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Investigation of High Temperature Co-fired Ceramic tapes lamination conditions
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CERAMICS INTERNATIONAL
Ceramics International 41 (2015) 7860–7871 www.elsevier.com/locate/ceramint
Investigation of High Temperature Co-fired Ceramic tapes lamination conditions Dominik Jurkówa,n, Johanna Stiernstedtb, Mateusz Dorczyńskia, Göran Wetterb a
Wroclaw University of Technology, Faculty of Microsystem Electronics and Photonics, 50-372 Wrocław, Poland b Swerea IVF AB, P.O. Box 104, SE-431 22 Mölndal, Sweden Received 30 December 2014; received in revised form 6 February 2015; accepted 23 February 2015 Available online 28 February 2015
Abstract The main goal of this paper was to analyze the influence of lamination process conditions and High Temperature Co-fired Ceramic (HTCC) tape composition on the lamination quality (existence of delaminations). The second aim was to estimate the influence of lamination conditions and HTCC tape composition on three process outputs: compressibility, surface roughness and density of High Temperature Co-fired Ceramics and to recognize if these outputs can be useful from lamination quality investigation point of view. The bonding quality was investigated using scanning acoustic microscopy (SAM). The analyzed ceramics was fabricated using water based slurries in the frame of tape casting process. The paper additionally discusses limitations and drawbacks of the used investigation methods and experiment design. & 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Keywords: Ceramics; Lamination; Water based tape casting; HTCC
1. Introduction Multilayer ceramic technology can be divided into two main parts: Low Temperature Co-fired Ceramics (LTCC) and High Temperature Co-fired Ceramics (HTCC). LTCC contains glass which gives a firing temperature compatible with silver and gold, and LTCC is utilized in the fabrication of wireless components (e.g. antennas), sensors, actuators, chemical reactors and microsystems [1–3]. HTCC is fired at higher temperature (1500–1600 1C) and is used in applications where higher chemical or thermal stability is needed [4], moreover, it can be used as well in RF devices or packages [5,6] and automotive applications [5]. Both LTCC and HTCC are fabricated in the frame of tape casting process from various slurries [7]. The slurry composition decides about mechanical and electrical properties of both green and fired tapes. The trend of toxicity reduction of materials caused the necessity of slurry composition changes. The possibility of utilizing more environmental and user friendly water based solvents instead of high flammable and toxic n
Corresponding author. E-mail address: [email protected] (D. Jurków).
http://dx.doi.org/10.1016/j.ceramint.2015.02.123 0272-8842/& 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
organic solvents was previously reported [8–10]. After tape casting the laser cutting systems, punching units or embossing machines permit the fabrication of structures in each single tape. The structured tapes are aligned and stacked, in order to build up 3D components. Then the lamination is conducted. This process is extremely important due to the fact that it affects the homogeneity of tapes in region of the tapes interface. In other words if the process is carried out improperly, delaminations between tapes on the tapes interfaces will occur. There are two groups of lamination techniques which are worth to be mentioned thermo-compressive lamination [11,12] and chemical laminations [13–15]. The usefulness of the chemical methods is mainly limited to the special complicated 3D structures without electrical components. On the other hand standard thermocompressive methods are widely used but can cause high deformation of 3D structures fabricated using single tapes. After lamination the tapes are co-fired in a furnace. This process drives off all organic materials from the tapes and permits sintering of the ceramic grains together. Hence, the hard dense ceramics is obtained. The quality of sintered ceramics can be investigated from several points of view, e.g. surface roughness, delaminations,
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compressibility or density value. Given the level of surface roughness for ceramics, the most useful method of measuring is mechanical profilometry. The surface roughness depends mainly on the size of the ceramic grains and its optimal level depends on the application. This material property is not correlated with the other ceramic properties mentioned above. Delamination is a frequently investigated output, since it can indicate an insufficient lamination process or variation in the material composition. The quality of sintered ceramics can be examined using several different inspection methods, of which the most promising are non-destructive [16], such as Scanning Acoustic Microscopy (SAM) [16,17]. SAM permits the detection of delaminations in ceramic structures [16,17] and therefore it is also very useful in LTCC and HTCC structures inspection [16,18,19]. SAM is a very sensitive control method of delaminations, since inclusion of air causes a total reflection in the signal. Therefore, SAM inspection was used as