An optimal yield mapping approach for the small and medium sized liquid crystal displays

DOI 10.1007/s00170-004-2266-5 O R I G I N A L A R T I C L E

Peng-Sen Wang · Chao-Ton Su

An optimal yield mapping approach

for the small and medium sized liquid crystal displays

Received: 23 February 2004 / Accepted: 18 May 2004 / Published online: 2 March 2005 ©Springer-Verlag London Limited 2005

Abstract The ability to improve yield in the manufacturing process is an important competitiveness determinant for LCD factories. The TFT-LCD contains three major manufacturing sec-tors: the array, cell, and module assembly processes. The yield loss from the cell process is one of the most critical steps. To increase the cell process yield, more conforming LCD panels must be produced from one glass substrate. The sorter is a robot used in LCD manufacturing systems to achieve higher yield for matching TFT and CF plates. This sorter contains several ports that can transfer CF glasses from CF cassettes to match TFT glasses. In this paper, the Hungarian method is applied to solve the yield-mapping problem with the sorter. This method provides an optimal solution to improve the cell process yield.

Keywords Hungarian method· Liquid crystal display (LCD) · Matching· TFT-LCD · Yield mapping

1 Introduction

Liquid crystal displays (LCDs) applications encompass a var-iety of consumer electronics including: personal digital assistants (PDA), cellular phones, digital cameras, computers, notebook computers, flat panel televisions, etc., because of its unsurpassed features in device size and radiation prevention compared with the conventional cathode radiation tube (CRT) device. LCDs can be divided into three major products: twisted nematic (TN), su-per twisted nematic (STN), and thin film transistor (TFT). The most widely used LCD for high information content displays is the TFT-LCD. In the 1980s, market demand forced a tran-P.-S. Wang

Department of Industrial Engineering & Management, National Chiao Tung University,

Hsinchu, Taiwan C.-T. Su (u)

Department of Industrial Engineering & Engineering Management, National Tsing Hua University, Hsinchu 300, Taiwan

E-mail: [email protected] Tel.: +886-3-5742936 Fax: +886-3-5722204

sition from twisted nematic displays to super twisted nematic displays. This higher-performance display is expected to grow rapidly and have a major market share in the display market. This led to today’s amorphous silicon and low temperature poly sil-icon (LTPS) TFT-LCD. LTPS production technology is aimed at manufacturing small and medium sized LCD panels and has gathered much attention from many display manufacturers be-cause it has several advantages over amorphous displays, e.g., built-in driver circuits, high-definition, and high-aperture ratio.

The manufacturing process for LCD may be likened to mak-ing a sandwich. The bottom substrate is the TFT array. The TFT fabrication process sequence is a series of deposition and etching sequences, as with integrated circuit fabrication. The top sub-strate is the color filter plate. Color filter (CF) glasses are usually purchased from outside vendors. A LCD cell process consists of one TFT and color filter line each, usually in parallel production steps. Both the TFT plate and color filter plate are first coated with a thin layer of polyimide [1]. The polyimide layers are then rubbed in prearranged directions to align the liquid-crystal direc-tor. The color filter plate is then sprayed with spherical plastic spacers. An epoxy seal material is applied to the color filter plate, which is then aligned to the TFT plate. The two substrates are laminated together and the glass plate is scribed to the appropri-ate display panel. A liquid crystal mappropri-aterial is injected into the gap between the glass plates to complete the assembly operation. The final step is module assembly, involves applying polarizers to both sides of the liquid-crystal cell and integrating the periph-eral drive IC circuit onto the substrate for driving the display. A typical LTPS process is shown in Fig. 1. For a concise pre-sentation, readers are referred to O’Mara [2] and Blake [3, 4] for a detailed discussion of the manufacturing process.

The yield loss occurs in three major manufacturing sectors: array, cell, and module assembly processes; however, the post-mapping yield loss from the cell process is one of the most critical steps. This paper aims to propose an efficient method to improve yield rate in the cell process.

