A Spine Layout Design Method For Semiconductor Fabrication Facilities Containing Automated Material Handling Systems
Taho Yang Brett A. Peters Department of Industrial Engineering Texas A&M University
December 19, 1996
This working paper is not to be copied, quoted, or cited without the permission of the authors. Address correspondence to Brett A. Peters, Dept. of Industrial Engineering, Texas A&M University, College Station, TX 77843–3131 or email to
[email protected]
A Spine Layout Design Method For Semiconductor Fabrication Facilities Containing Automated Material Handling Systems ABSTRACT A bay configuration arranged along a central spine and served by an automated monorail material handling system are common designs for the layout and material handling system in new semiconductor wafer fabrication facilities. This paper investigates the facility design problem in semiconductor fabrication facilities and proposes a procedure to determine the optimal spine layout design given a design of the material handling system. The procedure is explained and tested to demonstrate the use of the model for solving semiconductor facility design problems. The procedure is applicable for the important semiconductor industry as well as in other facilities that use a central spine layout configuration.
KEYWORDS: Layout, material handling, semiconductor fabrication facilities
A Spine Layout Design Method For Semiconductor Fabrication Facilities Containing Automated Material Handling Systems INTRODUCTION A bay configuration arranged along a central spine and served by an automated monorail material handling system are common designs for the layout and material handling system in new semiconductor wafer fabrication facilities (fabs). The resulting bay configuration provides many advantages in the semiconductor environment 1[ ]. In this approach, the facility is divided into a number of bays that contain processing equipment. Typically, the bays contain similar pieces of equipment. This situation creates a large amount of material flow between bays (interbay), since the semiconductor manufacturing process is highly reentrant. Overhead monorail systems have also been shown to be efficient in semiconductor fabrication environments due to their “clean” designs, gentle handling of wafers, and efficient use of overhead space [1]. For example, the installation of such a material handling system in Motorola’s Arizona MOS-12 fab significantly improved system inventory storage and distribution control and handling system reliability [2]. This bay configuration greatly simplifies the utility distribution systems. Due to having collocated processing equipment of the same type in a bay configuration, maintenance activities can often proceed without interrupting production activities. In addition, maintenance passages can be constructed between bays and separated from clean-room space. These features contribute to both reduced costs and simplified maintenance operations in the fabrication facility. Although other configurations are certainly possible, the semiconductor industry is slow to adopt these configurations due to the advantages available with the bay design. A newly built fab is usually equipped with an overhead monorail automated material handling system (AMHS) in conjunction with automated storage/retrieval systems (stockers) for interbay automation, as well as limited amounts of intrabay material handling automation 3]. [ Experimental results indicate the
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installation of an AMHS can significantly reduce shock and vibration during material movement compared with manual material handling methods, so consequently system yield is increased4]. [ An AMHS is usually associated with a spine layout configuration 3[ ], which forms a material flow loop within the facility as shown in Figure 1.
Crossover Turntable
1
6
4
3
Bay (Department) Travel Direction Material Handling System
7
2
9
5
8
Pickup/Deposit Point
Figure 1. Spine configuration The pickup/deposit (P/D) point of a bay is usually a stocker, which serves as both a work-in-process storage space and a wafer-lot transfer mechanism. The crossover turntable is used for changing travel directions. Judicious use of crossovers can significantly reduce the material handling time in large fabs. The impact of a layout design on the performance of a manufacturing system is widely acknowledged [5-6]. Because of the process layout of the semiconductor fab, the interbay material handling function is extremely important. Hence, a good layout design that gives adequate consideration to the automated material handling system design can significantly impact the performance of a fab in several areas, including facility operating cost, yield, work-in-process inventory levels, operator labor cost,etc. [7]. In this paper, a solution procedure, based on a modified quadratic set covering problem (QSCP) formulation, is proposed to solve the fab layout design problem with a spine configuration and an automated material handling system. This procedure jointly considers the facility layout and the material
2
handling system design. Given an AMHS design, including the specification of a set of crossover turntables, the proposed procedure determines the optimal fab layout.
