Neural network modeling of the cellgap process for ... - Semantic Scholar
Available online at www.sciencedirect.com
Expert Systems with Applications Expert Systems with Applications 35 (2008) 1311–1315 www.elsevier.com/locate/eswa
Neural network modeling of the cellgap process for liquid crystal display fabricated on plastic substrates Jung Hwan Lee a, Dong-Hun Kang a, Young-Don Ko a, Jaejin Jang b, Dae-Shik Seo a, Ilgu Yun a,* b
a Department of Electrical and Electronics Engineering, Yonsei University, 134 Shinchon-Dong, Seodaemun-Gu, Seoul 120-749, Republic of Korea Department of Industrial and Manufacturing Engineering, University of Wisconsin-Milwaukee, 3200 N. Cramer Street, Milwaukee, WI 53201, USA
Abstract In this paper, a neural network model is presented to characterize the thickness and the uniformity of the cellgap process for flexible liquid crystal display (LCD). Input factors are explored via a D-optimal design with 15 runs and used as training data in the neural network. In order to verify the fitness of the model, three more runs are added as test data. Latin hypercube sampling and error back-propagation algorithm are used to build the model. Latin hypercube sampling is used to generate initial weights and biases of the network. The thickness of cellgap is measured at five points: one at the center and four at the edges. The average thickness is used as cellgap thickness, and the uniformity is obtained by comparing the thickness at the center and edge points. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Neural networks; Latin hypercube sampling; Flexible LCD; Cellgap
1. Introduction Recently, the demand for flat panel display has rapidly increased. The flat panel display has certain advantages over the cathode-ray tube display, such as being thin, lightweight, and power efficient (Lueder, 2001). Liquid crystal display (LCD) is the most prevalent type of flat panel displays, being widely used in computers, mobile communication devices, and televisions. However, it has been mostly glass-based and does not bend. In recent years, there has been research on the development of flexible display technology (West, Wang, Ji, & Kelly, 1995; Yamamoto, Hasegawa, & Hatoh, 1996). The flexible displays based on polymer substrates for LCD have several advantages over displays using glass substrates (Lueder, 2001). In spite of these advantages, their production volume of flexible displays is still low and the costs of plastic substrates are high. Especially, flex-
ible display generates new problems that differ from those of glass display because of the low-temperature processing and flexibility of a plastic substrate. Neural network is a powerful data modeling tool that can capture and represent complex input/output relationships. To characterize a process, the neural network has been applied to various fields such as semiconductor manufacturing and LCD manufacturing (Han, Li, May, & Rohatgi, 1996; Kim & Hong, 2004; Ko et al., 2005; Su, Hung, Cheng, & Chen, 2006). In this paper, three input factors are considered to characterize the average thicknesses and the uniformity of thickness for LCD panels using an error back-propagation (BP) neural network. Latin hypercube sampling was used to generate initial weights and biases, which are the key parameters of neural network modeling. Input factors were explored via D-optimal experimental design. 2. Experiments
*
Corresponding author. Tel.: +82 2 2123 4619; fax: +82 2 313 2879. E-mail address: [email protected] (I. Yun).
0957-4174/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2007.08.027
The 200 lm thick polycarbonate (PC) films are used as substrates of the test LCD. In order to measure the cell
1312
J.H. Lee et al. / Expert Systems with Applications 35 (2008) 1311–1315 Table 2 The experimental design matrix
Fig. 1. Five measurement points on the cell.
