Modeling and optimization of the growth rate for ... - Semantic Scholar
Expert Systems with Applications 36 (2009) 4061–4066
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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
Modeling and optimization of the growth rate for ZnO thin films using neural networks and genetic algorithms Young-Don Ko a, Pyung Moon a, Chang Eun Kim a, Moon-Ho Ham b, Jae-Min Myoung b, Ilgu Yun a,* a b
Department of Electrical and Electronic Engineering, Yonsei University, 134 Shinchon-Dong, Seodaemun-Gu, Seoul 120-749, Republic of Korea Department of Metallurgy System Engineering, Yonsei University, 134 Shinchon-Dong, Seodaemun-Gu, Seoul 120-749, Republic of Korea
a r t i c l e Keywords: Process modeling Neural networks Genetic algorithms ZnO PLD
i n f o
a b s t r a c t The process modeling for the growth rate in pulsed laser deposition (PLD)-grown ZnO thin films was investigated using neural networks (NNets) based on the back-propagation (BP) algorithm and the process recipes was optimized via genetic algorithms (GAs). Two input factors were examined with respect to the growth rate as the response factor. D-optimal experimental design technique was performed and the growth rate was characterized by NNets based on the BP algorithm. GAs was then used to search the desired recipes for the desired growth rate on the process. The statistical analysis for those results was then used to verify the fitness of the nonlinear process model. Based on the results, this modeling methodology can explain the characteristics of the thin film growth mechanism varying with process conditions. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Recently, with the development of optoelectronic devices, ZnO becomes distinguished as one of the II–VI compound semiconductors because of the large exciton binding energy (60 meV), the wide band-gap semiconductor and the superior thermal stability. In applications, ZnO can be used for the optical device applications such as light emitting diodes, laser diodes and invisible field effect transistors towards a flat panel display due to exciting optical properties (Aoki et al., 2000; Nakayama and Murayama, 2000; Ryu et al., 2000). According to the previous researches (Chen, Ma, & Yang, 2006; Jiao et al., 2006; Xu et al., 2006), the superior ultraviolet (UV) luminescence from ZnO-based light-emitting diodes (LEDs) was reported and the positive advantages of that were potentially addressed. However, ZnO thin films having the high crystal quality and superior characteristics as the light-emitting device are difficult to characterize the manufacturing process for its nonlinear characteristic in general due to the nature and the unavoidable random variations of the process. Therefore, the response factor must be characterized with respect to the varying process conditions in order to manufacture ZnO thin films used for the optical devices. The relationship between the process input factors and the performance metrics with the process fluctuations needs to be analyzed statistically. In addition, the accurate explanation by the process model can significantly impact the values and the range of process input factors. The statistical variations * 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 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.03.010
of process input factors must be carefully examined to build the process model by considering the ranges and the values of process variables. Over a few years several methodologies for modeling and optimization of nonlinear characteristics that affect the device performance have been researched. In order to characterize the plasma enhanced chemical vapor deposition (PECVD) of SiO2 films deposited under varying conditions, Han and May (1997) performed NNets for the process modeling and optimized the varying condition on the predicted model via genetic algorithms (GAs). For constructing the model of the electron mobility of molecular beam epitaxy (MBE)-grown InAs/AsSb thin film for high electron mobility transistors (HEMT) applications, Triplett, May, and Brown (2002) applied NNets to the device manufacturing process. Hong, May, and Park (2003) investigated NNets of the reactive ion etching using optical emission spectroscopy data. Kim and May (1994) investigated the statistical experimental design and process model for plasma etching using NNets. In this paper, the modeling scheme applied to the thin film fabrication process by using NNets and GAs is presented. D-optimal design was used to make design matrix in this experiment and then carry out the modeling and the optimization. As the above mentioned, Han and May (1997) has been investigated SiO2 thin films by PECVD. Those films are used in the integrated circuit, MOS transistor and the multichip modules as the interlayer dielectrics and passivation layers. In case of the optimization for the modeling response, the comparison of the varying optimization methodology such as GAs, simplex method, Powell’s method and hybrid method as well as the optimal conditions were then
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analyzed, whereas ZnO used in this paper is the one of the various oxide layers, which is used in optoelectronic devices, such as light emitting diodes (LEDs). Additionally, comparing with the others (Han & May, 1997; Hong et al., 2003; Kim & May, 1994; Triplett et al., 2002), this paper focuses on the modeling for the growth rate having a strong effect in order to determine both the electrical and optical properties. Here, taking account of a nonlinear complexity, the predictive modeling and optimization were investigated through NNets and GAs. Considering the accuracy and compatibility of the model, the variations among the models that are the regression, quadratic and NNets were validated by the statistical methodology and the assumption of the model is also verified under the significance level.