LITERATURE REVIEW Most fab design problems use simulation approaches to provide system performance information about an existing fab layout and handling system design,e.g., Carpenter et al. [8] and Cardarelli and Pelagagge [1]. However, they do not provide information about how to create a good design. Langevin et al. [9] solved an undirected spine layout design problem by a two-step approach. The first step heuristically generates an ordered list of cells. Then, the second step transposes this ordered list into a net layout using an integer program formulation. Conceptually, this approach could be adapted to solve the spine fab layout design; however, it cannot take into account the following two important fab design factors. First, the ordered list from the first step could be an infeasible solution due to both the bay area and geometry constraints. Second, the integer program formulation from the second step neither enforces the exact cell geometry nor considers exact P/D point position. Therefore, building on this approach does not seem viable for the fab design problem. Kouvelis et al. [10] solved row layout problems with an equal area assumption. While this approach could be good for some manufacturing system design problems, it is not appropriate for solving the bay layout design problem due to lack of consideration for varying cell areas, a directed material flow path, and explicit P/D point position. Banerjee and Zhou [11] designed a directed, single loop machine layout by sequentially determining the flow sequence between machines and the layout of the machines. It solves an open-field type layout design which does not have a pre-determined layout configuration. Given a fixed single-loop material flow path, Wu and Egbelu 12] [ developed a procedure to determine an optimal layout design along this path. They assume that the P/D point of each department is located at the center of a department. The procedure arranges the departments continuously along the flow path. 3
However, it is unable to solve a fab design that has special structure such as: (1) the layout bays are separated into two rows as shown inFigure 1, (2) the P/D point may not be located at the department center, and (3) the flow path has crossover turntables to form shortcuts. The paper considers a directed material flow path as well as the special structure of a semiconductor fab configuration. It exploits this special structure to generate a bay layout along the spine configuration and generates a handling system design both of which are suitable for a semiconductor fabrication facility.
THE PROPOSED METHOD The proposed procedure formulates the spine fab layout design problem by exploiting the special structure found in semiconductor fabs. It then develops a solution procedure for this formulation. Given a set of shortcuts for the material handling system, the procedure determines the optimal layout design. Additionally, the procedure can iterate over alternative sets of shortcuts searching for the best overall solution. The background sectionprovides fundamental knowledge that is used to develop the proposed procedure and is followed by a detailed discussion of the model formulation in QSCP formulation section.
Background When modeling a fab layout with a spine configuration, three interesting aspects are noted. First, the material handling system can be modeled as a single loop material flow path with shortcuts. The locations of shortcuts are often specified a priori; for example, it could be a shortcut in the center, or two shortcuts to divide the AMHS loop into thirds. In developing the formulation, we assume that the set of shortcuts is known. However, the solution procedure can iterate over alternative shortcut designs to allow comparisons of the different alternatives, as shown in the empirical illustrations section. Second, the bay layout arrangement requires that each department have exactly one boundary on the center spine of the floor space in order to access the AMHS, which implies that exactly one department can be located in each bay.
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Finally, the bay height is usually constant across the entire length of the facility. However, the upper and lower row heights could be different. These heights are design parameters that are based on the desired bay configurations and available floor space and, hence, are specified prior to solving the layout problem.
QSCP Formulation The quadratic set covering problem (QSCP) formulation for a layout design problem13] [ can be extended to accurately model the layout design problem with a spine material handling system configuration. The typical QSCP approach divides the available floor space and departments into small equal-size blocks. When this approach is applied to the fab layout problem described in this paper, the floor space is divided intoequal area unit rectangular blocks. Each block extends the full height of the bay, with the width of the unit blocks depending on the height of the row. Each block is assigned a distinctive value as its address. Figure 2 illustrates the address assignment, which is used to determine the set of blocks that are occupied by each candidate location for a department. Note that, for modeling convenience, the numbering of the address assignments follows the AMHS flow direction with the upperleft corner block as the starting block. The width of a unit-rectangular block in the upper row is assumed to be 1. This width can be easily achieved by normalizing the scale. Then, the width of the unit-rectangular block in the lower row is b= H1/H2.
