# Technology Evaluation and Selection of 3DIC Integration Using a Three-Stage Fuzzy MCDM

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background and Motive for Study

#### 1.2. Technology Selection Using Fuzzy MCDM

## 2. Perspectives on 3DIC Integration Technologies

#### 2.1. 3DIC Packaging

#### 2.2. 3DIC TSV

#### 2.3. 3D Si TSV

#### 2.4. 2.5D TSI

## 3. Three-Stage Fuzzy MCDM for Evaluating 3DIC Integration Technologies

#### 3.1. Fuzzy Delphi Method

- (1)
- No overlap exists between the two triangular fuzzy numbers (${C}_{U}^{i}\le {O}_{L}^{i}$). The arithmetic mean is acquired through the geometric mean ${C}_{M}^{i}$ and ${O}_{M}^{i}$.
- (2)
- If ${C}_{U}^{i}\ge {O}_{L}^{i}$, the values of ${Z}^{i}={C}_{U}^{i}-{O}_{L}^{i}$ and ${M}^{i}={O}_{M}^{i}-{C}_{M}^{i}$ are first acquired. If the crosspoint of the two triangular fuzzy numbers is equal to the value of the experts’ consensus in the gray zone ${Z}^{i}\le {M}^{i}$, the level of membership in the gray zone is ${G}^{i}=\left\{{x}_{j}|\mathrm{max}{U}_{{F}^{i}}\left({x}_{j}\right)\right\}$, where ${F}^{i}\left({x}_{j}\right)=\{{\int}_{x}\left\{\mathrm{min}\left[{C}^{i}\left({x}_{j}\right),{O}^{i}\left({x}_{j}\right)\right]\right\}dx\}$.
- (3)
- If ${C}_{U}^{i}\ge {O}_{L}^{i}$ and ${Z}^{i}>{M}^{i}$, the value of the experts’ consensus cannot be converged, and the tests should be refined again, with the reference value $\left({C}_{M}^{i},{O}_{M}^{i}\right)$ attached.

#### 3.2. Fuzzy AHP

- (1)
- Establish a hierarchical structure.

- (2)
- Construct fuzzy decision matrices.

- (3)
- Test the consistency.

- (4)
- Perform defuzzification.

- (5)
- Establish an aggregate crisp decision matrix.

- (6)
- Calculate criteria weights.

