Hybrid Metamodel — NSGA-III — EDAS Based Optimal Design of Thin Film Coatings

: In this work, diamond-like carbon (DLC) thin ﬁ lm coatings are deposited on silicon substrates by using plasma-enhanced chemical vapour deposition (PECVD) technique. By varying the hydrogen ( H 2 ) ﬂ ow rate, CH 4 − Argon (Ar) ﬂ ow rate and deposition temperature ( T d ) as per a Box-Behnken experimental design (BBD), 15 DLC deposition experiments are carried out. The Young ’ s modulus (E) and the coef ﬁ cient of friction (COF) for the DLCs are measured. By using a second-order polynomial regression approach, two metamodels are built for E and COF, that establish them as functions of H 2 ﬂ ow rate, CH 4 -Ar ﬂ ow rate and T d . A non-dominated sorting genetic algorithm (NSGA-III) is used to obtain a set of Pareto solutions for the multi-objective optimization of E maximization and COF mini-mization. According to various practical scenarios, evaluation based on distance from average solution (EDAS) approach is used to identify the most feasible solutions out of the Pareto solution set. Con ﬁ rmation experiments are conducted which shows the ef ﬁ cacy of the polynomial regression — NSGA-III — EDAS hybrid approach. The surface morphology of the DLCs deposited as per the optimal pre-dictions is also studied by using atomic force microscopy.


Introduction
The excellent mechanical, tribological and optical properties of diamond-like carbon (DLC) coatings offer a wide application in the automotive and electronic industries. DLC coating is a mixture of both graphite-like sp2 bond and diamond-like sp3 bonds which shows that the properties of DLCs depend on the number of bonds present within the coatings. DLCs are considered to be the hybrid form of carbon which holds both graphite-like sp2 bond and diamond-like sp3 bonds [1]. It is well known that graphite (100% sp2) is having a zero-band gap whereas diamond (100% sp3 bond) has a bandgap of 5.5 eV and thus, by the synthesis of DLCs by using different methods the amount of sp3 and sp2 bonds can be altered [2]. Due to the mixture of sp2 and sp3 bonds within the DLC films, it possesses characteristics of both graphite and diamond. The good electrical and electronic properties of DLC are due to the sp2 hybridized carbon whereas, the tribological and mechanical properties are due to the sp3 hybridized carbon [3,4]. DLC films are also used for making surgical equipments, automotive engine parts, magnetic storage discs, micro-electromechanical devices (MEMS), etc.
Various chemical vapour deposition (CVD) techniques are used for the deposition of thin-film coatings and out of all the CVD techniques, plasma-enhanced chemical vapour deposition (PECVD) technique is most widely used for the DLC coating synthesis because of its quality coating at low temperature [5][6][7]. The different PECVD deposition parameters like gas flow rate, duty cycle, gas composition, deposition temperature, power supply etc. influence the properties of DLC thin films. In recent years, the selection of deposition parameters is a matter of prime concern for the researchers to get the desired properties of the films [8,9]. Singh et al. [10] used a Taguchi technique to find the combination of PECVD deposition parameters like bias voltage (V), bias frequency (f), gas composition, deposition pressure (P) of DLC coatings with PECVD technique to get optimum response parameters, i.e., roughness and hardness. Ghadai et al. [11] used particle swarm optimization (PSO) techniques to optimize the PECVD process parameters to get high hardness of the DLC coating. In an extension to the previous work, Ghadai et al. [12] found that symbolic regression metamodels are superior to traditional polynomial regression metamodels. The symbolic regression metamodels were form-free and thus, were better at modelling the inherent non-linearity in the deposition process. Ghadai et al. [13] also used a genetic algorithm to fine-tune the DLC deposition parameters in APCVD process.
Despite the considerable amount of work done on DLC thin film coatings, only a handful of works are seen on the implementation of advance computational intelligence techniques like multi-objective optimization based on metamodels. This work attempts to address this lacuna by building metamodels that express two different DLC performance parameters (Young's modulus and coefficient of friction) as functions of three DLC deposition process parameters (hydrogen flow rate, CH 4 -Argon flow rate and deposition temperature). The metamodels are then deployed in conjunction with the non-dominated sorting genetic algorithm (NSGA-III) for carrying out Pareto optimization. Finally, based on certain scenarios, a multi-criteria decision-making method called EDAS is used to identify the desirable solutions from the Pareto set. Surface morphologies of these optimal designs are studied by using atomic force microscopy.

