TOPSIS based Taguchi design optimization for CVD growth of graphene using different carbon sources: Graphene thickness, defectiveness and homogeneity

Accepted Manuscript TOPSIS based Taguchi design optimization for CVD growth of graphene using different carbon sources: Graphene thickness, defectiveness and homogeneity

Baris Simsek PII: DOI: Reference:

S1004-9541(18)30534-2 doi:10.1016/j.cjche.2018.08.004 CJCHE 1230

To appear in:

Chinese Journal of Chemical Engineering

Received date: Revised date: Accepted date:

12 April 2018 26 June 2018 5 August 2018

Please cite this article as: Baris Simsek , TOPSIS based Taguchi design optimization for CVD growth of graphene using different carbon sources: Graphene thickness, defectiveness and homogeneity. Cjche (2018), doi:10.1016/j.cjche.2018.08.004

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ACCEPTED MANUSCRIPT Article TOPSIS based Taguchi Design Optimization for CVD Growth of Graphene Using Different Carbon Sources: Graphene Thickness, Defectiveness and Homogeneity☆ Baris Simsek*

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Department of Chemical Engineering, Faculty of Engineering, Çankırı Karatekin University, Uluyazı Kampüsü 18200, Merkez, Çankırı, Turkey E-mail: [email protected] Supported by the Scientific Research Project of Çankırı Karatekin University (MF200217B05) and the

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Scientific Research Project Management Unit of Çankırı Karatekin University (ÇAKÜ-BAP).

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Abstract

Chemical inhomogeneity of CVD grown graphene compromises its usage in high-

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performance devices. In this study, TOPSIS based Taguchi optimization was performed to

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improve thickness uniformity and defect density of CVD grown graphene. 1.56% decrease in the mean 2D/G intensity ratio, 87.96% improvement in the mean D/G intensity ratio, 56.07% improvement in the standard deviation D/G intensity ratio, 25.21% improvement in the

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standard deviation 2D/G intensity ratio and 69.32% improvement in the surface roughness was achieved with TOPSIS based Taguchi optimization. The statistical differences between the copper and silicon substrates have been found significantly in terms of their impacts on

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the graphene’s properties with the 0.000 p-value for the mean D/G intensity ratio and with the

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0.009 p-value for the mean 2D/G intensity ratio, respectively. Graphene having 98% lower mean D/G intensity ratio (low defective graphene products) compared to the values given in the literature using single-response optimization was obtained using multi-response optimization. Keywords: Graphene Quality, Chemical Vapor Deposition (CVD), Multi-Response Optimization, TOPSIS based Taguchi Method, Statistical Comparison. 1. Introduction

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ACCEPTED MANUSCRIPT The most commonly used method for obtaining single-layer graphene is mechanical exfoliation from graphite i.e. “the scotch tape method” which was first demonstrated by Novoselov et al [1]. Scotch tape method is easy to apply and there is no need for fancy and costly equipment. However, it is time consuming, uncontrollable and not suitable for obtaining large area graphene sheets [2]. There has been great effort on developing non-

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graphitic alternative single layer graphene production methods such as epitaxial growth on

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silicon carbide [3-6], chemical vapor deposition (CVD) [7-16], and synthesizing from

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graphene flakes [17-19].

CVD method is more prominent that the other methods due to its ease of scalability to

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larger sheets and applicability to roll-to-roll manufacturing [20]. CVD growth process consists of heating, growth and cooling stages [21]. During each stage there are several

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factors such as substrate, substrate quality and substrate surface preparation, furnace pressure, source gases, carrier gases, gas flow rates, gas mixtures, heating and cooling ramp profiles,

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growth temperature, growth time and etc. that affect the quality characteristics of graphene

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such as defect density of the graphene sheet and number of graphene layers to be grown [22, 23]. Researchers have been investigating the effects of these factors in order to reduce defect

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density and control the number of graphene layers to be grown [14, 24-45]. Most of these studies have only been focused on investigating the effects of selected insufficient number of

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factors at a time without applying statistical experimental design methodologies [46]. Results of these kinds of investigation approaches might be enough for understanding specific growth behaviors for research purposes but would not be enough for industrialization of graphene growth. In recent years, researchers have been started investigating the experimental design based approaches to optimize CVD growth process for graphene [47]. However, these studies were limited to single-response optimization methodologies [22, 42, 43, 47-51]. Wissmann and Grover [50] used the sequential experimental design based D-optimal design to optimize