tially active and its density is easily controlled by changing the oxygen pressure. The c-axis oriented thin films related to the optical properties were attracted by the substrate temperature and the oxygen pressure effects on the crystal structure and morphology (Ryu et al., 2000). For these reasons, the substrate temperature (T) and the oxygen pressure (P) were selected to investigate the characterization of PLD process. Other process variables such as the repetition rate and the energy density of laser remain constant. The design matrix of PLD process, D-optimal experimental design with 17 runs, is presented in Table 2. The run order has been randomized to avoid statistically the effect of irrelevant factors, which may be present, but not considered in this study. 3.2. Neural network modeling
2. Experiments The initial substrate of n-type InP has doping concentrations of 3 1018 cm3. The PLD technique was used for the deposition of ntype ZnO layer. The chamber was evacuated by a turbomolecular pump to base pressure at 1 106 Torr. Pulsed Nd:YAG laser was operated at a 355-nm wavelength with 2 Hz repetition rate and 2.5 J/cm2 energy density. The ZnO films were deposited with varying substrate temperature in the range of 350–450 °C and oxygen pressure in the range of 250–450 mTorr. A substrate holder was placed at 5 cm from the target. After ZnO thin films were deposited by PLD process, the thicknesses of the ZnO thin films on InP substrate were measured by using the scanning electron microscopy (SEM). 3. Modeling scheme 3.1. D-optimal design Unlike the standard designs, the full factorial design and the fractional factorial design, which cannot cover the complexity of the problem for requiring the small runs, D-optimal design is generally used in a nonlinear design problem with either a constrained or irregularly shaped design space between the process variables (Brown & May, 2005). It allows the presence of qualitative parameters and can cover the continuous design space (Gianchandani & Crary, 1998). In optimal design, an optimal criterion is used for generating the design treatment runs. A general model is Y = XB + e, where Y is a vector of the observations, X is a matrix of the levels of the independent variables, B is a vector of the regression coefficient, and e is a vector of errors. From this model, D-optimal design is to minimize the determinant of (XTX)1 because the generalized variance of the unbiased estimator of B is proportional to (XTX)1. That represents a D-optimality criterion that result in minimizing the determinant of (XTX)1. It means that the volume of the joint confidence region on the vector of regression coefficients is also minimized by D-optimal design (Begot, Voisim, Hiebel, Artioukhine, & Kauffmann, 2002; Gianchandani & Crary, 1998; Myers & Montgomery, 1995). The input factors to characterize the growth rate in PLD-grown ZnO thin film are summarized in Table 1. PLD process is very unique for the growth of oxide films on a semiconductor substrate because the crystal structure of ZnO thin films on the substrate is critical and the oxygen plasma created by the pulsed laser is poten-
Table 1 Summary of process parameters Factor
Symbol
Unit
Range
Remark
Temperature Pressure
T P
°C mTorr
350–450 250–450
Controllable Controllable
NNets consist of several layers, which are input layer, hidden layer and output layer. The most popular method of training feed-forward NNets is the error BP algorithms. BP networks consist of several layers of neurons, which receive, process, and transmit critical information regarding the relationships between the input parameters and corresponding responses. Each neuron contains the weighted sum of its input filtered by a nonlinear transfer function. The typical feed-forward NNets are shown in Fig. 1. The NNet used in this work has 2–9–9–1 structure, which consists of 1 input layer, 2 hidden layers and 1 output layer. The tangent hyperbolic function is used in each node of the hidden layer as the activation function. The NNet structure consists of 9 nodes in each hidden layer. This network was trained on 15 experimental runs with the learning rate of 0.0025 and the momentum coefficient of 0.95. The additional two trials were used for testing data in order to verify the fitness of the NNet output for the results of the training data. The network training was completed when the root mean square error (RMSE) of training of 5% was achieved. 3.3. Recipe synthesis using genetic algorithms In order to find the optimum condition having the specified target response value, one of the methods for global searching algorithm is GAs. Generally, GAs consisted of parallel-search procedures and guided stochastic search techniques based on the mechanics of genetics. In addition, as GAs explore the entire design space by the genetic manipulations, it does not easily fall into a certain local minima or maxima (Chen, 1996).
Table 2 D-optimal design Run
T (°C)
P (mTorr)
Growth rate (lm)
Remark
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
400 400 375 350 425 425 400 450 425 375 400 450 400 350 350 375 450
450 300 350 250 400 300 400 350 350 400 350 450 250 450 350 300 250
0.35 0.42 0.44 0.20 0.20 0.30 0.30 0.20 0.42 0.25 0.48 0.22 0.20 0.23 0.15 0.30 0.20
TR TR TR TE TR TR TR TR TR TE TR TR TR TR TR TR TR
TR, training data. TE, testing data.
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Responses
y1
yj
....
Start
yn
....
Create initial population
Output Layer
Evaluation of each string W 1j
W oj
....
h1
hk
....
ho
Reproduction Hidden Layer(s)
Selection W 11
W mo
....
x1
xi
....
xm
Mutation
Input Layer
Inputs
Calculate fitness function for new generation
Fig. 1. Typical feed-forward neural networks.
In coding genetic searches, binary strings are typically used. One successful method for coding multiparameter optimization problem is concatenated, multiparameter, mapped, fixed-point coding (Goldberg, 1989). If x 2 [0, 2b] is the parameter of interest (where b is the number of bits in the string), the decoded unsigned integer x can be mapped linearly from [0, 2b] to a specified interval [Umin Umax]. In this way, both the range and precision of the decision variables can be controlled. To construct a multiparameter coding, required each single parameter can simply be concatenated. Each coding may have its own sub-length (i.e., its own Umin and Umax). An example of a two-parameter coding with four bits in each parameter is shown in Fig. 2. The ranges of the first and second parameters are 4 and 3.5, respectively. GA operates iteratively through of simple cycle of four stages (Kim & May, 1999): (1) creation of a population of strings; (2) evaluation of each string (3) selection of the best strings; and (4) genetic manipulation to create a new population of strings. GA starts off with the initial populations, which are randomly chosen in the design space and searches the input range effectively for required output variables by means of reproduction, crossover, and mutation. The initial population strings with large fitness values (Fi’s) are assigned a proportionately higher probability of survival into the next generation. This probability is defined as (Han & May, 1996; Thongvigitmanee & May, 2002): Fi P select i ¼ Pn
Evaluation No Yes End Fig. 3. The optimization process flow chart of GAs.