gap of this flexible LCD, a cell was fabricated as a sandwich with an anti-parallel structure, and the 4 lm thick spacers were used to maintain a uniform space between the two polymer substrates. The spacers were positioned in between the two polymer films by spraying, and the number of spraying spacers was considered as one of the input factors. The pressing machine was then pressed with three types of sheets, which were rubber, teflon and iron sheets, that was considered as an input factor. Here, the pressure was also considered as the other input factor. A mixture of nematic liquid crystal was then injected in isotropic phases. The liquid crystal cells were then cooled to room temperature. The cell gaps were then measured by CGMS-150 at five points: one at the center and four at the edges of a cell. The schematic of the measurement points is illustrated in Fig. 1. 3. Modeling scheme 3.1. Design of experiments Three input factors were selected to characterize the average thickness and the uniformity of flexible displays: type of sheet, number of spray and pressure in Table 1. Table 1 Input factors and ranges Factor
Symbol
Type of sheet
S
Number of spray Pressure
N P
Unit
Range
EA kg/5.29 cm2
Type1 (rubber) Type2 (Teflon) Type3 (iron) 1, 4, 7 1, 3, 5
Runs
Type of sheet
Pressure [kg/ 5.29 cm2]
Number of spray [EA]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
2 3 1 3 2 2 1 1 2 2 3 2 3 3 2 1 1 3
3 5 3 3 1 3 2 5 5 1 1 5 5 3 3 1 3 1
4 1 7 7 1 4 7 4 7 7 7 1 4 1 4 4 1 4
Train/ test Test
Test
Test
These input factors were explored via D-optimal design with 15 runs and used as training data of a neural network, and three more as the test data to verify the fitness of the models. All experimental runs were made in random order. The experimental design matrix is summarized in Table 2. 3.2. Latin hypercube sampling Latin hypercube sampling (LHS) is used in this study to select randomized values for the weights and the biases of the neural networks. LHS is a stratified sampling technique where the random variable distributions are divided into equal probability intervals. The LHS generates a sample size n from the N variables with same probability from within each interval that is partitioned into n nonoverlapping ranges (Swidzinski & Chang, 2000). Unlike the simple random sampling, the LHS can cover the full sampling range by maximally satisfying each marginal distribution. The distributions of sampling of the selection methods are illustrated in Fig. 2. One hundred sample points were generated in the range of (0.5, 0.5). It indicates that the sampling values of the LHS are uniformly distributed compared with that of the random sampling. Therefore, the unbiased random values of the weights and biases for the neural networks were selected via the LHS. 3.3. Neural networks Neural networks are used to model the nonlinear relationship between inputs and outputs in semiconductor processing. A general neural network consists of the three layers: the input, hidden and the output layers. That is comprised of simple processing units called neurons, interconnection, and weights that are assigned to the interconnection between neurons. Each neuron keeps the weighted sum of its input filtered by a nonlinear sigmoid
14
14
12
12
10
10
Frequency
Frequency
J.H. Lee et al. / Expert Systems with Applications 35 (2008) 1311–1315
8 6
8 6
4
4
2
2
0
-0.5 -0.4 -0.3 -0.2 -0.1
0.0
0.1
0.2
0.3
0.4
0.5
1313
0
-0.5 -0.4 -0.3 -0.2 -0.1
0.0
0.1
0.2
0.3
0.4
0.5
Value
Value
Fig. 2. The sampling result of two difference distributions: (a) the simple random sampling, (b) Latin hypercube sampling.
transfer function. The schematic of a general feed-forward neural network is shown in Fig. 3. The neural network in this research is trained by the error BP algorithm. The error BP neural networks consist of several layers of neurons which receive, process and transmit critical information regarding the relationships between the input parameters and corresponding responses. The general weight mechanism of the BP algorithm is given in the following equation (Chen, 1996):
This algorithm has been shown to be very effective in learning arbitrary nonlinear mappings between noisy sets of input and output factors. The parameters of the neural network used in this study are summarized in Table 3.
wijk ðn þ 1Þ ¼ wijkðnÞ þ gDwijk ðnÞ
The thickness of cell gaps was measured at five points. The measured vs. the predicted values by the neural network are plotted in Fig. 4a, where the squares (‘j’) represent the training data and the circles (‘d’) represent the testing data. The plots exhibit a good agreement between the predicted and the actual values. Root mean square errors (RMSEs) of the average cellgap thickness for the training and testing cases are 0.152 and 0.178, respectively. The residual plot for average cellgap is also illustrated in Fig. 4b. It is shown that the residuals are randomly distributed without either biased or special patterns. The response surfaces of the average cellgap for the different types of sheets are shown in Fig. 5. The r2 of model is 90%. It is shown that increasing the number of sprays with low pressure makes the average cellgap thickness increase, but with low pressure the number of sprays does not have a significant effect on the average cellgap thickness. In addition, higher pressure with a large number of sprays decreases the average cellgap thickness; however, with a small number of sprays, the effect of pressure is not significant. The result indicates that more spacers to maintain the cellgap need higher pressure to control cellgap thickness. When too many spacers are inserted, they can usually be distributed with some non-uniformity. This can result from the stacking of the spacers. Therefore, it can increase the cellgap thickness when there is not enough pressure.
