IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 28, NO. 3, AUGUST 2015
367
A Practical Two-Phase Approach to Scheduling of Photolithography Production Andy Myoungsoo Ham and Myeonsig Cho
Abstract—The introduction of real-time dispatching (RTD) to semiconductor manufacturing has greatly improved productivities for the last two decades. Recently, researchers have revealed that data available and complexity of the algorithms to the dispatcher are limited—in effect the dispatcher has tunnel vision, dutifully rank ordering the lots in the queue, but oblivious to what is happening around it, which leads to the poor results compared to other modern optimization-based approaches. However, the author admits that most semiconductor manufacturing companies are still using RTD not only as a last-minute loading-check, but also as a scheduling logichub. Here comes a business need of improving the brainpower of RTD by using the optimization technologies. In this paper, we propose an integration of RTD with linear programming technique in photolithography area by using two-stage modeling. The transportation model at the first stage finds the least-cost means of assigning jobs to reticles and machines. Then, the sequencing module provides an expository sequencing decision by inheriting the same dispatching business rules. The experimental study demonstrates the proposed method can reduce the count of reticle delivery by 40.5% in a low-mix fab instances. Index Terms—Litho, programming.
reticle,
scheduling,
mixed
integer
I. I NTRODUCTION Y 2016, the minimum capital expenditure budget needed to justify the building of a new fab will range from $8 billion to $10 billion for logic, $3.5 billion to $4.5 billion for DRAM and $6 to $7 billion for NAND flash, according to Gartner [1]. Furthermore, by 2020, current cost trends will lead to an average cost of between $15 billion and $20 billion for a leading-edge fab, according to the report. Owing to this tremendous capital expenditure, the great advancement in automation and robotics can be well noticed in semiconductor manufacturing industry. Automatic material handling system (AMHS) replaces a manual delivery, automatic real-time dispatching (RTD) replaces a manual decision, and advanced process control (APC) replaces a manual process control. This trend of computerization would be peak in coming years as Frey and Osborne [2] estimated 47% of U.S. employment is replaced by automation and robotics in the
B
Manuscript received January 2, 2015; revised June 1, 2015; accepted June 8, 2015. Date of publication June 30, 2015; date of current version July 31, 2015. A. M. Ham is with Texas A&M University—Commerce, Commerce, TX 75429-3011 USA (e-mail:
[email protected]). M. Cho is with Kyonggi University, Suwon 443-760, Korea. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSM.2015.2451512
next twenty years. How could this estimation be true to semiconductor industry considering the past matchless accomplishment in automation? In order to provide an answer, we now zoom in our focus on a high-precision automatic RTD dispatching solutions. Although the industry successfully shifted a manual dispatching to an automatic decision process, the dispatching algorithm of computer program is far from perfection so that the industry creates remote operating center (ROC) [3] where highly skilled engineers override the automatic decision often. The highest manual intervention occurs in lithography area due to its complexities. Hereby, the motivation of this paper is to provide a highprecision automatic dispatching/scheduling solutions for the lithography area in semiconductor manufacturing empowered by Mixed Integer Programming (MIP), aiming to generate an efficient solution in a short-time. All jobs which are currently awaiting and future arriving to lithography area are both considered. The processing time of each layer on machine per each job is known. Acknowledging that most semiconductor manufacturing companies are still using RTD not only as the last-minute loading-check, but also as a business logic-hub in lithography area, we improve the brainpower of RTD by using MIP. II. P REVIOUS R ELATED W ORK We look into the literatures from the three different angles: dispatching, scheduling, and hybrid method. A. Dispatching Approaches to Lithography Production Researchers have noticed that no dispatching rule is known to be globally better than other. Their efficiency depends on the characteristics of the system, operating condition and their objectives. Furthermore, the development of customized dispatching rules is usually a tedious procedure requiring a significant amount of expertise, coding-effort and time. Therefore, researchers applied several machine-learning algorithms in order to dynamically generate and customize dispatching rules [4]–[7]. However, those approaches are not much applicable to lithography area due to its unique constraints, which will be discussed in the later section. Dispatching rules, which have the tunnel vision [8], simply cannot generate the comprehensive dispatching decisions. B. Scheduling Approaches to Lithography Production INTEL Corporation [9] reports a ground-break work with a remarkable improvement of 26% cycle time reduction in
c 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. 0894-6507 See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
368
IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 28, NO. 3, AUGUST 2015
lithography production after deploying linear programming based scheduling system. They define a dual role of realtime dispatching system: 1) for less complex areas, dispatching serves as the primary logic engine to determine lot-machine assignments in real-time; 2) for complex areas, the scheduling system serves as the primary logic engine with dispatching as the last set of preflight checks before the decisions are executed. However, we are aware that the so-called less complex areas such as Deposition, Planarization, Oxidation, and Implantation also have a great need of improving the brainpower of dispatching system. The critical factors to be considered in those areas include, but not be limited to, chamber conflict avoidance, sequence dependent setup minimization, as well as job priority, queue-time, production target, etc. AMAT [10] proposes the constraint-programming (CP) based lithography scheduler and records over 2% increase of wafers out and 1% increase of machine utilization in a real deployment. Although the results are not impressive and the details of the mathematical model are not provided, their cutting-edge approach to the lithography scheduling problem should be highly regarded. CP is a new programming paradigm wherein relationships between variables are stated in the form of constraints. CP began from artificial intelligence world. While MIP has the focus on the objective function and its optimality, CP focuses on the constraints and their feasibilities so that it promises a fast run-time. Yan et al. [11] discover that the decision space is difficult to delineate because of certain complicating constraints in lithography. A two-phase approach is therefore developed. In the first phase, a simplified problem with those complicating constraints dropped is efficiently solved to establish ranges of decision variables. The problem with the full set of constraints is then solved in the second phase with a much reduced decision space. This two-phase approach generated a nearoptimal schedule in 27 seconds in their third example, which has 7 layers, 11 machines, and 71 reticles. Although the results (5.5% relative gap) is promising, the CPU time seems to be worrisome specially when there exists much larger number of layers and machines in practice. Doleschal et al. [12] examine the benefits of a MIPbased reticle allocation in comparison to a classical rule-based heuristic. The experimental study shows very large benefits. However, they find implementing their approach in the real fab comes along with many integration challenges, resulting from not only their complex three-stage MIP models but also the data-interface between RTD and MIP models. Cakici and Mason [13] study a photolithography scheduling problem in a parallel machine environment and set the weighted sum of completion times as a sole objective. We also use this same objective as one of our objective elements. They represent the system as a disjunctive programming formulation, which is extremely slow when it deals with a large size of problem. The very limited size of problems (number of machine