P1
0 1 0 1 1 0
The fitness for an individual string is n times better than another will produce n times the number of offspring in the subsequent generation. After the strings were reproduced, they are stored in a ‘‘mating pool” whose strings then take the process of the crossover and mutation. This operation flowchart is illustrated in Fig. 3. The crossover operator interchanges the behind bit strings of where the crossover point was randomly chosen. The mutation
1 1 0 0 1 10 0 1 0 1 0 0 00 0 0 0 0 0 1st parameter = 4
2st parameter = 3.5
Range [2,4.5]
Range [2.5,4.5]
Precision=0.0025
Precision=0.002
Fig. 2. Example of multiparameter coding.
0 1 0 1 0 1
O1
0 0 0 0 1 0
O2
Crossover Point
P2
0 0 0 0 0 1 Crossover operation
0 0 0 0 0 0 Mutation Point
0 0 0 0 1 0
ð1Þ
i¼1 F
Crossover
Mutation operation Fig. 4. The crossover and mutation operation for GAs.
operator changes a bit string for a certain point from 0 to 1 or from 1 to 0 with the mutation probability. The process schematic for each operator is described in Fig. 4. The parameter values in this study used for searching the optimal conditions are summarized in Table 3. The fitness function for searching the performance index is defined as (Yun & May, 1999): F fit ¼
1þ
Pn
1
2 i¼1 ðymeasured i ypredicted i Þ
ð2Þ
where n is the number of response, ymeasured is the measured response value, ypredicted is the predicted response value.
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Table 3 Parameter values for GAs
Table 5 Summary of RMSE
Parameter
Value
Population size Probability crossover Probability mutation Chromosome length
17 0.95 0.03 20 bits
NNet training RMSE NNet prediction RMSE NNet testing RMSE RMSE for regression model Improvement (%)
5.09 5.22 8.54 10.50 49.71
rffiffiffiffiffiffiffiffiffiffiffiffi SSE n1
4. Results and discussion
RMSE ¼
In order to analyze the deviation and the variation of the response, each sum of square terms was calculated (Myers, 1990). The total deviation consists of the sum between the deviation of b i Þ around the mean ðYÞ and the deviation of the fitted value ð Y the observation (Yi) around fitted regression line. The measure of total variation, denoted by SSTO (total sum of square), is the sum of the squared deviations. SSR (regression sum of square) and SSE represent the sum of square of the regression and error, respectively. The relationship among the each sum of square error and the notations are the following form:
where n is the sample size. The plot of residuals versus fitted values is shown in Fig. 5. One of the assumptions in this analysis is that the residuals are both normally and randomly distributed (Montgomery, 2001). It is observed that the residuals should be scattered evenly around zero and there is no special features or patterns in residuals. The predicted values versus measured values are illustrated in Fig. 6. It is verified that the linear relationship between the network output values and the experimental data. The ‘N’ and the ‘’ points designate the training data and testing data, respectively. It is shown that the modeling output belongs to the range of prediction under the RMSE of training of 5%. The 3-D surface plot of response model for the growth rate is shown in Fig. 7. It is observed that the growth rate for PLD-grown ZnO thin film is near the maximum growth rate when the temperature is in the range of 330–350 °C and the pressure is in the range of 390–410 mTorr. Zn and O2 molecules do not have enough thermal energy to form stoichiometry ZnO thin film so that Zn and O2 molecules need enough thermal energy in order to react up to the maximum growth rate. As the temperature and the pressure increase, the reaction between Zn and O2 molecules actively occurs, and the growth rate increases with the improvement of the oxygen-deficient stoichiometry ZnO thin film simultaneously. Above the maximum growth rate, the increased temperature affects the number of Zn due to Zn evaporation leading to inferior stoichiometric ZnO as Zn has melting point at 693 K (Bae, Lee, Jin, & Im, 2001). With the change of Zn increment, oxygen vacancies are decreased under the increase of the oxygen pressure at the same time (Jin, Bae, Lee, & Im, 2000; Jin, Woo, Im, Base, & Lee, 2001). From the above reasons, the oxygen composition and the change of temperature affect the deposition of the thin film in the circumstance. The growth rate was decreased on the circumstance fully filled with oxygen to limit the crystallite size of the thin film on the higher substrate temperature. The NNet model suggested in this study
SSE ¼ SSTO SSR X X X b i Þ2 b i YÞ2 ¼ ðY i YÞ2 ðY i Y ðY
ð3Þ ð4Þ
b i is the ith predicted value, and Y where Yi is the ith observations, Y is the mean of the fitted values. The R2 value represents the proportion of variation in the response explained by the model. Therefore, the R2 value can be expressed the reduction in variation (SSTO SSE = SSR) as a proportion of the total variation: SSR SSE ¼1 SSTO SSTO
ð5Þ
Generally, the four types of model are used to compare with the NNet model. The regression model and the response surface model that consists of the quadratic terms are the following that: The regression models have the following that (Myers, 1990): y ¼ a0 þ a1 u1 þ a2 u2 þ a3 u1 u2 þ e
ð6Þ
where y is a response variable, ui’s are the two process variables, ai’s are regression coefficients estimated using the least squares method and e is a modeling error. Response surface models may be represented as the full quadratic model (Montgomery, 2001): y ¼ b0 þ
n X
bi X i þ
i¼1
n n X X j¼iþ1 i¼1
bij X i X j þ
n X
bij X 2i
ð7Þ
i¼1
where y is the response variable, n is the number of independent process factor, b’s are model coefficient, and Xi are process factor values. The R2 values for those models are summarized in Table 4. From Table 4, the R2 values for all models are the lower than the NNet model. Therefore, the portion of the model explanation in NNets is better than the portion of the regression model. The RMSE values for the each models developed via regression models are summarized in Table 5. The RMSE is defined as
0.10 0.08 0.06 0.04 Residuals
R2 ¼
ð8Þ
0.02 0.00 -0.02 -0.04
Table 4 Summary of R2 values
-0.06
Model
R2 (%)
NNets Full quadratic Linear with square term Linear with interaction term Regression
76.8 53.8 50.8 2.90 1.30
-0.08 -0.10 1
2
3
4
5
6
7 8 9 10 11 12 13 14 15 Run order
Fig. 5. The residuals plot by run order for the growth rate.
