The Estimation of Thin Film Properties by Neural Network

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1 Automaton, Control and Intellgent Systems 2016; 4(2): do: /j.acs ISS: (Prnt); ISS: (Onlne) The Estmaton of Thn Flm Propertes by eural etwork Ch-Yen Shen 1, Yu-Ju Chen 2, Shumng T. Wang 1, Chuo-Yean Chang 3, Rey-Chue Hwang 1, * 1 Electrcal Engneerng Department, I-Shou Unversty, Kaohsung Cty, Tawan 2 Informaton Management Department, Cheng-Shu Unversty, Kaohsung Cty, Tawan 3 Electrcal Engneerng Department, Cheng-Shu Unversty, Kaohsung Cty, Tawan Emal address: cyshen@su.edu.tw (Ch-Yen Shen), yjchen@su.edu.tw (Yu-Ju Chen), smwang@su.edu.tw (S. T. Wang), cychang@csu.edu.tw (Chuo-Yean Chang), rchwang@su.edu.tw (Rey-Chue Hwang) * Correspondng author To cte ths artcle: Ch-Yen Shen, Yu-Ju Chen, Shumng T. Wang, Chuo-Yean Chang, Rey-Chue Hwang. The Estmaton of Thn Flm Propertes by eural etwork. Automaton, Control and Intellgent Systems. Vol. 4, o. 2, 2016, pp do: /j.acs Receved: February 22, 2016; Accepted: March 21, 2016; Publshed: March 25, 2016 Abstract: Ths paper presents a method based on neural network () for estmatng the propertes of semconductor thn flm. Through the effectve learnng process, s able to catch the relatonshp between nput and output pars bypassng the complcated statstcal steps such as model hypothess, dentfcaton, estmaton of model parameters, and verfcaton. Such an estmator then can be developed to be a smart mechansm whch can help the techncan to set the relevant control parameters n the manufacturng process of thn flm. In ths research, the thckness and refractve ndex (RI) of thn flm were estmated by the well learned model. From the studed results shown, the propertes of thn flm ndeed could be estmated n advance accordng to the relevant control parameters n the manufacturng process. That also means the estmator we developed could be bult and fulflled ts functon. Keywords: eural etwork, Thn Flm, Manufacturng Process 1. Introducton In recent twenty years, the hgh-tech sklls have been developed wdely and vtally n varous electronc applances, such as photoelectrc, semconductor and bomedcal chps. The electronc ndustry has become the focus of economc development for many countres. Besdes, due to the fast mprovement of manufacturng technque, more and more electronc products are requested to be small and exquste. Ther functon s requested to be more powerful ether. It s well-known that thn flm s an mportant and ndspensable part for many electronc products. Takng the wafer manufacturng as an example, the flmng process plays an mportant and key role n the wafer front-end manufacturng step. Fgure 1 shows the flowchart of wafer manufacturng process [1]. Thus, f the relevant manufacturng parameters of flmng process could be set quckly and accurately, not only the effcency of workng machne can be greatly mproved, but also the tme and frequency of machne test can be reduced effectvely. Fgure 1. The manufacturng process of wafer.