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ACCEPTED MANUSCRIPT the surface roughness of the synthesized film via CVD process. They achieved the desired film roughness of 7±1.65 nm with the use of atomic force microscopy across a 2×2 µm area of the wafer. Santangelo et al. [22] optimized the properties of the graphene films by the copper catalyzed ethanol decomposition with the use of Taguchi design. They determined the 2D/G intensity ratio and D/G intensity ratio as 1.28 and 0.03 under the optimum conditions,

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respectively. Alrefae et al. [51] improved the D/G intensity ratio value from 1.4 to 0.7 in a

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plasma CVD system with the use of stochastic optimization methods. In order to make it

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possible for graphene to be produced at the industrial scale and enable industrial usage of graphene; effects of all of the growth factors have to be taken into account with a statistically

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meaningful multi-response optimization methodology.

In the literature, the optimization studies about the properties of CVD graphene

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usually involve only one response optimizations. On the other hand, it is not enough to define a single feature of an industrial product. When considering a graphene synthesized as a thin

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film, it will not be enough to optimize only graphene defectiveness. In order to increase the

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industrial usability of the product, it will be necessary to consider properties such as thickness, surface roughness and product homogeneity features as well as graphene

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defectiveness. It is also known that some of the CVD process operating parameters has an effect on film quality. With the experimental design method used, the factors’ effects on the

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responses can be revealed and can be optimized simultaneously. A factor has a positive effect on the one response (for example graphene defectiveness), causing a negative effect on the other factor (for example surface roughness). For this reason, it is necessary to analyze and optimize the conflicting criteria simultaneously. The proposed easy to apply TOPSIS (Technique of Ordering Preferences by Similarity to Ideal Solutions) -based Taguchi method such a robust design also provides a systematic and efficient methodology for determining the optimum combination of the design factors such that the product is effective and has high

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ACCEPTED MANUSCRIPT performance, and also is robust to the noise factors [52]. The noise factors are known as the uncontrollable factors (In CVD process, these factors can be laboratory temperature, moisture and etc.). In this study, multi-featured graphene product design was made robust to the factors that cannot be controlled such as laboratory temperature, moisture and etc., using controllable factors such as the type of hydrocarbon source, annealing time, flow rate of hydrocarbon

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source, H2 flow rate, argon flow rate, reaction time, reaction temperature and cooling type.

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The main novelty of this work is that we involved not only mean D/G intensity ratio

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but also standard deviation value to optimization study different from other studies in literature. So we aimed to synthesize both smaller mean D/G intensity ratio and CVD

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graphene having smaller variance of the intensity of D-peak to G-peak ratio. Especially, manufacturing with small variance is very important for mass production of nano materials.

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The graphene quality has been improved with the reduction in variability in the same experimental conditions. Decreasing of standard deviation means an obtaining of a product

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having graphene property close to each other. Thus, it will be possible to produce a high

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amount of homogeneous CVD graphene films. In this way, homogeneous products will exhibit their expected properties (high electrical conductivity or mechanical strength and etc.)

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more successfully. Finally, the copper and silicon substrates have been compared statistically in terms of the production.

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2. Materials

Ethanol and methanol which are low cost and non-hazardous [22] comparing to other alternative source gasses and environment friendly because they can be produced from solid waste material recycling [53, 54] were selected as gas sources. 1cm×1 cm copper foils having 99.8% purity and 0.025 mm thickness (99.8%) were used as growth substrates. Organic contaminants on copper surface were cleaned with acetone in ultrasonic cleaner for 15

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ACCEPTED MANUSCRIPT minutes. Cleaned substrates were transferred to CVD furnace immediately after cleaning to prevent contamination. 3. Methodology There are 9 flow steps in the determination of the optimal operating parameters of the graphene growth with the use of CVD process (Fig.1). Mean D/G and 2D/G intensity ratios

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values, the standard deviation D/G and 2D/G intensity ratios which have been obtained by

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Raman spectroscopy as integrated intensity ratios, the surface roughness which have been

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obtained by the atomic force microscopy (AFM) have been determined as the graphene quality criteria. The optimal operating levels of the type of hydrocarbon source, annealing

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time, flow rate of hydrocarbon source, H2 flow rate, argon flow rate, reaction time, reaction temperature and cooling type have been determined with the use of TOPSIS based Taguchi

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method. The TOPSIS procedure as a kind of multi-criteria decision method was used

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integrally with the Taguchi method to solve multi-response optimization problems.

