The optimization of chemical mechanical planarization process-parameters of c-plane gallium-nitride using Taguchi method and grey relational analysis

Materials and Design 104 (2016) 392–403

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The optimization of chemical mechanical planarization process-parameters of c-plane gallium-nitride using Taguchi method and grey relational analysis D.M. Nelabhotla a, T.V. Jayaraman b,⁎, K. Asghar a, D. Das a,⁎ a b

School of Engineering Sciences and Technology, University of Hyderabad, Hyderabad 500046, India Department of Mechanical Engineering, University of Michigan, Dearborn, MI 48128, USA

a r t i c l e

i n f o

Article history: Received 5 February 2016 Received in revised form 22 April 2016 Accepted 11 May 2016 Available online 12 May 2016 Keywords: Chemical mechanical planarization c-plane GaN Taguchi method Grey relational analysis

a b s t r a c t In this work, Taguchi-based grey relational analysis (TGRA) was adopted for the optimization of chemical mechanical planarization (CMP) process-parameters of c-plane gallium-nitride (GaN), in a potassium-permanganate/alumina (KMnO4/Al2O3) slurry. The TGRA suggests, the combination of process–parameters—slurry pH = 2, KMnO4 conc. = 0.3 M, Al2O3% = 2.50, down-pressure = 38 kPa, and platen RPM = 90—provides the optimum combination of response variables: material removal rate (MRR) ~ 142 nm/h and root-mean-square surface roughness (RMS) ~ 22 nm. The optimum condition provides a marked improvement in the multiple performance, grey relational grade (GRG), as high as ~0.86. The strongest influence on GRG was slurry pH, followed by down-pressure, platen RPM, Al2O3%, and KMnO4 conc. The combination of CMP process-parameters suggested by TGRA provides a superior combination of MRR and RMS compared to the combination of process-parameters suggested by Taguchi—larger is better MRR (TMRR) and Taguchi—smaller is better RMS (TRMS). Comparing optimal condition for TGRA to that of TMRR indicates marginal reduction (~8%) in MRR, and significant improvement (~21%) in RMS. Similarly, comparison of optimal condition for TGRA to that of TRMS indicates increase in RMS by a miniscule ~5% and a dramatic increase in MRR by ~48%. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction The III-V nitride systems were widely viewed as promising candidates for semiconductor device applications in the blue and ultra-violet (UV) wavelength spectrum [1]. Currently, gallium-nitride (GaN) is a popular candidate material for applications in high frequency and high power opto-electronic devices, owing to wide bandgap, high carrier mobility, high saturated electron drift velocity, and high breakdown field [2,3]. Some of the challenges in the development and commercialization of GaN based power- or opto-electronic devices have been including, but not limited to non-availability of suitable device grade wafers (GaN being hard and chemically inert makes it difficult to obtain crystals with a low number of lattice defects and high quality surface), difficulties in growing bulk GaN wafer in homoepitaxial substrates, and relatively poor quality of GaN films in heteroepitaxial growth on sapphire substrates [2,4,5]. Large differences in the thermal expansion, coupled with the lattice mismatch between sapphire and GaN, introduces relatively large crystal defects and, rough surface generated during the growth process limits its application [6,7]. Hence it is

⁎ Corresponding authors. E-mail addresses: [email protected] (T.V. Jayaraman), [email protected] (D. Das).

imperative to produce an atomic scale flat, smooth, and defect free GaN surface. Chemical mechanical planarization (CMP), a surface polishing/ finishing/planarization technology, is known for providing global planarization [8–11]. It is a surface smoothening process aided by chemical corrosion and mechanical grinding. The basic principle of CMP is to rotate the wafer surface (held by a carrier) with a rotating polishing pad (in a platen) under a certain down-pressure with a constant flow of a suitable slurry that consists of ultra-fine abrasive particles and chemical oxidizer in a liquid medium. This technique originated from glass polishing and brought into the semiconductor industry by IBM [12, 13]. Fig. 1 shows the schematic of a CMP process. The key challenge in CMP is to simultaneously achieve a high material removal rate (MRR) and low non-uniformity of the polished/planarized surface i.e. rootmean-square surface roughness (RMS). Many factors (process–parameters) control the CMP process response variables—MRR and RMS. The CMP process–parameters (attributes) can be broadly classified into: a) Slurry attributes (viz. slurry pH, oxidizer concentration, abrasive concentration, slurry flow rate, surfactant dose etc.); b) Platen attribute (eg. platen RPM, type/nature of the pad, pad asperity etc.); and c) Carrier attributes (viz. carrier RPM, down pressure, rotation direction with respect to the pad rotation etc.). Ability to control all these factors/attributes to obtain optimum combination of MRR and RMS is an important research subject in CMP process and numerous optimization works are

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was estimated from the difference in the weight—measured using a Sartorius Model# CPA225D high precision electronic balance—before and after each experimental run. The wafer surface features were characterized using Bruker Optical Surface Profiler (Model Contour GT-K0). The root-mean-square surface roughness (RMS) was estimated over a scan area of 0.70 × 0.96 mm2 after each experimental run. The post CMP cleaning was performed by repeated cleaning of the GaN wafer surface using alcohol, acetone, and deionized water after each experimental run. 2.2. Design of experiments and analysis

Fig. 1. Schematic of a chemical mechanical planarization (CMP) process.