2 Automaton, Control and Intellgent Systems 2016; 4(2): Generally, Chemcal Vapor Deposton (CVD) s the popular method used n the feld of thn flm manufacturng process. In CVD process, many complcated and nonlnear chemcal and physcal reactons are hardly analyzed. The phenomena of partcle drft and varaton are happened very often n the flmng process ether. Undoubtedly, these uncontrolled factors wll affect the qualty of flmng process very serously. Thus, how to set the adequate manufacturng parameters for mprovng the yeld rate and reducng the tmes of machne test has become the most mportant work n the thn flm manufacturng process. Unfortunately, tral-and-error s stll the common method taken by the techncans n many companes. As we know, the number of faled manufacturng process and the defectve product could be possbly rased, f the manufacturng parameters were determned by the techncan based on personal experence only. Thus, several studes about the optmal thn flm manufacturng have been proposed [2-5]. Recently, due to the fast development of artfcal ntellgent technques, some studes about the optmal control of flm manufacturng process were reported. For nstance, the genetc algorthm (GA) had been used for searchng the optmal parameters of physcal vapor deposton manufacturng control process [4]. Hseh, Tong, Cu and Hwang et al. proposed the flm s control and estmaton by usng technques [5-14]. Snce the powerful learnng and modelng capabltes, has been wdely used n dfferent applcatons, such as the sgnal processng and control [15-19]. Bascally, through the well learnng, could generate an effcent mappng between nput and output pars bypassng the complcated statstcal steps. The well-traned model then can be used for the specfc work. In ths research, an artfcal ntellgent (AI) system based on model for the estmaton of flm propertes s studed. Its am s that accordng to the estmaton nformaton provded, the junor techncan wth no full experence s able to make a good settng work for the manufacturng parameters n the flmng process. Thus, such an AI system can not only help the techncan to do the work of flm manufacturng very effcently and easly, but also reduce the rate of defectve products and then save the producton cost. 2. eural etwork technque s the man tool used for constructng the estmator of flm propertes. As prevous descrptons, the relatonshp between nput and output pars s expected to be obtaned through the well learnng of. The structure commonly known as mult-layered feed-forward network s used n ths study. The supervsed wth error back-propagaton (BP) learnng algorthm s taken for s tranng [15-17]. An example of a three-layered feed-forward archtecture as shown n Fgure 2 s the model of selected topology. Each layer s connected to a layer above t n a feed-forward manner, whch means no feed-back from the same layer or a layer above. All connectons have a multplyng weght assocated wth them. Tranng s equvalent to fnd the proper weghts for all connectons such that a desred output s generated for a gven nput set. Once the neural network s well traned, the proper nput nformaton could be nferred n accordance wth an expected output. In other words, the useful nformaton can be found for helpng the techncan to do the well control n the manufacturng process. Fgure 2. A three-layered feed-forward archtecture. In ths study, the error back-propagaton (BP) learnng algorthm s used for s tranng. The major steps of BP learnng rule algorthm s brefly summarzed as follows [15-17]. 1 st step: Intalze all weghts (ω j ) to the small random values frstly. 2 nd step: Present an nput pattern wth the correspondng desred outputs and then calculate the outputs. 3 rd step: Fnd the error term for all nodes. 4 th step: Adjust weghts by ω j( n + 1) = ωj(n) + αδ jx + ζ( ωj(n)- ωj(n-1)) (1) where n+1, n and n-1 are the next, present, and prevous teraton numbers, respectvely. δ s the error of node j and j X s the th nput of node j. α s the learnng rate, the step sze n the gradent search algorthm. ζ s the momentum and ts value s between 0 and 1. 5 th step: Present another nput pattern and go back to 2 nd step. 3. Experments In our study, the thn flm data manufactured by usng two recpes, LDRXX and XX, were collected and smulated. Table 1 and Table 2 present the examples of two collected data sets. The numbers of LDRXX and XX data sets are 102 and 89, respectvely.

3 17 Ch-Yen Shen et al.: The Estmaton of Thn Flm Propertes by eural etwork Table 1. The examples of data manufactured by usng recpe LDRXX. Manufacturng Parameters DT cshdst factor (mgm) HE O 2 HFRF LFRF Thn Flm Propertes Thckness RI Table 2. The examples of data manufactured by usng recpe XX. Manufacturng Parameters DT cshdst factor (mgm) HE O 2 HFRF LFRF Thn Flm Propertes Thckness RI The values of thckness and RI of thn flm are expected to be estmated by the well-traned model. In order to farly demonstrate the effectveness of model n the estmaton of thn flm propertes, three same sze data sets,.e. LDR-1a, LDR-1b, and LDR-1c, are randomly reorganzed from data LDRXX. Smlarly, three same sze data sets, -1a, -1b and -1c, are randomly reorganzed from data XX. In the smulatons of data LDR-1a, LDR-1b and LDR-1c, 70 sets were used for s tranng and 32 sets were used for testng. For data -1a, -1b and -1c, 59 sets were used for s tranng and 30 sets were used for testng. For all data sets, the sze of n thckness estmaton s The nputs are DT, factor, HFRF, LFRF. In RI estmaton, the sze of s The nputs are DT, factor, HFRF, LFRF and thckness. The mean absolute error (MAE) and mean absolute percentage error (MAPE) are used as the estmated measurements. MAPE MAE = = = 1 y y ˆ y ˆ y y = 1 100% Where, y and ŷ are actual and estmated values. s the total number of estmaton data. In order to observe the dstrbuton behavors of all tranng and test data sets, the smple statstcal analyss was done. For example, Table 3 lsts the nformaton of mean value, varance and standard devaton for the whole LDR-1a data, LDR-1a 70 tranng data and 32 LDR-1a test data. Smlarly, Table 4 and Table 5 lst the statstcs of data LDR-1b and LDR-1c, respectvely. Table 6 lsts the estmaton errors of LDRXX data seres performed by. For XX data, Table 7, Table 8 and Table 9 lst the statstcs of data -1a, -1b and -1c, respectvely. Table 10 presents the estmaton errors of XX data seres performed by. Total Data (LDR-1a) Table 3. The dstrbuton behavors of data LDR-1a. Mean Var Std Tranng Data (LDR-1a) Mean Var Std Test Data (LDR-1a) Mean Var Std (2) (3)