Figure 1 Proposed methodology 4. Identifying Performance Optimization Conditions 4.1.Graphene quality criteria 5

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First quality criterion is the mean D/G intensity ratio value which informs about the graphene defectiveness of graphene which is one of the most important structural features. The graphene which has got low D/G intensity ratio is a graphene type that there is a little structural defectiveness. The mean 2D/G intensity ratio, which should be maximum, gives

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information about the number of layer (in other words thickness). The higher 2D/G intensity ratio values (especially larger than 2 value) prove the high crystalline quality monolayer

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graphene [21]. The second and fourth quality criteria have been selected as the standard

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deviation D/G and 2D/G intensity ratio, respectively. The production with low variance means the high quality graphene synthesis. The last criterion has been selected as the surface

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roughness which is important for hydrophilicity/hydrophobicity [55] and graphene thickness

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[56]. The same weight for five performance criteria has been designated and presented in Table 1.

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Table 1 Quality characteristic and their weights Symbol

Description

Information

Target values for graphene

1

R1

Mean D/G intensity ratio

Defect in structure

Smaller is better

2

R2

Standard deviation D/G intensity ratio

Number of layers

Larger is better

3

R3

5 Totalª

R4 R5 5

Mean 2D/G intensity ratio

Graphene homogeneity

Smaller is better

Standard deviation 2D/G intensity ratio

Graphene homogeneity

Smaller is better

Surface roughness (nm)

Graphene thickness

Smaller is better

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Quality Criteria

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ªSame weights are assigned to all responses.

4.2.Definition of factors One factor has two level and seven factors that each has three control levels affects the selected graphene quality criteria. The type of hydrocarbon source, annealing time, flow rate of hydrocarbon source, H2 flow rate, argon flow rate, reaction time, reaction temperature and cooling type have been selected as the factors (in other words, the operating parameters). The symbols X1, X2, X3, X4, X5, X6, X7 and X8 were used to define these factors, respectively (Table 2). 6

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Table 2 Factors and their levels Bounds Factors

Definition First bound

Second bound

Third bound

The type of hydrocarbon source

Ethanol

Methanol

N/A

X2

Annealing time/min

5

15

25

X3

Flow rate of hydrocarbon source/sscm

1

5

10

X4

H2 flow rate/sscm

1

5

10

X5

Argon flow rate/sscm

10

X6

Reaction time/min

10

X7

Reaction temperature/°C

970

X8

Cooling rate

Low

100

20

30

1000

1030

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50

Moderate

High

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4.3.Selecting the experimental design

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X1

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L18 Taguchi orthogonal array (21*37) has been chosen to record the experiment results. In Table 3, columns 2–9 represent the seven control factors and their uncoded levels. This

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orthogonal array has ensured the five performance measures simultaneously to analyze the factor effects.

The type of hydrocarbon source

Annealing time/min

Flow rate of hydrocarbon source /sscm

H2 flow rate /sscm

Ar flow rate /sscm

Reaction time /min

5

1

1

10

10

970

Low

5

5

5

50

20

1000

Moderate

5

10

10

100

30

1030

High

15

1

1

50

20

1030

High

15

5

5

100

30

970

Low

15

10

10

10

10

1000

Moderate

25

1

5

10

30

1000

High

Ethanol

CVD 3

Ethanol

CVD 4

Ethanol

CVD 5

Ethanol

CVD 6

Ethanol

CVD 7

Ethanol

CVD 8 CVD 9 CVD 10 CVD 11

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Ethanol

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CVD1 CVD 2

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Exp. No

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Table 3 Factors and their levels Reaction temperature /°C

Cooling rate

Ethanol

25

5

10

50

10

1030

Low

Ethanol

25

10

1

100

20

970

Moderate

Metanol

5

1

10

100

20

1000

Low

Metanol

5

5

1

10

30

1030

Moderate

CVD 12

Metanol

5

10

5

50

10

970

High

CVD 13

Metanol

15

1

5

100

10

1030

Moderate

CVD 14

Metanol

15

5

10

10

20

970

High

CVD 15

Metanol

15

10

1

50

30

1000

Low

CVD 16

Metanol

25

1

10

50

30

970

Moderate

CVD 17

Metanol

25

5

1

100

10

1000

High

CVD 18

Metanol

25

10

5

10

20

1030

Low

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4.4.Experiment conditions The first experiment run has been described as follows. Ethanol (X1) with the reason that it is relatively cheap has been used for carbon source material. CVD process was started