ð1Þ
where wijk is the connection strength between the jth neuron in layer (k 1) and the ith neuron in layer k, Dwijk is the calculated change in that weight that reduces the error of the networks, and g is the learning rate.
Responses
y1
....
yj
....
W 1j
Output Layer
ho
Hidden Layer(s)
W oj
....
h1
yn
hk
....
W 11
W mo
....
x1
xi
....
xm
Input Layer
Inputs
Fig. 3. Typical feed-forward neural networks.
Table 3 Summary of network parameters
Structure Learning rate Momentum
4. Results and discussion 4.1. Average cellgap thickness
4.2. Uniformity of cellgap thickness
Average of cellgap
Uniformity of cellgap
3–4–3–1 0.0051 0.05
3–4–2–1 0.0034 0.04
There are a few different ways to calculate uniformity. One common method is comparing the difference between the edge values and the center values, which is shown in Eq. (2).
J.H. Lee et al. / Expert Systems with Applications 35 (2008) 1311–1315
6.0
0.4
5.5
0.2
Residuals
Predicted data
1314
5.0 4.5
0.0 -0.2
4.0
-0.4 4.0
4.5
5.0
5.5
6.0
0
2
4
6
Experimental datai
8
10
12
14
16
Runs
Fig. 4. The neural network modeling results for average thickness of cellgap: (a) the measured vs. the predicted values and (b) the residual plot.
Fig. 5. The response surface plots for average thickness of cellgap: (a) rubber, (b) teflon and (c) iron.
C M e 100 U ¼ 100 C
ð2Þ
where U is the uniformity of cellgap thickness, C is the center point value, and Me is the average of edge point values.
The plot of the measured and the predicted values of the uniformity of cellgap thickness is given in Fig. 6a, where the squares (‘j’) represent the training data and the triangles (‘m’) represent the testing data. The plot shows a good agreement between the modeled and the measured
100 1.5 98 1.0
Residuals
Predicted data
96 94 92
0.5 0.0
90
-0.5
88
-1.0 -1.5
86 86
88
90
92
94
Experimental data
96
98
100
0
2
4
6
8
10
12
14
16
Runs
Fig. 6. The neural network modeling results for uniformity of cellgap: (a) the measured vs. the predicted values and (b) the residual plot.
J.H. Lee et al. / Expert Systems with Applications 35 (2008) 1311–1315
1315
Fig. 7. The response surface plots for uniformity of cellgap: (a) rubber, (b) teflon and (c) iron.