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Y.-D. Ko et al. / Expert Systems with Applications 36 (2009) 4061–4066 Table 7 Verification of optimization results for GAs
Growth rate [μ m] (Network output)
0.6
0.5
0.4
Input set
Optimized
Measured
T (°C)
P (mTorr)
Film thickness (Å)
T (°C)
P (mTorr)
Film thickness (Å)
Set 1 Set 2
400 380
398 390
3540 3536
400 375
400 400
3500 3480
0.3 Table 8 Performance parameter fluctuations for each process parameter variation
0.2
Process variable
0.1
Training data Testing data
0.0 0.0
0.1
0.2
0.3
0.4
0.5
P (mTorr)
Film thickness
400–450 400
350 300–425
0.088 0.098
0.6 used to analyze the statistical variation for the film thickness on the process. The statistical variations of thin film thickness for each process parameter variation were summarized in Table 8. The standard deviation for changing temperature has small variation than the effect of pressure. However, there is no heavily unbiased variation for the each input factor on the process.
Growth rate [μ m](Experimental data) Fig. 6. Neural network modeling result for the growth rate.
Growth rate [ m] [μm]
Statistical variation (SD)
T (°C)
5. Conclusion
1 0. 0.5 0 450 400
350 375
350
Pressure [mTorr]
400
300
425 250
Temperature [ºC]
450
Fig. 7. The surface plot of neural network model for the growth rate.
are in good agreement with the growth rate related to the characteristics of ZnO thin film such as photoluminescence (PL) and crystallinity, and X-ray diffraction (XRD) (Kim et al., 2004; Shim, Kang, Kang, Kim, & Lee, 2002). These models can explain the constrained conditions between the control variables for the response depending on the variation of the process, which the regression and quadratic models do not predict the response. Two recipe sets with respect to the desired growth rate and the fitness value were summarized in Table 6. In addition, in order to verify the recipe synthesis and the response value, the input recipes via GAs were used in the model and those film thicknesses were predicted 3540 Å and 3536 Å when the desired value is fixed to 3500 Å, respectively. To comparing with the measured data, the each film thickness results between the optimized sets and the measured sets approaching the optimized conditions for input sets were observed and summarized in Table 7. The designated condition ranges with respect to the effect of process parameters are Table 6 Optimization results for genetic algorithms Optimized input set
T (°C)
P (mTorr)
Fitness value
Set 1 Set 2
400 380
398 390
0.996 0.998
The characterization of the growth rate of ZnO thin film fabricated by PLD process has been investigated. D-optimal design was performed and the regression and the NNet model were evaluated. Based on the modeling results, the NNet model was more accurate model than the other models that are the regression and quadratic models, indicating that the NNet model can explain the nonlinear characteristics of the PLD process. The film growth mechanism of the PLD process is also well explained by the NNet model. In addition, it was verified that GAs could find a desired process condition for a certain growth rate of ZnO thin film deposited by PLD process. Finally, even though the modeling methodology used in this work was based on the statistical assumption and analysis, the desired recipes on the semiconductor manufacturing process can be provided with the acceptable tolerance by GAs and improve a prediction accuracy for the response on a certain process. Acknowledgements This work was supported by Yonsei University Institute of TMS Information Technology, a Brain Korea 21 program, Korea and by the Korea Science and Engineering Foundation(KOSEF) grant funded by the Korea government(MOST) (No. R01-2007-00020143-0). References Aoki, T., Hatanaka, Y., & Look, D. C. (2000). ZnO diode fabricated by excimer-laser doping. Applied Physics Letters, 76(22), 3257–3258. Bae, S. H., Lee, S. Y., Jin, B. J., & Im, S. (2001). Growth and characterization of ZnO films grown by pulse laser deposition. Applied Surface Science, 525–528. Begot, S., Voisim, E., Hiebel, P., Artioukhine, E., & Kauffmann, J. M. (2002). D-optimal experimental design applied to a linear magnetostatic inverse problem. IEEE Transactions on Magnetics, 38(2), 1065–1068. Brown, T. D., & May, G. S. (2005). Hybrid neural network modeling of anion exchange at the interface of mixed anion III–V heterostructures grown by molecular beam epitaxy. IEEE Transactions on Semiconductor Manufacturing, 18(4), 614–621. Chen, C. H. (1996). Fuzzy logic and neural network handbook. New York: McGrawHill.