a reference investigation method in order to validate the other inspection methods applied in this work. Measurement of density through the Archimedes method permits detection of closed porosity; if any close gas voids exits between layers the measured density will be lower than the expected mean value. However, the limitation is the fact that open delaminations will not be detected by this method. The compressibility is correlated with delaminations through the expectation that some compressibility is needed for proper lamination, hence, if the compressibility is low, this indicates delaminations. The measurement of compressibility is, however, dependent on the tape thickness variation and might be misleading. In the present study delaminations were detected only for samples with low compressibility. Optimization from laser cutting and sintering point of views of the tapes presented in this paper were done before [20,21]. The aim of this paper was to investigate the influence of the lamination process conditions and tape composition on the lamination quality (existence of delaminations). Three measures of quality of lamination were proposed in this paper: compressibility and surface roughness of the green tapes, and density of the fired tapes. The usefulness of these three outputs on the lamination quality analysis was verified in the frame of the experiment. Moreover, the tape compressibility, sintered ceramics surface roughness and density were investigated for different values of a number of process parameters, and the bonding quality was investigated using Scanning Acoustic Microscopy (SAM). The experiment was planned using Design of the Experiment (DoE) [20,21] and the data were analyzed using analysis of variance and orthogonal contrasts methods [20,21]. The paper additionally discusses limitations and drawbacks of the used investigation methods and experiment design.
binder content and binder composition. The investigated inputs are given in Table 1. The preheating means that tapes were left in the laminating machine for a particular period before the lamination pressure was turn on. This solution is used to provide even temperature distribution for all laminated tapes. The value of each of the lamination conditions as well as binder content and tapes composition was chosen based on the expert knowledge. This knowledge was gained in the frame of earlier investigations [20,21]. The samples used in the study were laminates of two HTCC square tapes 20 20 mm2, around 180 mm thick (in green state). The tapes were made by aqueous tape casting using alumina powder (AKP30, Sumitomo Chemical), dispersant (Dolapix PC21, Zschimmer & Schwarz) and latex binder (Resicel E50N, Lamberti Speciality Chemicals, or LDM 7651S, Celanese Emulsions). The compressibility was calculated as the ratio between prelaminated green tape and laminated sample thicknesses multiplied by 100. The density was measured using the Archimedes method in water and its value is given as a relative value of theoretical alumina density given in percent. The average roughness results were calculated based on 10 mm long surfaces scans of the ceramic (Taylor-Hobson mechanical profilometer). The experiment consists of three runs; three samples were measured from up and down sides (total cardinality was equal to 108). The cardinality of each of the runs for compressibility verification was 10 with two replications (total cardinality was equal to 360). The density was measured as average density of 3 samples with three replications (total cardinality was equal to 162). The results are given only as average values of all achieved results to simplify the form of tables. All statistical calculations were conducted according to an analysis of variance method (ANOVA) and the type influence of inputs on outputs was found using an orthogonal contrasts method. The second solution permits to find if the relation between input and output is linear, square or mixed linearsquare [22].
2. Experiment
3. Design of the Experiment (DoE)
In the investigation of lamination quality, the compressibility of the tapes, and surface roughness and density of sintered samples were analyzed and the following process conditions were investigated: duration time of tapes preheating at lamination tempera ture, lamination time, lamination temperature, lamination pressure,
Taking account that influence of 6 inputs were investigated at once it was decided to apply Design of the Experiment (DoE) methodology in the analysis [22,23]. This solution permits the reduction of costs and time of the experiment. The most sufficient experiment design would be full factorial design, which enables
Table 1 Investigated process parameters. Factor
Preheating of structure at lamination temperature Lamination time Lamination temperature Lamination pressure Binder content Resicel/LDM ratio
Factor acronym
Factor level 1
0
þ1
A
10 min –
0 min
B C D E F
2 min 26 1C 5 MPa 20% 100/0
20 min 80 1C 20 MPa 30% 0/100
11 min 50 1C 12.5 MPa 25% 50/50
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Table 2 Experiment design and results of compressibility, surface roughness and density analysis. set Preheating Lamination time Lamination temperature Lamination pressure Binder content Binder ratio Compressibility analysis