responses. The root mean square errors (RMSEs) of the uniformity for cellgap for the training and test cases are 0.832 and 1.575, respectively. The residual for the uniformity of cellgap is shown in Fig. 6b. It is also observed that the residuals are randomly distributed without either biased nor special patterns. The response surface plots of the uniformity of cellgap thickness for different types of sheets are shown in Fig. 7. It is indicated that the uniformity of cellgap for LCD fabricated on plastic substrates is near the maximum uniformity when the pressure is low and number of sprays is adequate for each type of sheet in general. It is also found that more spacers make the uniformity increase. However, if too many spacers are inserted without enough pressure, the uniformity of the cellgap is decreased since the probability for thickness variation caused by the number of stacked spacers is increased. 5. Conclusion The average cellgap thickness and the uniformity of cellgap have been investigated using the error BP (Back Propagation) neural network models. Latin hypercube sampling was used to generate the initial weights and the biases to improve the training speed of the neural networks. The models represent comprehensive characterizations of cellgap fabrication process. These results show that low pressure and an adequate number of sprays are critical for both high uniformity and low thickness of cellgap. The neural network modeling results show good agreement with the experimental data. Therefore, the neural net-
work modeling allows us to predict cellgap properties for different sets of process conditions. References Chen, C. H. (1996). Fuzzy logic and neural network handbook. McGrawHill. Han, S.-S., Li, C., May, G. S., & Rohatgi, A. (1996). Modeling the growth of PECVD silicon nitride films for solar cell applications using neural networks. IEEE Transactions on Semiconductor Manufacturing, 9, 303–311. Kim, B., & Hong, W.-S. (2004). Use of neural network to characterize a low pressure temperature effect on refractive property of silicon nitride film deposited by PECVD. IEEE Transactions on Plasma Science, 32, 84–89. Ko, Y.-D., Kang, H. S., Jeong, M.-C., Lee, S. Y., Myoung, J.-M., & Yun, I. (2005). Neural network based modeling of PL intensity in PLDgrown ZnO thin films. Journal of Materials Processing Technology, 159, 159–163. Lueder, L. (2001). Liquid crystal displays: Addressing schemes & electrooptical effects. John Wiley & Sons. Su, Y.-C., Hung, M.-H., Cheng, F.-T., & Chen, Y.-T. (2006). A processing quality prognostics scheme for plasma sputtering in TFT-LCD manufacturing. IEEE Transactions on semiconductor manufacturing, 19, 183–194. Swidzinski, J. F., & Chang, K. (2000). Nonlinear statistical modeling and yield estimation technique for use in Monte Carlo simulations. IEEE Transactions on Microwave Theory and Techniques, 48, 2316–2324. West, J.L., Wang, X., Ji, Y., & Kelly, J.R., (1995). Polarized UV-exposed poly-imide films for liquid-crystal alignment. In Proceedings of SID’95 digest (pp. 703). Yamamoto, T., Hasegawa, M., & Hatoh, H., (1996). Liquid-crystal alignment by slantwise irradiation of non-polarized UV light on a polyimide layer. In Proceedings of SID’96 digest (pp. 642).
Expert Systems with Applications Expert Systems with Applications 35 (2008) 1311–1315 www.elsevier.com/locate/eswa
Neural network modeling of the cellgap process for liquid crystal display fabricated on plastic substrates Jung Hwan Lee a, Dong-Hun Kang a, Young-Don Ko a, Jaejin Jang b, Dae-Shik Seo a, Ilgu Yun a,* b
a Department of Electrical and Electronics Engineering, Yonsei University, 134 Shinchon-Dong, Seodaemun-Gu, Seoul 120-749, Republic of Korea Department of Industrial and Manufacturing Engineering, University of Wisconsin-Milwaukee, 3200 N. Cramer Street, Milwaukee, WI 53201, USA
Abstract In this paper, a neural network model is presented to characterize the thickness and the uniformity of the cellgap process for flexible liquid crystal display (LCD). Input factors are explored via a D-optimal design with 15 runs and used as training data in the neural network. In order to verify the fitness of the model, three more runs are added as test data. Latin hypercube sampling and error back-propagation algorithm are used to build the model. Latin hypercube sampling is used to generate initial weights and biases of the network. The thickness of cellgap is measured at five points: one at the center and four at the edges. The average thickness is used as cellgap thickness, and the uniformity is obtained by comparing the thickness at the center and edge points. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Neural networks; Latin hypercube sampling; Flexible LCD; Cellgap
1. Introduction Recently, the demand for flat panel display has rapidly increased. The flat panel display has certain advantages over the cathode-ray tube display, such as being thin, lightweight, and power efficient (Lueder, 2001). Liquid crystal display (LCD) is the most prevalent type of flat panel displays, being widely used in computers, mobile communication devices, and televisions. However, it has been mostly glass-based and does not bend. In recent years, there has been research on the development of flexible display technology (West, Wang, Ji, & Kelly, 1995; Yamamoto, Hasegawa, & Hatoh, 1996). The flexible displays based on polymer substrates for LCD have several advantages over displays using glass substrates (Lueder, 2001). In spite of these advantages, their production volume of flexible displays is still low and the costs of plastic substrates are high. Especially, flex-
ible display generates new problems that differ from those of glass display because of the low-temperature processing and flexibility of a plastic substrate. Neural network is a powerful data modeling tool that can capture and represent complex input/output relationships. To characterize a process, the neural network has been applied to various fields such as semiconductor manufacturing and LCD manufacturing (Han, Li, May, & Rohatgi, 1996; Kim & Hong, 2004; Ko et al., 2005; Su, Hung, Cheng, & Chen, 2006). In this paper, three input factors are considered to characterize the average thicknesses and the uniformity of thickness for LCD panels using an error back-propagation (BP) neural network. Latin hypercube sampling was used to generate initial weights and biases, which are the key parameters of neural network modeling. Input factors were explored via D-optimal experimental design. 2. Experiments
*
Corresponding author. Tel.: +82 2 2123 4619; fax: +82 2 313 2879. E-mail address: [email protected] (I. Yun).