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Chen, P., Ma, X., & Yang, D. (2006). Fairly pure ultraviolet electroluminescence from ZnO-based light-emitting devices. Applied Physics Letters, 89, 111–112. Gianchandani, Y. B., & Crary, S. B. (1998). Parametric modeling of a microaccelerometer: Comparing I- and D-optimal design of experiments for finite-element analysis. Journal of Microelectromechanical Systems, 7(2), 274–282. Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Addison Wesley. Han, S.-S., & May, G. S. (1996). Optimization of neural network structure and learning parameters using genetic algorithms. In Proceedings of 8th international conference on tools with artificial intelligence (pp. 200–206). Han, S.-S., & May, G. S. (1997). Using neural network process models to perform PECVD silicon dioxide recipe synthesis via genetic algorithms. IEEE Transactions on Semiconductor Manufacturing, 10(2), 279–287. Hong, S. J., May, G. S., & Park, D.-C. (2003). Neural network modeling of reactive ion etching using optical emission spectroscopy data. IEEE Transactions on Semiconductor Manufacturing, 16(4), 598–608. Jiao, S. J., Zhang, Z. Z., Lu, Y. M., Sehn, D. Z., Yao, B., Zhang, J. Y., et al. (2006). ZnO p–n junction light-emitting diodes fabricated on sapphire substrates. Applied Physics Letters, 88, 031911. Jin, B. J., Woo, H. S., Im, S., Base, S. H., & Lee, S. Y. (2001). Relationship between photoluminescence and electrical properties of ZnO thin films grown by pulsed laser deposition. Applied Surface Science, 169–170, 521–524. Jin, B. J., Bae, S. H., Lee, S. Y., & Im, S. (2000). Effects of native defects on optical and electrical properties of ZnO prepared by pulsed laser deposition. Applied Surface Science B, 71, 301–305. Kim, B., & May, G. S. (1994). An optimal neural network process model for plasma etching. IEEE Transactions on Semiconductor Manufacturing, 7(1), 12–21. Kim, M.-S., Ko, Y.-D., Hong, J.-H., Jeong, M.-C., Myoung, J.-M., & Yun, I. (2004). Characteristics and processing effects of ZrO2 thin films grown by metal-organic molecular beam epitaxy. Applied Surface Science, 227, 387–398.
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Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
Modeling and optimization of the growth rate for ZnO thin films using neural networks and genetic algorithms Young-Don Ko a, Pyung Moon a, Chang Eun Kim a, Moon-Ho Ham b, Jae-Min Myoung b, Ilgu Yun a,* a b
Department of Electrical and Electronic Engineering, Yonsei University, 134 Shinchon-Dong, Seodaemun-Gu, Seoul 120-749, Republic of Korea Department of Metallurgy System Engineering, Yonsei University, 134 Shinchon-Dong, Seodaemun-Gu, Seoul 120-749, Republic of Korea
a r t i c l e Keywords: Process modeling Neural networks Genetic algorithms ZnO PLD
i n f o
a b s t r a c t The process modeling for the growth rate in pulsed laser deposition (PLD)-grown ZnO thin films was investigated using neural networks (NNets) based on the back-propagation (BP) algorithm and the process recipes was optimized via genetic algorithms (GAs). Two input factors were examined with respect to the growth rate as the response factor. D-optimal experimental design technique was performed and the growth rate was characterized by NNets based on the BP algorithm. GAs was then used to search the desired recipes for the desired growth rate on the process. The statistical analysis for those results was then used to verify the fitness of the nonlinear process model. Based on the results, this modeling methodology can explain the characteristics of the thin film growth mechanism varying with process conditions. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Recently, with the development of optoelectronic devices, ZnO becomes distinguished as one of the II–VI compound semiconductors because of the large exciton binding energy (60 meV), the wide band-gap semiconductor and the superior thermal stability. In applications, ZnO can be used for the optical device applications such as light emitting diodes, laser diodes and invisible field effect transistors towards a flat panel display due to exciting optical properties (Aoki et al., 2000; Nakayama and Murayama, 2000; Ryu et al., 2000). According to the previous researches (Chen, Ma, & Yang, 2006; Jiao et al., 2006; Xu et al., 2006), the superior ultraviolet (UV) luminescence from ZnO-based light-emitting diodes (LEDs) was reported and the positive advantages of that were potentially addressed. However, ZnO thin films having the high crystal quality and superior characteristics as the light-emitting device are difficult to characterize the manufacturing process for its nonlinear characteristic in general due to the nature and the unavoidable random variations of the process. Therefore, the response factor must be characterized with respect to the varying process conditions in order to manufacture ZnO thin films used for the optical devices. The relationship between the process input factors and the performance metrics with the process fluctuations needs to be analyzed statistically. In addition, the accurate explanation by the process model can significantly impact the values and the range of process input factors. The statistical variations * 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 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.03.010
of process input factors must be carefully examined to build the process model by considering the ranges and the values of process variables. Over a few years several methodologies for modeling and optimization of nonlinear characteristics that affect the device performance have been researched. In order to characterize the plasma enhanced chemical vapor deposition (PECVD) of SiO2 films deposited under varying conditions, Han and May (1997) performed NNets for the process modeling and optimized the varying condition on the predicted model via genetic algorithms (GAs). For constructing the model of the electron mobility of molecular beam epitaxy (MBE)-grown InAs/AsSb thin film for high electron mobility transistors (HEMT) applications, Triplett, May, and Brown (2002) applied NNets to the device manufacturing process. Hong, May, and Park (2003) investigated NNets of the reactive ion etching using optical emission spectroscopy data. Kim and May (1994) investigated the statistical experimental design and process model for plasma etching using NNets. In this paper, the modeling scheme applied to the thin film fabrication process by using NNets and GAs is presented. D-optimal design was used to make design matrix in this experiment and then carry out the modeling and the optimization. As the above mentioned, Han and May (1997) has been investigated SiO2 thin films by PECVD. Those films are used in the integrated circuit, MOS transistor and the multichip modules as the interlayer dielectrics and passivation layers. In case of the optimization for the modeling response, the comparison of the varying optimization methodology such as GAs, simplex method, Powell’s method and hybrid method as well as the optimal conditions were then
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analyzed, whereas ZnO used in this paper is the one of the various oxide layers, which is used in optoelectronic devices, such as light emitting diodes (LEDs). Additionally, comparing with the others (Han & May, 1997; Hong et al., 2003; Kim & May, 1994; Triplett et al., 2002), this paper focuses on the modeling for the growth rate having a strong effect in order to determine both the electrical and optical properties. Here, taking account of a nonlinear complexity, the predictive modeling and optimization were investigated through NNets and GAs. Considering the accuracy and compatibility of the model, the variations among the models that are the regression, quadratic and NNets were validated by the statistical methodology and the assumption of the model is also verified under the significance level.