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with oxide removal under H2 flow. Copper foils loaded into the furnace were first exposed to H2 and Ar gases flow of 500 sscm each at 5800 mtorr pressure for 15 minutes. Then, Ar gas

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flow was turned off and H2 gas flow rate was reduced to 100 sscm at 670 mtorr. After 5

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minutes of waiting, furnace was heated from room temperature to process temperature, 970° C, with a constant slope heating ramp of 2 min. After the heating completed, copper foils

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were annealed for oxide removal under 100 sscm H2 (standard cm3·min-1 in the stable

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temperature and pressure) gas flow at constant temperature (970 °C) for 5 min (X2). After the annealing, growth phase of the process was started by turning on ethanol (X3) source gas, H2

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(X4) reductant gas and Ar (X5) carrier gas with 1, 1 and 10 sscm flow rates respectively at 200

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mtorr furnace pressure. The growth was performed for 10 min (X6) under constant gas flow, furnace temperature 970 °C (X7) and pressure (200 mtorr). In this step, the reactor pressure

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has been stabilized at 200 mtorr manually. After the growth phase, the samples were left for cooling slowly (X8) to room temperature under constant H2 flow of 100 sscm for 15 minutes

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and then Ar flow of 100 sscm for 10 min. Cooling phase was completed and the samples were unloaded from the furnace for further processing Graphene growth was observed on the top side of the copper foil substrates. In order to protect graphene layer from mechanical stress and breaking during the releasing process, graphene sheets were coated with 4% Polymethyl methacrylate (PMMA) anisole solution. PMMA coated graphene sheets were released from copper substrates by dissolving the substrates in iron (III) chloride (Fe3Cl) acid for 1 h. After the copper substrates were completely dissolved and graphene/PMMA sheets released from the substrates and started to 8

ACCEPTED MANUSCRIPT float on top of the acid, they were fished out of the acid using a tweezer, rinsed in di-water by five consecutive dipping into water and left graphene side down floating on di-water. Rinsed samples were fished out of di-water using Si/SO2 substrates on which graphene sheets would be transferred to. Fished samples were left for annealing-drying on hot plate at 60°C for 15 min. In order to remove PMMA layer and complete the transfer of graphene sheets on to

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Si/SiO2 substrates, samples were put into acetone at 30°C. After 30 min, PMMA layers were

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completely removed and graphene sheets were successfully transferred on to Si/SiO2

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substrates [57]. 5. Optimization of Graphene

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5.1.Characterization of the synthesized graphene by L18 Taguchi design Raman spectroscopy is quite a useful tool to characterize the carbon based materials

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such as graphene, carbon nanotubes and etc. [58-60]. The Raman spectra of the graphene samples show three apparent peaks at the positions around the D, G and 2D bands of pristine

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graphite with the differences in the position and relative intensity [61, 62]. The Raman

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spectrum of graphene samples which are synthesized by L18 orthogonal arrays exhibits a Gband at 1590 cm-1, D band at 1350 cm-1, 2D band at 2700 cm-1, respectively [63] (Fig.2). The

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excitation wavelength and the excitation leaser energy have been used as 532 nm and 10 mV, respectively. Raman results also demonstrate that the synthesis of graphene by CVD process

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has been made succeeded for the each experimental runs (Fig.2). The obtained mean and standard deviation D/G and 2D/G intensity ratio for each experiment runs have been given in Table 4. AFM images can be used to characterize the surface morphology properties of graphene such as the average surface roughness, prediction of the thickness deviation and analyzing the surface morphology [64]. AFM analysis has been performed to the graphene on the copper with two replicates and the average surface roughness for all the experimental runs

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ACCEPTED MANUSCRIPT has been calculated with the use of AFM device for a 5 µm×5µm sample area (please see the

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Fig.3 for replicate 1) and transferred to Table 4.

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Figure 2Raman spectra of graphene prepared by L18 Taguchi design (a) replicate 1, (b) replicate 2 and (c) replicate 3

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Table 4 Responses for graphene obtained by L18 Taguchi design Exp. No.