Surface roughness analysis
Average density analysis
Δz=z0 [%] V [%] Ra [nm] V [%] ρ [%] V [%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
A
B
C
D
E
F
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1
1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1
1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0
1 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1 1
1 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0
to obtain the most correct results and analyze influence of main effects as well as interaction between inputs. It has to be mentioned that it is expected that interactions exist between the analyzed inputs. However, the full factorial design on three levels demands to conduct test for 3n=36=729 combination of inputs values (where: n – number of inputs). This is in practice impossible. Another type of design which could be applied would be one of the fractional (or partial) factorial designs where the number of needed combinations can be reduced meanwhile some interactions still can be investigated [22]. The most reduced experiment designs which enable investigation of only main effects without interactions were proposed mainly by Taguchi [23] and are called screening designs. Using of such designs permits only very rough estimation of results and experiment findings correctness is endangered by existence of aliasing between main effects and interactions. The aim of this experiment was to get basic knowledge about the lamination process and to roughly verify the variability of results and usefulness of outputs from lamination quality point of view, hence it was decided to use fractional factorial design L18 which was proposed by Taguchi. This matrix is presented in Table 2 and is widely used by many authors [23] who indicate that aliasing of main effects and interactions of this design is very efficient from the analysis point of view. However, as it will be discussed further in this paper this aliasing pattern is not always sufficient This problem was reported by other authors who proposed some ways of coping with this using orthogonal contrasts procedure [24], but this procedure was also found incorrect by other statisticians. The confounding of L18 design exclude the possibility of any more precise analysis, which is limiting the usefulness of this design only for very simple verification of processes where no interactions occur. The chosen screening design permits the investigation of the influences of up to 8 inputs on outputs at once and one second level interaction. The aliasing pattern which occurs between main effects
1.774 2.673 4.390 1.410 2.149 2.931 1.992 3.259 4.334 3.757 1.549 2.650 1.672 3.797 1.833 2.971 1.546 2.791
31.89 50 13.11 72 4.53 123 30.01 57 0.52 74 0.48 74 4.26 70 4.89 83 21.46 69 4.73 87 12.35 70 5.99 75 2.07 77 9.10 77 9.89 70 4.53 77 49.09 76 2.10 59
18.03 3.79 18.69 6.39 2.17 2.54 2.87 4.68 3.76 8.80 10.45 5.51 9.96 7.38 4.13 2.38 6.96 1.45
92.32 98.86 96.84 94.54 93.97 95.75 94.38 98.12 94.64 91.23 94.19 93.98 93.80 95.32 96.68 93.78 95.21 95.92
0.97 0.52 2.27 1.21 0.89 1.58 1.19 1.36 0.47 0.30 2.04 2.30 1.06 1.71 0.61 1.29 0.98 0.89
and second order interactions were as well calculated and is presented in the Appendix A to this paper. This appendix explains the limitation of the used design and indicates the risk which is present when researchers are using such design. Moreover, the fact of existence of such complex aliasing pattern can lead to wrong conclusions, hence, the analysis of results has to be conducted very carefully. 4. Analysis of variance (ANOVA) The results of the experiment were analyzed using analysis of variance (ANOVA) [22]. This statistical method permits to find which of the factors is significantly important from results (outputs) point of view. The calculated results of analysis of variance are presented in an ANOVA table, which consists of several columns: f – number of degrees of freedom, SS – Sum of Squares, SM – square mean, F – estimated Fisher coefficient, Fc – critical value of the Fisher test, SS' – pure sum of squares, P – percent contribution, error – influence of not investigated inputs. The meaning of the coefficients which were listed above and are present in Tables 3–5 can be found in [22]. The most important from the analysis understanding point of view are F, Fc and P, hence, these coefficients will be additionally explained. If F is smaller than Fc then the factor is insignificant. This means that its influence on the result shall not be investigated. Otherwise it is significant. The significance of a factor is indicated additionally by asterisk (n) placed after the Fc value in Tables 3–5. For all significant factors it is possible to calculate the percentage influence of this factor on the output, which indicates more visually how important a particular factor is. The significance level, α, for which all statistical tests were conducted was fixed for the whole experiment at α=0.05. The significance level can be defined as likelihood of accepting the result as significant when
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Table 3 Filled ANOVA table (compressibility measurements). The letters L or Q after acronym indicates the type of relation between factor and output [L – linear or Q – quadratic].