tially active and its density is easily controlled by changing the oxygen pressure. The c-axis oriented thin films related to the optical properties were attracted by the substrate temperature and the oxygen pressure effects on the crystal structure and morphology (Ryu et al., 2000). For these reasons, the substrate temperature (T) and the oxygen pressure (P) were selected to investigate the characterization of PLD process. Other process variables such as the repetition rate and the energy density of laser remain constant. The design matrix of PLD process, D-optimal experimental design with 17 runs, is presented in Table 2. The run order has been randomized to avoid statistically the effect of irrelevant factors, which may be present, but not considered in this study. 3.2. Neural network modeling
2. Experiments The initial substrate of n-type InP has doping concentrations of 3 1018 cm3. The PLD technique was used for the deposition of ntype ZnO layer. The chamber was evacuated by a turbomolecular pump to base pressure at 1 106 Torr. Pulsed Nd:YAG laser was operated at a 355-nm wavelength with 2 Hz repetition rate and 2.5 J/cm2 energy density. The ZnO films were deposited with varying substrate temperature in the range of 350–450 °C and oxygen pressure in the range of 250–450 mTorr. A substrate holder was placed at 5 cm from the target. After ZnO thin films were deposited by PLD process, the thicknesses of the ZnO thin films on InP substrate were measured by using the scanning electron microscopy (SEM). 3. Modeling scheme 3.1. D-optimal design Unlike the standard designs, the full factorial design and the fractional factorial design, which cannot cover the complexity of the problem for requiring the small runs, D-optimal design is generally used in a nonlinear design problem with either a constrained or irregularly shaped design space between the process variables (Brown & May, 2005). It allows the presence of qualitative parameters and can cover the continuous design space (Gianchandani & Crary, 1998). In optimal design, an optimal criterion is used for generating the design treatment runs. A general model is Y = XB + e, where Y is a vector of the observations, X is a matrix of the levels of the independent variables, B is a vector of the regression coefficient, and e is a vector of errors. From this model, D-optimal design is to minimize the determinant of (XTX)1 because the generalized variance of the unbiased estimator of B is proportional to (XTX)1. That represents a D-optimality criterion that result in minimizing the determinant of (XTX)1. It means that the volume of the joint confidence region on the vector of regression coefficients is also minimized by D-optimal design (Begot, Voisim, Hiebel, Artioukhine, & Kauffmann, 2002; Gianchandani & Crary, 1998; Myers & Montgomery, 1995). The input factors to characterize the growth rate in PLD-grown ZnO thin film are summarized in Table 1. PLD process is very unique for the growth of oxide films on a semiconductor substrate because the crystal structure of ZnO thin films on the substrate is critical and the oxygen plasma created by the pulsed laser is poten-
Table 1 Summary of process parameters Factor
Symbol
Unit
Range
Remark
Temperature Pressure
T P
°C mTorr
350–450 250–450
Controllable Controllable
NNets consist of several layers, which are input layer, hidden layer and output layer. The most popular method of training feed-forward NNets is the error BP algorithms. BP networks consist of several layers of neurons, which receive, process, and transmit critical information regarding the relationships between the input parameters and corresponding responses. Each neuron contains the weighted sum of its input filtered by a nonlinear transfer function. The typical feed-forward NNets are shown in Fig. 1. The NNet used in this work has 2–9–9–1 structure, which consists of 1 input layer, 2 hidden layers and 1 output layer. The tangent hyperbolic function is used in each node of the hidden layer as the activation function. The NNet structure consists of 9 nodes in each hidden layer. This network was trained on 15 experimental runs with the learning rate of 0.0025 and the momentum coefficient of 0.95. The additional two trials were used for testing data in order to verify the fitness of the NNet output for the results of the training data. The network training was completed when the root mean square error (RMSE) of training of 5% was achieved. 3.3. Recipe synthesis using genetic algorithms In order to find the optimum condition having the specified target response value, one of the methods for global searching algorithm is GAs. Generally, GAs consisted of parallel-search procedures and guided stochastic search techniques based on the mechanics of genetics. In addition, as GAs explore the entire design space by the genetic manipulations, it does not easily fall into a certain local minima or maxima (Chen, 1996).
Table 2 D-optimal design Run
T (°C)
P (mTorr)
Growth rate (lm)
Remark
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
400 400 375 350 425 425 400 450 425 375 400 450 400 350 350 375 450
450 300 350 250 400 300 400 350 350 400 350 450 250 450 350 300 250
0.35 0.42 0.44 0.20 0.20 0.30 0.30 0.20 0.42 0.25 0.48 0.22 0.20 0.23 0.15 0.30 0.20
TR TR TR TE TR TR TR TR TR TE TR TR TR TR TR TR TR
TR, training data. TE, testing data.
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Responses
y1
yj
....
Start
yn
....
Create initial population
Output Layer
Evaluation of each string W 1j
W oj
....
h1
hk
....
ho
Reproduction Hidden Layer(s)
Selection W 11
W mo
....
x1
xi
....
xm
Mutation
Input Layer
Inputs
Calculate fitness function for new generation
Fig. 1. Typical feed-forward neural networks.