#### 3.3. Fuzzy TOPSIS

- (1)
- Obtain the fuzzy weights of the criteria.This study employs the fuzzy AHP to obtain the fuzzy preference weights of the criteria.
- (2)
- Construct the fuzzy decision matrix and determine the appropriate linguistic variables for the alternatives, with respect to criteria:$$\tilde{D}={[{\tilde{D}}_{ij}]}_{m\times n}=\begin{array}{c}\\ \begin{array}{c}{\mathrm{A}}_{1}\\ {\mathrm{A}}_{2}\\ \vdots \\ {\mathrm{A}}_{m}\end{array}\end{array}\begin{array}{c}\begin{array}{cccc}{\mathrm{C}}_{1}& {\mathrm{C}}_{2}& \cdots & {\mathrm{C}}_{n}\end{array}\\ \left[\begin{array}{cccc}{\tilde{a}}_{11}& {\tilde{a}}_{12}& \cdots & {\tilde{a}}_{1n}\\ {\tilde{a}}_{21}& {\tilde{a}}_{22}& \cdots & {\tilde{a}}_{2n}\\ \vdots & \vdots & \ddots & \vdots \\ {\tilde{a}}_{m1}& {\tilde{a}}_{m2}& \cdots & {\tilde{a}}_{mn}\end{array}\right]\end{array}$$$$\begin{array}{c}i=1,2,\dots ,m;j=1,2,\dots ,n\\ {\tilde{a}}_{ij}=\frac{1}{K}\left({\tilde{a}}_{ij}^{1}\oplus {\tilde{a}}_{ij}^{2}\oplus \cdots \oplus {\tilde{a}}_{ij}^{K}\right)\end{array}$$
- (3)
- Normalize the fuzzy decision matrix.The normalized fuzzy decision matrix $\tilde{R}$ can be expressed as:$$\tilde{R}={\left[{\tilde{r}}_{ij}\right]}_{m\times n},i=1,2,\dots ,m;j=1,2,\dots ,n$$$$\mathrm{where}\text{\hspace{1em}}{\tilde{r}}_{ij}=\left(\frac{{l}_{ij}}{{u}_{j}^{+}},\frac{{m}_{ij}}{{u}_{j}^{+}},\frac{{u}_{ij}}{{u}_{j}^{+}}\right),{u}_{j}^{+}=\underset{i}{\mathrm{max}}\left\{{u}_{ij}|i=1,2,\dots ,m;j=1,2,\dots ,n\right\}$$Then the weighted fuzzy normalized decision matrix $\tilde{V}$ can be expressed as:$$\tilde{V}={\left[{\tilde{v}}_{ij}\right]}_{m\times n},i=1,2,\dots ,m;j=1,2,\dots ,n$$$$\mathrm{where}\text{\hspace{1em}}{\tilde{v}}_{ij}={\tilde{r}}_{ij}\otimes {\tilde{w}}_{j}$$
- (4)
- Determine the fuzzy positive ideal solution (FPIS) and the fuzzy negative ideal solution (FNIS).The FPIS ${A}^{+}$ (aspiration levels) and FNIS ${A}^{-}$ (worst levels) can be defined as [26,27]:$${A}^{+}=\left({\tilde{v}}_{1}^{+},\dots ,{\tilde{v}}_{j}^{+},\dots ,{\tilde{v}}_{n}^{+}\right)=\left\{\underset{i}{\mathrm{max}}{v}_{ij}|i=1,2,\dots ,n\right\}$$$${A}^{-}=\left({\tilde{v}}_{1}^{-},\dots ,{\tilde{v}}_{j}^{-},\dots ,{\tilde{v}}_{n}^{-}\right)=\left\{\underset{i}{\mathrm{min}}{v}_{ij}|i=1,2,\dots ,n\right\}$$

- (5)
- Calculate the distance of each alternative from the FPIS and the FNIS.

- (6)
- Obtain the closeness coefficients and improve the gap degrees for achieving the aspiration levels:$${\tilde{CC}}_{i}=\frac{{\tilde{d}}_{i}^{-}}{{\tilde{d}}_{i}^{+}+{\tilde{d}}_{i}^{-}}=1-\frac{{\tilde{d}}_{i}^{+}}{{\tilde{d}}_{i}^{+}+{\tilde{d}}_{i}^{-}},i=1,2,\dots ,m$$

## 4. Empirical Analysis of Taiwanese Semiconductor Industry

#### 4.1. First Stage: Determine Important Criteria Using Fuzzy Delphi Method

No. | Criteria | Gray Zone | Consensus | Result |
---|---|---|---|---|

1 | Technological innovation | (5, 6) | 5.44 | Ingored |

2 | Technical feasibility | (7, 8) | 7.62 | Selected |

3 | Manufacturing capability | (7, 8) | 7.37 | Selected |

4 | Patent portfolio | (4, 6) | 4.93 | Ingored |

5 | Strategic importance | (4, 6) | 5.18 | Ingored |

6 | Market potential | No overlap | 9.05 | Selected |

7 | Market application | (4, 5) | 4.53 | Ingored |

8 | Time-to-market | (8, 9) | 8.86 | Selected |

9 | Customer satisfaction | (4, 6) | 5.07 | Ingored |

10 | Product performance | (8, 9) | 8.46 | Selected |

11 | Cost effectiveness | (4, 6) | 4.89 | Ingored |

12 | Heterogeneous integration | (8, 9) | 8.61 | Selected |

13 | Supply chain management | (4, 5) | 4.54 | Ingored |

14 | Profitability | (3, 5) | 4.12 | Ingored |

#### 4.2. Second Stage: Derive the Weights of Criteria Using Fuzzy AHP

- (1)
- Design the questionnaire.

- (2)
- Construct fuzzy decision matrices.

- (3)
- Test the consistency.