Mean D/G intensity ratio, R1

Standard deviation D/G intensity ratio, R2

Mean 2D/G intensity ratio, R3

Standard deviation 2D/G intensity ratio, R4

Surface roughness, R5 /nm

0.04701

0.57647

0.181297

30.8

5.14315

0.14054

0.105491

290.1

0.21392 3.26969

CVD 3

3.42525

5.01432

0.03340

0.025430

142.1

CVD 4

2.62186

4.03482

0.01519

0.002301

60.5

CVD 5

2.76896

4.54966

0.16344

0.259585

71.2

CVD 6

1.77710

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CVD1 CVD 2

0.58501

0.242060

100.4

0.12076

0.06388

0.028513

182.2

2.23709

0.17637

0.37553

0.231432

132.8

2.16468

0.35488

0.13136

0.105416

135.2

CVD 10

1.30631

0.08547

0.15981

0.120242

63.5

CVD 11

1.05735

0.79735

0.26319

0.124786

94.1

CVD 12

3.01785

4.98724

0.12855

0.150589

86.8

CVD 13

2.94258

4.58530

0.02736

0.007734

96.1

CVD 14

2.25998

0.22771

0.13616

0.029364

56.5

CVD 15

1.42721

0.52948

1.04753

0.884648

51.2

CVD 16

2.54405

4.17120

0.05192

0.084143

120.3

CVD 17

0.96717

0.68870

0.10123

0.030682

60.7

CVD 18

2.23556

3.62522

0.01485

0.015489

74.6

CVD 8 CVD 9

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0.10714

1.48165

CVD 7

10

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CVD2

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CVD5

CVD6

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CVD4

CVD3

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CVD1

CVD8

CVD9

CVD11

CVD12

CVD14

CVD15

CVD17

CVD18

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CVD10

D

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CVD7

AC

CVD13

CVD16

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ACCEPTED MANUSCRIPT Figure 3 AFM images for CVD graphene (Replicate 1)

5.2.TOPSIS Based Taguchi Optimization The Taguchi experiment design method is used for optimization of a single response

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like other experimental design methods such as response surface methodology and full

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factorial design. However; if there is more than one quality criterion to be optimized, different

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methods should be used with the Taguchi method to convert the multiple response problems to one response optimization problem. For multi-response optimization applications, the most

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prominent optimization techniques with the Taguchi method are linear or goal programming and multi-criteria decision making techniques. Linear programming involves complex

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mathematical operations when the objective function and constraint functions are involved, or requires knowledge of the algorithm and the ability to use the programming tools such as

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Minitab®, Matlab® or Lindo® software.

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However, multi-criteria decision making techniques can be easily integrated with the Taguchi method. The signal-to-noise (S/N) ratios are the smaller-the-better and the larger-the-

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better for each response is calculated using experimental results obtained with the Taguchi design. Experimental results that are converted to signal to noise ratios are called decision

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matrices. Then the sequence consists of the following stages such as forming the standard decision matrix, forming the weighted normalized decision matrix, identification of positive and negative ideal solutions, calculation of the separation measures, and calculation of ideal solving relative proximity as ranking score. Detailed information about TOPSIS method can be found in Şimşek et al. (2013)’s study [52]. Multi-response-optimization problem containing five performance measures (graphene quality criteria) can be easily optimized using TOPSIS based Taguchi method simultaneously.

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ACCEPTED MANUSCRIPT The S/N ratios, for the smaller and larger is better, are calculated with the use of Eq. (1) and (2) for each response [52, 64, 65]. The design of experiment and the S/N ratios as the decision matrix are shown in Table 5, columns 2-6. The TOPSIS method transforms the multi-response optimization problem into a single response problem [66]. The final results are showed in Table 5, at the last column [65].

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The S/N ratios for the lower-the-better and the-higher-the-better responses are

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calculated by with the use of Eq. (1) and (2) respectively for each response. The experimental design and the S/N ratios are given in Table 10, columns 2-10 [52, 64, 65].

