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For the purpose of the sustainable development in the global semiconductor industry, emerging three-dimensional integrated circuit (3DIC) integration technologies have demonstrated their importance as potential candidates for extending the lifespan of Moore’s Law. This study aimed to explore a technology selection process involving a three-stage fuzzy multicriteria decision-making (MCDM) approach to facilitate the effective assessment of emerging 3DIC integration technologies. The fuzzy Delphi method was first used to determine the important criteria. The fuzzy analytic hierarchy process (fuzzy AHP) was then adopted to derive the weights of the criteria. The fuzzy technique for order of preference by similarity to ideal solution (fuzzy TOPSIS) was finally deployed to rate the alternatives. Empirical results indicate that market potential, time-to-market, and heterogeneous integration are the top three decision criteria for the selection of 3DIC integration technologies. Furthermore, 2.5D through-silicon interposer (TSI) is of primary interest to the Taiwanese semiconductor industry, followed by 3DIC through-silicon via (TSV), 3D packaging, and 3D silicon TSV (Si TSV). The proposed three-stage fuzzy decision model may potentially assist industry practitioners and government policy-makers in directing research and development investments and allocating resources more strategically.

After six years since the introduction of the first commercial planar transistor in 1959, Moore’s Law has been recognized as a golden rule guiding the technological evolution of the semiconductor industry [

Several research studies used fuzzy MCDM approaches to evaluate, prioritize, and select the optimal emerging technologies. Tavana,

In consideration of the relevant literature mentioned above, this study’s contribution is the proposal of a technology selection process consisting of a three-stage fuzzy MCDM approach to facilitate the effective assessment of emerging 3DIC integration technologies. Furthermore, none of the research conducted so far has used the fuzzy MCDM to evaluate 3DIC integration technologies. Hence, this study could be a forerunner by using fuzzy MCDM methods to specifically evaluate 3DIC integration technologies. As shown in

The three-stage technology selection process.

The rest of this paper was organized as follows.

While significant R and D efforts have been expended on various planar approaches, 3DIC integration technologies are undoubtedly gaining momentum as potential pioneers in the challenge to meet the demands of the form factor, performance, and cost through this decade and beyond [

The most prevalent technology for 3DIC integration appears to be 3DIC packaging. The 3DIC packaging technologies exploit a z-axis dimension to provide a volumetric packaging solution for higher integration and performance, as well as to save space by stacking either separate chips or separate packages in a single package [

The 3DIC TSV is an innovative interconnection technology that involves stacking individual wafers or individual dies to create customized multilayer multifunctional devices. They are vertically bonded together in either the wafer-to-wafer (W2W) or die-to-wafer form, using metalized pillars as the interconnection matter [

The 3D Si TSV concept is little different from that of 3DIC TSV. The major distinction is that 3DIC TSV stacks up the chips with TSV and solder bumps, while 3D Si TSV stacks up the wafers with TSV alone (

The 2.5D TSI uses one layer of either the silicon or glass interposer to connect different dies on the same horizon with package substrates [

Compared to traditional binary sets, fuzzy logic variables may have a membership value that ranges in degree between 0 and 1 [

Noorderhaven [

No overlap exists between the two triangular fuzzy numbers (

If

If

Double triangular fuzzy numbers.

Finally, the important criteria can be selected if the consensus values

The AHP is one of the MCDM methods based on an additive weighting process, in which the multi-attribute weight measurements are calculated through pairwise comparisons of the relative importance of every pair of criteria [

Establish a hierarchical structure.

Determine the important criteria screened by fuzzy Delphi investigations to establish the hierarchical structure.

Construct fuzzy decision matrices.

Compare the relative importance of the criteria in pairs, and convert crisp values to fuzzy numbers for constructing fuzzy decision matrices based on a defined membership function of linguistic variables.

A fuzzy decision matrix can be defined as:

Test the consistency.

