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Designing MIMO controller by neuro-traveling particle swarm optimizer approach
Expert Systems with Applications Expert Systems with Applications 32 (2007) 848–855 www.elsevier.com/locate/eswa
Designing MIMO controller by neuro-traveling particle swarm optimizer approach Chwen-Tzeng Su *, Jui-Tsung Wong Department of Industrial Engineering and Management, National Yunlin University of Science and Technology, 123, Section 3, University Road, Touliu, Yunlin 640, Taiwan, ROC
Abstract A nonlinear, multiple input–multiple output controller called the quality controller of neuro-traveling particle swarm optimizer (QC/ NTPSO) approach has been proposed in this paper. A reliable controller must stabilize the quality during the manufacturing process and bring the quality characteristics of the manufacturing process close to the target. This controller must also have an adequate feedback system with estimation technology and optimization algorithm. In addition, the artificial intelligence has reasonably been matured and is often used in dealing with construction problems. Therefore, this work constructed a controller with artificial intelligence technology by first using an artificial neural network as the predictor and then using the traveling particle swarm optimizer that is ideal for continuous optimization problems as the algorithm for optimization. The proposed approach has been tested through chemical mechanical polishing (CMP), an important process in semiconductor manufacturing. The result of the test shows that the proposed approach can bring quality characteristics closer to the target than any other approaches. 2006 Elsevier Ltd. All rights reserved. Keywords: Multiple input–multiple output; Particle swarm optimizer; Artificial neural network
1. Introduction The manufacturing of high-tech products in the present day involves precision and complexity. Under such circumstances, designing a highly efficient control system to control multiple quality characteristics is of extreme importance. This controller should be able to adjust controllable and meaningful parameters, bringing the quality characteristics in manufacturing close to the target. Research in this direction indeed demands our attention. Over the past decade, artificial intelligence (AI) has witnessed rapid development, and is widely used in different domains. Artificial neural network (ANN) is a powerful tool in construction, and is generally used as a model in simulating the manufacturing process (Chen, 2001; Lee * Corresponding author. Tel.: +886 05 5342 601x5114; fax: +886 05 5321 719. E-mail addresses: [email protected] (C.-T. Su), g9221802@ yuntech.edu.tw (J.-T. Wong).
0957-4174/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2006.01.023
et al., 2000; Verikas & Bacauskiene, 2003). It is also frequently combined with heuristic algorithms such as genetic algorithm (Chen & Ramaswamy, 2002; Cook, Ragsdale, & Major, 2000; Su & Chiang, 2002), tabu search (Hsu, 2004), simulated annealing (Tarng, Ma, & Chung, 1995) to find the optimal parameter in the manufacturing process. These approaches are only used in optimizing the parameter of static manufacturing process, i.e., time series is not being taken into consideration. In actual semiconductor manufacturing, time series is an important factor causing changes, such as in the wire etching process and in chemical mechanical polishing. The process of adjusting multiple controllable parameters in the dynamic model in order to bring multiple quality characteristics closer to the target is called multiple input–multiple output (MIMO) control of the manufacturing process. Therefore, how to adjust controllable parameters in order to bring multiple quality characteristics close to the target and to maintain its stability is the focus of the research dealing with such problems. The feedback model often contains a predictive model and
C.-T. Su, J.-T. Wong / Expert Systems with Applications 32 (2007) 848–855
an optimization algorithm. Therefore, this paper proposed an effective controller of quality characteristics with artificial intelligence. Particle swarm optimizer (PSO) is an evolutionary computation algorithm first proposed by Eberhart and Kennedy (1995). Its development is based on the observation of animals’ social behavior, such as bird flocking, fish schooling and swarm theory. In implementing PSO, every individual particle moves in accordance with a randomized velocity in the flying experience of itself and others in the same swarm. Unlike a typical genetic algorithm, PSO has memory, and each particle can memorize its best solution. In addition, if another particle discovers a better solution, it will be shared among other particles. The best solution is thus memorized. Every particle will move toward this best solution, but yet, not fully accept this experience. PSO is mainly used for solving continuous optimization problems, and is also frequently used in optimizing parameters in the manufacturing process (Costa, Lage, & Biscaia, 2003; Ourique, Biscaia, & Pinto, 2002). Artificial intelligence is still not widely used in the dynamic control model of manufacturing. Therefore, this work proposed artificial intelligence-based framework of a hybrid system for the controller, quality controller of neuro-traveling particle swarm optimizer (QC/NTPSO). This system is constructed with a PSO algorithm suitable for continuous optimization problems and ANNs. First, the ANN generates a predicted value. After being adjusted, the predicted value generates a feedback value, which can be used in estimating the target of quality characteristics in the next run. In other words, this method uses an artificial neural network to forecast the track of quality characteristics optimization in each run. Traveling particle swarm optimizer algorithm is then used to find the optimal parameter for each run. In the NTPSO, every particle must travel every controllable parameter (i.e., they must make decisions with every controllable parameter), as shown in Fig. 1. This work tests the efficiency of this approach through the chemical mechanical polishing (CMP) process in semiconductor manufacturing. This is a nonlinear MIMO model. The applicability of the proposed approach