2 Yield mapping

A given substrate (plate or glass) could contain different numbers of cells (panels) depending on its embedded cell size, e.g., one piece of the PDA display. The size of a cell varies from the small size used in a camera viewfinder to the large diagonal panel used in a television display. The cell mapping process combines one TFT and one CF plate to form both sides of a LCD. This mapping process has a one-to-one match between the relative positions of cells in both plates. A matched LCD cell is “good” only when both the CF and TFT cells are “good”. When one of the cells from either the TFT or CF plate is bad, the matched LCD cell is bad and results in a post-mapping yield loss. The cell mapping information is shown in Fig. 2.

The sorter is a robot used in LCD manufacturing systems to achieve higher yield for matching TFT and CF plates. This sorter usually contains r ports that can handle the r−1 CF cassettes and

Fig. 2. The cell mapping

Fig. 3. Plates matching (A plate has 30 panels)

r− 1 TFT cassettes matching problem. Assume that there are N TFT and N CF cassettes in queue. Each cassette contains typic-ally 20 glasses (plates). The mapping process first places three CF cassettes and one empty cassette onto a sorter to matching in-dicated TFT cassettes for a sorter with four ports. Assume that sixty plates from the TFT cassettes and CF cassettes are num-bered T1, T2, . . . , T60 and C1, C2, . . . , C60, respectively. The

matching process chooses one TFT plate (Ti) and one CF plate (Cj) to form a matched LCD plate. This step is called “plates-matching” as illustrated in Fig. 3.

In practice, the large-sized displays usually scribe glass in advance and then into cell process. For the small and medium size LCD panels, scribing glass in advance and then during the cell process produces lower economy of scale. For example, per plate contains 50 panels scribing glass in advance that must per-form the cell process 50 times. An efficient method is desired to improve yield rate for the small and medium size LCD panels.

3 Proposed approaches

This research proposes a linear programming (LP) formulation to maximize the yield rate through an optimal matching process to obtain a greater number of acceptable LCD panels to improve the cell process yield. The results were benchmarked against two heuristics used in practice. The two heuristics will be discussed first followed by the proposed LP approach.

A. Random mapping

The simplest method is to match TFT and CF using a random approach. This approach randomly chooses a pair of plates into the cell process and does not need to use the sorter. The advan-tages of random matching are that it is quick and easy to perform. A possible disadvantage is that not considering glass yield infor-mation might lead to LCD scrap and yield losses.

B. Greedy algorithm

A greedy algorithm makes a locally optimal choice and hopes with a globally optimal solution. Hence, the algorithm does not always yield the optimal solution. We discuss the greedy algorithm for plates-matching for a sorter with four ports as follows:

Step 1: Sort the sixty TFT plates in descending order by yield rate.

Step 2: Based on the sequence from step 1, perform the “best” plates-matching sequentially. “Best” indicates the high-est yield. For example, the first TFT plate has the highhigh-est priority to choose the “best” matching CF plate from those 60 CF plates. When a TFT plate and a CF plate are chosen, their post-mapping yield is a direct compound as shown in Fig. 2. The second TFT plate then chooses its “best” matching CF plate from those remaining 59 plates. This matching procedure continues until the last TFT plate is matched with the last CF plate.

C. Linear programming formulation

Linear programming (LP) involves restrictions or constraints for determining optimal solutions to problems. An assignment prob-lem is a special type of linear programming probprob-lem. The usual assignment problem is given the same number of jobs and ma-chines. Each assignment, assigning the job to the machine, has a fixed profit. This problem assigns each machine a unique job such that the sum of the profit of the machines is maximum. Without loss of generality, we will refer to jobs as TFT plates, machines as CF plates, and the profit as the matching yield for the TFT and CF plate. Therefore, the plates-matching can be for-mulated as a linear programming problem. Notation is defined before the LP formulation as follows:

n= The cell quantities of plate (substrate).

r= The number of ports of the sorter.