reported for various combinations of wafer materials (eg. Si, Cu, polymers etc.) and slurries [10,12,14–20]. In the past, studies on c-plane GaN using colloidal SiO2 showed success in planarization to defect-free GaN surfaces [21]—specifically polishing of N polar (0001) GaN surface was relatively more effective than the Ga polar (0001) GaN surface. Over the past, the studies on CMP slurries for GaN were focused on various abrasives particles (Al2O3 and SiO2) and chemical oxidizers—KOH, sodium-hypochlorite, H2O2 and KMnO4 [22–29]. Recently, CMP studies [28] on (0001) GaN with slurry having KMnO4 as an oxidizer indicate that the MRR for Al2O3 (as abrasive) containing slurry is significantly higher (~double) than that for the slurry having SiO2 (as abrasive). However KMnO4/ SiO2 slurry produced better surface quality in terms of surface roughness (RMS) and relatively defect-free surface compared to the KMnO4/ Al2O3 slurry. Till date there have been no studies on the optimization of process parameters of CMP of c-plane GaN. This paper focuses on the optimization of the CMP process–parameters of c-plane GaN in KMnO4/Al2O3 slurry, using Taguchi method (TM) [30–32] and Grey Relational Analysis (GRA) [33]—also referred as grey-based Taguchi method [34–38] or Taguchi-based grey relational analysis [39–41]—in order to achieve an optimum combination of MRR and RMS. 2. Experimental 2.1. Materials and methods Commercially available c-plane (0001) GaN film grown on 2″ sapphire substrate was used in this study. The CMP experimental runs were carried out on a Buehler Ecomet 250 variable speed Grinder Polisher having Automet 250 power head. The GaN wafer was mounted on a 2″ stainless steel carrier using a Crystal Bond 509 epoxy resin and polished/planarized on a Cabot D100 pad. The CMP slurries consisted of the oxidizer—potassium permanganate (KMnO4) and abrasive particles—colloidal alumina (Al2O3). The colloidal Al2O3 had the mean size ~ 50 nm with a solid loading of ~ 40%. The slurry was delivered to the polishing pad by a peristaltic pump (Ravel, Model# RH-P100VS-100) at a flow rate of 10 ml/min while the carrier velocity was maintained a constant—30 RPM. The rotation direction of platen and carrier were opposite to one another. The typical time for each of the experimental runs was ~ 15 min coupled with intermittent conditioning of the pad after every 5 min, using a diamond pad conditioner (M/s Abrasive Technology Asia Pacific Ltd. Singapore, Model# S341038N-2A2). A series of designed experimental runs (details in Section 2.2) involved variation of the following control factors: slurry pH (a slurry attribute), oxidizer —KMnO4—concentration (a slurry attribute), abrasive (Al2O3) concentration (a slurry attribute), down pressure (a carrier attribute), and platen velocity (a platen attribute); followed by the measurement of the following response variables: MRR (nm/h) and RMS (nm). The MRR

The traditional experimental techniques that involves varying one parameter at a time while keeping other parameters constant, suffer from the major drawback of either being ‘unbalanced’ or having a large number of experiments that leads to increase in the cost of experiments coupled with inherent complexity. In this study, a Taguchi orthogonal array was adopted to observe the influence of the CMP process–parameters on the c-plane GaN. Table 1 lists the five controlled factors (attributes) and their respective levels. While the control factor slurry pH has two levels, rest of the control factors have three levels each. The plan of experiments in this study follows an orthogonal array (OA) L18 (21 × 37) table. The layout of the OA is given in Table 2. This array is a specially designed array since the interaction is built in between the first two columns and the interaction information can be obtained without sacrificing any other column. Interactions between three-level columns are distributed more or less uniformly to all the other three-level columns, which permits the investigation of main effects and thus it is a highly recommended array for experiments [30]. In the case of the usual Factorial Design it would require 162 experimental conditions (runs), whereas the Taguchi OA reduces it to exclusively 18 different experimental conditions (runs) providing a significant advantage in terms of experimental resources, time, and cost. Additionally the duplicate runs of each experimental condition lead to an overall 36 experimental runs (again significantly b 162) and improved accuracy. The response variables of the CMP process investigated are i) MRR (nm/h) and ii) RMS (nm). The Taguchi method employs the signal to noise (S/N) ratio, to measure the performance of the process response. S/N ratio being the ratio of mean to standard deviation can effectively consider the variation encountered in a set of experimental runs [31]. Based on the objective of the experimental response variables, the characteristics of the S/N ratio is categorized into three criteria: larger is better (LB), smaller is better (SB), and nominal is best (NB) [31,32]. The factor-level combination that maximized to the appropriate S/N ratio is the optimal setting. In this work the LB and SB were selected to obtain the performance characteristics for MRR and RMS respectively, using Eqs. (1) and (2) respectively. Larger is better (LB):
 S 1 n ¼ 10 log  ∑ 1=y2MRR N n i¼0

ð1Þ

Table 1 Chemical mechanical planarization control factors and levels. Levels Control factors A: Slurry pH B: Oxidizer concentration (M) (KMnO4 conc.) C: Abrasive concentration (wt.%) (Alumina–Al2O3%) D: Carrier down pressure (kPa) E: Platen velocity (RPM)

I

II

III

2 0.1

3 0.2

0.3

1.25

2.50

3.75

24 60

31 90

38 100

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Table 2 The layout of the L18 (21 × 37) OA. A, B, C, D, and E represent control factors while 1, 2, and 3 represent the levels. Experiment #

A

B

C

D

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2

1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2

1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1

Level

n

S 1 ¼ 10 log  ∑ y2 N n i¼0 RMS

A (Slurry pH)

B (KMnO4 conc.)