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in the manufacturing process of such characteristics can be determined. 2. Quality controller of MIMO process The most obvious difference between the MIMO process and single input–single output (SISO) process lies in that there are complicated interactions among the parameters in the MIMO process, which makes it difficult to estimate and adjust parameters. This is why some of the traditional control approaches in the SISO system are not suitable for direct implementation on MIMO systems. Run-to-Run controller (R2R-controller) has recently been emerged as a dynamic control approach in the manufacturing process. It has been successfully used in controlling the manufacturing process in the semiconductor industry (Butler & Stefani, 1994; Chen & Guo, 2001; Del Castillo & Yeh, 1998; Joweet & Morozov, 2002). With the controller of statistical process control, R2R controller mainly reduces the cost stemmed from adjusting the controllable parameters. Using the typical control chart to monitor the process, however, leaves great room for discussion (see Woodall, 2002 for the controversy regarding the statistical process control). However, this will not be discussed in this paper, which emphasizes that parameters, within an acceptable range of adjustment, can bring quality characteristics closer to the target. Moreover, some artificial intelligence-based approaches are being used in controllers. Yeh and Huang (2003) proposed an MIMO controller based on the Hammerstein model and genetic algorithm. In this case, the constraint of quality characteristics is the basis for adjusting the timing. Yi, Sheng, and Xu (2003) proposed two artificial neural networks, which are to be used in the predictive model and control model, but are only limited to use in multiple input–single output system. There are other controllers based on the fuzzy model being used in the MIMO system (Lian & Huang, 2001; Zhang & Bien, 2000). The ultimate goal of these approaches is to construct an efficient controller. Therefore, this paper adopts a convenient method using efficient controller in nonlinear MIMO system. 3. QC/NTPSO implementation
p1
1
p2
1
p3
1
0.67 0.18
– 0.32
Fig. 1. Concept of a particle’s travel in multiple controllable parameters: a particle must complete the travel to all controllable parameters in order to generate a parameter combination P = {piji = 1, 2, 3}.
3.1. The controller for the MIMO system The controller in this discrete MIMO system mainly monitors the present output value, and makes adequate feed back value for the difference between the output value and the target value in the manufacturing process. Next, it uses optimization technology to find the optimal controllable parameter for the next run. First, artificial neural network is used to forecast the output value of quality characteristics in the next run. The error is then used to estimate the expected target of quality characteristics in the next run. Second, NTPSO algorithm determines the optimal parameter in the next run, as shown in Fig. 2,
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ut
1
Equipment
y t Feedback model
yˆt+1 B
TPSO
yt and t
ANN-predict
~ yt+1 Target Weight
Fig. 3. The three-layered BPN architecture of the predictor.
Constrain
QC/NTPSO
Initial model
Fig. 2. The QC/NTPSO framework of the control system.
Process model
where B is the discrete control process. The error computation and feedback computation are shown in Eqs. (1) and (2) ejt ¼ y jt ^y jt ;
ð1Þ
^y j;tþ1 ¼ ~y j;tþ1 ejt ;
ð2Þ
where ejt is the error value of quality characteristic j in the tth run. yt, ~y jt and ^y jt , respectively, represent the output value in the equipment, the output value of ANN and the adjusted output value of quality characteristic j in the tth run. 3.2. Construction of the ANN-based predictive model An account of the training process of the ANN is provided in this section. The ANN imitates the informationprocessing system of the biological neural network. Within it, layers, created by neurons, form the network. Artificial neural networks are effective models for prediction. One supervised ANN of paramount importance is the backpropagation network (BPN) because of its simplicity and efficiency. Therefore, this paper adopted BPN as the model for prediction. More on BPN can be found in Negnevitsky (2002). In MIMO systems, it is difficult to bring every quality characteristic close to the target. Therefore, the attainable target of the predictive model of this controller is to obtain quality characteristics in the optimization technology, providing a basis for adjustment for the feedback model. There are three nodes in the input layer of this ANN, which are the optimal quality characteristics obtained by TPSO (the testing example of this paper includes two quality characteristics) and run number. The output layer consists of the quality characteristic obtained by TPSO in the next run. This BPN model is shown as in Fig. 3. In Fig. 4, TPSO algorithm is used to obtain the optimal quality characteristics in each run number, and then the standardization of the obtained quality characteristics is carried out. The construction of the BPN model involves training and testing stage.
TPSO for optimization data
BPN model constructed
Training data
Obtain attainable quality characteristic by TPSO at each run
Training
Testing
Standardization quality characteristic
Fig. 4. The training flow for this predictor.
3.3. TPSO for optimization model The TPSO algorithm updates the velocity of the particle as shown in Eq. (3) k k k vkþ1 ih ¼ wvih þ c1 /1 ðpbest ih sih Þ þ c2 /2 ðgbest h sih Þ;
ð3Þ
where vkih is the velocity of the particle i in the kth iteration of the controllable parameter h in the manufacturing process. w is the inertia weight within the range [0, 1]. c1 and c2 are two constants (i.e., the cognitive and social parameter, respectively). /1 and /2 are two uniformly random real value [0, 1]. skih is the position (solution) of particle i in the controllable parameter h in the kth iteration. pbestih is the present optimum solution found in individual particle i in the controllable parameter h. gbesth is the present optimum solution found in the particles in the controllable parameter h of the manufacturing process. As can be seen in Eq. (3), TPSO algorithm, with the present optimum solution, moves the position of the particles toward the optimum solution. The movement of particles is also influenced by individual particles. Eq. (4) shows the update of the solution for every particle k kþ1 skþ1 ih ¼ sih þ vih .
ð4Þ
C.-T. Su, J.-T. Wong / Expert Systems with Applications 32 (2007) 848–855
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Fig. 5. TPSO in determining the optimal parameters.