Triangular Fuzzy Numbers | Linguistic Variables |
---|---|

$\tilde{1}$ = (1, 1, 1) | Equally important |

$\tilde{2}$ = (1, 2, 3) | Intermediate |

$\tilde{3}$ = (2, 3, 4) | Moderately more important |

$\tilde{4}$ = (3, 4, 5) | Intermediate |

$\tilde{5}$ = (4, 5, 6) | Strongly more important |

$\tilde{6}$ = (5, 6, 7) | Intermediate |

$\tilde{7}$ = (6, 7, 8) | Very strongly more important |

$\tilde{8}$ = (7, 8, 9) | Intermediate |

$\tilde{9}$ = (8, 9, 9) | Extremely more important |

Criteria | C1 | C2 | C3 | C4 | C5 | C6 |
---|---|---|---|---|---|---|

C1 | (1, 1, 1) | (1, 2, 3) | (1/6, 1/5, 1/4) | (1/5, 1/4, 1/3) | (1/3, 1/2, 1) | (1/4, 1/3, 1/2) |

C2 | (1/3, 1/2, 1) | (1, 1, 1) | (1/7, 1/6, 1/5) | (1/6, 1/5, 1/4) | (1/4, 1/3, 1/2) | (1/5, 1/4, 1/3) |

C3 | (4, 5, 6) | (5, 6, 7) | (1, 1, 1) | (1, 2, 3) | (3, 4, 5) | (2, 3, 4) |

C4 | (3, 4, 5) | (4, 5, 6) | (1/3, 1/2, 1) | (1, 1, 1) | (2, 3, 4) | (1, 2, 3) |

C5 | (1, 2, 3) | (2, 3, 4) | (1/5, 1/4, 1/3) | (1/4, 1/3, 1/2) | (1, 1, 1) | (1/3, 1/2, 1) |

C6 | (2, 3, 4) | (3, 4, 5) | (1/4, 1/3, 1/2) | (1/3, 1/2, 1) | (1, 2, 3) | (1, 1, 1) |

_{max}= 6.122; CI = 0.024; RI = 1.25; CR = 0.020 ≤ 0.1.

- (4)
- Perform defuzzification.

Criteria | C1 | C2 | C3 | C4 | C5 | C6 |
---|---|---|---|---|---|---|

C1 | 1.000 | 1.955 | 0.201 | 0.253 | 0.568 | 0.345 |

C2 | 0.561 | 1.000 | 0.168 | 0.203 | 0.355 | 0.258 |

C3 | 4.964 | 5.929 | 1.000 | 2.071 | 4.000 | 3.036 |

C4 | 3.967 | 4.928 | 0.540 | 1.000 | 3.007 | 2.046 |

C5 | 2.007 | 2.935 | 0.252 | 0.342 | 1.000 | 0.558 |

C6 | 2.981 | 3.929 | 0.340 | 0.549 | 2.032 | 1.000 |

Criteria | C1 | C2 | C3 | C4 | C5 | C6 |
---|---|---|---|---|---|---|

C1 | 1.000 | 1.768 | 0.514 | 0.566 | 0.881 | 0.658 |

C2 | 0.874 | 1.000 | 0.481 | 0.516 | 0.667 | 0.570 |

C3 | 4.527 | 5.366 | 1.000 | 1.884 | 3.625 | 2.786 |

C4 | 3.593 | 4.491 | 0.853 | 1.000 | 2.756 | 1.858 |

C5 | 1.819 | 2.686 | 0.564 | 0.654 | 1.000 | 0.870 |

C6 | 2.731 | 3.554 | 0.903 | 0.861 | 1.845 | 1.000 |

- (5)
- Calculate overall criteria weights

Criteria | Weights | Rank |
---|---|---|

(C1) Technical feasibility | 0.092 | 5 |

(C2) Manufacturing capability | 0.074 | 6 |

(C3) Market potential | 0.312 | 1 |

(C4) Time-to-market | 0.228 | 2 |

(C5) Product performance | 0.121 | 4 |

(C6) Heterogeneous integration | 0.174 | 3 |

#### 4.3. Third Stage: Rate the Alternatives Using Fuzzy TOPSIS

- (1)
- Determine the appropriate linguistic variables, and construct the fuzzy decision matrix.