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Address assignment 1
H1
2
3
4
5
Crossover Turntable AMHS
H2
10
9
8
7
6
Unit block
Figure 2. Address assignment for spine configuration The position of a P/D point of a department is represented by its distance from the starting block boundary which is part of the department boundary; hence, it is the distance from the left-hand side of the starting block when the department is located in the upper row, while it is the distance from the right-hand side of the starting block when the department is located in the lower row. In addition, a P/D point is located on the lower side of a department when the department is located on the upper row of the floor space while the P/D point is located on the upper side of a department when the department is located on the lower row of the floor space. Figure 3 illustrates example departments and P/D point locations. 0.5
: P/D Point
Department 1
Department 2
Department 3
Figure 3. Example departments A department’s candidate location is represented by its starting block, area, and P/D point position. The starting block is the one with the smallest address number and the area is represented by the number of unit-rectangular blocks. For example, when the starting point of department 1 inFigure 3 is block 1 (from
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the floor space in Figure 2), then the blocks occupied by department 1 are blocks 1, 2, and 3. The P/D point is at 0.5 for this candidate location. This example forms one candidate location for department 1. There is an additional location with P/D point at 2.5 and starting point at block 1 that comes from flipping the department horizontally. With block 2 as the starting block of department 1, there are two additional candidate locations for the department. Continuing in this manner, all possible candidate locations for department 1 can be enumerated. Note that blocks 4 and 5 are not valid starting blocks for department 1 because the department will extend beyond the floor space boundary. Note that there is a minimum clearance between a crossover turntable and the nearest P/D point, as well as between two crossover turntables. This clearance is due to the hardware constraints from particular material handling system technologies. Hence, a candidate location for a department whose P/D point is less than the minimum clearancedistance from the nearest crossover turntable must be excluded from the candidate location set. The addition of a crossover turntable creates a shortcut in the AMHS loop. The flow distance from the P/D point of a department to the P/D point of another department, in a loop with shortcuts, is the shortest path in this flow network. For example, let department 1 fromFigure 3 use blocks 1, 2, and 3 from Figure 2 with the P/D point being at 0.5, and let department 2 fromFigure 3 use blocks 9 and 10 from Figure 2 with the P/D point being at 1.0. Assume that there is a shortcut located at 2.5 distance units from the left boundary of block 1 in Figure 2. Let a be the fixed distance across the center spine and assume thatb is equal to 1. Then, the flow distance from the candidate location of department 1 to the candidate location of department 2 can be formulated simply as network flow problem and can be efficiently solved using a shortest path algorithm. The resulting network flow is illustrated inFigure 4 and its formulation can be derived using equations 1( ) − (3), which are discussed below.
7
2.0
3
1 1.5+a
a
5.0+a
2 1.5
4
Figure 4. Shortest path network flow example In general, the network flow formulation is represented asG = (V, E), where V and E are the set of nodes and arcs, respectively. The set of nodes,V, consists of the P/D points of each department and the endpoints of each shortcut. The set of arcs, E, connects adjacent nodes along the material handling loop and connects the two nodes representing the shortcut. The following additional notation is needed to develop the network formulation. Let xij : the flow on the directed arc (i, j) cij : the flow distance for arc (i, j) Then, the shortest path problem is formulated as follows. Minimize
∑
(1)
cij xij
( i , j )∈E
st:
−1 if j = dropoff point xij − ∑ x ji = 1 if j = pickup point ∑ i ∈V i ∈V 0 otherwise
0 ≤ xij ≤ 1
∀(i, j) ∈ E
∀j ∈ V
(2)
(3)
Since the shortest path network formulation is quite straight forward and its solution is well known, it is not discussed in more detail here. Let the directed flow distance from thekth candidate location of department i to the lth candidate location of departmentj be δikjl. Then, δikjl is the solution of the shortest path from the network flow formulation in equations 1) ( − (3).
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The following additional notation is needed to represent the QSCP formulation for the optimal spine layout design problem given an AMHS design with shortcuts. N = the total number of departments in the layout i, j : indices for departments; i, j = 1,…,N t : index for the unit rectangular block in the floor space uij = the directed flow density from departmenti to department j εij = the cost per unit distance for a unit of flow from departmenti to department j I(i): the set of candidate locations of departmenti k : index for candidate locations;k = 1,…,I(i) ξik = 1 if department i is assigned to its kth candidate location; otherwise it is equal to 0 Ji(k): the set of blocks occupied by departmenti if it is assigned to its kth location αikt = 1 if t ∈ Ji(k); otherwise it is equal to 0 The integrated design problem can then be formulated as follows. N
Minimize
N
I (i ) I ( j )
∑ ∑ ∑ ∑ε
u δ ikjl ξ ik ξ jl
(4)
ij ij
i =1 j =1 k =1 l =1
I (i )
Subject to
∑ξ
ik
=1
∀i
(5)
∀t
(6)
for i = 1,..,N and ∀k ∈ I(i)
(7)
k =1
N
I (i )
∑ ∑α
ikt
ξ ik ≤ 1
i =1 k =1
ξik ∈ {0, 1}
In the above formulation, equation (4) is the objective function of the optimal spine layout design problem. Constraint (5) ensures that exactly one candidate location will be chosen for each department. Constraint (6) ensures that a block can be occupied by at most one department in the final layout. Equation (7) specifies the variable bounds.