C (Al2O3%)

D (Down pressure)

E (Platen RPM)

S/N ratios 1 41.89 2 35.84 3 Delta 6.05 Rank 1

39.13 38.40 39.08 0.74 5

39.53 38.45 38.62 1.08 4

36.78 39.30 40.52 3.74 2

38.29 38.36 39.95 1.67 3

Mean 1 2 3 Delta Rank

97.92 91.93 99.09 7.16 5

96.06 92.20 100.48 8.28 4

77.29 98.55 112.90 35.61 2

89.88 92.75 106.00 16.01 3

127.35 65.14 62.21 1

correspond to the larger is better (LB) and smaller is better (SB) criterion respectively and are expressed as: Larger is better (LB):

Smaller is better (SB):


Table 4 Response table for S/N ratios and means for Material Removal Rate (MRR)—Larger is better.

h i h i xij ¼ yij − minyij = maxyij − minyij

 ð2Þ

where yMRR and yRMS represent the response for MRR and RMS respectively, and n denotes the number of experiments. While the traditional Taguchi method utilizes a well-balanced experimental design (OA design to optimize a single response at a time) it is not suitable to optimize multiple-responses simultaneously. This is overcome by coupling Taguchi method with grey relational analysis (GRA) [34–42]. The GRA, a part of grey system theory, was proposed by Deng [33] as a relatively accurate method for multiple attribute decision making that is based on the minimization of maximum distance from the ideal referential alternative. In this method several response variables are converted into single response function—a representative of all desired response characteristics of the process—and the single response function is maximized. In GRA, the experimental data (from the Taguchi OA) is first normalized ranging from zero to one—a data preprocessing step known as grey relational generation. The normalized data in the present study for the response variables MRR and RMS

ð3Þ

Smaller is better (SB): h i h i xij ¼ maxyij −yij = maxyij − minyij

ð4Þ

where xij is the normalized value i.e. value after grey relational generation of ith response variable in the jth experiment, minyij and maxyij are the smallest and the largest value respectively, of yij for the ith response variable among j experiments. This normalization avoids the pitfalls of adopting different units and reduces the variability. Subsequently, the grey relational coefficients (GRC) are calculated from the normalized data to represent a correlation between the desired and the actual experimental data. GRC (ξij) is calculated as     ξij ¼ mini jX j −xij j þ ψ maxi jX j −xij j = jX j −xij j þ ψ maxi jX j −xij j ð5Þ where Xj is the ideal normalized value i.e. the maximum of the normalized S/N ratio (since large S/N ratio is preferred) for the jth response variable and ψ is the distinguishing or identification co-efficient, which is

Table 3 The experimental runs and results–OA L18 (21 × 37) and computation of means (average) and S/N ratios for Material Removal Rate (MRR)—Larger is better and Surface Roughness (RMS)— Smaller is better. Exp

A

B

C

D

E

# 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 Grand average

0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3

1.25 2.50 3.75 1.25 2.50 3.75 1.25 2.50 3.75 1.25 2.50 3.75 1.25 2.50 3.75 1.25 2.50 3.75

24 31 38 24 31 38 31 38 24 38 24 31 31 38 24 38 24 31

60 90 100 90 100 60 60 90 100 100 60 90 100 60 90 90 100 60

MRR

RMS

#1

#2

Avg.

S/N(LB)

#1

#2

Avg.

S/N(SB)

82.8 145.8 152.4 92.8 96.1 155.7 129.2 139.1 149.1 86.1 53.0 59.6 102.7 62.9 33.1 76.2 46.4 56.3

86.1 149.1 149.1 96.1 99.4 159.0 125.9 142.5 142.4 89.5 56.3 62.9 106.0 62.9 36.4 79.4 53.0 49.7

84.5 147.4 150.7 94.4 97.7 157.4 127.5 140.8 145.7 87.8 54.7 61.3 104.4 62.9 34.8 77.8 49.7 53.0 96.3

38.53 43.37 43.56 39.50 39.80 43.94 42.11 42.97 43.26 38.86 34.74 35.74 40.37 35.98 30.80 37.81 33.87 34.43 38.87

32.6 23.0 30.4 24.4 29.5 27.6 30.1 21.5 29.2 24.9 23.3 24.6 24.4 26.3 25.1 24.8 25.9 28.3

30.6 22.7 30.0 23.7 27.3 26.6 27.2 21.4 27.6 24.8 22.6 24.4 23.1 25.7 23.6 24.6 25.7 26.6

31.6 22.9 30.2 24.1 28.4 27.1 28.7 21.5 28.4 24.9 23.0 24.5 23.8 26.0 24.4 24.7 25.8 27.5 26.0

−30.00 −27.18 −29.60 −27.62 −29.07 −28.66 −29.15 −26.63 −29.07 −27.91 −27.22 −27.98 −27.52 −28.30 −27.73 −27.85 −28.23 −28.78 −28.2

D.M. Nelabhotla et al. / Materials and Design 104 (2016) 392–403 Table 5 Response table for S/N ratios and means for Surface Roughness (RMS)—Smaller is better.