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1 n 2   yijk   n k 1 

1

ij  10 log 10 

n



1   yijk2 

(1)

(2)

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 n ki1

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 ij  10 log 10 

In the equations (1-2); ηij is the S/N ratio for the response j of experimental number i,

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and yijk is the experiment result for the response j of the experiment i, in the k th replication; n

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is the total number of replications [52, 64, 65]. In Table 5, columns 2-6 are exampled as the decision matrix for the first step of the

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TOPSIS method which transforms the multi-response optimization problem into a single response problem [52]. A sample calculation for the weighted normalized matrix is showed in

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Table 5 [52]. Calculation of the positive ideal solution (A*) and the negative ideal solution (A−) can be seen in Table 5 [52, 65]. In each scenario, the calculation of the similarity of the ideal solutions, C i* (deputy response) can be also seen in the same Table [52, 64]. The recent results are showed in Table 5, at the last column. The maximum surrogate response Ci*has been selected as the optimum parameter design [52, 65, 67].

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Table 5 S/N ratios calculated by Minitab®, and TOPSIS method implementation for CVD grown graphene Decision Matrix (S/N Ratios) R1

R2

R3

R4

R5

Weight

0.200

b

0.200

0.200

0.200

0.200

GO1

13.40b

26.56

-4.78

14.8

GO2

-10.29

-14.22

-17.0

GO3

-10.69

-14.00

-29.5

GO4

-8.37

-12.12

GO5

-8.85

-13.16

GO6

-4.99

GO7 GO8

Si*

Si-

Ci*

vi2

vi3

vi4

vi5

-29.8

0.08b

0.09

-0.01

0.03

-0.04

0.07c

0.21d

0.76e

19.5

-49.2

-0.06

-0.05

-0.04

0.03

-0.06

0.21

0.05

0.20

31.9

-43.0

-0.07

-0.05

-0.07

0.06

-0.05

0.06

0.21

-36.4

52.8

-35.6

-0.05

-0.04

-0.08

0.09

-0.04

0.20

0.10

0.32

-15.

11.7

-37.0

-0.05

-0.04

-0.03

0.02

-0.04

0.21

0.05

0.21

19.40

-4.7

12.3

-40.0

-0.03

0.06

-3.41

18.36

-23.9

30.9

-45.2

-0.02

0.06

-6.99

15.07

-8.51

12.7

-42.5

-0.04

0.05

0.21

-0.01

0.02

-0.05

0.14

0.14

0.50

-0.05

0.06

-0.05

0.13

0.13

0.50

-0.02

0.02

-0.05

0.15

0.12

0.44

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vi1

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Response

Weighted Normalized Decision Matrix

-6.71

9.00

-17.6

19.1

-42.6

-0.04

0.03

-0.04

0.03

-0.05

0.16

0.10

0.38

-2.32

21.36

-15.9

18.4

-36.1

-0.01

0.07

-0.04

0.03

-0.04

0.12

0.14

0.53

GO11

-0.48

1.97

-11.6

18.1

-39.5

0.00

0.01

-0.03

0.03

-0.05

0.14

0.10

0.43

GO12

-9.59

-13.96

-17.8

16.4

-38.8

-0.06

-0.05

-0.04

0.03

-0.05

0.21

0.05

0.20

GO13

-9.37

-13.23

-31.3

42.2

-39.6

-0.06

-0.04

-0.07

0.08

-0.05

0.21

0.08

0.27

GO14

-7.08

12.85

-17.3

30.6

-35.0

-0.04

0.04

-0.04

0.05

-0.04

0.15

0.11

0.44

GO15

-3.09

5.52

0.40

1.06

-34.2

-0.02

0.02

0.00

0.00

-0.04

0.15

0.12

0.43

GO16

-8.11

-12.41

-25.7

21.5

-41.6

-0.05

-0.04

-0.06

0.04

-0.05

0.20

0.05

0.19

GO17

0.29

3.24

-19.9

30.2

-35.7

0.00

0.01

-0.04

0.05

-0.04

0.13

0.11

0.47

GO18

-6.99

-11.19

-36.57

36.20

-37.4

-0.04

-0.04

-0.08

0.06

-0.04

0.20

0.07

0.26

32.2a

61.3

90.0

112.0

116.8

D

PT E

a

MA

GO9 GO10

A*=

0.08

0.09

0.00

0.09

-0.04

A- =

-0.07

-0.05

-0.08

0.00

-0.06

CE

The square root of sum of squares of each element in the columns From [59-61]: 0.1200*[(13.40)/(32.2)]=0.08; c From [59-61]: {[(0.08)-(0.08)]2+ ……+ [-(0.04)-(-0.04)]2}1/2=0.07 d From [59-61]: {[(0.08)-(-0.07)]2………+ [-(0.04)-(-0.06)]2}1/2=0.21 e From [59-61] : 0.21/(0.07+0.21)=0.76

AC

b

5.3.Optimum operating parameters The quality contributions of S/N ratios for selected five criteria have been estimated with the use of an optimal mixture level to estimate the improvement rate under the determined optimum conditions between the predicted (CVD1) mixture levels. The remarkable improvement rate which is achieved by TOPSIS-Taguchi method is given in Table 6 [52, 65].