Source of variation
Degrees of freedom Acronyms f
Preheating of structure at lamination Al temperature Lamination time Bl BQ Lamination temperature Cl CQ Lamination pressure Dl DQ Binder content El EQ Resicel/LDM ratio Fl FQ Interaction AB AlBl AlBQ Replications R Error Total
Sum of squares SS
Square mean SM
Empiric Fisher coefficient F
Critical Fisher coefficient Fc
Pure sum of squares SS'
Percent contribution P [%]
1
0.6112
0.6112
3.1370
4.3248
–
–
1 1 1 1 1 1 1 1 1 1 1 1 2 21 35
0.0016 2.0695 4.7762 0.3637 12.4944 1.8033 1.5138 0.5306 0.1847 4.3117 0.3247 1.2726 0.0972 4.0913 34.4465
0.0016 2.0695 4.7762 0.3637 12.4944 1.8033 1.5138 0.5306 0.1847 4.3117 0.3247 1.2726 0.0972 0.1948
0.0083 10.6226 24.5156 1.8668 64.1321 9.2559 7.7701 2.7235 0.9482 22.1312 1.6666 6.5323 0.4988
4.3248 4.3248n 4.3248n 4.3248 4.3248n 4.3248n 4.3248n 4.3248 4.3248 4.3248n 4.3248 4.3248n 4.3248
– 1.8479 4.5546 – 12.2728 1.5817 1.2922 – – 4.0901 – 1.0510 – 7.7562
– 5.36 13.22 – 35.63 4.59 3.75 – – 11.87 – 3.05 – 22.52 100
Table 4 Filled ANOVA table (surface roughness). Source of variation
Acronyms
f
SS
SM
F
Fc
S'
P
Preheating of structure at lamination temperature Lamination time
Al Bl BQ Cl CQ Dl DQ El EQ Fl FQ AB R –
1 1 1 1 1 1 1 1 1 1 1 2 2 38 53
2.60 473.06 243.60 646.01 29.87 4109.88 338.32 2794.88 118.23 592.11 455.92 320.54 223.06 2988.94 13,337.03
2.60 473.06 243.60 646.01 29.87 4109.88 338.32 2794.88 118.23 592.11 455.92 320.54 111.53 78.66
0.0331 6.0143 3.0970 8.2130 0.3798 52.2511 4.3012 35.5329 1.5031 7.5278 5.7964 4.0752 1.4180 –
4.0982 4.0982n 4.0982 4.0982n 4.0982 4.0982n 4.0982n 4.0982 4.0982n 4.0982n 4.0982n 3.2448n 3.2448 –
– 391.10 – 564.05 – 4027.92 256.36 2712.92 – 510.15 373.96 156.61 – 4343.96
– 2.93 – 4.23 – 30.20 1.92 20.34 – 3.83 2.80 1.17 – 32.57 100
Lamination temperature Lamination pressure Binder content Resicel/LDM ratio Interaction AB Replications Error Total
it was insignificant in reality. Exemplary calculations can be found in [22]. One extra factor called replications was investigated for each analysis in this paper. This is a noise factor which indicates if separate runs of measurements for the same process conditions vary significantly between each other. Hence, it indicates if uncontrolled process conditions were constant and were the same for all conducted measurements. In other words, let us assume that three different samples were fabricated at the same process conditions. The expectation is that the properties of all samples will be approximately the same. Unfortunate it can happen that one of the process conditions which was uncontrolled during the process can affect the samples properties significantly e.g. temperature variations. If it will happen then properties of three fabricated samples can very much vary from each other. If e.g. three different samples were fabricated in process conditions
which are expected to be same, experimenter can define one extra input factor in the analysis (replication). This factor has number of levels which is equal to the number of samples in this case 3. In the frame of statistical analysis using ANOVA it is possible to verify if this factor (replication) is significant or not. Thanks to this, it can be estimated if uncontrolled process conditions which were initially recognized as constant are really constant or not. 5. Results and discussion 5.1. Maximal compressibility analysis The aim of the first investigation was to estimate the influence of the lamination process conditions and HTCC composition on compressibility of tapes. It was expected that
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Table 5 Filled ANOVA table (density analysis). Source of variation
Acronyms
f
SS
SM
F
Fc
SS'
P [%]
Preheating of structure at lamination temperature Lamination time
Al Bl BQ Cl CQ Dl DQ El EQ Fl FQ AlBl AlBQ R –
1 1 1 1 1 1 1 1 1 1 1 1 1 2 38 53
15.62 4.16 0.12 47.21 24.13 4.41 0.04 0.43 25.91 0.10 0.00 10.57 17.87 0.99 92.93 244.47
15.6167 4.1558 0.1161 47.2079 24.1288 4.4066 0.0392 0.4268 25.9101 0.1027 0.0003 10.5716 17.8706 0.4927 2.4455
6.3860 1.6994 0.0475 19.3041 9.8667 1.8019 0.0160 0.1745 10.5951 0.0420 0.0001 4.3229 7.3076 0.2015
4.0982n 4.0982 4.0982 4.0982n 4.0982n 4.0982 4.0982 4.0982 4.0982n 4.0982 4.0982 4.0982n 4.0982n 3.2448
13.42 – – 45.01 21.93 – – – 23.72 – – 8.38 15.68 – 116.33
5.49 – – 18.41 8.97 – – – 9.70 – – 3.43 6.41 – 47.59 100
Lamination temperature Lamination pressure Binder content Resicel/LDM ratio Interaction AB Replications Error Total