Level

A (Slurry pH)

S/N ratios 1 −28.55 2 −27.92 3 Delta 0.63 Rank 3 Means 1 2 3 Delta Rank

26.97 24.93 2.04 3

B (KMnO4 conc.)

C (Al2O3%)

D (Down pressure)

E (Platen RPM)

−28.28 −28.15 −28.29 0.13 5

−28.34 −27.77 −28.60 0.83 2

−28.31 −28.25 −28.16 0.15 4

−28.68 −27.47 −28.57 1.22 1

26.16 25.61 26.07 0.55 4

26.27 24.57 27.00 2.43 2

26.19 25.93 25.72 0.47 5

27.29 23.65 26.90 3.64 1

395

used to adjust the difference of the relational coefficient, usually ψ ϵ (0, 1). ψ generally weakens the effect of maxi |Xj − xij | when it gets too big, enlarging the different significance of the relational coefficient. The suggested value of ψ is 0.5 due to the moderate distinguishing effects and good stability of outcomes [33]. Finally, grey relational grade (GRG) is calculated by averaging the GRC. GRC (γ) is computed as: γ ¼ ð1=nÞ∑ξij

ð6Þ

The GRG is treated as the overall response of the process instead of the multiple responses—MRR and RMS. The higher value of γ represents that the corresponding factors (process–parameters) combination is closer to the optimal condition. Additionally, the optimum process condition is evaluated from the main effect plot of GRC. Thus the optimization of the multiple process response is converted into optimization of a single GRG [33–43]. After evaluating the optimal process parameters

Fig. 2. Main effect plots showing the effect of control factors (slurry pH, KMnO4 conc. Al2O3%, down pressure, and platen RPM) on the response variable MRR (nm/h); a) Mean of S/N ratios and b) Mean of Means.

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Fig. 3. Main effect plots showing the effect of control factors (slurry pH, KMnO4 conc. Al2O3%, down pressure, and platen RPM) on the response variable RMS (nm); a) Mean of S/N ratios and b) Mean of Means.

settings the enhancement of the performance/quality characteristics using the optimal parameters/factors combination was predicted and verified through confirmation tests. 3. Results and discussion The results (response variables—MRR and RMS) for the various CMP experimental runs based on the Taguchi–OA L18 (21 × 37) are presented in Table 3. Each combination of experimental conditions (experiment#) was duplicated, and overall there were 36 experimental runs. For each experimental condition the average value (mean) of MRR and RMS were determined and their respective S/N ratios—larger is better for MRR and smaller is better RMS—were calculated based on Eqs. (1) and (2) and, the results are tabulated (Table 3). The data analysis of the experimental results were performed using the commercial statistical software MINITAB® 17, at 95% confidence level. The response table of S/N ratios and means (average values) for MRR (larger is better) and RMS (smaller is better) are presented in Tables 4 and 5 respectively. A

response table provides information regarding the nature of the process under consideration. The highest difference (based on means) in the control factors indicates the strongest influence on the response variable. The strongest influence on MRR (Table 4) is slurry pH, followed by down-pressure, platen RPM, Al2O3%, and KMnO4 conc. in that order; while the strongest influence for RMS (Table 5) is platen RPM followed by Al2O3%, slurry pH, KMnO4 conc., and down-pressure in that order. Among all the factors the KMnO4 conc. has least influence on both MRR and RMS. Figs. 2 and 3 show the main effect plots (S/N ratios and means) for MRR and RMS respectively. The main effect plots show how each factor effects the response characteristic. By comparing the slopes of the lines the relative magnitude of the factor effect is known. Additionally, the main effect plots are used to determine the optimum factor levels (based on S/N ratio) for each response variables. For MRR (Fig. 2a) it is evident that the optimum level of factors for the performance characteristics—larger is better—is A1B1C1D3E3 (slurry pH = 2, KMnO4 conc. = 0.1 (M), Al2O3% = 1.25, down-pressure = 38 kPa, and platen RPM =

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Fig. 4. Interaction plots showing the interaction among control factors (slurry pH, KMnO4 conc. Al2O3%, down pressure, and platen RPM) on the response variables a) MRR (nm/h) and b) RMS (nm).

100). On the other hand for RMS (Fig. 3a) the optimum level of factors for the performance characteristics—smaller is better—is A2B2C2D3E2 (i.e. slurry pH = 3, KMnO4 conc. = 0.2 (M), Al2O3% = 2.50, down-pressure = 38 kPa, and platen RPM = 90). Fig. 4 shows the interaction plots

for MRR and RMS. Interaction plots assess the two-way interactions among factors to the response variable. In the case of MRR (Fig. 4a) interaction effect is observed between slurry pH and Al2O3%, between KMnO4 conc. and down-pressure, between KMnO4 conc. and platen

Table 6 The Analysis of Variance (ANOVA) table for Material Removal Rate—MRR (DOF is degrees of freedom, Seq. SS is sequential sum of squares, Adj. SS is adjusted sum of squares, Adj. MS is adjusted mean of squares).