14

ACCEPTED MANUSCRIPT Table 6 Improvement ratio between CVD6 and CVD1 grown graphene Responses

Definition

CVD6

CVD1

Improvement rate¹/%

1

Mean D/G intensity ratio

1.777

0.214

87.96

2

Standard deviation D/G intensity ratio

0.107

0.047

56.07

3

Mean 2D/G intensity ratio

0.585

0.576

-1.54

4

Standard deviation 2D/G intensity ratio

0.242

0.181

25.21

5

Surface roughness/nm

100.4

30.8

69.32

ºPredicted levels before the experimental design (reference graphene) *Experiment results with the highest grading score (optimum graphene)

¹[(

1.777 1.777

) ∗ 100] = 87.96

PT

6. Results and discussions

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6.1. Main effect analysis

As shown in the main effect plot for the mean D/G intensity ratio (R1), the D/G

SC

intensity ratio of graphene increased with increasing of flow rate of hydrocarbon source, H2,

NU

argon and reaction time [Fig.4(a)]. The mean D/G intensity ratio has not been changed significantly with the change of the hydrocarbon type. It has been found that the high reaction

MA

temperature and cooling rate have negative impact on the mean D/G intensity ratio. When the main effect plot for the standard deviation D/G intensity ratio (R2) has been

D

analyzed, it has been concluded that the standard deviation D/G intensity ratio of CVD grown

PT E

graphene decreased as increasing the annealing time [Fig.4(b)]. However, it can be said that the high flow rate of gases such as hydrocarbon source, H2, argon has increased significantly

CE

the standard deviation D/G intensity ratio [Fig.4(b)]. Moreover, the standard deviation D/G

[Fig.4(b)].

AC

intensity ratio has been affected significantly as increasing the reaction temperature and time

It can be interpreted in the main effect plot for the mean 2D/G intensity ratio (R3), it has increased as raising the hydrocarbon source flow rate [Fig.4(c)]. The mean 2D/G intensity ratio of graphene has not been changed significantly as changing the hydrocarbon source type such as ethanol or methanol. The slow cooling rate has a positive impact on the mean 2D/G intensity ratio of graphene, but also has a negative impact on the standard deviation 2D/G intensity ratio [Fig.4(d)].

15

ACCEPTED MANUSCRIPT Methanol should be preferred to obtain the CVD grown graphene which has low surface roughness. The surface roughness of CVD graphene decreased with the decreasing the flow rate of hydrocarbon source, H2 and argon [Fig.4(e)]. The CVD graphene which has low surface roughness can be obtained with the low reaction time and cooling rate.

A

NU

SC

RI

PT

B

D

PT E

D

MA

C

AC

CE

E

Figure 4 Main effect plots for responses 6.2. Copper substrates versus silicon substrates Eighteen experiments have been performed in order to compare the copper and silicon substrates in terms of the graphene quality and the results have been transferred in Table 7. The paired-t-test has been applied to reveal differences in graphene quality. There is 16

ACCEPTED MANUSCRIPT statistically significant difference which has been found between the copper and silicon substrate on graphene quality.

Copper substrate

Silicone substrate

Exp. No.

