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International Symposium on Semiconductor Manufacturing Intelligence (ISMI 2015) Optimizing Multiple Response Variables of CMP Process for Semiconductor Fabrication Using a Clustering Method Jaehyun Park and Dong-Hee Lee* *Corresponding author

SLIDE 1

Jaehyun Park and Dong-Hee Lee*

*Corresponding author Tel.: +82-2-2220-0502; E-mail addresses: dh@hanyang.ac.kr

Optimizing Multiple Response Variables of CMP Process for Semiconductor Fabrication Using a Clustering Method

International Symposium on Semiconductor Manufacturing Intelligence (ISMI 2015)

SLIDE 2

응용시스템학과

Dept. of Applied Systems

CMP Process

CMP slurry Conditioner Head Wafer Platen Pad

Slurry Head Polishing pad Wafer

Schematic illustration of CMP process

Chemical and Mechanical Planarization (CMP) Process
One of unite processes for semiconductor fabrication
aims to achieve high planarity across the wafer surface (i.e., minimize roughness)

Definition of Roughness

2/10

SLIDE 3

응용시스템학과

Dept. of Applied Systems

Problem Statements

Process Variables Response Variables

Slurry material composition

(x1, x2, x3: proportions of pure slurries of which particle sizes are 30nm, 70nm, 200nm respectively)

Operation condition: pH of Slurry, Temperature
Rq: Roughness on the wafer surface

(Smaller the better)

Ra: Removal rate of material that should

be removed (Larger the better)

Rb: Removal rate of material that should

be protected from removal (Smaller the better)

Rotating speed of wafer and platen
Pressure between the wafer

surface and polishing pad

ptimize

𝐲

𝑆𝑏 𝐲 , 𝑆𝑐 𝐲 , 𝑆𝑟 𝐲

s. t. 𝑦1 + 𝑦2 + 𝑦3 = 100%

Three response variables should be optimized, simultaneously  “Multiresponse optimization method” is needed

3/10

SLIDE 4

응용시스템학과

Dept. of Applied Systems

Three Stages for Optimization

Posterior preference articulation approach to MultiResponse Surface

Optimization based on Clustering method (PMRSOC) (Lee and Lee, 2015) is adopted for the optimization

Stages of PMRSOC Action for the suggested CMP problem Applied Method

1. Model Building

Mixture experiments are conducted to build a reliable statistical models of Rq, Ra, Rb Simplex centroid design

2. Nondominated Solutions

Generation Candidate solutions are generated ε-constraints method

(Haimes et al., 1971)

3. Best Solution Selection

Best solution is selected from the candidate solutions K-means clustering 4/10

SLIDE 5

응용시스템학과

Dept. of Applied Systems

Stage 1. Model Building

Simplex of three input variables and its coordinate system

Design points (𝒚𝟐, 𝒚𝟑, 𝒚𝟒)

𝑺𝒃 𝑺𝒄 𝑺𝒓

(1, 0, 0) 909.21 122.86 8.57 (0, 1, 0) 728.95 102.52 10.20 (0, 0, 1) 323.90 32.33 13.26 (1/2, 1/2, 0) 824.82 116.18 9.20 (1/2, 0, 1/2) 1138.98 160.44 8.49 (0, 1/2, 1/2) 690.93 98.35 7.72 (1/3, 1/3, 1/3) 1325.55 185.77 6.47 (4/6, 1/6, 1/6) 1272.40 181.59 7.68 (1/6, 4/6, 1/6) 1042.86 139.24 8.00 (1/6, 1/6, 4/6) 1008.46 132.95 8.65

𝑧𝑆𝑏 𝐲 = 916.9𝑦1 + 731.1𝑦2 + 325.0𝑦3 + 42.6𝑦1𝑦2 + 2107.1𝑦1𝑦3 + 664.5𝑦2𝑦3 + 10473.0𝑦1𝑦2𝑦3, 𝑧𝑆𝑐 𝐲 = 125.56𝑦1 + 101.16𝑦2 + 31.61𝑦3 + 16.66𝑦1𝑦2 + 335.36𝑦1𝑦3 + 119.56𝑦2𝑦3 + 1327.48𝑦1𝑦2𝑦3, 𝑧𝑆𝑟 𝐲 = 8.6𝑦1 + 10.24𝑦2 + 13.27𝑦3 − 0.6𝑦1𝑦2 − 9.64𝑦1𝑦3 − 15.97𝑦2𝑦3 − 29.84𝑦1𝑦2𝑦3. The R2 (R2

adj) of the three models for Ra, Rb, and Rq are 99.64%

(98.91%), 99.38% (98.13%), and 99.59% (98.78%), respectively,

5/10

SLIDE 6

응용시스템학과

Dept. of Applied Systems

Stage 2. Nondominated Solutions Generation

Definition of nondominated solution
A solution

𝐲 is said to be nondominated if and only if there does not exist any

ther 𝐲 ∈ 𝛁 such that

𝑧𝑆𝑏(x) ≥ 𝑧𝑆𝑏( 𝐲), 𝑧𝑆𝑐(x) ≤ 𝑧𝑆𝑐( 𝐲), 𝑧𝑆𝑟(x) ≤ 𝑧𝑆𝑟( 𝐲), and x≠ 𝐲 .

ε-constraints method: Maximize

𝑧𝑆𝑏(𝐲) by restricting 𝑧𝑆𝑐(𝐲) and 𝑧𝑆𝑟(𝐲) Maximize 𝑧𝑆𝑏 𝐲

s. t.