Source

DOF

Seq. SS

Adj. SS

Adj. MS

A: Slurry pH B: KMnO4 conc. C: Al2O3% D: Down-pressure E: Platen RPM A ∗ C: Slurry pH ∗ Al2O3% Error Total

1 2 2 2 2 2 6 17

17,415.7 173.6 206.0 3852.1 879.2 3206.7 1499.4 27,232.6

17,415.7 173.6 206.0 1296.7 502.3 3206.7 1499.4

17,415.7 86.8 103.0 648.3 251.1 1603.4 249.9

contribution %

F value

p value

63.95 0.64 0.76 14.15 3.23 11.78 5.51 100

69.69 0.35 0.41 2.59 1.00 6.42

0.000 0.720 0.680 0.154 0.420 0.032

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Table 7 The Analysis of Variance (ANOVA) table for Surface Roughness—RMS (DOF is Degrees of Freedom, Seq. SS is sequential sum of squares, Adj. SS is adjusted sum of squares, Adj. MS is adjusted mean of squares). Adj. MS

Source

DOF Seq. SS

Adj. SS

A: Slurry pH B: KMnO4 conc. C: Al2O3% D: Down pressure E: Platen RPM A ∗ B: Slurry pH ∗

1 2 2 2 2 2

18.707 1.054 18.560 0.679 47.955 11.714

18.707 18.707 1.054 0.527 20.117 10.059 0.679 0.339 47.955 23.978 11.714 5.857

KMnO4 conc. A ∗ D: Slurry pH ∗

2

7.48

down pressure Error Total

4 17

7.48

21.472 21.472 127.622

contribution F p % value value 14.66 0.83 14.54 0.53 37.58 9.18

3.48 0.10 1.87 0.06 4.47 1.09

0.135 0.909 0.267 0.940 0.096 0.419

3.740

5.86

3.74

0.550

5.368

16.82 100

RPM, between Al2O3% and down-pressure RPM, and between Al2O3% and platen RPM. The interaction effect between slurry pH and Al2O3% indicates that the relationship between slurry pH and MRR, depends on Al2O3%. For example, use of low KMnO4 conc. is associated with high MRR for higher platen RPM. For RMS (Fig. 4b), interaction effect is observed between slurry pH and KMnO4 conc., between slurry pH and Al2O3%, between slurry pH and down-pressure, between slurry pH and platen RPM, between KMnO4 conc. and Al2O3%, between KMnO4 conc. and down-pressure, between Al2O3% and down-pressure, and between Al2O3% and platen RPM. In order to observe the practical (% contribution ≥ 10%) and statistical (p ≤ 0.05) significance of various factors (slurry pH, KMnO4 conc., Al2O3%, down-pressure, and platen RPM) on MRR and RMS, Analysis of Variance (ANOVA) was performed with the experimental data with 95% confidence level. Tables 6 and 7 show the results of ANOVA for MRR and RMS respectively. It is evident (Table 6) that the effect of slurry pH (% contribution ~ 64 and p b 0.001) on MRR is of both statistical and practical significance while the effect of down pressure (% contribution ~ 14 and p = 0.154) on MRR is moderately significant. The effect of rest of the factors— KMnO4 conc., Al2O3%, and platen RPM—on MRR is insignificant. The interaction of slurry pH and Al2O3% (% contribution ~ 12 and p = 0.032) have significant effect (both statistical and practical) on MRR. Additionally, the percentage contribution of combined error is relatively small (~6%) which indicates that no further important factors were missed in the Taguchi approach and the arrangement of the experimental trials in the current study is complete. Similarly, it is evident from Table 7 that the effect of platen RPM (% contribution ~ 38% and p = 0.096) on RMS is significant while the effect of slurry pH (% contribution ~ 15% and p = 0.135) and Al2O3% (% contribution ~ 15% and p = 0.267) on RMS is moderately significant. The factors—KMnO4 conc. and down-pressure have insignificant effect on RMS. The significance of interaction between slurry pH and KMnO4 conc. (% contribution ~ 9% and p = 0.419) is also moderate. The percentage contribution of combined error is ~17% which indicates

Table 8 Comparison of predicted and confirmatory experimental results MRR (nm/h) and RMS (nm) based on Taguchi—Larger is better for MRR and Smaller is better for RMS. Response variables

Initial condition

Grey relational generation

Grey relational coefficient

Exp #

MRR

RMS

MRR

RMS

Grey relational grade

Grey order

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0.5885 0.9568 0.9716 0.6621 0.6849 1.0000 0.8610 0.9265 0.9489 0.6140 0.3002 0.3760 0.7283 0.3944 0.0000 0.5340 0.2336 0.2769

0.0000 0.8370 0.1180 0.7048 0.2746 0.3969 0.2506 1.0000 0.2755 0.6207 0.8255 0.6573 0.7365 0.5039 0.6719 0.6363 0.5240 0.3630

0.5486 0.9205 0.9462 0.5968 0.6134 1.0000 0.7825 0.8718 0.9072 0.5643 0.4167 0.4448 0.6479 0.4522 0.3333 0.5176 0.3948 0.4088

0.3333 0.7541 0.3618 0.6288 0.4080 0.4533 0.4002 1.0000 0.4083 0.5687 0.7413 0.5933 0.6549 0.5020 0.6038 0.5789 0.5123 0.4397