As the purpose of this paper is to bring quality characteristics closer to the target (the testing examples have two quality characteristics), it is always better to have smaller errors. Therefore, the optimization model is mainly about finding solution to minimization problems. The objective function can be shown as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f ðy i Þ ¼ aðy 1 T 1 Þ2 þ ð1 aÞðy 2 T 2 Þ2 ; where a is the adjustable weight. T1 and T2 represent the target of quality characteristics 1 and 2, respectively. Fig. 5 delineates the steps to optimize the output process parameters close to the desired target using the TPSO.
4. The result of QC/NTPSO testing for CMP process 4.1. Tested example Fig. 6 shows that CMP is a method for polishing wafer surface. The wafer is placed between the carrier and the polishing pad of the rotating platen. Slurry is placed between the wafer and the polishing pad. The main purpose of the CMP process in the semiconductor industry is to make the wafer surface even and smooth. A SEMATECH-based 4 · 2 CMP process (Del Castillo & Yeh, 1998) is used to test the proposed idea. Eqs. (5) and (6) represent the equipment model of quality characteristics 1 and 2, respectively, in the actual manufacturing process as
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C.-T. Su, J.-T. Wong / Expert Systems with Applications 32 (2007) 848–855 0.1 0.09
RMSE
Wafer Carrier Slurry
Wafer
Polishing Pad
0.06 0.03 0 0
1
2
3
4
Platen
5 4
Training epoch
x 10
Fig. 7. The convergence process of BPN training. Fig. 6. A typical CMP structure in the semiconductor manufacturing industry.
y 1 ¼ 1563:5 þ 159:3u1 38:2u2 þ 178:9u3 þ 24:9u4 67:2u1 u2 46:2u21 19:2u22 28:9u23 12u1 t0 2
þ 116u4 t0 50:4t0 þ 20:4ðt0 Þ þ e1t ; y 2 ¼ 254 þ 32:6u1 þ 113:2u2 þ 32:6u3 þ 37:1u4
ð5Þ
36:8u1 u2 þ 57:3u4 t0 2:42t0 þ e2t ;
ð6Þ
where t 0 = (t 53)/52; e1t N(0, 602); e2t N(0, 302). Note that ui is the classic controllable parameter in the CMP process, which include u1: platen speed, u2: back pressure, u3: polishing downforce and u4: profile of the conditioning system. The value of every controllable parameter is standardized, which means ui is a real number between range [1, 1]. Quality characteristics include y1: the removal rate of silicon dioxide and y2: within-wafer nonuniformity. In this testing, the target values of quality characteristics are y1 = 2000 and y2 = 100, respectively. The constraints are y1 > 1700 and y2 < 200 (Yeh & Huang, 2003). Eqs. (7) and (8) represent the initial models used for testing as y 1 ¼ 1600 þ 150u1 40u2 þ 180u3 þ 25u4 30u21 20u22 25u23 60u1 u2 90t; ð7Þ y 2 ¼ 250 þ 30u1 þ 100u2 þ 20u3 þ 35u4 30u1 u2 þ 0:05t. ð8Þ 4.2. Constructing the artificial neural network In this section, the BPN model is used for constructing the predictor of the controller in the CMP process. Trained data is based on the optimal quality characteristics
obtained through the TPSO in each run. Before implementing the training of ANN, preprocessing must be done, which means the standardization of data in order to avoid drastic changes in the numerical range of variables and eliminate overlooking the importance of the variables in smaller numerical ranges. Fig. 7 shows the convergence of BPN when the learning rate equals 0.08, and the hidden number equals 3 under the 50,000 training epochs. Under this BPN parameter at the 10 runs, the average of training root mean square error (RMSE) is 0.0002. The data shows a better performance of the BPN model. The average RMSE of the testing is 0.0067. Fig. 7 shows that the process is steadily converging and that the RMSE is small, which implies that the predictive model of this controller is ideal for constructing BPN. 4.3. Controller tested for the CMP process Three methods, QC/NTPSO, OAQC (Del Castillo & Yeh, 1998) and GAQC (Yeh & Huang, 2003), were compared. The parameters for the TPSO algorithm of this research are: number of particles K equals 30, inertia at weight w equals 0.8 and two positive constants c1 equals 2 and c2 equals 1.4. The objective of this testing is to bring quality characteristics y1 and y2 close to the target. The performance measures are computed as: y i represent the average output value of the quality characteristic i; S y i represents the standard deviation of the quality characteristic i; Mi represents the root mean square error of the quality characteristic i; ui represents the average of the parameter i; S ui represents the standard deviation of the parameter i. Table 1 shows the result of the average output when executing the experiment 20 times at 50 runs each. This shows that under the control of QC/NTPSO, quality characteris-
Table 1 Simulated result of this 4 · 2 CMP process Efficiency indicator
OAQC GAQC QC/NTPSO
y 1
y 2
S y1
S y2
u1
u2
u3
u4
S u1
S u2
S u3
S u4
M1
M2
1719.7 1748.6 1798.5
168.4 161.7 167.6
70.4 74.5 84.0
40.1 36.8 37.0
0.4 0.1 0.0
1.0 0.9 1.0
0.80 0.5 1.0
0.8 0.8 1.0
0.3 0.1 0.4
0.1 0.1 0.0
0.2 0.2 0.1
0.2 0.2 0.1
299.8 262.3 218.1
79.2 71.9 76.8
C.-T. Su, J.-T. Wong / Expert Systems with Applications 32 (2007) 848–855
Quality charcteristic
tics are congruent with the constraints, and that the two quality characteristics under QC/NTPSO are closer to the target than those of OAQC. Compared with the GAQC method, quality characteristic y1 rendered better result with the proposed approach of this paper. In terms of the deviation of the parameters, except for parameter u1, the deviations of other parameters of the proposed approach are all smaller than those of OAQC and GAQC. Fig. 8 shows that the controller provided by this proposed approach stabilizes the quality characteristics and brings quality characteristics closer to the target by adjusting the parameter in the manufacturing process. As far as the controllable parameters of this testing is concerned, two parameters, the platen speed and polishing downforce, have greater variations. Fig. 9 shows that under the control of QC/NTPSO, many quality characteristic samples were congruent with
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the constraints and the 99% confidence intervals of quality characteristics y1 and y2 were also congruent with the constraints. The result shows that the QC/NTPSO controller proposed can effectively control the process. This section analyzes the importance of BPN in the proposed controller. Under the control of QC/NTPSO, many samples of quality characteristics are in control with the control limits of the exponentially weighted moving average (EWMA), as shown in Fig. 10(a). Without the BPN model, many samples of quality characteristics are still in control, but the output value of the two quality characteristics demonstrated a downward trend as shown in Fig. 10(b). Table 2 shows that the BPN predictor in the QC/ NTPSO controller has statistically significant influence on the quality characteristics y1 and y2. In other words, the BPN predictor is effective.