4 Automaton, Control and Intellgent Systems 2016; 4(2): Table 4. The dstrbuton behavors of data LDR-1b. Total Data (LDR-1b) Mean Var Std Tranng Data (LDR-1b) Mean Var Std Test Data (LDR-1b) Mean Var Std Table 5. The dstrbuton behavors of data LDR-1c. Total Data (LDR-1c) Mean Var Std Tranng Data (LDR-1c) Mean Var Std Test Data (LDR-1c) Mean Var Std Table 6. The statstcs of estmatons for data LDRXX. LDR-1a MAE MAPE % % % % Statstcs LDR-1b Thckness RI MAE MAPE % % % % Statstcs LDR-1c Thckness RI MAE MAPE % % % % Table 7. The dstrbuton behavors of data -1a. Total Data (-1a) Mean Var Std Tranng Data (-1a) Mean Var Std Test Data (-1a) Mean Var Std Table 8. The dstrbuton behavors of data -1b. Total Data (-1b) Mean Var Std Tranng Data (-1b) Mean Var Std Test Data (-1b) Mean Var Std Table 9. The dstrbuton behavors of data -1c. Total Data (-1c) Mean Var Std Tranng Data (-1c) Mean Var Std Test Data (-1c) Mean Var Std

5 19 Ch-Yen Shen et al.: The Estmaton of Thn Flm Propertes by eural etwork Table 10. The statstcs of estmatons for data -xx. Statstcs -1a Thckness RI MAE MAPE 0.812% % 0.040% 0.022% Statstcs -1b Thckness RI MAE MAPE 0.852% % % % Statstcs -1c Thckness RI MAE MAPE 0.823% % % % Fgure 5. The superposton plot of RI for s tranng. The examples of superposton plot for thckness estmaton are shown n Fgure 3 and Fgure 4. Fgure 3 shows the example of s tranng result and Fgure 4 shows the example of s testng results. In fgures, the sold lne stands the actual thckness values and the dotted lne stands s estmated values. Fgure 6. The superposton plot of RI for s test. 4. Results & Dscusson Fgure 3. The superposton plot of thckness for s tranng. It s known that many unknown factors wll affect the propertes of thn flm n ts real manufacturng process. These unknown factors are usually uncontrolled and can be treated as the dsturbances. Besdes, dfferent manufacturng machnes have dfferent physcal characterstcs. All these condtons mght make the flms have dfferent propertes even they are flmed under the same manufacturng parameters. In our study, we tred to use technque to catch the relatonshps among the flm s propertes and the relevant manufacturng parameters so that the flm s propertes could be estmated n advance. From the smulaton results shown, the relatonshps between the flm s propertes and the manufacturng parameters ndeed can be obtaned by a well-traned model. For both thckness and RI estmatons, the plots show that the trends of flm s propertes stll can be estmated by. 5. Concluson Fgure 4. The superposton plot of thckness for s test. Smlarly, the examples of superposton plot for RI estmaton are shown n Fgure 5 and Fgure 6. Fgure 5 shows the example of s tranng result and Fgure 6 shows the example of s testng result. Same as above fgures, the sold lne stands the actual thckness values and the dotted lne stands s estmated values. In ths research, the estmaton for the propertes of semconductor s thn flm based on technque was studed. From the study results shown, we conclude that model ndeed has the ablty to estmate the propertes of thn flm f was well-traned. In other words, these well-traned estmators could provde the mportant nformaton to the techncan for settng the proper manufacturng parameters n the flmng process. The

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