Optimal Preventive Maintenance Scheduling in Semiconductor Manufacturing Systems: Software Tool & Simulation Case Studies

Transcription

1 1 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 Optimization 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 José A. Ramírez-Hernández, and Emmanuel Fernandez are affiliated with the Department of Electrical and Computer Engineering, University of Cincinnati, OH , USA ( s: ramirejs@mail.uc.edu; emmanuel.fernandez@uc.edu; address: 822 Rhodes Hall, University of Cincinnati, PO Box , Cincinnati, Ohio Jason Crabtree is with Integral Analytics Inc., Cincinnati, OH, ( jason.crabtree@integralanalytics.com). Xiaodong Yao is with SAS Institute, Inc., ( xiaodong.yao@sas.com). Michael C. Fu and Steven I. Marcus are with the Institute for Systems Research, University of Maryland, College Park, MD 20742, USA, s: {mfu; marcus}@isr.umd.edu. Mani Janakiram is with Intel Corp., Chandler, AZ, USA mani.janakiram@intel.com. 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 ( nipa.patel@amd.com; address: 5204 E. Ben White Blvd. M/S 563, Austin, TX 78741; phone: ; fax: ).

2 2 I. INTRODUCTION In semiconductor manufacturing systems, Preventive Maintenance (PM) is performed by taking 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 implementation 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.

3 3 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 noncalendar 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 noncalendar 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)

4 4 formulation [3], [4], [5] at the lower level, as depicted in Fig. 1 below. Objective Failure Dynamics Demand Pattern Upper MDP PM Policy WIP Lower MIP PM Schedule Constraints 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 solutions, 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 T p ( ) ρ M i max b i V i (t) c I i I i (t) c l i a l i(t), (1) t=1 i=1 l=1

5 5 T p max MIP Objective 2 ( ) ρ M i b i X i (t) c l i a l i(t), (2) t=1 i=1 l=1 where, using the same notation as in [3], [4], [5], T p represents the number of time units or periods in the PM scheduling horizon, M is the number of tools (or tool chambers), V i (t) is availability of tool i in period t, b i is the profit coefficient for availability of tool i, I i (t) is the workload level (i.e., WIP) for tool i in period t, c I i is the cost coefficient for inventory in tool i, ρ i is the number of PM tasks on tool i, a l i(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 c l i is the cost of performing PM task l on tool i. Moreover, in MIP Objective 2 the quantity X i (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.

6 6 Tool Tool 3 Warning Due Late Tool 2 Tool 1 Present Schedul ing Horizon Time (day) 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 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.

7 7 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. A set of tools Initial schedule (PM tasks) Scheduling horizon Projected Incoming WIP Cost Parameters and constraints Available resources PM Optimization Scheduling Model/algorithm Optimized Schedule Estimated Availability Estimated 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

8 8 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 programming 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

9 9 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].

10 10 PM Optimal Scheduling Tool (PMOST) pmost_ui.exe START User input -Scheduling horizon -Tools family -Number of Technicians pmost.exe Read Input Data Write MPS file MPS file -Tool data files Baseline PM -PM data files Schedule -PM schedule -Estimated WIP data files -Conversion of PM Schedule to calendar-time format (conv2cal.exe) Fab Simulation LP/MIP SOLVER Parse Solution Solution file Output: PM Orders Solution file in calendar-time format 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.

11 11 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.

12 12 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

13 13 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 downtimes 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

14 14 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.

15 15 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 considered 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.

16 16 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

17 17 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

18 18 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 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 20 Table I COMPARISON 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 II PERFORMANCE RESULTS FROM CASE STUDY I: PERCENTAGE CHANGE FOR BASELINE VS. OPTIMAL PM SCHEDULE Statistic Max.(%) Min.(%) Avg. (%) WCOMPS AVAIL UTIL 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 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,, 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 22 Table III COMPARISON 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 3 7 Tool18_CH2 3 7 Tool19_CH1 5 1 Tool19_CH2 5 1 Tool20_CH1 1 2 Tool25_CH1 4 4 Tool25_CH2 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 IV PERFORMANCE RESULTS FROM CASE STUDY II: HEURISTIC VS. OPTIMAL PM SCHEDULE Statistic Change (%) WCOMPS 0 AVAIL 0.03 UTIL 0.01

23 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 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 deposition 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,, 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 25 Table V COMPARISON 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 4 MDep2_PMW1 5 4 MDep3_PMW3 5 2 MDep3_PMW1 3 2 MDep4_PMW3 4 2 MDep5_PMW3 7 5,, : Dates with consolidated PM tasks in a tool. Table VI PERFORMANCE RESULTS FROM CASE STUDY III: PERCENTAGE CHANGE FOR BASELINE VS. OPTIMAL PM SCHEDULE Statistic Max.(%) Min.(%) Avg. (%) WCOMPS AVAIL UTIL 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,,, and. The first column of the table provides the modified PM names. Each PM name

26 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.