2500 2000 1700 1500 y1 y2
1000 500 200 0 0
10
20
30
40
50
Controllable parameter
Run number 1 0.5 u1 u2 u3 u4
0 -0.5 -1 0
10
20
30
40
50
Run Number Fig. 8. The process of implementing the controller.
Fig. 9. Histogram of quality characteristics. This sample is obtained by executing 10 times at 50 runs each. (a) The output of the removal rate, and its 99% confidence interval is [1789.67, 1781.42]. (b) The output of the within-wafer nonuniformity, and its 99% confidence interval is [159.86, 156.39].
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C.-T. Su, J.-T. Wong / Expert Systems with Applications 32 (2007) 848–855 EWMA,Zi
Removal Rate
1800 1781 1750
1843
EWMA
EWMA
1843
1718 0
10
20
30
40
1800 1781 1700
1600
50
1718
0
10
Run number
150
152
104 50
100
(a)
30
EWMA
EWMA
199
20
30
40
50
Within-Wafer Nonuniformity
200
10
20
Run number
Within-Wafer Nonuniformity
0
Control Limits
1900
1850
1700
EWMA,Zi
Removal Rate
Control Limits
1900
40
200
199
150
152
100 0
(b)
Run number
104 10
20
30
40
50
Run number
Fig. 10. The EWMA control chart of quality characteristics: (a) the result with the BPN model; (b) the result without the BPN model.
Table 2 T-test of the effect of BPN model on the result of the controller Factors
T-value
P-value
Removal rate Within-wafer nonuniformity
8.53 8.35
0.00* 0.00*
*
P < 0.05.
5. Conclusions This paper proposed QC/NTPSO approach, a controller constructed with artificial intelligence by adjusting of the parameters in the manufacturing process in order to minimize the error between quality characteristics and the target. This controller adopted ANN as the predictor and TPSO algorithm as the model for optimizing the parameter. CMP, an important process in semiconductor manufacturing, is then used to test the proposed approach. The result has shown that in this example, the quality characteristics of this controller are closer to the target than those of OAQC’s. Only one quality characteristic, however, is closer to the target when compared with GAQC. When adjusting the parameter in the process, the parameters of the proposed approach rendered smaller standard deviation than those of GAQC’s. Among these parameters, there is greater variation in platen speed. In the actual manufacturing process, however, it is a parameter that can be easily controlled. In addition, this paper also tried to uncover how ANN model can influence this controller. The result indicated that under the predictive model without ANN, the output quality characteristics of this controller tended to deviate. The semiconductor industry today faces a manufacturing environment that is becoming more and more complex, and the AI technology relatively
matured. Therefore, using AI tools to settle the difficulties in construction is indeed an important task. References Butler, S. W., & Stefani, J. A. (1994). Supervisory run-to-run control of a polysilicon gate etch using in situ ellipsometry. IEEE Transactions on Semiconductor Manufacturing, 7(2), 193–201. Chen, A., & Guo, R. S. (2001). Age-based double EWMA controller and its application to CMP processes. IEEE Transactions on Semiconductor Manufacturing, 14(1), 11–19. Chen, C. R., & Ramaswamy, H. S. (2002). Modeling and optimization of variable retort temperature (VRT) thermal processing using coupled neural networks and genetic algorithms. Journal of Food Engineering, 53(3), 209–220. Chen, M. C. (2001). Tolerance synthesis by neural learning and nonlinear programming. International Journal of Production Economics, 70(1), 55–65. Cook, D. F., Ragsdale, C. T., & Major, R. L. (2000). Combining a neural network with a genetic algorithm for process parameter optimization. Engineering Applications of Artificial Intelligence, 13(4), 391–396. Costa, E. F., Jr., Lage, P. L. C., & Biscaia, E. C., Jr., (2003). On the numerical solution and optimization of styrene polymerization in tubular reactors. Computers and Chemical Engineering, 27(11), 1591–1604. Del Castillo, E., & Yeh, J. (1998). An adaptive run-to-run optimizing controller for linear and nonlinear semiconductor processes. IEEE Transactions on Semiconductor Manufacturing, 11(2), 285–295. Eberhart, R., & Kennedy, J. (1995). A new optimizer using particle swarm theory. In Proceedings of sixth international symposium on micro machine and human science (pp. 39–43), Nagoya, Japan. Hsu, C. M. (2004). An integrated approach to enhance the optical performance of couplers based on neural networks, desirability functions and tabu search. International Journal of Production Economics, 92(3), 241–254. Joweet, P., & Morozov, V. (2002). Shallow trench isolation run-to-run control project at infineon technologies richmond. In IEEE/SEMI advanced semiconductor manufacturing conference (pp. 107–112), Boston, USA.