𝑧𝑆𝑐 𝑦 ≤ 𝜁𝑆𝑐, 𝑧𝑆𝑟 𝑦 ≤ 𝜁𝑆𝑟

150 100 8 10 12 14 50 400 800 1200

𝑧𝑆𝑟 𝑧𝑆𝑐 𝑧𝑆𝑏 200 nondominated solutions

6/10

SLIDE 7

응용시스템학과

Dept. of Applied Systems

Stage 3. Best Solution Selection (1/3)

Grouping and Selection Strategy

Step 1: Divide the nondominated solutions into two groups by using K-means clustering Step 2: Select a preferred group Step 2: Are the solutions

f the selected group

close to each other? Start End Step 3: Select a final solution from the solutions

f the selected group

no yes

7/10

SLIDE 8

응용시스템학과

Dept. of Applied Systems

Stage 3. Best Solution Selection (2/3)

K-means Clustering
attempts to group a set of nondominated solutions in such a way that the solutions

in the same group are similar to each other than to those in other groups.

Algorithm

1: Determine K value 2: Select K solution randomly for the set of nondominated solutions as the initial centroids 3: repeat 4: Form K clusters by assigning all solutions to the closest centroid 5: Update the centroid of each cluster 6: until the centroids don’t change 8/10

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응용시스템학과

Dept. of Applied Systems

Stage 3. Best Solution Selection (3/3)

Iteration Group 1 Group 2 Selected group Ranges of solutions of selected group Centroid (ŷRa, ŷRb, ŷRq) Number of Solutions Centroid (ŷRa, ŷRb, ŷRq) Number of Solutions

1 (911.79, 125.15, 8.12) 82 (533.36, 70.62, 9.21) 118 1 (521.56, 70.74, 3.24) 2 (820.03, 112.70, 8.45) 52 (1070.85, 146.72, 7.53) 30 1 (247.69, 30.74, 2.72) 3 (768.41, 106.47, 8.57) 32 (902.63, 122.67, 8.26) 20 1 (114.24, 11.54, 2.52) 4 (797.51, 110.86, 8.48) 16 (739.32, 102.07, 8.67) 16 2 (35.34, 3.67, 2.39) 5 (742.14, 102.53, 8.96) 12 (730.84, 100.71, 7.80) 4 1 (29.11, 2.93, 2.16) 6 (737.09, 102.94, 9.30) 8 (752.24, 101.7, 8.27) 4 2 (12.93, 2.80, 0.72)

Summary of iterations of Steps 1 and 2

Input variable (x1, x2, x3) Estimated Response (ŷRa, ŷRb, ŷRq)

(3.24%, 34.97%, 61.80%) (745.72, 101,00, 8.20) (4.00%, 31.33%, 64.67%) (750.29, 101.00, 8.40) (4.75%, 28.10%, 67.15%) (754.30, 101.00, 8.60) (0.20%, 63.22%, 36.57%) (758.65, 103.80, 7.88)

Final 4 solutions in Step 3

Input variable (x1, x2, x3) Response (𝑺𝒃, 𝑺𝒄, 𝑺𝒓) (0%, 100%, 0%) (728.95, 102.52, 10.20)

Performance at the existing slurry 9/10

SLIDE 10

응용시스템학과

Dept. of Applied Systems

Concluding Remarks

Summary
The optimal blend of the mixture slurry was determined by applying PMRSOC
We showed that 𝑆𝑏, 𝑆𝑐, and 𝑆𝑟 at the obtained setting are better than those at

the existing pure slurry composition.

Limitation
No confirmation run
Future research issues
Effects of other process variables such as pH of Surry, Temperature need to be

investigated

Variability of Ra, Rb, and Rq needs to be investigated

10/10

Jaehyun Park and Dong-Hee Lee*

Optimizing Multiple Response Variables of CMP Process for Semiconductor Fabrication Using a Clustering Method

CMP Process

Schematic illustration of CMP process

Definition of Roughness

Problem Statements

Process Variables Response Variables

𝑆𝑏 𝐲 , 𝑆𝑐 𝐲 , 𝑆𝑟 𝐲

Suggested CMP problem Difficulty

Three response variables should be optimized, simultaneously  “Multiresponse optimization method” is needed

Three Stages for Optimization

Optimization based on Clustering method (PMRSOC) (Lee and Lee, 2015) is adopted for the optimization

Stages of PMRSOC Action for the suggested CMP problem Applied Method

Stage 1. Model Building

Simplex of three input variables and its coordinate system

Stage 2. Nondominated Solutions Generation

𝐲 is said to be nondominated if and only if there does not exist any

𝑧𝑆𝑏(x) ≥ 𝑧𝑆𝑏( 𝐲), 𝑧𝑆𝑐(x) ≤ 𝑧𝑆𝑐( 𝐲), 𝑧𝑆𝑟(x) ≤ 𝑧𝑆𝑟( 𝐲), and x≠ 𝐲 .

𝑧𝑆𝑏(𝐲) by restricting 𝑧𝑆𝑐(𝐲) and 𝑧𝑆𝑟(𝐲) Maximize 𝑧𝑆𝑏 𝐲

𝑧𝑆𝑐 𝑦 ≤ 𝜁𝑆𝑐, 𝑧𝑆𝑟 𝑦 ≤ 𝜁𝑆𝑟

𝑧𝑆𝑟 𝑧𝑆𝑐 𝑧𝑆𝑏 200 nondominated solutions

Stage 3. Best Solution Selection (1/3)

Step 1: Divide the nondominated solutions into two groups by using K-means clustering Step 2: Select a preferred group Step 2: Are the solutions

close to each other? Start End Step 3: Select a final solution from the solutions

no yes

Stage 3. Best Solution Selection (2/3)

in the same group are similar to each other than to those in other groups.

Stage 3. Best Solution Selection (3/3)

Concluding Remarks

the existing pure slurry composition.

investigated