Experimental Procedure
In the work, the synthesis of DLC coatings over silicon (Si) was done by using PECVD deposition technique. To remove the oxide layer, the substrates were dipped into 2% HF solution for 4 min followed by ultrasonic cleaning in deionized water for 10 min. Tab. 1 shows the details of input parameters like hydrogen (H 2 ) flow rate, CH 4 -Argon (Ar) flow rate and temperature for the deposition (T d ) of DLC coatings. The morphological analysis of the DLC coating is done with the help of Innova SPM atomic force microscope. The Young's modulus (E) of the DLC coatings were calculated by using a nanohardness tester (NHTX-55-0019) of CSM Instruments having Berkovich indentor. The radius of curvature of the indentor (B-I 93) is 20 μm. The indentation was considered at three different locations and the average of that value is considered and the maximum load is taken as 10 mN. The Oliver-Pharr method [14] is applied for the calculation of Young's modulus (E). The nano scratch tests were performed over the coating by using CSM instrument with a sphero-conical diamond indenter (R = 2 µm, SB-A63), by applying a load of 20 mN with a scratch speed of 1 mm/min over a 0.5 mm scratch length.

Predictive Modeling with Polynomial Regression
In this work, the metamodels for Young's modulus and the coefficient of friction are built by fitting a second-order polynomial regression equation of the following form.
Here b 0 s are the coefficients of regression. These coefficients of regression help in describing the response (y i ) as a function of predictor variables (x 0 s). x 1 ; x 2 and x 3 represent hydrogen (H 2 ) flow rate, CH 4 -Argon (Ar) flow rate and deposition temperature (T d ) respectively.
Using the Box-Behnken experimental design in Tab. 1, Eq. (1) is fitted based on multiple regression fitting scheme. The difference between the predicted value (b y i ) and the actual experimental value (y i ) of the response is called the residue [15].
(1) are computed such that the residual sum of squared (RSS) is minimized.
where n is the number of experimental points in Tab. 1.

Optimization with NSGA-III
In this work, non-dominated sorting genetic algorithm III (NSGA-III) [16,17] is used for carrying out the Pareto optimization. The multi-objective optimization problem is stated as, In Eq. (4), Y 1 and Y 2 are Young's modulus (E) and coefficient of friction (COF) respectively.
NSGA-III is realized in this work by using the following pseudo-code. Report the Pareto front having P nd non-dominated solutions END ________________________________________________________________________