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International Journal of Machine Tools and Manufacture, 35(12), 1693–1701. Verikas, A., & Bacauskiene, M. (2003). Using artificial neural networks for process and system modeling. Chemometrics and Intelligent Laboratory Systems, 67(2), 187–191. Woodall, W. H. (2002). Controversies and contradictions in statistical process control. Journal of Quality Technology, 32(4), 341–378. Yeh, J. Y, & Huang, B. H. (2003). Genetic algorithm based semiconductor manufacturing process controller for chemical mechanical planarization. Journal of the Chinese Institute of Industrial Engineers, 20(6), 625–635. Yi, J., Sheng, Y., & Xu, C. S. (2003). Neural network based uniformity profile control of linear chemical–mechanical planarization. IEEE Transactions on Semiconductor Manufacturing, 16(4), 609–620. Zhang, H., & Bien, Z. (2000). Adaptive fuzzy control of MIMO nonlinear systems. Fuzzy Sets and Systems, 115(2), 191–204.
Designing MIMO controller by neuro-traveling particle swarm optimizer approach Chwen-Tzeng Su *, Jui-Tsung Wong Department of Industrial Engineering and Management, National Yunlin University of Science and Technology, 123, Section 3, University Road, Touliu, Yunlin 640, Taiwan, ROC
Abstract A nonlinear, multiple input–multiple output controller called the quality controller of neuro-traveling particle swarm optimizer (QC/ NTPSO) approach has been proposed in this paper. A reliable controller must stabilize the quality during the manufacturing process and bring the quality characteristics of the manufacturing process close to the target. This controller must also have an adequate feedback system with estimation technology and optimization algorithm. In addition, the artificial intelligence has reasonably been matured and is often used in dealing with construction problems. Therefore, this work constructed a controller with artificial intelligence technology by first using an artificial neural network as the predictor and then using the traveling particle swarm optimizer that is ideal for continuous optimization problems as the algorithm for optimization. The proposed approach has been tested through chemical mechanical polishing (CMP), an important process in semiconductor manufacturing. The result of the test shows that the proposed approach can bring quality characteristics closer to the target than any other approaches. 2006 Elsevier Ltd. All rights reserved. Keywords: Multiple input–multiple output; Particle swarm optimizer; Artificial neural network
1. Introduction The manufacturing of high-tech products in the present day involves precision and complexity. Under such circumstances, designing a highly efficient control system to control multiple quality characteristics is of extreme importance. This controller should be able to adjust controllable and meaningful parameters, bringing the quality characteristics in manufacturing close to the target. Research in this direction indeed demands our attention. Over the past decade, artificial intelligence (AI) has witnessed rapid development, and is widely used in different domains. Artificial neural network (ANN) is a powerful tool in construction, and is generally used as a model in simulating the manufacturing process (Chen, 2001; Lee * Corresponding author. Tel.: +886 05 5342 601x5114; fax: +886 05 5321 719. E-mail addresses: [email protected] (C.-T. Su), g9221802@ yuntech.edu.tw (J.-T. Wong).