0.4409 0.8373 0.6540 0.6128 0.5107 0.7266 0.5914 0.9359 0.6578 0.5665 0.5790 0.5191 0.6514 0.4771 0.4686 0.5483 0.4536 0.4243

17 2 5 7 13 3 8 1 4 10 9 12 6 14 15 11 16 18

that the factors (and few of their interactions in Table 7) chosen in the Taguchi approach for the experimental trials in the current study explain the variations in RMS. The predicted mean of MRR (MRRpredict) at the optimum levels (performance characteristics – larger is better) of control factors— A1B1C1D3E3 was computed using the following equation [31]:           −Y þ C1  −Y þ D3  −Y −Y þ B1 MRRpredict ¼ Y þ A1    −Y þ E3

ð7Þ

where Y (is the grand average of MRR (corresponding to all the 36  , B1  , C1  , D3  , and E3  are the average (18 × 2) readings in Table 3, and A1 values of MRR with process parameters at their respective optimum levels (Table 4). The predicted MRR for the combination of control factors A1B1C1D3E3 was ~155 nm/h. Similarly, the predicted mean of RMS (RMSpredict) at the optimum levels (performance characteristics – smaller is better) of control factors—A2B2C2D3E2 was computed as:           −Y þ C2  −Y þ D3  −Y RMSpredict ¼ Y þ A2 −Y þ B2     þ E2 −Y

ð8Þ

where Y (is the grand average of RMS (corresponding to all the 36  , B2  , C2  , D3  , and E2  are the average (18 × 2) readings in Table 3, and A2 values of RMS with process parameters at their respective optimum levels (Table 5). The predicted RMS for the combination of control factors A2B2C2D3E2 was ~ 21 nm. The predicted results (based on 95% confidence interval) of MRR and RMS are tabulated (Table 8) along with the corresponding results from the confirmatory experimental runs. The difference between the predicted results and the experimental results is negligible and the experimental values of MRR and RMS are within the confidence interval of the predicted MRR and RMS Table 10 Response table for means of grey relational grade (GRG).

Optimum condition Predicted

Table 9 Computed Grey relational generation, Grey relational coefficient for MRR (nm/h) and RMS (nm), Grey relational grade, and Grey order (rank).

Experimental Level

Material Removal Rate (MRR) Level A1B1C1D1E1 Mean/Average 84.5 S/N ratio 38.5

A1B1C1D3E3 155.1 ± 1.9 45.6

A1B1C1D3E3 154.9 ± 1.2 43.8

Surface Roughness (RMS) Level A1B1C1D1E1 Mean/Average 31.6 S/N ratio −30.00

A2B2C2D3E2 20.7 ± 0.3 −26.52

A2B2C2D3E2 20.9 ± 0.1 −26.44

1 2 3 Delta Rank

A (Slurry pH)

B (KMnO4 conc.)

C (Al2O3%)

D (Down-pressure)

E (Platen RPM)

0.6630 0.5209

0.5995 0.5745 0.6019 0.0273 5

0.5685 0.6323 0.5751 0.0637 4

0.5354 0.5890 0.6514 0.1160 2

0.5399 0.6536 0.5823 0.1138 3

0.1422 1

Total mean of grey relational grade = 0.5920. The bold font signifies the highest GRG for respective process-parameters.

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399

Fig. 5. Main effect plots showing the effect of control factors (slurry pH, KMnO4 conc. Al2O3%, down pressure, and platen RPM) on the response variable grey relational grade (GRG).

respectively. While the MRR at the combination of control factors A1B1C1D3E3—performance characteristics larger is better—from the confirmatory runs was ~ 155 nm/h the RMS at this condition was ~28 nm. Similarly for the combination of control factors A2B2C2D3E2 —performance characteristics smaller is better—the RMS was ~21 nm and MRR at this condition was ~74 nm/h. The optimum factor levels for MRR (larger is better) and RMS (smaller is better) differ from one another. A slurry with a relatively lower pH favors higher MRR while, a slurry with higher pH favors lower RMS. An industrial requirement prefers that the CMP process be performed at the same level of design and process parameters to get the optimized MRR and RMS. The traditional Taguchi method is suitable to optimize single response variable at a time, but it is not suitable to

optimize multiple-responses simultaneously. To achieve the optimization of multiple responses, both responses (MRR and RMS) are converted into a single response—grey relational grade—based on grey relational analysis [33–43]. The grey relational generation (a data preprocessing step based on Eqs. (3) and (4) (larger is better for MRR and smaller is better for RMS), the grey relational coefficient calculation based on Eq. (5), and the grey relational grade (Eq. (6)) are tabulated (Table 9). The distinguishing coefficient (in Eq. (5)) was taken as 0.5 since the importance of MRR and RMS were assumed to be equal, and equal weights of GRC was considered for GRG calculation (Eq. (6)). The grey relational grade corresponding to each of the experiments runs are ranked (highest is ranked one and so on)—also known as grey order. The experiment# 8 has the highest grey

Fig. 6. Interaction plots showing the interaction among the control factors (slurry pH, KMnO4 conc. Al2O3%, down pressure, and platen RPM) on the response variable grey relational grade (GRG).