fij= The mapping function represents the matching yield for the ith plate from TFT cassettes and the jth plate from CF cassettes. Let two ordered n-tuples

p= (p1, p2, . . . , pn) and q = (q1, q2, . . . , qn) repre-sent panels of TFT plate and corresponding CF plate. Where p1, p2, . . . , pn, q1, q2, . . . , qn = 0 (bad panel) or 1 (good panel). Then fij= p ·q = p1q1+ p2q2+. . .+

pnqn.

xij= 1 When the ith plate from TFT cassettes is matched with the jth plate from CF cassettes. Otherwise, xij = 0. This is the decision variable from the plates-matching LP for-mulation.

The plates-matching problem can then be formulated as Eqs. 1– 4. Maximize Z= 20
(r−1) i=1 20
(r−1) j=1 fijxij (1) Subject to 20
(r−1) i=1 xij= 1 for j = 1, 2, · · · , 20(r − 1) (2) 20
(r−1) j=1 xij= 1 for i = 1, 2, · · · , 20(r − 1) (3) and xij∈ {0, 1} (4)

Equation 1 is the objective function for maximizing the yield when the TFT cassettes and the CF cassettes are chosen. Equa-tion 2 assures that each CF plate has exactly one matching TFT plate. Equation 3 assures that each TFT plate has exactly one matching CF plate. Equation 4 is the {0, 1} constraint for the de-cision variables. Using Eqs. 1– 4, we can solve various ports in the post-mapping yield problem.

Although the proposed LP approach formulation is a combi-natorial Problem, it has the typical assignment problem structure that can be solved efficiently using a special algorithm, the Hun-garian method. In the HunHun-garian method a one-to-one match is

required. The first Hungarian method for the assignment problem was proposed by Kuhn [5] in 1955. Another approach to solv-ing the assignment problem is referred to Hung and Rom [6]. Readers are referred to Taha [7] and Winston [8] for a detailed discussion of the assignment problem and Hungarian method. In the literature, the Hungarian method has been applied to solve matching problems. For example, Hsieh et al. [9] apply the Hun-garian method to solve a bipartite weighted matching problem for online Chinese character recognition and propose a greedy al-gorithm based on the Hungarian method by restricting the above matching which satisfies the constraints of geometric relation.

4 Results and discussion

To illustrate the effectiveness of the proposed optimal solution approach, a case study was adapted from a LTPS TFT-LCD manufacturing firm in Hsinchu, Taiwan. In this case study, the plate size was 620 mm× 750 mm. Four different cell sizes use the same plate. The larger the cell size, the fewer the number of cells used for a single plate. The corresponding number of cells for a given cell size is shown in Table 1.

The TFT average yield rate is about 90% for LCD factories. Color filter (CF) glasses are usually purchased from outside ven-dors. Therefore, the CF yield rate has many choices. The higher the CF yield rate, the higher the cost. Based on the company’s historical data, four scenarios were investigated in this study. In practice, the data can only be obtained through extra proced-ures with special equipment. Without losing its reality, random numbers were used to simulate the defective cells on a plate for a given plate yield rate. A random number generator output a value of 0 or 1 is determined using the Bernoulli distribution. If the output value is 1, the cell is good. If the output value is 0, the cell is defective. Ten replications were performed to construct a 95% confidence interval on the mean for each experimental scenario [10].

B. Numerical results and discussion

LCD plates have some defect types. The sources of defect types are from different stages of the manufacturing process. Mate-rials, equipment, operations, etc., can cause the problems. We compare the performance of different algorithms for the follow-ing four defects types of LCD plates:

1) The defective panels scatter randomly on the TFT plate as il-lustrated in Fig. 4a.

2) There are 80% defective panels gathered at the second quad-rant of the TFT plate as illustrated in Fig. 4b.

Table 1. Cell size versus number of cells

Number of panels (n) 30 50 70 100

Fig. 4. Defect types

3) There are 80% defective panels gathered at the center of the TFT plate as illustrated in Fig. 4c.