PT

Table 7 Responses for graphene obtained by L18 Taguchi design T-test Statistics‡

p-value*

0.464

5.06¹

0.000¹

0.232

-2.94²

0.009²

Mean 2D/G intensity ratio²

Mean D/G intensity ratio¹

Mean 2D/G intensity ratio²

CVD1

0.214

0.576

0.129

CVD 2

3.270

0.141

1.589

CVD 3

3.425

0.033

0.881

CVD 4

2.622

0.015

1.623

CVD 5

2.769

0.163

1.370

CVD 6

1.777

0.585

1.193

CVD 7

1.482

0.064

1.201

CVD 8

2.237

0.376

1.313

4.850

RI

Mean D/G intensity ratio¹

0.048 0.461 1.050

CVD 9

2.165

0.131

1.336

1.813

1.306

0.160

1.035

0.092

CVD 11

1.057

0.263

2.252

0.231

CVD 12

3.018

0.129

0.983

0.178

CVD 13

2.943

0.027

1.109

0.490

CVD 14

2.260

0.136

1.085

0.604

CVD 15

1.427

1.048

CVD 16

2.544

CVD 17

0.967

D

2.033

0.216

2.363

0.101

0.005

0.339

0.015

0.629

1.245

PT E

0.455

0.052

2.236

CE

¹ Graphene on copper substrate ² Graphene on silicon substrate *Null hypothesis H0= The Xi’s are interdependent and identically distributed random variables with distribution function F. Since the pvalue, 0.000 and 0.009 <0.05, null hypothesis would reject for (test statistics value: ‡

𝑑̅ √𝑛 𝑠𝑑

)

The silicon substrate which has higher 2D peak intensity allows the higher quality

AC

CVD 18

MA

0.095

CVD 10

NU

SC

2.181

monolayer graphene production with the lower layer thickness (Fig.5).

Cu

>1 layer

1 layer

17

ACCEPTED MANUSCRIPT

Si

1 layer

RI

PT

Figure 5 CVD 6 a) Raman spectroscopy b) AFM image of graphene on copper substrate and c) AFM image of graphene on silicon substrate

SC

6.3. Comparison with the literature

When it has been compared with the literature, a D/G intensity ratio of 0.216 on the

NU

copper substrate for CVD 16 has been similar result to the literature (D/G intensity ratio of

MA

0.2) [21]. The single component narrow 2D peak and low D/G intensity ratio prove the high crystalline quality monolayer graphene which has low the defect density. 2D/G intensity ratio

D

obtained using silicon substrate (2.363 for CVD 16) higher than 2 value supports the evidence

PT E

of a single layer structure [68]. The surface roughness of the CVD grown graphene on silicon substrate for CVD 16 with the use of AFM device for a 2 µm×2µm sample area has been determined as 7.80 nm that is consistent with the literature [50]. As can be seen from these

CE

results, these findings of the study are very compatible with the literature. In this study,

AC

approximately 87.96% improvement rate has been obtained for the mean D/G intensity ratio with the use of TOPSIS based Taguchi design. The highest improvement rate of the mean D/G intensity ratio in the literature has been found as 78.57% with the use of only Taguchi method. Since there is no information in the literature on the standard deviation, the comparison has been made with the results obtained from this study. The improvement rates of 56.07% for standard deviation D/G and 25.21% for standard deviation 2D/G intensity ratio are quite remarkable and these rates are important for the high quality graphene manufacturing. 18

ACCEPTED MANUSCRIPT 7. Conclusions Graphene quality features were successfully optimized using the approached used in this study. The results show that the source (hydrocarbon) gas and gas flow rates are the most affective factors on graphene defect density and the source gas is the most affective factor on the number of graphene layers.

PT

In conclusion, unlike the previously proposed single response experimental design and optimization approaches, by using TOPSIS based Taguchi Multi-Response Optimization

RI

Approach, we managed to statistically optimize and improve multiple graphene quality

SC

criteria simultaneously. The results show that graphene quality criteria such as defect density,

NU

number of layers, sheet layer uniformity and growth repeatability were significantly improved. This indicates that the approach that was proposed in this study makes it possible

MA

to optimize the growth process and develop a proper growth recipe for a selected system with limited number of experiments which can only be done with large number of experiments and

D

large amount of time using previously demonstrated single-response approaches.

PT E

Additionally, the standard deviation data show that the results of growth to growth variation were significantly reduced. Because the repeatability of a manufacturing process is

CE

the prerequisite for the industrialization of a product, the main contribution of this study stands out as improvement in the process repeatability.

AC

As a result, this study shows the multi-response optimization approach in which we merged TOPSIS and Taguchi optimization methods to make it possible to optimize multiple responses simultaneously can be applied not only for CVD growth optimization of graphene but also for optimization of any kind of similar growth processes and materials. Acknowledgements Graphene growth by CVD process was performed by Graphene Biotech. Raman spectroscopy analyses and AFM were carried out by the Thermo DXR Raman,

19

ACCEPTED MANUSCRIPT Nanomagnetics Instruments AFM plus device in Namık Kemal University Central Research Laboratory. References

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