To verify whether a pairwise comparison matrix is sufficiently consistent, the maximum eigenvalue

Saaty [

The consistency ratio (

The matrix will be considered consistent if the resulting ratio is less than 0.1. Csutora and Buckley [

Perform defuzzification.

Adopt the method of converting fuzzy data to crisp scores (CFCS), developed by Opricovic and Tzeng [

Step 1. Perform normalization:

Step 2. Compute the lower (

Step 3. Compute the total normalized crisp value:

Step 4. Compute the crisp value:

Step 5. Integrate the crisp values:

Establish an aggregate crisp decision matrix.

Calculate criteria weights.

Obtain eigenvector value

Following the above-mentioned procedures of the fuzzy AHP, the weights of the criteria can be effectively obtained.

Hwang and Yoon [

Obtain the fuzzy weights of the criteria.

This study employs the fuzzy AHP to obtain the fuzzy preference weights of the criteria.

Construct the fuzzy decision matrix and determine the appropriate linguistic variables for the alternatives, with respect to criteria:

Normalize the fuzzy decision matrix.

The normalized fuzzy decision matrix

Then the weighted fuzzy normalized decision matrix

Determine the fuzzy positive ideal solution (FPIS) and the fuzzy negative ideal solution (FNIS).

The FPIS

Calculate the distance of each alternative from the FPIS and the FNIS.

The distances (

Obtain the closeness coefficients and improve the gap degrees for achieving the aspiration levels:

Following the above-mentioned procedures of fuzzy TOPSIS, the alternative 3DIC integration technologies can be effectively prioritized and selected.

The effective selection and investment in 3DIC integration technologies under strategic planning help the Taiwanese semiconductor industry stay competitive in the global market. In this regard, this section formulated and described an empirical analysis on the basis of the aforementioned methodology.

This study first explored 14 criteria associated with technology evaluation themes through the literature review and expert interviews. Sixteen experts—sourced from the entire supply chain of Taiwan’s semiconductor industry—used an interval range (0–10) to evaluate the 14 criteria. The opinions of the 16 experts, as expressed in the fuzzy Delphi questionnaires, were then converted to triangular fuzzy numbers. Next, the consensus value of each criterion was obtained through the fuzzy Delphi calculation, as shown in

Fuzzy Delphi screening results.

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 |

A hierarchical model of the 3DIC integration technology selection was established (as shown in

Hierarchical model of 3DIC integration technology selection.

Next, the weights of the criteria were calculated through the fuzzy AHP steps, as follows:

Design the questionnaire.

A typical AHP questionnaire to obtain the 16 experts’ perceptions was designed in the form of pairwise comparisons based on the hierarchical structure. The questionnaire used a nine-point rating scale representing the relative importance of each criterion in the hierarchical model.

Construct fuzzy decision matrices.

The crisp values sourced from the assessment of relative importance of the criteria in pairs were converted to fuzzy numbers, according to the definition of triangular fuzzy numbers in

Test the consistency.

The consistency of fuzzy decision matrices was tested by using Equations (5) and (6). If the subjective judgments of the 16 experts were inconsistent, the author asked them to repeat the pairwise comparison processes until the CI and CR values were less than 0.1.

Triangular fuzzy numbers.

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

Equally important | |

Intermediate | |

Moderately more important | |

Intermediate | |

Strongly more important | |

Intermediate | |

Very strongly more important | |

Intermediate | |

Extremely more important |

Fuzzy decision matrix for evaluator 1.

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;

Perform defuzzification.

This study adopted the aforementioned CFCS method to perform defuzzification. Equations (7)–(14) were applied to obtain the crisp decision matrices of the 16 experts.

Crisp decision matrix for evaluator 1.

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 |

Aggregate crisp judgment matrix.

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 |

Calculate overall criteria weights

Equation (17) was used to calculate the weight of each criterion.

Weights of criteria for 3DIC integration technology selection.