0957-4174/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2007.08.027
The 200 lm thick polycarbonate (PC) films are used as substrates of the test LCD. In order to measure the cell
1312
J.H. Lee et al. / Expert Systems with Applications 35 (2008) 1311–1315 Table 2 The experimental design matrix
Fig. 1. Five measurement points on the cell.
gap of this flexible LCD, a cell was fabricated as a sandwich with an anti-parallel structure, and the 4 lm thick spacers were used to maintain a uniform space between the two polymer substrates. The spacers were positioned in between the two polymer films by spraying, and the number of spraying spacers was considered as one of the input factors. The pressing machine was then pressed with three types of sheets, which were rubber, teflon and iron sheets, that was considered as an input factor. Here, the pressure was also considered as the other input factor. A mixture of nematic liquid crystal was then injected in isotropic phases. The liquid crystal cells were then cooled to room temperature. The cell gaps were then measured by CGMS-150 at five points: one at the center and four at the edges of a cell. The schematic of the measurement points is illustrated in Fig. 1. 3. Modeling scheme 3.1. Design of experiments Three input factors were selected to characterize the average thickness and the uniformity of flexible displays: type of sheet, number of spray and pressure in Table 1. Table 1 Input factors and ranges Factor
Symbol
Type of sheet
S
Number of spray Pressure
N P
Unit
Range
EA kg/5.29 cm2
Type1 (rubber) Type2 (Teflon) Type3 (iron) 1, 4, 7 1, 3, 5
Runs
Type of sheet
Pressure [kg/ 5.29 cm2]
Number of spray [EA]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
2 3 1 3 2 2 1 1 2 2 3 2 3 3 2 1 1 3
3 5 3 3 1 3 2 5 5 1 1 5 5 3 3 1 3 1
4 1 7 7 1 4 7 4 7 7 7 1 4 1 4 4 1 4
Train/ test Test
Test
Test
These input factors were explored via D-optimal design with 15 runs and used as training data of a neural network, and three more as the test data to verify the fitness of the models. All experimental runs were made in random order. The experimental design matrix is summarized in Table 2. 3.2. Latin hypercube sampling Latin hypercube sampling (LHS) is used in this study to select randomized values for the weights and the biases of the neural networks. LHS is a stratified sampling technique where the random variable distributions are divided into equal probability intervals. The LHS generates a sample size n from the N variables with same probability from within each interval that is partitioned into n nonoverlapping ranges (Swidzinski & Chang, 2000). Unlike the simple random sampling, the LHS can cover the full sampling range by maximally satisfying each marginal distribution. The distributions of sampling of the selection methods are illustrated in Fig. 2. One hundred sample points were generated in the range of (0.5, 0.5). It indicates that the sampling values of the LHS are uniformly distributed compared with that of the random sampling. Therefore, the unbiased random values of the weights and biases for the neural networks were selected via the LHS. 3.3. Neural networks Neural networks are used to model the nonlinear relationship between inputs and outputs in semiconductor processing. A general neural network consists of the three layers: the input, hidden and the output layers. That is comprised of simple processing units called neurons, interconnection, and weights that are assigned to the interconnection between neurons. Each neuron keeps the weighted sum of its input filtered by a nonlinear sigmoid
14
14
12
12
10
10
Frequency
Frequency
J.H. Lee et al. / Expert Systems with Applications 35 (2008) 1311–1315
8 6
8 6
4
4
2
2
0
-0.5 -0.4 -0.3 -0.2 -0.1
0.0
0.1
0.2
0.3
0.4
0.5
1313
0
-0.5 -0.4 -0.3 -0.2 -0.1
0.0
0.1
0.2
0.3
0.4
0.5
Value
Value
Fig. 2. The sampling result of two difference distributions: (a) the simple random sampling, (b) Latin hypercube sampling.