Linguistic Variables | Triangular Fuzzy Numbers |
---|---|

Very low (VL) | $\tilde{0}$ = (0, 0, 2) |

Low (L) | $\tilde{2}$ = (0, 2, 4) |

Medium (M) | $\tilde{4}$ = (2, 4, 6) |

High (H) | $\tilde{6}$ = (4, 6, 8) |

Very high (VH) | $\tilde{8}$ = (6, 8, 10) |

Excellent (E) | $\tilde{10}$ = (8, 10, 10) |

Criteria | 3D Packaging | 2.5D TSI | 3DIC TSV | 3D Si TSV |
---|---|---|---|---|

C1 | (2.80, 4.80, 6.80) | (7.07, 9.07, 10) | (5.33, 7.33, 9.2) | (1.87, 3.87, 5.87) |

C2 | (2.80, 4.80, 6.80) | (5.87, 7.87, 9.33) | (4.00, 6.00, 8.00) | (2.00, 4.00, 6.00) |

C3 | (2.80, 4.80, 6.80) | (6.53, 8.53, 9.87) | (4.53, 6.53, 8.4) | (1.73, 3.73, 5.73) |

C4 | (3.47, 5.47, 7.47) | (4.53, 6.53, 8.4) | (5.47, 7.47, 9.33) | (1.47, 3.47, 5.47) |

C5 | (2.80, 4.80, 6.80) | (6.80, 8.80, 9.87) | (4.80, 6.80, 8.40) | (1.33, 3.33, 5.33) |

C6 | (2.80, 4.80, 6.80) | (5.87, 7.87, 9.33) | (3.47, 5.47, 7.47) | (1.60, 3.60, 5.60) |

- (2)
- Check the consistency of the experts’ opinions.

Expert | 3D Packaging | 2.5D TSI | 3DIC TSV | 3D Si TSV |
---|---|---|---|---|

E1 | 6 | 10 | 8 | 4 |

E2 | 4 | 8 | 6 | 2 |

E3 | 6 | 10 | 6 | 4 |

E4 | 8 | 10 | 8 | 6 |

E5 | 4 | 8 | 8 | 4 |

E6 | 6 | 10 | 8 | 4 |

E7 | 4 | 8 | 6 | 2 |

E8 | 6 | 10 | 6 | 4 |

E9 | 8 | 10 | 8 | 6 |

E10 | 4 | 8 | 8 | 4 |

E11 | 6 | 10 | 8 | 4 |

E12 | 4 | 8 | 6 | 2 |

E13 | 6 | 10 | 6 | 4 |

E14 | 8 | 10 | 8 | 6 |

E15 | 4 | 8 | 8 | 4 |

E16 | 6 | 10 | 8 | 4 |

3D Packaging | 2.5D TSI | 3DIC TSV | 3D Si TSV | ||
---|---|---|---|---|---|

E1 | 3D packaging | 1.00 | 0.60 | 0.75 | 1.50 |

2.5D TSI | 1.67 | 1.00 | 1.25 | 2.50 | |

3DIC TSV | 1.33 | 0.80 | 1.00 | 2.00 | |

3D Si TSV | 0.67 | 0.40 | 0.50 | 1.00 | |

CR = 0.000 | |||||

E2 | 3D packaging | 1.00 | 0.50 | 0.67 | 2.00 |

2.5D TSI | 2.00 | 1.00 | 1.33 | 4.00 | |

3DIC TSV | 1.50 | 0.75 | 1.00 | 3.00 | |

3D Si TSV | 0.50 | 0.25 | 0.33 | 1.00 | |

CR = 0.025 | |||||

E3 | 3D packaging | 1.00 | 0.60 | 1.00 | 1.50 |

2.5D TSI | 1.67 | 1.00 | 1.67 | 2.50 | |

3DIC TSV | 1.00 | 0.60 | 1.00 | 1.50 | |

3D Si TSV | 0.67 | 0.40 | 0.67 | 1.00 | |

CR = 0.012 |

- (3)
- Normalize the fuzzy decision matrix.