compressibility can be a good quality measure for lamination analysis. Higher compressibility would in such case indicate better lamination. All verifications were conducted at significance level equal to 0.05. The results of all investigated factors are given as average value and variability coefficient in Table 2. Using analysis of variance (ANOVA) an estimation of the relative importance of the input factors is made, which is presented in Table 3. According to ANOVA all factors are in some way important from the compressibility point of view however, the relation between inputs and outputs and their percentage influence can vary. Most important is lamination pressure, which contributes to compressibility in approximately 41%. It is well related with expectation because the used binders have low Tg (transient glass temperature) so they can in theory be laminated at room temperature. Next significant factors are lamination temperature (around 13%) and Resicel/LDM ratio (around 12%). The lamination temperature affects the rheology of the organic binder, hence the higher temperature the more soft this material is and can be more compressed. The Resicel/LDM binder ratio decides about rheology properties of green tapes because each of these two binders has different properties [20]. The relation which is as well interesting is interaction between preheating of structure at lamination temperature and lamination time. It was found at first that preheating of structure at lamination temperature is insignificant. However, the interaction which contains this factor is significant. This indicates how important interactions are and the fact that analysis of results without investigation of interactions is much less precise. Because of the significance of interaction the factor preheating is significant as well. The reason of this significance from physics point of view is relatively easy to explain. The lamination time is needed for ensuring proper temperature homogeneity of the laminated tapes. If the temperature of lamination is equal to room temperature, the influence of preheating is insignificant but if temperature is much higher, then it takes more time to get uniform temperature distribution and this factor starts to be significant. Hence again investigation of interactions can be essential and gives much more information than analysis without interaction investigation [24]. Therefore, the
used experiment design might be limited, but on the other hand it permits significant cost reduction of the experiment [23] by the cost of investigation quality [24]. The relation between inputs and outputs can also be investigated using main effects analysis, which is presented in Fig. 1. These graphs permit to have a look at retaliation between process conditions and compressibility value. These graphs can be used to investigate how a value of an input factor affects the value of the output and to present it graphically, but they do not show the relative importance of the factors. It was expected that longer lamination time will make the compressibility higher (see Fig. 1a). Meanwhile the compressibility for the nominal value of lamination time (11 min) gives much lower compressibility than for 2 min lamination. This result can be caused by the drawback of the used design which is related with confounding between main effects and interaction (see Appendix A). On the other hand the variation of green tapes thicknesses could affect this result as well. The second uncertainty relation can be observed in Fig. 1f, there is observed significant decrease of compressibility for nominal lamination time equal to 11 min (Aþ B0). Moreover, the compressibility decreases for longer lamination times if there is no preheating. These relations cannot be logically explained. This can be only assumed that it is related to green tape variation or drawbacks of the used experiment design. All other retaliations are consistent with expectations. The factor which was called replications, which is useful in the indicating if not investigated process conditions were constant, was found insignificant. In other words it means that process conditions from the analysis point of view were constant. This indicates that all measurements were carried out at similar constant conditions. Thanks to ANOVA it was possible to conduct a rough estimation of compressibility at optimal conditions together with results of confirmation test (see Table 6). 5.2. Surface roughness analysis The influence of the investigated lamination and tapes parameters on sintered ceramic average surface roughness was
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Fig. 1. Main effects analysis – maximal compressibility, (a) lamination time, (b) lamination temperature, (c) lamination pressure, (d) binder content, (e) Resicel/LDM ratio, and (f) interaction AB.