0957-4174/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2006.01.023
et al., 2000; Verikas & Bacauskiene, 2003). It is also frequently combined with heuristic algorithms such as genetic algorithm (Chen & Ramaswamy, 2002; Cook, Ragsdale, & Major, 2000; Su & Chiang, 2002), tabu search (Hsu, 2004), simulated annealing (Tarng, Ma, & Chung, 1995) to find the optimal parameter in the manufacturing process. These approaches are only used in optimizing the parameter of static manufacturing process, i.e., time series is not being taken into consideration. In actual semiconductor manufacturing, time series is an important factor causing changes, such as in the wire etching process and in chemical mechanical polishing. The process of adjusting multiple controllable parameters in the dynamic model in order to bring multiple quality characteristics closer to the target is called multiple input–multiple output (MIMO) control of the manufacturing process. Therefore, how to adjust controllable parameters in order to bring multiple quality characteristics close to the target and to maintain its stability is the focus of the research dealing with such problems. The feedback model often contains a predictive model and
C.-T. Su, J.-T. Wong / Expert Systems with Applications 32 (2007) 848–855
an optimization algorithm. Therefore, this paper proposed an effective controller of quality characteristics with artificial intelligence. Particle swarm optimizer (PSO) is an evolutionary computation algorithm first proposed by Eberhart and Kennedy (1995). Its development is based on the observation of animals’ social behavior, such as bird flocking, fish schooling and swarm theory. In implementing PSO, every individual particle moves in accordance with a randomized velocity in the flying experience of itself and others in the same swarm. Unlike a typical genetic algorithm, PSO has memory, and each particle can memorize its best solution. In addition, if another particle discovers a better solution, it will be shared among other particles. The best solution is thus memorized. Every particle will move toward this best solution, but yet, not fully accept this experience. PSO is mainly used for solving continuous optimization problems, and is also frequently used in optimizing parameters in the manufacturing process (Costa, Lage, & Biscaia, 2003; Ourique, Biscaia, & Pinto, 2002). Artificial intelligence is still not widely used in the dynamic control model of manufacturing. Therefore, this work proposed artificial intelligence-based framework of a hybrid system for the controller, quality controller of neuro-traveling particle swarm optimizer (QC/NTPSO). This system is constructed with a PSO algorithm suitable for continuous optimization problems and ANNs. First, the ANN generates a predicted value. After being adjusted, the predicted value generates a feedback value, which can be used in estimating the target of quality characteristics in the next run. In other words, this method uses an artificial neural network to forecast the track of quality characteristics optimization in each run. Traveling particle swarm optimizer algorithm is then used to find the optimal parameter for each run. In the NTPSO, every particle must travel every controllable parameter (i.e., they must make decisions with every controllable parameter), as shown in Fig. 1. This work tests the efficiency of this approach through the chemical mechanical polishing (CMP) process in semiconductor manufacturing. This is a nonlinear MIMO model. The applicability of the proposed approach
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in the manufacturing process of such characteristics can be determined. 2. Quality controller of MIMO process The most obvious difference between the MIMO process and single input–single output (SISO) process lies in that there are complicated interactions among the parameters in the MIMO process, which makes it difficult to estimate and adjust parameters. This is why some of the traditional control approaches in the SISO system are not suitable for direct implementation on MIMO systems. Run-to-Run controller (R2R-controller) has recently been emerged as a dynamic control approach in the manufacturing process. It has been successfully used in controlling the manufacturing process in the semiconductor industry (Butler & Stefani, 1994; Chen & Guo, 2001; Del Castillo & Yeh, 1998; Joweet & Morozov, 2002). With the controller of statistical process control, R2R controller mainly reduces the cost stemmed from adjusting the controllable parameters. Using the typical control chart to monitor the process, however, leaves great room for discussion (see Woodall, 2002 for the controversy regarding the statistical process control). However, this will not be discussed in this paper, which emphasizes that parameters, within an acceptable range of adjustment, can bring quality characteristics closer to the target. Moreover, some artificial intelligence-based approaches are being used in controllers. Yeh and Huang (2003) proposed an MIMO controller based on the Hammerstein model and genetic algorithm. In this case, the constraint of quality characteristics is the basis for adjusting the timing. Yi, Sheng, and Xu (2003) proposed two artificial neural networks, which are to be used in the predictive model and control model, but are only limited to use in multiple input–single output system. There are other controllers based on the fuzzy model being used in the MIMO system (Lian & Huang, 2001; Zhang & Bien, 2000). The ultimate goal of these approaches is to construct an efficient controller. Therefore, this paper adopts a convenient method using efficient controller in nonlinear MIMO system. 3. QC/NTPSO implementation
p1
1
p2
1
p3
1
0.67 0.18
– 0.32
Fig. 1. Concept of a particle’s travel in multiple controllable parameters: a particle must complete the travel to all controllable parameters in order to generate a parameter combination P = {piji = 1, 2, 3}.
3.1. The controller for the MIMO system The controller in this discrete MIMO system mainly monitors the present output value, and makes adequate feed back value for the difference between the output value and the target value in the manufacturing process. Next, it uses optimization technology to find the optimal controllable parameter for the next run. First, artificial neural network is used to forecast the output value of quality characteristics in the next run. The error is then used to estimate the expected target of quality characteristics in the next run. Second, NTPSO algorithm determines the optimal parameter in the next run, as shown in Fig. 2,
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ut
1
Equipment
y t Feedback model
yˆt+1 B
TPSO
yt and t
ANN-predict
~ yt+1 Target Weight
Fig. 3. The three-layered BPN architecture of the predictor.
Constrain
QC/NTPSO
Initial model
Fig. 2. The QC/NTPSO framework of the control system.
Process model
where B is the discrete control process. The error computation and feedback computation are shown in Eqs. (1) and (2) ejt ¼ y jt ^y jt ;
ð1Þ
^y j;tþ1 ¼ ~y j;tþ1 ejt ;
ð2Þ
where ejt is the error value of quality characteristic j in the tth run. yt, ~y jt and ^y jt , respectively, represent the output value in the equipment, the output value of ANN and the adjusted output value of quality characteristic j in the tth run. 3.2. Construction of the ANN-based predictive model An account of the training process of the ANN is provided in this section. The ANN imitates the informationprocessing system of the biological neural network. Within it, layers, created by neurons, form the network. Artificial neural networks are effective models for prediction. One supervised ANN of paramount importance is the backpropagation network (BPN) because of its simplicity and efficiency. Therefore, this paper adopted BPN as the model for prediction. More on BPN can be found in Negnevitsky (2002). In MIMO systems, it is difficult to bring every quality characteristic close to the target. Therefore, the attainable target of the predictive model of this controller is to obtain quality characteristics in the optimization technology, providing a basis for adjustment for the feedback model. There are three nodes in the input layer of this ANN, which are the optimal quality characteristics obtained by TPSO (the testing example of this paper includes two quality characteristics) and run number. The output layer consists of the quality characteristic obtained by TPSO in the next run. This BPN model is shown as in Fig. 3. In Fig. 4, TPSO algorithm is used to obtain the optimal quality characteristics in each run number, and then the standardization of the obtained quality characteristics is carried out. The construction of the BPN model involves training and testing stage.