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Table 11 Comparison of initial condition and optimal condition—predicted and experimental results MRR (nm/h), RMS (nm), and grey relational grade—from Taguchi-based grey relational analysis. Initial condition

Optimal condition

Experimental

Predicted

Levels

A1B1C1D1E1

A1B3C2D3E2 A1B3C2D3E2

Factors Slurry pH KMNO4 conc.(M) Al2O3% Down-pressure (kPa) Platen RPM

2 0.1 1.25 24 60

2 0.3 2.5 38 90

2 0.3 2.5 38 90

84.1

NA

141.9

30.1 0.4333

NA 0.8342

21.6 0.8591

Response variables Material removal rate-MRR (nm/h) Surface roughness-RMS (nm) Grey relational grade

Experimental

NA – Not applicable. (Note: The prediction is only for the grey relational grade).

relational grade (0.9359) and has the optimal parameters setting for best multi-response-characteristics. The response table of means (average values) for GRG (larger is better) is presented in Table 10. The strongest influence on GRG is slurry

pH, followed by down-pressure, platen RPM, Al2O3% and KMnO4 conc. The optimum parameter levels for maximizing grey relational grade is obtained from the main effect plot (Fig. 5). The optimum level of factors for the performance characteristics—maximizing GRG—is A1B3C2D3E2 (slurry pH = 2, KMnO4 conc. = 0.3 (M), Al2O3% = 2.50, down-pressure = 38 kPa, and platen RPM = 90). Fig. 6 shows the interaction plots for GRG. Interaction effects are observed between slurry pH and KMnO4 conc., slurry pH and Al2O3%, between slurry pH and down pressure, between slurry pH and platen RPM, between KMnO4 conc. and Al2O3%, between KMnO4 conc. and down-pressure, and between KMnO4 conc. and platen RPM. For example, the interaction effect between slurry pH and Al2O3% indicates that the relationship between slurry pH and GRG, depends on Al2O3%. The confirmation test was conducted to validate the analysis. The experiment was conducted according to the optimal parameter settings. The predicted grey relational grade (based on grey relational analysis) using optimal process parameters is given by the equation: γ ¼ γm þ ∑ðγn −γm Þ

ð9Þ

where γm is the total mean grey relational grade; γn is the mean grey relational grade at the optimum level—obtained from the response table of GRG (Table 10). Table 11 shows the comparison of predicted GRC and that obtained through confirmatory experimental run; coupled with the comparison of experimental initial condition and the optimal

Fig. 7. Optical surface profiler images of the c-plane GaN surface after confirmatory chemical mechanical planarization run—initial condition (A1B1C1D1E1). a) 2D and b) 3D.

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401

Fig. 8. Optical surface profiler images of the c-plane GaN surface after confirmatory chemical mechanical planarization runs—optimum condition (A1B3C2D3E2) based on grey relational analysis. a) 2D and b) 3D.

settings based on grey relational analysis. The initial condition is where the factors were set to their respective lowest levels (A1B1C1D1E1). The comparison of experimental initial condition with that of optimum condition indicates that the MRR increased from 84.1 nm/h to 141.9 nm/h (~ 69% increase), RMS decreased from 30.1 nm to 21.6 nm (~ 27% decrease), and the grey relational grade increased from 0.4333 to 0.8591, respectively—a clear improvement in the multiple performance characteristics. Figs. 7 and 8 compares the optical surface profiler images of the c-plane GaN surface after the confirmatory CMP runs based on initial (A1B1C1D1E1) and optimum (A1B3C2D3E2) conditions respectively. The RMS was estimated over a scan area ~0.70 × 0.96 mm2 after CMP. It is evident from the surface profile that the surface quality for the optimum condition, based on grey relational analysis, is significantly superior to the initial condition. Fewer pits observed probably originate from the threading dislocation created during GaN growth and open up or became visible during CMP. The opening up of the dislocations due to the chemical etching effect during CMP is well known as observed in other investigations [28,44,45]. Regarding occasional scratches found after CMP using optimum condition, it is owing to mechanical abrasion by relatively harder Al2O3 particles. The Taguchi grey relational analysis based optimization of CMP process–parameters of c-plane GaN, for a KMnO4/Al2O3 slurry, suggest the process–parameters—A1B3C2D3E2 (slurry pH = 2, KMnO4 conc. = 0.3 M, Al2O3% = 2.50, down-pressure = 38 kPa, and platen RPM = 90)—provide the optimum combination of response variables

MRR ~ 142 nm/h and RMS ~ 22 nm. In comparison, the Taguchi (only) —Larger is Better MRR suggest the process parameters—A1B1C1D3E3 (slurry pH = 2, KMnO4 conc. = 0.1 M, Al2O3% = 1.25, down-pressure = 38 kPa, and platen RPM = 100) that gives the following combination of MRR ~ 155 nm/h and RMS ~ 28 nm. While MRR reduces only marginally by 8%, the RMS significantly improves by ~21%. However, in comparison, the Taguchi—Smaller is Better RMS, process-parameters— A2B2C2D3E2 (i.e. slurry pH = 3, KMnO4 conc. = 0.2 M, Al2O3% = 2.50, down-pressure = 38 kPa, and platen RPM = 90) provides the following combination of RMS ~ 21 nm/h and MRR ~ 74 nm. The improvement in RMS (in comparison Taguchi-based grey relational analysis based optimization) is relatively minuscule ~ 5% while MRR reduces dramatically by 48%. The CMP process parameters (for KMnO4/Al2O3 based slurry) suggested by Taguchi-based grey relational analysis provides a relatively superior combination of MRR and RMS. Past works [21,23,26,28,46] based on traditional experimental techniques—varying one parameter at a time while keeping other parameters constant— have shown that a KMnO4/SiO2 based slurry provides MRR b ~40 nm/ h and RMS ~ b ~ 10 nm. Though the MRR for c-plane GaN for the KMnO4/SiO2 based slurry is significantly lower than that for KMnO4/ Al2O3 based slurry (from Taguchi-based grey relational analysis), the RMS for KMnO4/SiO2 or H2O2/SiO2 based slurry is significantly superior. This suggests that the CMP of c-plane GaN could possibly be performed in a two-step process: i) a coarse-polishing step using a KMnO4/Al2O3 based slurry (MRR ~ 140 nm/h dominating, coupled with relatively

