Results presented here

also demonstrated an increase in tool production. As such, the utilization of a PM optimization

algorithm can lead to significant improvements in marginal profits.

By presenting here an architecture and the corresponding software implementation of the PM

optimization algorithm, i.e., PMOST, we also aimed to provide guidelines and a template, as

well as experimental data, that can help in the adoption of these by others, and also perhaps


29

serve as the basis for generic third-party commercial tools. Moreover, the current version of

PMOST is subject to further improvements. For instance, PMOST currently does not use a

MDL for the optimization model and to generate the corresponding MPS file used by the LP/MIP

solver. However, future versions or modifications of PMOST could include interfaces with MDL

software to facilitate implementation and portability.

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