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Using the specific characteristics of the fab layout design problem, efficiencies in modeling and solving the problem can be obtained. In particular, we have used the actual AMHS design configuration to compute the distances between departments in the layout. These distances are then incorporated into the QSCP formulation to determine the assignment of departments to bays to minimize the material handling cost. In this paper, the QSCP formulation is solved by an embedded nonlinear integer programming solver in a commercial code, LINGO® [14]. It can also be solved by a standard branch-and-bound based linear programming solver. This is achieved through the introduction of one additional variable to substitute each quadratic term in the objective function as shown in equation(8), and two additional constraints to warrant the logical relationship between the quadratic term and its linearized variable as shown in equations9)( and (10) [15]. Yikjl = ξikξjl
(8)
ξik + ξ jl − Yikjl ≤ 1
(9)
−ξik −ξ jl + 2Yikjl ≤ 0
(10)
Our preliminary experiments indicated that the increase in problem size more than offset the efficiencies gained by using the linear optimizer for solving the modified formulation; therefore, the nonlinear optimizer is directly used to solve the problems in this paper. Since the QSCP is in the class of an NP-hard problem [16], it will be computationally inefficient to solve a large scale fab design problem,e.g., a 25-bay problem. Most of the current fab designs involved 10 to 20 bays and therefore this reduced QSCP approach seems be reasonable. Other, more efficient, solution techniques for large scale problems will be investigated as part of our future research efforts.
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EMPIRICAL ILLUSTRATIONS In order to demonstrate the proposed procedure, an example problem is generated. In this example, bay sizes and P/D point positions are generated using problem data in Carpenteret al. [8] as a guide. Since there is no interbay flow density information in Carpenteret al. [8], the interbay flow density matrix is adopted from an example industrial study contained in Meller 17]. [ The area and P/D point position information for each department as well as the interbay flow density matrix are summarized in the Appendix. This example problem assumes that: (1) bothH1 and H2 are equal to 4 distance units; (2) the length between the two bay rows is 1 distance unit; (3) the minimum clearance distance between a P/D point and a crossover turntable is 0.4 distance units. The proposed procedure is coded in C programming language and is implemented on an IBM RS/6000 computer. The shortest path network flow formulation is solved using a special network optimizer provided by CPLEX® [18] in a callable library. In general, the location of a shortcut is input information for the procedure. In this study, four cases are considered. The first case has no shortcuts in the material flow path. The second case has only one shortcut located at the center of the floor width (7.5 distance units from left boundary). The third case has two shortcuts located at 5.0 and 10.0 distance units from the left boundary. Finally, there are three shortcuts for case 4, located at 4.0, 8.0, and 12.0 distance units from the left boundary. The resulting material handling costs are shown inTable 1. Figure 5 through Figure 8 show the resulting facility layout designs for each of the four alternative material handling system designs. Table 1. Material handling costs for example problems Number of shortcuts
0
1
2
3
Material handling cost
3782
3702
2794
2572
11
1 2
3 4
7
5 6
6
5
7
8
9 10 11 12 13 14 15
9
1
10
2
8
3
4
11
30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
Figure 5. Optimal layout design - no shortcut 1 2
3 4
5 6
7 8
9
10
6
5
1
9 10 11 12 13 14 15
7
2
8
3
4
11
30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
Figure 6. Optimal layout design - 1 shortcut 1 2
3 4
9
10
6
5 6
5
7 8
9 10 11 12 13 14 15
7
1
11
3
2
8
4
30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
Figure 7. Optimal layout design - 2 shortcuts
12
1 2
3 4
7
5 6
7 8
6
5
9 10 11 12 13 14 15
9
1
11
10
8
2
3
4
30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
Figure 8. Optimal layout design - 3 shortcuts As expected, the material handling costs decrease as the number of shortcuts increases, although not necessarily in a linear manner. This relationship is illustrated for the example problem inFigure 9. A facility planner can then determine whether or not the reduction in material handling costs outweighs the investment cost of additional crossover turntables.
4000 3782 3702 Costs
3500
3000
2794 2572
2500 0
1
2
3
Number of shortcuts Figure 9. Material handling costs versus number of shortcuts
CONCLUSIONS The proposed procedure successfully solves an fab layout design problem with a spine configuration given a predetermined AMHS flow path with shortcuts. It can also be adapted to solve an intrabay layout design problem, with a spine-type material handling system. The resulting design will be able to improve
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the system performance and help justify the high investment costs for a semiconductor fabrication facility. The computational results with the proposed procedure indicate that it is a viable solution method for use during the design stage of a semiconductor fab. Currently, research efforts are aimed at developing a design procedure to integrate a shortcut design with a layout design problem, in that a candidate shortcut becomes a decision variable with fixed cost for installing a crossover turntable. When there is no specific desired shortcut position, the integrated layout and material handling system design procedure is conceptually better than the sequential design of a material handling system and a facility layout. Additional research efforts e.g., ( [19]) are being directed at this approach.