4) There are 80% defective panels gathered at the edge of the TFT plate as illustrated in Fig. 4d.

The total average yield rates for four defect types of TFT and CF plates were set at 90% and 85%, respectively. The

numeri-Table 2. Mapping results in 95% confidence interval for defective panels scatter randomly on the plate with TFT average yield 90% and CF average yield 85%

Method Random mapping Greedy algorithm Hungarian method Improvement yield

Panels 30 76.4867± 0.0161 79.7000± 0.2393 81.2889± 0.1040 4.8022%, 1.5889% 50 76.4880± 0.0214 78.8267± 0.1010 80.1200± 0.0796 3.6320%, 1.2933% 70 76.4916± 0.0061 78.3524± 0.1169 79.5905± 0.0400 3.0989%, 1.2381% 100 76.5094± 0.0163 78.0367± 0.0909 79.0417± 0.0585 2.5323%, 1.0050% Average 76.4939% 78.7290% 80.0103% 3.5164%, 1.2813%

Table 3. Mapping results in 95% confidence interval for 80% defective panels gathered at the second quadrant of the plate with TFT average yield 90% and CF average yield 85%

Method Random mapping Greedy algorithm Hungarian method Improvement yield

Panels 30 76.5082± 0.0870 78.8389± 0.1701 80.5611± 0.2373 4.0529%, 1.7222% 50 76.5190± 0.0273 78.2667± 0.1211 79.7333± 0.0665 3.2143%, 1.4666% 70 76.4912± 0.0321 78.0119± 0.1224 79.2048± 0.0618 2.7136%, 1.1929% 100 76.4895± 0.0495 77.6517± 0.0802 78.6917± 0.0832 2.2022%, 1.0400% Average 76.5020% 78.1923% 79.5477% 3.0458%, 1.3554%

Table 4. Mapping results in 95% confidence interval for 80% defective panels gathered at the center of the plate with TFT average yield 90% and CF average yield 85%

Method Random mapping Greedy algorithm Hungarian method Improvement yield

Panels 30 76.5193± 0.0801 78.8222± 0.2270 80.5333± 0.2079 4.0140%, 1.7111% 50 76.4841± 0.0412 78.2367± 0.1033 79.7333± 0.0954 3.2492%, 1.4966% 70 76.5391± 0.0199 78.0833± 0.1293 79.3571± 0.0440 2.8180%, 1.2738% 100 76.5186± 0.0249 77.7733± 0.0554 78.7967± 0.0533 2.2781%, 1.0234% Average 76.5153% 78.2289% 79.6051% 3.0898%, 1.3762%

cal results for random mapping, greedy algorithm and Hungarian method mapping using a sorter with four ports are summarized in Tables 2, 3, 4 and 5. The greedy algorithm is implemented on a program. The LP formulation is solved by a commercial mathe-matical programming solver, LINGO. Both the greedy algorithm and LP formulation computation time is about 1 s.

As we can see, the Hungarian method consistently gener-ated a superior solution compared to the other algorithms for the four defect types with TFT average yield 90% and CF aver-age yield 85%. In Table 2, the Hungarian method for the averaver-age improvement yield from random mapping and the greedy al-gorithm were 3.5164% and 1.2813%, respectively. Considering the costly TFT and CF plates, the expected improvement repre-sents a significant profit increase. In the case study example, the monthly throughput was 30 000 LCD plates. The average cost per LCD plate is about US$876. The expected monthly profit increases from random mapping and the greedy algorithm were about US$924 000 and US$337 000, respectively. Similarly, in Tables 3, 4, and 5, the expected monthly profit increase from ran-dom mapping and greedy algorithm were about US$800 000 and US$356 000, US$812 000 and US$362 000, and US$876 000 and US$392 000, respectively.