TPSO for optimization data
BPN model constructed
Training data
Obtain attainable quality characteristic by TPSO at each run
Training
Testing
Standardization quality characteristic
Fig. 4. The training flow for this predictor.
3.3. TPSO for optimization model The TPSO algorithm updates the velocity of the particle as shown in Eq. (3) k k k vkþ1 ih ¼ wvih þ c1 /1 ðpbest ih sih Þ þ c2 /2 ðgbest h sih Þ;
ð3Þ
where vkih is the velocity of the particle i in the kth iteration of the controllable parameter h in the manufacturing process. w is the inertia weight within the range [0, 1]. c1 and c2 are two constants (i.e., the cognitive and social parameter, respectively). /1 and /2 are two uniformly random real value [0, 1]. skih is the position (solution) of particle i in the controllable parameter h in the kth iteration. pbestih is the present optimum solution found in individual particle i in the controllable parameter h. gbesth is the present optimum solution found in the particles in the controllable parameter h of the manufacturing process. As can be seen in Eq. (3), TPSO algorithm, with the present optimum solution, moves the position of the particles toward the optimum solution. The movement of particles is also influenced by individual particles. Eq. (4) shows the update of the solution for every particle k kþ1 skþ1 ih ¼ sih þ vih .
ð4Þ
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Fig. 5. TPSO in determining the optimal parameters.
As the purpose of this paper is to bring quality characteristics closer to the target (the testing examples have two quality characteristics), it is always better to have smaller errors. Therefore, the optimization model is mainly about finding solution to minimization problems. The objective function can be shown as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f ðy i Þ ¼ aðy 1 T 1 Þ2 þ ð1 aÞðy 2 T 2 Þ2 ; where a is the adjustable weight. T1 and T2 represent the target of quality characteristics 1 and 2, respectively. Fig. 5 delineates the steps to optimize the output process parameters close to the desired target using the TPSO.
4. The result of QC/NTPSO testing for CMP process 4.1. Tested example Fig. 6 shows that CMP is a method for polishing wafer surface. The wafer is placed between the carrier and the polishing pad of the rotating platen. Slurry is placed between the wafer and the polishing pad. The main purpose of the CMP process in the semiconductor industry is to make the wafer surface even and smooth. A SEMATECH-based 4 · 2 CMP process (Del Castillo & Yeh, 1998) is used to test the proposed idea. Eqs. (5) and (6) represent the equipment model of quality characteristics 1 and 2, respectively, in the actual manufacturing process as
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RMSE
Wafer Carrier Slurry
Wafer
Polishing Pad
0.06 0.03 0 0
1
2
3
4
Platen
5 4
Training epoch
x 10
Fig. 7. The convergence process of BPN training. Fig. 6. A typical CMP structure in the semiconductor manufacturing industry.
y 1 ¼ 1563:5 þ 159:3u1 38:2u2 þ 178:9u3 þ 24:9u4 67:2u1 u2 46:2u21 19:2u22 28:9u23 12u1 t0 2
þ 116u4 t0 50:4t0 þ 20:4ðt0 Þ þ e1t ; y 2 ¼ 254 þ 32:6u1 þ 113:2u2 þ 32:6u3 þ 37:1u4
ð5Þ
36:8u1 u2 þ 57:3u4 t0 2:42t0 þ e2t ;
ð6Þ
where t 0 = (t 53)/52; e1t N(0, 602); e2t N(0, 302). Note that ui is the classic controllable parameter in the CMP process, which include u1: platen speed, u2: back pressure, u3: polishing downforce and u4: profile of the conditioning system. The value of every controllable parameter is standardized, which means ui is a real number between range [1, 1]. Quality characteristics include y1: the removal rate of silicon dioxide and y2: within-wafer nonuniformity. In this testing, the target values of quality characteristics are y1 = 2000 and y2 = 100, respectively. The constraints are y1 > 1700 and y2 < 200 (Yeh & Huang, 2003). Eqs. (7) and (8) represent the initial models used for testing as y 1 ¼ 1600 þ 150u1 40u2 þ 180u3 þ 25u4 30u21 20u22 25u23 60u1 u2 90t; ð7Þ y 2 ¼ 250 þ 30u1 þ 100u2 þ 20u3 þ 35u4 30u1 u2 þ 0:05t. ð8Þ 4.2. Constructing the artificial neural network In this section, the BPN model is used for constructing the predictor of the controller in the CMP process. Trained data is based on the optimal quality characteristics
obtained through the TPSO in each run. Before implementing the training of ANN, preprocessing must be done, which means the standardization of data in order to avoid drastic changes in the numerical range of variables and eliminate overlooking the importance of the variables in smaller numerical ranges. Fig. 7 shows the convergence of BPN when the learning rate equals 0.08, and the hidden number equals 3 under the 50,000 training epochs. Under this BPN parameter at the 10 runs, the average of training root mean square error (RMSE) is 0.0002. The data shows a better performance of the BPN model. The average RMSE of the testing is 0.0067. Fig. 7 shows that the process is steadily converging and that the RMSE is small, which implies that the predictive model of this controller is ideal for constructing BPN. 4.3. Controller tested for the CMP process Three methods, QC/NTPSO, OAQC (Del Castillo & Yeh, 1998) and GAQC (Yeh & Huang, 2003), were compared. The parameters for the TPSO algorithm of this research are: number of particles K equals 30, inertia at weight w equals 0.8 and two positive constants c1 equals 2 and c2 equals 1.4. The objective of this testing is to bring quality characteristics y1 and y2 close to the target. The performance measures are computed as: y i represent the average output value of the quality characteristic i; S y i represents the standard deviation of the quality characteristic i; Mi represents the root mean square error of the quality characteristic i; ui represents the average of the parameter i; S ui represents the standard deviation of the parameter i. Table 1 shows the result of the average output when executing the experiment 20 times at 50 runs each. This shows that under the control of QC/NTPSO, quality characteris-