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low RMS ~ 21 nm) followed by, ii) a fine-polishing step adopting a KMnO4/SiO2 based slurry (superior surface finish RMS b ~10 nm over same scan area). 4. Conclusion In order to achieve an optimum combination of MRR and RMS, in this work, a Taguchi-based grey relational analysis was adopted for the optimization of chemical mechanical planarization process parameters for c-plane GaN in a KMnO4/Al2O3 slurry. The Taguchi-based grey relational analysis suggest, the combination of process-parameters— A1B3C2D3E2 (slurry pH = 2, KMnO4 conc. = 0.3 M, Al2O3% = 2.50, down-pressure = 38 kPa, and platen RPM = 90)—provide the optimum combination of response variables MRR ~ 142 nm/h and RMS ~ 22 nm. The optimum condition provides a clear improvement in the multiple performance—grey relational grade (GRG)—from ~0.43 to ~0.86. Compared to the initial condition, MRR increased by ~ 69% and RMS decreased by ~ 27%. The strongest influence on GRG was slurry pH, followed by down-pressure, platen RPM, Al2O3% and KMnO4 conc., in that order. The CMP process parameters suggested by Taguchi based grey relational analysis provide a superior combination of MRR and RMS compared to the process parameters suggested by Taguchi—larger is better MRR and Taguchi—smaller is better RMS. Comparing optimal condition obtained from Taguchi based grey relational analysis to that from Taguchi—larger is better MRR indicates that MRR reduces only marginally by 8% and, the RMS significantly improves by ~21%. Similarly, comparison of optimal condition obtained from Taguchi based grey relational analysis to that from Taguchi—smaller is better RMS indicates increase in RMS by a minuscule ~5% and a dramatic increase in MRR by 48%.The Taguchi based grey relational analysis indicates that the lowest RMS (KMnO4/Al2O3 slurry) that could be reached while maintaining a reasonably high MRR (~ 142 nm/h) is ~ 22 nm. Any change in process parameters to reduce RMS further (b 22 nm) reduces MRR dramatically. Consequently, the CMP for of c-plane GaN could possibly be performed in a two-step process—a coarse-polishing step using a KMnO4/Al2O3 based slurry that facilitates a high MRR (N ~140 nm/h) while maintaining RMS ~ 22 nm, followed by a fine-polishing step using a KMnO4/SiO2 based slurry that maintains RMS b ~10 nm. Acknowledgements The financial support from Department of Science and Technology (DST), Government of India through project grant# SR/S2/CMP-0009/ 2011 and partial support from the Board of Research in Nuclear Sciences (BRNS), Department of Atomic Energy (DAE), Government of India (Grant# 34/14/43/2014-BRNS) with ATC, are highly acknowledged. Infrastructure support from the School of Engineering Sciences and Technology, University of Hyderabad and the Department of Mechanical Engineering, College of Engineering and Computer Science, at the University of Michigan in Dearborn, are truly appreciated. References [1] S. Strite, H. Morkoc, GaN, AlN, and InN: a review, J. Vac. Sci. Technol. B 10 (1992) 1237–1266. [2] S. Nakamura, T. Mukai, M. Senoh, Candela-class high-brightness InGaN/AlGaN double heterostructure blue-emitting diodes, Appl. Phys. Lett. 64 (1994) 1687. [3] H. Kim, V. Tilak, B.M. Green, J.A. Smart, W.J. Schaff, J.R. Shealy, L.F. Eastman, Reliability evaluation of high power AlGaN/GaN HEMTs on SiC substrate, Phys. Status Solidi A 188 (1) (2001) 203–206. [4] X.H. Wu, P. Fini, S. Keller, E.J. Tarasa, B. Heying, U.K. Mishra, S.P. Debbaars, J.S. Speck, Morphological and structural transitions in GaN films grown on sapphire by metalorganic chemical vapor deposition, Jpn. J. Appl. Phys. 35 (1996) L1648–L1651. [5] R.P. Vando, X. Xu, A. Salant, J. Malcame, G.R. Brandes, Characteristics of semi-insulating , Fe-doped GaN substrates, Phys. Status Solidi A 200 (2003) 18. [6] M. Puchinger, T. Wagner, P. Fini, D. Kisailus, U. Beck, J. Bill, F. Aldinger, E. Arzt, F.F. Lange, Chemical solution deposition derived buffer layers for MOCVD-grown GaN films, J. Cryst. Growth 233 (2001) 57–67.

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