transfer function. The schematic of a general feed-forward neural network is shown in Fig. 3. The neural network in this research is trained by the error BP algorithm. The error BP neural networks consist of several layers of neurons which receive, process and transmit critical information regarding the relationships between the input parameters and corresponding responses. The general weight mechanism of the BP algorithm is given in the following equation (Chen, 1996):
This algorithm has been shown to be very effective in learning arbitrary nonlinear mappings between noisy sets of input and output factors. The parameters of the neural network used in this study are summarized in Table 3.
wijk ðn þ 1Þ ¼ wijkðnÞ þ gDwijk ðnÞ
The thickness of cell gaps was measured at five points. The measured vs. the predicted values by the neural network are plotted in Fig. 4a, where the squares (‘j’) represent the training data and the circles (‘d’) represent the testing data. The plots exhibit a good agreement between the predicted and the actual values. Root mean square errors (RMSEs) of the average cellgap thickness for the training and testing cases are 0.152 and 0.178, respectively. The residual plot for average cellgap is also illustrated in Fig. 4b. It is shown that the residuals are randomly distributed without either biased or special patterns. The response surfaces of the average cellgap for the different types of sheets are shown in Fig. 5. The r2 of model is 90%. It is shown that increasing the number of sprays with low pressure makes the average cellgap thickness increase, but with low pressure the number of sprays does not have a significant effect on the average cellgap thickness. In addition, higher pressure with a large number of sprays decreases the average cellgap thickness; however, with a small number of sprays, the effect of pressure is not significant. The result indicates that more spacers to maintain the cellgap need higher pressure to control cellgap thickness. When too many spacers are inserted, they can usually be distributed with some non-uniformity. This can result from the stacking of the spacers. Therefore, it can increase the cellgap thickness when there is not enough pressure.
ð1Þ
where wijk is the connection strength between the jth neuron in layer (k 1) and the ith neuron in layer k, Dwijk is the calculated change in that weight that reduces the error of the networks, and g is the learning rate.
Responses
y1
....
yj
....
W 1j
Output Layer
ho
Hidden Layer(s)
W oj
....
h1
yn
hk
....
W 11
W mo
....
x1
xi
....
xm
Input Layer
Inputs
Fig. 3. Typical feed-forward neural networks.
Table 3 Summary of network parameters
Structure Learning rate Momentum
4. Results and discussion 4.1. Average cellgap thickness
4.2. Uniformity of cellgap thickness
Average of cellgap
Uniformity of cellgap
3–4–3–1 0.0051 0.05
3–4–2–1 0.0034 0.04
There are a few different ways to calculate uniformity. One common method is comparing the difference between the edge values and the center values, which is shown in Eq. (2).
J.H. Lee et al. / Expert Systems with Applications 35 (2008) 1311–1315
6.0
0.4
5.5
0.2
Residuals
Predicted data
1314
5.0 4.5
0.0 -0.2
4.0
-0.4 4.0
4.5
5.0
5.5
6.0
0
2
4
6
Experimental datai
8
10
12
14
16
Runs
Fig. 4. The neural network modeling results for average thickness of cellgap: (a) the measured vs. the predicted values and (b) the residual plot.
Fig. 5. The response surface plots for average thickness of cellgap: (a) rubber, (b) teflon and (c) iron.