Table 1 Simulated result of this 4 · 2 CMP process Efficiency indicator
OAQC GAQC QC/NTPSO
y 1
y 2
S y1
S y2
u1
u2
u3
u4
S u1
S u2
S u3
S u4
M1
M2
1719.7 1748.6 1798.5
168.4 161.7 167.6
70.4 74.5 84.0
40.1 36.8 37.0
0.4 0.1 0.0
1.0 0.9 1.0
0.80 0.5 1.0
0.8 0.8 1.0
0.3 0.1 0.4
0.1 0.1 0.0
0.2 0.2 0.1
0.2 0.2 0.1
299.8 262.3 218.1
79.2 71.9 76.8
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Quality charcteristic
tics are congruent with the constraints, and that the two quality characteristics under QC/NTPSO are closer to the target than those of OAQC. Compared with the GAQC method, quality characteristic y1 rendered better result with the proposed approach of this paper. In terms of the deviation of the parameters, except for parameter u1, the deviations of other parameters of the proposed approach are all smaller than those of OAQC and GAQC. Fig. 8 shows that the controller provided by this proposed approach stabilizes the quality characteristics and brings quality characteristics closer to the target by adjusting the parameter in the manufacturing process. As far as the controllable parameters of this testing is concerned, two parameters, the platen speed and polishing downforce, have greater variations. Fig. 9 shows that under the control of QC/NTPSO, many quality characteristic samples were congruent with
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the constraints and the 99% confidence intervals of quality characteristics y1 and y2 were also congruent with the constraints. The result shows that the QC/NTPSO controller proposed can effectively control the process. This section analyzes the importance of BPN in the proposed controller. Under the control of QC/NTPSO, many samples of quality characteristics are in control with the control limits of the exponentially weighted moving average (EWMA), as shown in Fig. 10(a). Without the BPN model, many samples of quality characteristics are still in control, but the output value of the two quality characteristics demonstrated a downward trend as shown in Fig. 10(b). Table 2 shows that the BPN predictor in the QC/ NTPSO controller has statistically significant influence on the quality characteristics y1 and y2. In other words, the BPN predictor is effective.
2500 2000 1700 1500 y1 y2
1000 500 200 0 0
10
20
30
40
50
Controllable parameter
Run number 1 0.5 u1 u2 u3 u4
0 -0.5 -1 0
10
20
30
40
50
Run Number Fig. 8. The process of implementing the controller.
Fig. 9. Histogram of quality characteristics. This sample is obtained by executing 10 times at 50 runs each. (a) The output of the removal rate, and its 99% confidence interval is [1789.67, 1781.42]. (b) The output of the within-wafer nonuniformity, and its 99% confidence interval is [159.86, 156.39].
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C.-T. Su, J.-T. Wong / Expert Systems with Applications 32 (2007) 848–855 EWMA,Zi
Removal Rate
1800 1781 1750
1843
EWMA
EWMA
1843
1718 0
10
20
30
40
1800 1781 1700
1600
50
1718
0
10
Run number
150
152
104 50
100
(a)
30
EWMA
EWMA
199
20
30
40
50
Within-Wafer Nonuniformity
200
10
20
Run number
Within-Wafer Nonuniformity
0
Control Limits
1900
1850
1700
EWMA,Zi
Removal Rate
Control Limits
1900
40
200
199
150
152
100 0
(b)
Run number
104 10
20
30
40
50
Run number
Fig. 10. The EWMA control chart of quality characteristics: (a) the result with the BPN model; (b) the result without the BPN model.
Table 2 T-test of the effect of BPN model on the result of the controller Factors
T-value
P-value
Removal rate Within-wafer nonuniformity
8.53 8.35
0.00* 0.00*
*
P < 0.05.
5. Conclusions This paper proposed QC/NTPSO approach, a controller constructed with artificial intelligence by adjusting of the parameters in the manufacturing process in order to minimize the error between quality characteristics and the target. This controller adopted ANN as the predictor and TPSO algorithm as the model for optimizing the parameter. CMP, an important process in semiconductor manufacturing, is then used to test the proposed approach. The result has shown that in this example, the quality characteristics of this controller are closer to the target than those of OAQC’s. Only one quality characteristic, however, is closer to the target when compared with GAQC. When adjusting the parameter in the process, the parameters of the proposed approach rendered smaller standard deviation than those of GAQC’s. Among these parameters, there is greater variation in platen speed. In the actual manufacturing process, however, it is a parameter that can be easily controlled. In addition, this paper also tried to uncover how ANN model can influence this controller. The result indicated that under the predictive model without ANN, the output quality characteristics of this controller tended to deviate. The semiconductor industry today faces a manufacturing environment that is becoming more and more complex, and the AI technology relatively
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