analyzed next. The results which are given as an average value and variability coefficient are shown in Table 2. The filled ANOVA table is presented in Table 4 (see description in Section 2). All factors influence the surface roughness in some way according to the conducted analysis of variance. Again, the influence of preheating is significant because of interaction AB significance. The highest impact on surface roughness has lamination pressure (around 30%) and binder content (around 20%). The trends observed in the frame of main effects analysis are shown in Fig. 2. The explanation of the high impact of these two factors is quite easy. The topology of steel plates which are used during the lamination of tapes can be transferred into tapes during thermo-compression of tapes. Furthermore any defects which are presented on these steel plates e.g. scratches can be transferred as well. The higher the lamination pressure and binder content, the softer the tapes are. Hence, this transfer can be conducted easier. The influence of all other factors on output can be explained in the same way. Higher roughness will be achieved for all combination of factors which make the tapes softer and hence make it easier to transfer steel plate's topology into laminated tapes [20]. So obtained results are only true for
the particular steel plates which were used during lamination. The only conclusion which can be done at this stage is that steel plates shall be as smooth as possible. Otherwise the surface roughness of ceramic tapes would be disturbed by unwanted topology transfer from steel plates into green ceramic surface. Hence, this output of lamination quality analysis is useless from the practical point of view. The factor which was called replications was found insignificant. This indicates that all measurements were carried out at similar constant conditions. The comparison of the estimated value of surface roughness and the result of confirmation test is given in Table 6. The correlation can be said to be quite good. 5.3. Density analysis The influence of investigated lamination conditions and tapes parameters on sintered ceramic density was analyzed next. The density is shown as a relative value of theoretical alumina density given in percent. The results are given as average value and variability coefficient in Table 2. The filled ANOVA table is presented in Table 5. In the frame of the analysis it was found that
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Table 6 ANOVA optimization. Significance of factor
Influence on compressibility
Surface roughness Ra [nm]
Density
Preheating Lamination time Lamination temperature Lamination pressure Binder content Resicel/LDM
Yes (10 min) 20 min 80 1C 20 MPa 30% 50/50
Yes (10 min) 11 min 26 1C 5 Mpa 20% 50/50
Yes (10 min) 2 min (according to experiment) (used 10 min)a 50 1C Insignificant 25% Insignificant
Optimization Estimated optimal value Measured optimal value
5.42% 4.12%
43 nm 53 nm
98% 96%
a
a
See explanation in text above.
Resicel/LDM ratio and lamination pressure are insignificant from the density point of view. The factor which was called replications was found insignificant. This indicates that all measurements were carried out at similar constant conditions. The lamination time is significant because of significance of interaction AB. Unexpectedly it was found that the higher impact on density has lamination temperature (totally around 27%), next is interaction AB (around 10%) and binder content (around 10%). This indicates that the best proportion of LDM to Resiscel is 50/50%. Moreover, thanks to interaction AB investigation as well as to main effects analysis of (Fig. 3) preheating, it also can be said that higher density can be achieved if preheating is used. It was expected that lamination temperature does not play significant role because of low Tg of used binders [20]. However, even if a low Tg means that complete lamination is possible at room temperature, the binder becomes softer at higher temperatures; its rheology [25] decreases, the bonding becomes stronger and the space between ceramic grains decreases. This closer distance between ceramic grains make it easier to sinter grains together after debinding. Lamination time was found insignificant. However, due to the fact that interaction between preheating and lamination time was found significant also lamination time plays a role in the density analysis. The explanation of lamination time vs. density is more complicated. It was found that higher density is achieved for shorter lamination times. This result was probably obtained due to confounding which exists between main effects and interactions in Taguchi design [24] or by measuring errors and this result is not logic. The influence of instability of sintering conditions is visible through error factor. This value is very high for density analysis (around 48%). 5.4. Scanning Acoustic Microscopy (SAM) analysis Beside of compressibility analysis as an initial verification, the lamination quality can be as well investigated through the SAM (Scanning Acoustic Microscope) analysis. This method provides vital information about a missing part of the investigation – delamination. The lamination quality was tested for all samples (all combinations are given in Table 2) using SAM in three modes: backecho, topecho and midecho. The most useful mode from the analysis point of view was backecho which permits to have a look through the whole substrate. The SAM analysis