Predictive Modeling
Using the training data listed in Tab. 1, second-order polynomial regression metamodels are developed for the prediction of Young's modulus (E) and the coefficient of friction (COF). The coefficients of regression for the metamodels of E and COF are mentioned in Tab. 2. Fig. 1 shows the variation of the predicted values of E and COF for their respective experimental values. It should be noted that closer the values are to the diagonal (identity) line in Fig. 1, better are the estimations of the metamodel. In general, the metamodel for E is seen to have better performance than COF. To further analyze the utility of the two metamodels, the residuals in each case are evaluated against their respective predicted values, as shown in Fig. 2. A random scatter is seen in both cases, which indicates that the residues do not show any trend with the predicted values. Thereby it can be concluded that the metamodels are appropriate as they can quantify the variance in the training data. Further analysis of the residuals is done by plotting their normal probability plots in Fig. 3. No outliers are seen in Fig. 3, which further confirms the efficacy of the metamodels. Fig. 4 shows the effect of H 2 and CH 4 ÀAr flow rate on Young's modulus (E) of the DLCs. It is seen that deposition temperature (T d ) has a significant effect on the role that of H 2 and CH 4 ÀArgon flow rate plays on E. For example-at a lesser T d , the E of the DLCs increase with the increase in CH 4 ÀArgon flow rate but the E decreases with an increase in H 2 flow rate. The trend is the opposite when higher levels of T d is considered. Similarly, Fig. 5 shows the interactive effect of T d and CH 4 ÀAr flow rate on E at various levels of H 2 flow. It is observed that the E increases as the T d and CH 4 ÀArgon flow rate increases. Fig. 6 shows that the increase in H 2 flow, in general, decreases the E of the DLCs. Fig. 7 shows the effect of H 2 and CH 4 ÀAr flow rate on the coefficient of friction (COF) of the DLCs. It is seen that the trend of the COF of the DLCs is also significantly affected by the T d . At low T d , the increase in H 2 and CH 4 ÀArgon flow rate increases the COF of the DLCs, whereas at higher levels of T d , the COF decreases with an increase in H 2 flow rate but CH 4 ÀArgon flow rate has a negligible effect on it. In Fig. 8, the trend of COF with T d and CH 4 ÀArgon flow rate is similar for mid and high level H 2 flow rate but is significantly different for low H 2 flow rate. At mid and high H 2 flow rate, the COF increases with a decrease in T d , but is not much affected by variation in CH 4 ÀArgon flow rate. However, as seen in Fig. 9, the behaviour of the COF of the DLCs is similar at all levels of CH 4 ÀArgon flow rate.

Pareto Optimization
Based on the discussion on the effect of the DLC deposition process parameters on Young's modulus and COF in the previous two sections, it is seen that the optimal setting of the two response parameters has conflicting requirements in terms of process parameter settings. Thus, it is not possible to arbitrary decide the optimal parameter combination that would simultaneously maximize the E and minimize the COF. Thus, a Pareto optimization using non-dominated sorting genetic algorithm is carried out and depicted in Fig. 10. The continuous Pareto front in Fig. 10b shows that as the E of the DLCs improve, there is an increase in COF as well. Thus, each solution within the Pareto front in Fig. 10b represents a possible compromise solution to the multi-objective problem. Since it is not possible to arbitrarily draw a particular solution out of the Pareto front to represent a feasible solution, a multi-criteria decision-making approach called EDAS is used to select the most plausible solutions pertaining to certain practical scenarios and are presented in Tab. 3.

Experimental Confirmation of Optimal Results
Confirmation experiments as per the optimal process parameters are conducted and the experimental values are reported in Tab  temperature are the same, however, the CH 4 ÀArgon flow rate is different. From the experimental results shown in Tab. 3, it is observed that the COF of the DLC coating decreases with an increase in the CH 4 ÀArgon flow rate. From the AFM images, it is observed that the DLC coating having less COF has a smooth surface and result is confirmed from the R a value. Overall, the confirmation experiment values are seen to be close to the predicted optimal solutions.

Conclusion
Finding an optimal combination of process parameters that enhances the performance of a process is a realistic goal with tremendous practical implications. In this work, such an effort for optimizing the DLC deposition process parameters is undertaken to suitably enhance Young's modulus and coefficient of friction of DLC thin film coatings. Based on the study the following conclusion are made Second-order polynomial regressions can serve as reliable metamodels for DLC process modelling that can be subsequently used for process parameter effect study or in case of optimization scenarios. Non-dominated sorting genetic algorithm (NSGA-III) is a viable tool for Pareto optimization of such critical processes. Improvement in Young's modulus of the DLCs was in general accompanied by worsening of the coefficient of friction. Thus, given such conflicting process performance, the Pareto set, as opposed to single-objective solutions, can provide the designer with a lot of flexibility regarding setting the preferred process parameters. In general, a higher level of hydrogen flow rate and deposition temperature was found to be suitable in augmenting the young's modulus of the DLCs. Confirmation experiments conducted as per the optimal process parameters showed that the polynomial regression-NSGA-III-EDAS approach is reliable and accurate.

Conflicts of Interest:
The authors declare that they have no conflicts of interest to report regarding the present study.