Table 5. Mapping results in 95% confidence interval for 80% defective panels gathered at the edge of the plate with TFT average yield 90% and CF average yield 85%

Method Random mapping Greedy algorithm Hungarian method Improvement yield

Panels 30 76.4869± 0.0262 79.0611± 0.2048 81.1111± 0.1060 4.6242%, 2.0500% 50 76.5294± 0.0293 78.5033± 0.1392 80.0000± 0.0803 3.4706%, 1.4967% 70 76.4811± 0.0293 78.0786± 0.0779 79.4095± 0.0845 2.9284%, 1.3309% 100 76.4896± 0.0146 77.7200± 0.0878 78.8050± 0.0500 2.3154%, 1.0850% Average 76.4968% 78.3408% 79.8314% 3.3347%, 1.4907%

Table 6. Mapping results in 95% confidence interval for defective panels scatter randomly

Method Random mapping Hungarian method Difference Conditions TFT yield n= 30 85.5009± 0.0194 88.4833 ± 0.1634 2.9824% 90% n= 50 85.5039± 0.0091 87.8633 ± 0.0307 2.3594% CF yield n= 70 85.5095± 0.0097 87.5952 ± 0.0501 2.0857% 95% n= 100 85.5007 ± 0.0091 87.2000 ± 0.0329 1.6993% TFT yield n= 30 86.3970± 0.0130 88.9389 ± 0.0687 2.5419% 90% n= 50 86.4057± 0.0085 88.5700 ± 0.0650 2.1643% CF yield n= 70 86.3989± 0.0087 88.2333 ± 0.0513 1.8344% 96% n= 100 86.3974 ± 0.0073 87.9550 ± 0.0342 1.5576% TFT yield n= 30 87.2971± 0.0131 89.4056 ± 0.0623 2.1085% 90% n= 50 87.3016± 0.0064 89.1567 ± 0.0374 1.8551% CF yield n= 70 87.2980± 0.0093 88.8810 ± 0.0681 1.5830% 97% n= 100 87.2985 ± 0.0074 88.6583 ± 0.0370 1.3598% TFT yield n= 30 88.2010± 0.0115 89.7444 ± 0.0598 1.5434% 90% n= 50 88.2019± 0.0064 89.5833 ± 0.0377 1.3814% CF yield n= 70 88.2006± 0.0071 89.4262 ± 0.0498 1.2256% 98% n= 100 88.1981 ± 0.0059 89.3000 ± 0.0446 1.1019% TFT yield n= 30 89.0996± 0.0079 89.9167 ± 0.0429 0.8171% 90% n= 50 89.0981± 0.0063 89.8933 ± 0.0293 0.7952% CF yield n= 70 89.1007± 0.0033 89.8524 ± 0.0287 0.7517% 99% n= 100 89.0998 ± 0.0039 89.8000 ± 0.0210 0.7002%

In Tables 2, 3, 4 and 5, the average yield ratio from random mapping, without respect to the panel quantities per substrate. This is unlike the others algorithm where average yield ratio in-creased as the panel quantities dein-creased. This implies that if the displays size is very small or if CF is purchased by a very high yield rate, random mapping is feasible.

Table 6 represents the numerical results for defective panels scatter randomly on the plate with TFT total average yield rates 90% and CF total average yield rates 95% to 99%. According to LCD firm estimation, the difference between random mapping and using sorter mapping does not exceed yield 1%. Therefore, LCD firms should purchase CF with yield rates no less than 99% for using random mapping with TFT yield 90%.

5 Conclusions

Yield control is an important factor for a TFT LCD manufac-turing firm to gain a competitive edge. The post-mapping yield control problem has a significant impact on TFT LCD manufac-turing. For the small to medium sized displays, scribing glass in advance and then during the cell process produces a lower econ-omy of scale. A judicious matching policy is very cost effective because it does not require a significant investment to produce yield improvement. This research proposed a linear program-ming formulation to maximize the yield rate through an optimal matching process to obtain a greater number of acceptable LCD panels to improve the cell process yield. The results were com-pared with two heuristics seen in practice and showed superior solution quality. Implementation results revealed that the pro-posed approach is effective in solving a practical problem.

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