In coding genetic searches, binary strings are typically used. One successful method for coding multiparameter optimization problem is concatenated, multiparameter, mapped, fixed-point coding (Goldberg, 1989). If x 2 [0, 2b] is the parameter of interest (where b is the number of bits in the string), the decoded unsigned integer x can be mapped linearly from [0, 2b] to a specified interval [Umin Umax]. In this way, both the range and precision of the decision variables can be controlled. To construct a multiparameter coding, required each single parameter can simply be concatenated. Each coding may have its own sub-length (i.e., its own Umin and Umax). An example of a two-parameter coding with four bits in each parameter is shown in Fig. 2. The ranges of the first and second parameters are 4 and 3.5, respectively. GA operates iteratively through of simple cycle of four stages (Kim & May, 1999): (1) creation of a population of strings; (2) evaluation of each string (3) selection of the best strings; and (4) genetic manipulation to create a new population of strings. GA starts off with the initial populations, which are randomly chosen in the design space and searches the input range effectively for required output variables by means of reproduction, crossover, and mutation. The initial population strings with large fitness values (Fi’s) are assigned a proportionately higher probability of survival into the next generation. This probability is defined as (Han & May, 1996; Thongvigitmanee & May, 2002): Fi P select i ¼ Pn
Evaluation No Yes End Fig. 3. The optimization process flow chart of GAs.
P1
0 1 0 1 1 0
The fitness for an individual string is n times better than another will produce n times the number of offspring in the subsequent generation. After the strings were reproduced, they are stored in a ‘‘mating pool” whose strings then take the process of the crossover and mutation. This operation flowchart is illustrated in Fig. 3. The crossover operator interchanges the behind bit strings of where the crossover point was randomly chosen. The mutation
1 1 0 0 1 10 0 1 0 1 0 0 00 0 0 0 0 0 1st parameter = 4
2st parameter = 3.5
Range [2,4.5]
Range [2.5,4.5]
Precision=0.0025
Precision=0.002
Fig. 2. Example of multiparameter coding.
0 1 0 1 0 1
O1
0 0 0 0 1 0
O2
Crossover Point
P2
0 0 0 0 0 1 Crossover operation
0 0 0 0 0 0 Mutation Point
0 0 0 0 1 0
ð1Þ
i¼1 F
Crossover
Mutation operation Fig. 4. The crossover and mutation operation for GAs.
operator changes a bit string for a certain point from 0 to 1 or from 1 to 0 with the mutation probability. The process schematic for each operator is described in Fig. 4. The parameter values in this study used for searching the optimal conditions are summarized in Table 3. The fitness function for searching the performance index is defined as (Yun & May, 1999): F fit ¼
1þ
Pn
1
2 i¼1 ðymeasured i ypredicted i Þ
ð2Þ
where n is the number of response, ymeasured is the measured response value, ypredicted is the predicted response value.
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Table 3 Parameter values for GAs
Table 5 Summary of RMSE
Parameter
Value
Population size Probability crossover Probability mutation Chromosome length
17 0.95 0.03 20 bits
NNet training RMSE NNet prediction RMSE NNet testing RMSE RMSE for regression model Improvement (%)
5.09 5.22 8.54 10.50 49.71
rffiffiffiffiffiffiffiffiffiffiffiffi SSE n1
4. Results and discussion
RMSE ¼
In order to analyze the deviation and the variation of the response, each sum of square terms was calculated (Myers, 1990). The total deviation consists of the sum between the deviation of b i Þ around the mean ðYÞ and the deviation of the fitted value ð Y the observation (Yi) around fitted regression line. The measure of total variation, denoted by SSTO (total sum of square), is the sum of the squared deviations. SSR (regression sum of square) and SSE represent the sum of square of the regression and error, respectively. The relationship among the each sum of square error and the notations are the following form:
where n is the sample size. The plot of residuals versus fitted values is shown in Fig. 5. One of the assumptions in this analysis is that the residuals are both normally and randomly distributed (Montgomery, 2001). It is observed that the residuals should be scattered evenly around zero and there is no special features or patterns in residuals. The predicted values versus measured values are illustrated in Fig. 6. It is verified that the linear relationship between the network output values and the experimental data. The ‘N’ and the ‘’ points designate the training data and testing data, respectively. It is shown that the modeling output belongs to the range of prediction under the RMSE of training of 5%. The 3-D surface plot of response model for the growth rate is shown in Fig. 7. It is observed that the growth rate for PLD-grown ZnO thin film is near the maximum growth rate when the temperature is in the range of 330–350 °C and the pressure is in the range of 390–410 mTorr. Zn and O2 molecules do not have enough thermal energy to form stoichiometry ZnO thin film so that Zn and O2 molecules need enough thermal energy in order to react up to the maximum growth rate. As the temperature and the pressure increase, the reaction between Zn and O2 molecules actively occurs, and the growth rate increases with the improvement of the oxygen-deficient stoichiometry ZnO thin film simultaneously. Above the maximum growth rate, the increased temperature affects the number of Zn due to Zn evaporation leading to inferior stoichiometric ZnO as Zn has melting point at 693 K (Bae, Lee, Jin, & Im, 2001). With the change of Zn increment, oxygen vacancies are decreased under the increase of the oxygen pressure at the same time (Jin, Bae, Lee, & Im, 2000; Jin, Woo, Im, Base, & Lee, 2001). From the above reasons, the oxygen composition and the change of temperature affect the deposition of the thin film in the circumstance. The growth rate was decreased on the circumstance fully filled with oxygen to limit the crystallite size of the thin film on the higher substrate temperature. The NNet model suggested in this study
SSE ¼ SSTO SSR X X X b i Þ2 b i YÞ2 ¼ ðY i YÞ2 ðY i Y ðY
ð3Þ ð4Þ
b i is the ith predicted value, and Y where Yi is the ith observations, Y is the mean of the fitted values. The R2 value represents the proportion of variation in the response explained by the model. Therefore, the R2 value can be expressed the reduction in variation (SSTO SSE = SSR) as a proportion of the total variation: SSR SSE ¼1 SSTO SSTO
ð5Þ
Generally, the four types of model are used to compare with the NNet model. The regression model and the response surface model that consists of the quadratic terms are the following that: The regression models have the following that (Myers, 1990): y ¼ a0 þ a1 u1 þ a2 u2 þ a3 u1 u2 þ e
ð6Þ
where y is a response variable, ui’s are the two process variables, ai’s are regression coefficients estimated using the least squares method and e is a modeling error. Response surface models may be represented as the full quadratic model (Montgomery, 2001): y ¼ b0 þ
n X
bi X i þ
i¼1
n n X X j¼iþ1 i¼1
bij X i X j þ
n X
bij X 2i
ð7Þ
i¼1
where y is the response variable, n is the number of independent process factor, b’s are model coefficient, and Xi are process factor values. The R2 values for those models are summarized in Table 4. From Table 4, the R2 values for all models are the lower than the NNet model. Therefore, the portion of the model explanation in NNets is better than the portion of the regression model. The RMSE values for the each models developed via regression models are summarized in Table 5. The RMSE is defined as
0.10 0.08 0.06 0.04 Residuals
R2 ¼
ð8Þ
0.02 0.00 -0.02 -0.04
Table 4 Summary of R2 values
-0.06
Model
R2 (%)
NNets Full quadratic Linear with square term Linear with interaction term Regression
76.8 53.8 50.8 2.90 1.30
-0.08 -0.10 1
2
3
4
5
6
7 8 9 10 11 12 13 14 15 Run order
Fig. 5. The residuals plot by run order for the growth rate.