REFERENCES 1. Cardarelli, G. and Pelagagge, P.J., “Simulation Tool for Design and Management Optimization of Automated Interbay Material Handling and Storage Systems for Large Wafer Fab”,IEEE Transactions on Semiconductor Manufacturing, Vol. 8, No. 1, 1995, pp. 44-49. 2. Davis, J., and Weiss, M., “Addressing automated materials handling in an existing wafer fab”, Semiconductor International, June, 1995, pp. 125-128. 3. Weiss, M., “Semiconductor factory automation”,Solid State Technology, Vol. 39, No. 1, pp. 89-96. 4. Wowk, V. and Billings, R., Vibration and shock from manual and automated material movement, SEMATECH Technology Transfer Document No. 94102603A-GEN, SEMATECH, Austin, TX, November, 1994. 5. Allegri, T.M., Material Handling: Principles and Practices, Van Nostrand, New York, NY, 1984. 6. Francis, R.L., McGinnis, L.F., and White, J.A., Facility Layout and Location: An Analytical Approach, Prentice-Hall, Englewood Cliffs, NJ, 1992. 7. Weiss, M., “Using flexible factory automation systems to allow alternative fab layouts”,Semicon Southwest, October, 1995. 8. Carpenter, B., Gibson, R., and Pierce, N., Generic interbay automated material handling system discrete-event simulation, SEMATECH Technology Transfer Document No. 93011441A-GEN, SEMATECH, Austin, TX, January, 1993. 9. Langevin, A., Montreuil, B., and Riopel, D., “Spine layout design”,International Journal of Production Research, Vol. 32, No. 2, 1994, pp. 429-442.
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10. Kouvelis, P., Chiang, W.-C., and Yu, G., “Optimal algorithms for row layout problems in automated manufacturing systems”, IIE Transactions, Vol. 27, 1995, pp. 99-104. 11. Banerjee, P., and Zhou, Y., “Facility layout design optimization with single loop material flow path configuration,” International Journal of Production Research, Vol. 33, No. 1, 1995, pp. 183-204. 12. Wu, C. T., and Egbelu, P. J., “Concurrent design of shop layout and material handling”, Proceedings of the International Material Handling Research Colloquium, Grand Rapids, MI, June 13-15, 1994, pp. 119-140. 13. Bazarra, M.S., “Computerized layout design: a branch and bound approach”, AIIE Transactions, Vol. 7, No. 4, 1975, pp. 423-438. 14. LINGO User’s Manual, LINDO System Inc., Chicago, IL, 1994. 15. Watters, L.J., “Reduction on integer polynomial programming problems to zero-one linear programming”, Operations Research, Vol. 15, 1967, pp. 1171-1174. 16. Sahni, S., and Gonzalez, T., “P-complete approximation problem”,Journal of ACM, Vol. 23, No. 3, 1976, pp. 555-565. 17. Meller, R.D., Layout Algorithms for Single and Multiple Floor Facilities, Ph.D. Dissertation, Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI, 1992. 18. CPLEX user’s manual, Version 3.0, CPLEX Optimization Inc., Incline Village, NV, 1994. 19. Peters, B.A. and Yang, T.H., “Integrated facility layout and material handling system design in semiconductor fabrication facilities”, Working Paper, Dept. of Industrial Engineering, Texas A&M University, College Station, TX, 1996.
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APPENDICES
A1. Department area information for the example problem Department Area (x4) P/D offset
1 3 1.5
2 2 1.0
3 4 1.0
4 2 1.0
5 3 1.5
6 4 1.5
7 2 1.0
8 3 1.5
9 2 1.0
10 2 1.0
11 3 1.0
A2. From-to departmental flow matrix for the example problem From\To 1 2 3 4 5 6 7 8 9 10 11
1 0 0 0 0 0 0 0 0 0 0 146
2 10 0 0 0 10 0 0 0 0 0 0
3 0 10 0 0 0 10 0 0 0 0 0
4 0 0 10 0 0 0 0 0 0 0 0
5 140 0 0 0 0 0 0 0 0 0 0
16
6 90 0 0 0 0 0 0 0 0 0 0
7 20 0 0 0 40 0 0 0 0 0 0
8 0 0 0 0 0 0 10 0 0 0 0
9 40 0 0 0 0 20 0 0 0 0 0
10 0 0 0 0 20 0 0 0 20 0 0
11 0 0 0 4 0 0 0 10 0 20 0