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 |

In view of the fuzzy AHP results, the first two important criteria for the 3DIC integration technology selection are market potential (0.312) and time-to-market (0.228). Moreover, the least important criterion is manufacturing capability (0.074).

The four alternative emerging 3DIC integration technologies formulated in

Determine the appropriate linguistic variables, and construct the fuzzy decision matrix.

The 16 experts were requested to express their perceptions about the rating of every 3DIC integration technology regarding each criterion of linguistic variables, shown in

Linguistic scales for the rating of each alternative.

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

Very low (VL) | |

Low (L) | |

Medium (M) | |

High (H) | |

Very high (VH) | |

Excellent (E) |

The fuzzy decision matrix.

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) |

Check the consistency of the experts’ opinions.

A comparison matrix was established, based on each expert opinion for each alternative, using Saaty’s technique.

An example for the rating of the alternatives with respect to C1.

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 |

An example for the comparison of the alternatives with respect to C1.

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 | |

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 | |

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 | |

Normalize the fuzzy decision matrix.

Using Equations (20) and (21), the fuzzy decision matrix was normalized to eliminate the deviations induced by different measurement units and scales, as shown in

The normalized 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) |

Establish the weighted fuzzy normalized decision matrix.

Using Equations (22) and (23), the weighted fuzzy normalized decision matrix was established, as shown in

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) |

Determine the FPIS and FNIS reference points

Using Equations (24) and (25), FPIS

FPIS and FNIS.

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

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) |

Estimate the performance, and rank the alternatives.

The distances of each alternative from the FPIS and FNIS reference points were calculated through Equations (26) and (27). The closeness coefficients of the four alternatives were then obtained by using Equation (28) (as shown in

The closeness coefficients for the four alternatives.

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 |

According to the results of

Taiwan is one of the world’s largest suppliers of semiconductors and occupies an important position in the global semiconductor industry. Effective evaluation and selection of emerging 3DIC integration technologies under strategic planning help the Taiwanese semiconductor industry stay competitive in the global market. However, evaluating and selecting appropriate emerging technologies are among the most complex decision-making problems encountered by the top management of semiconductor firms. Several studies indicated that technology evaluation and selection constitute an MCDM issue that can be improved by integrating different methods. In recent years, an increasing number of studies have used either a fuzzy MCDM method or a hybrid fuzzy MCDM approach for selecting appropriate emerging technologies because they could deal with both multiple criteria issues and the linguistic ambiguity of experts’ judgments.

This study has also explored a technology selection process involving a three-stage fuzzy MCDM approach to facilitate the effective assessment of emerging 3DIC integration technologies. Each stage in the technology selection process has deployed a corresponding fuzzy MCDM method to achieve its function. First, the fuzzy Delphi method has been used to determine the six important criteria among 14 options: technical feasibility, manufacturing capability, market potential, time-to-market, product performance, and heterogeneous integration. Next, the fuzzy AHP has been adopted to derive the weights of the criteria. Market potential, time-to-market, and heterogeneous integration are the top three decision criteria with respect to the 3DIC integration technology selection. The empirical results indicated that the most important factor before proceeding with a technology is determining its market potential. Time-to-market is also an essential factor in fast-moving industries where products are quickly available for sale. Heterogeneous integration concerning the fusion degree of multifunctionality can effectively facilitate system miniaturization. Finally, the fuzzy TOPSIS has been deployed to rate these alternatives. The empirical results indicated that 2.5D TSI is of primary interest to the Taiwanese semiconductor industry, followed by 3DIC TSV, 3D packaging, and 3D Si TSV. The proposed three-stage fuzzy decision model can potentially assist industry practitioners and government policy-makers in directing R and D investments and allocating resources more strategically.

We are grateful to the experts who are willing to take their time for our questionnaires and interviews.

Yen-Chun Lee designed and proposed the concept of this research. Both Yen-Chun Lee and C. James Chou performed research, analyzed the data and wrote the paper.

The authors declare no conflict of interest.