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Growth rate [μ m] (Network output)
0.6
0.5
0.4
Input set
Optimized
Measured
T (°C)
P (mTorr)
Film thickness (Å)
T (°C)
P (mTorr)
Film thickness (Å)
Set 1 Set 2
400 380
398 390
3540 3536
400 375
400 400
3500 3480
0.3 Table 8 Performance parameter fluctuations for each process parameter variation
0.2
Process variable
0.1
Training data Testing data
0.0 0.0
0.1
0.2
0.3
0.4
0.5
P (mTorr)
Film thickness
400–450 400
350 300–425
0.088 0.098
0.6 used to analyze the statistical variation for the film thickness on the process. The statistical variations of thin film thickness for each process parameter variation were summarized in Table 8. The standard deviation for changing temperature has small variation than the effect of pressure. However, there is no heavily unbiased variation for the each input factor on the process.
Growth rate [μ m](Experimental data) Fig. 6. Neural network modeling result for the growth rate.
Growth rate [ m] [μm]
Statistical variation (SD)
T (°C)
5. Conclusion
1 0. 0.5 0 450 400
350 375
350
Pressure [mTorr]
400
300
425 250
Temperature [ºC]
450
Fig. 7. The surface plot of neural network model for the growth rate.
are in good agreement with the growth rate related to the characteristics of ZnO thin film such as photoluminescence (PL) and crystallinity, and X-ray diffraction (XRD) (Kim et al., 2004; Shim, Kang, Kang, Kim, & Lee, 2002). These models can explain the constrained conditions between the control variables for the response depending on the variation of the process, which the regression and quadratic models do not predict the response. Two recipe sets with respect to the desired growth rate and the fitness value were summarized in Table 6. In addition, in order to verify the recipe synthesis and the response value, the input recipes via GAs were used in the model and those film thicknesses were predicted 3540 Å and 3536 Å when the desired value is fixed to 3500 Å, respectively. To comparing with the measured data, the each film thickness results between the optimized sets and the measured sets approaching the optimized conditions for input sets were observed and summarized in Table 7. The designated condition ranges with respect to the effect of process parameters are Table 6 Optimization results for genetic algorithms Optimized input set
T (°C)
P (mTorr)
Fitness value
Set 1 Set 2
400 380
398 390
0.996 0.998
The characterization of the growth rate of ZnO thin film fabricated by PLD process has been investigated. D-optimal design was performed and the regression and the NNet model were evaluated. Based on the modeling results, the NNet model was more accurate model than the other models that are the regression and quadratic models, indicating that the NNet model can explain the nonlinear characteristics of the PLD process. The film growth mechanism of the PLD process is also well explained by the NNet model. In addition, it was verified that GAs could find a desired process condition for a certain growth rate of ZnO thin film deposited by PLD process. Finally, even though the modeling methodology used in this work was based on the statistical assumption and analysis, the desired recipes on the semiconductor manufacturing process can be provided with the acceptable tolerance by GAs and improve a prediction accuracy for the response on a certain process. Acknowledgements This work was supported by Yonsei University Institute of TMS Information Technology, a Brain Korea 21 program, Korea and by the Korea Science and Engineering Foundation(KOSEF) grant funded by the Korea government(MOST) (No. R01-2007-00020143-0). References Aoki, T., Hatanaka, Y., & Look, D. C. (2000). ZnO diode fabricated by excimer-laser doping. Applied Physics Letters, 76(22), 3257–3258. Bae, S. H., Lee, S. Y., Jin, B. J., & Im, S. (2001). Growth and characterization of ZnO films grown by pulse laser deposition. Applied Surface Science, 525–528. Begot, S., Voisim, E., Hiebel, P., Artioukhine, E., & Kauffmann, J. M. (2002). D-optimal experimental design applied to a linear magnetostatic inverse problem. IEEE Transactions on Magnetics, 38(2), 1065–1068. Brown, T. D., & May, G. S. (2005). Hybrid neural network modeling of anion exchange at the interface of mixed anion III–V heterostructures grown by molecular beam epitaxy. IEEE Transactions on Semiconductor Manufacturing, 18(4), 614–621. Chen, C. H. (1996). Fuzzy logic and neural network handbook. New York: McGrawHill.
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