Criteria | 3D Packaging | 2.5D TSI | 3DIC TSV | 3D Si TSV |
---|---|---|---|---|

C1 | (0.28, 0.48, 0.68) | (0.71, 0.91, 1) | (0.53, 0.73, 0.92) | (0.19, 0.39, 0.59) |

C2 | (0.3, 0.51, 0.73) | (0.63, 0.84, 1) | (0.43, 0.64, 0.86) | (0.21, 0.43, 0.64) |

C3 | (0.28, 0.49, 0.69) | (0.66, 0.86, 1) | (0.46, 0.66, 0.85) | (0.18, 0.38, 0.58) |

C4 | (0.37, 0.59, 0.8) | (0.49, 0.7, 0.9) | (0.59, 0.8, 1) | (0.16, 0.37, 0.59) |

C5 | (0.28, 0.49, 0.69) | (0.69, 0.89, 1) | (0.49, 0.69, 0.85) | (0.14, 0.34, 0.54) |

C6 | (0.3, 0.51, 0.73) | (0.63, 0.84, 1) | (0.37, 0.59, 0.8) | (0.17, 0.39, 0.6) |

- (4)
- Establish the weighted fuzzy normalized decision matrix.

Criteria | 3D Packaging | 2.5D TSI | 3DIC TSV | 3D Si TSV |
---|---|---|---|---|

C1 | (0.03, 0.04, 0.06) | (0.06, 0.08, 0.09) | (0.05, 0.07, 0.08) | (0.02, 0.04, 0.05) |

C2 | (0.02, 0.04, 0.05) | (0.05, 0.06, 0.07) | (0.03, 0.05, 0.06) | (0.02, 0.03, 0.05) |

C3 | (0.09, 0.15, 0.21) | (0.21, 0.27, 0.31) | (0.14, 0.21, 0.27) | (0.05, 0.12, 0.18) |

C4 | (0.08, 0.13, 0.18) | (0.11, 0.16, 0.21) | (0.13, 0.18, 0.23) | (0.04, 0.08, 0.13) |

C5 | (0.03, 0.06, 0.08) | (0.08, 0.11, 0.12) | (0.06, 0.08, 0.1) | (0.02, 0.04, 0.07) |

C6 | (0.05, 0.09, 0.13) | (0.11, 0.15, 0.17) | (0.06, 0.10, 0.14) | (0.03, 0.07, 0.10) |

- (5)
- Determine the FPIS and FNIS reference points

Criteria | FPIS A^{+} | FNIS A^{−} |
---|---|---|

C1 | (0.09, 0.09, 0.09) | (0.02, 0.02, 0.02) |

C2 | (0.07, 0.07, 0.07) | (0.02, 0.02, 0.02) |

C3 | (0.31, 0.31, 0.31) | (0.05, 0.05, 0.05) |

C4 | (0.23, 0.23, 0.23) | (0.04, 0.04, 0.04) |

C5 | (0.12, 0.12, 0.12) | (0.02, 0.02, 0.02) |

C6 | (0.17, 0.17, 0.17)) | (0.03, 0.03, 0.03) |

- (6)
- Estimate the performance, and rank the alternatives.

${d}_{i}^{-}$ | ${d}_{i}^{+}$ | $C{C}_{i}^{-}$ | $C{C}_{i}^{+}$ | Rank | |
---|---|---|---|---|---|

3D packaging | 0.386 | 0.514 | 0.429 | 0.571 | 3 |

2.5D TSI | 0.657 | 0.242 | 0.731 | 0.269 | 1 |

3DIC TSV | 0.541 | 0.358 | 0.602 | 0.398 | 2 |

3D Si TSV | 0.268 | 0.645 | 0.294 | 0.706 | 4 |

## 5. Concluding Remarks

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Lee, Y.-C.; Chou, C.J.
Technology Evaluation and Selection of 3DIC Integration Using a Three-Stage Fuzzy MCDM. *Sustainability* **2016**, *8*, 114.
https://doi.org/10.3390/su8020114

**AMA Style**

Lee Y-C, Chou CJ.
Technology Evaluation and Selection of 3DIC Integration Using a Three-Stage Fuzzy MCDM. *Sustainability*. 2016; 8(2):114.
https://doi.org/10.3390/su8020114

**Chicago/Turabian Style**

Lee, Yen-Chun, and C. James Chou.
2016. "Technology Evaluation and Selection of 3DIC Integration Using a Three-Stage Fuzzy MCDM" *Sustainability* 8, no. 2: 114.
https://doi.org/10.3390/su8020114