C M e 100 U ¼ 100 C
ð2Þ
where U is the uniformity of cellgap thickness, C is the center point value, and Me is the average of edge point values.
The plot of the measured and the predicted values of the uniformity of cellgap thickness is given in Fig. 6a, where the squares (‘j’) represent the training data and the triangles (‘m’) represent the testing data. The plot shows a good agreement between the modeled and the measured
100 1.5 98 1.0
Residuals
Predicted data
96 94 92
0.5 0.0
90
-0.5
88
-1.0 -1.5
86 86
88
90
92
94
Experimental data
96
98
100
0
2
4
6
8
10
12
14
16
Runs
Fig. 6. The neural network modeling results for uniformity of cellgap: (a) the measured vs. the predicted values and (b) the residual plot.
J.H. Lee et al. / Expert Systems with Applications 35 (2008) 1311–1315
1315
Fig. 7. The response surface plots for uniformity of cellgap: (a) rubber, (b) teflon and (c) iron.
responses. The root mean square errors (RMSEs) of the uniformity for cellgap for the training and test cases are 0.832 and 1.575, respectively. The residual for the uniformity of cellgap is shown in Fig. 6b. It is also observed that the residuals are randomly distributed without either biased nor special patterns. The response surface plots of the uniformity of cellgap thickness for different types of sheets are shown in Fig. 7. It is indicated that the uniformity of cellgap for LCD fabricated on plastic substrates is near the maximum uniformity when the pressure is low and number of sprays is adequate for each type of sheet in general. It is also found that more spacers make the uniformity increase. However, if too many spacers are inserted without enough pressure, the uniformity of the cellgap is decreased since the probability for thickness variation caused by the number of stacked spacers is increased. 5. Conclusion The average cellgap thickness and the uniformity of cellgap have been investigated using the error BP (Back Propagation) neural network models. Latin hypercube sampling was used to generate the initial weights and the biases to improve the training speed of the neural networks. The models represent comprehensive characterizations of cellgap fabrication process. These results show that low pressure and an adequate number of sprays are critical for both high uniformity and low thickness of cellgap. The neural network modeling results show good agreement with the experimental data. Therefore, the neural net-
work modeling allows us to predict cellgap properties for different sets of process conditions. References Chen, C. H. (1996). Fuzzy logic and neural network handbook. McGrawHill. Han, S.-S., Li, C., May, G. S., & Rohatgi, A. (1996). Modeling the growth of PECVD silicon nitride films for solar cell applications using neural networks. IEEE Transactions on Semiconductor Manufacturing, 9, 303–311. Kim, B., & Hong, W.-S. (2004). Use of neural network to characterize a low pressure temperature effect on refractive property of silicon nitride film deposited by PECVD. IEEE Transactions on Plasma Science, 32, 84–89. Ko, Y.-D., Kang, H. S., Jeong, M.-C., Lee, S. Y., Myoung, J.-M., & Yun, I. (2005). Neural network based modeling of PL intensity in PLDgrown ZnO thin films. Journal of Materials Processing Technology, 159, 159–163. Lueder, L. (2001). Liquid crystal displays: Addressing schemes & electrooptical effects. John Wiley & Sons. Su, Y.-C., Hung, M.-H., Cheng, F.-T., & Chen, Y.-T. (2006). A processing quality prognostics scheme for plasma sputtering in TFT-LCD manufacturing. IEEE Transactions on semiconductor manufacturing, 19, 183–194. Swidzinski, J. F., & Chang, K. (2000). Nonlinear statistical modeling and yield estimation technique for use in Monte Carlo simulations. IEEE Transactions on Microwave Theory and Techniques, 48, 2316–2324. West, J.L., Wang, X., Ji, Y., & Kelly, J.R., (1995). Polarized UV-exposed poly-imide films for liquid-crystal alignment. In Proceedings of SID’95 digest (pp. 703). Yamamoto, T., Hasegawa, M., & Hatoh, H., (1996). Liquid-crystal alignment by slantwise irradiation of non-polarized UV light on a polyimide layer. In Proceedings of SID’96 digest (pp. 642).