showed that delaminations occur only for one set of process conditions (set 1 in Table 2). An example of a delamination is presented in Fig. 4a, where the delamination can be recognized as a dark region. Hence, it can be said that from this initial analysis point of view all combinations of process conditions, except set 1, are sufficient for laminating the investigated HTCC green tapes. Hence, it is obvious that density analysis can give more precise information than that and its usefulness is clearer at this point. 5.5. Optimization The findings which of the factors are significant and how much is surly important but it is not all information which can be expected from the analysis point of view. The experiment is conducted to get some estimation how the combination of particular factors values will contribute to the output. Three outputs were investigated in the frame of this investigation. The aim of dividing this work into three parts was to find if these outputs are or are not useful in the lamination quality investigation. The results of compressibility were expected to be similar to the density investigation results at the beginning of the experiment. However, density analysis results vary from compressibility one. This is an effect of additional process occurrence – sintering. The final bonding strength between green ceramic tapes depends on three mechanisms [3]: joining of softened resinous constituents (occurs at lamination stage), mechanical joining of unevenness in the joint surface (occurs at lamination stage), and grains sintering (occurs at sintering stage). This variation is also affected by the relation of compressibility from amount of binder content, more binder higher compressibility. An effect of high binder content is that averagely the ceramic grains are far from each other and it can cause formation of more porosity after sintering, hence, lower density ceramics. In the previous work it was found that the deviation of sintering process conditions has very high impact on the density [21].This impact is also visible in this paper through the error input contribution (see Table 5, row called Error). This factor is relatively high and is approximately 48%. Due to this fact the correlation between density and compressibility analysis is not so obvious. Based on this result it has to be said that it is useless to conduct compressibility analysis if someone wants to verify lamination quality through density
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Fig. 2. Main effects analysis – minimal surface roughness, (a) lamination time, (b) lamination temperature, (c) lamination pressure, (d) binder content, (e) Resicel/LDM ratio, and (f) interaction AB.
analysis. The compressibility test can be used as initial verification, which can be used for initial excluding bad laminating conditions. At this stage it can be said that density analysis make the biggest sense from practical point of view,
because only this analysis gives information which can be useful – higher density is a result of better process conditions. In case of surface roughness analysis the noise which was introduced by topology of steel pates was too high to obtain
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Fig. 3. Main effects analysis – maximal density, (a) preheating, (b) lamination temperature, (c) binder content, and (d) interaction AB.
any useful information beside of conclusion that plates have to be as smooth as possible. As it was earlier written in this paper during density analysis it was unexpectedly found that higher density is achieved for shorter lamination times. This result was probably obtained due to confounding which exists between main effects and interactions in Taguchi design [24] or by measuring errors and this result is not logic. Therefore, the value of this factor in the confirmation test (see Table 6) was set to 10 min which is more logical. If at least two outputs would be recognized as valuable from the lamination quality point of view it would be as well worth to conduct multivariate analysis of variance (MANOVA) [26] which permits to find overall optimal process conditions from the all outputs point of view. However, in this case this solution is not needed because only one output is useful. The optimal process condition which was found for each process output is presented in Table 6. Moreover, this table consists of information about expected value of output for optimal process conditions (estimated optimal value) and real value of this output measured using samples fabricated at optimal process conditions (measured optimal value). The correlation between estimation and real value is not so bad. However, it can be
observed that real values are lower, what indicates imperfection of experiment design which was used in the frame of analysis. This effect is probably caused by complex aliasing structure of the design and extremely limited analysis of interactions which were conducted in this verification. Moreover, word “optimal” has to be used here very carefully. Because this optimal conditions were found for this particular analysis and if another, more precisely design of the experiment was used then other optimal conditions could be found. As it was previously said from the practical point of view only column density is worth to be recognized as valuable information from the lamination quality point of view. 6. Conclusions The most useful measure of the lamination quality is density of sintered ceramic tapes, according to the conducted analysis. This output is much more sufficient because it includes influence of all three ceramic tapes boning mechanics on the bonding strength: joining of melted resinous constituents (occurs at lamination stage), mechanical joining of unevenn ess in the joint surface (occurs at lamination stage), the glass
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Fig. 4. SAM pictures in backecho mode for two samples per set of lamination conditions for (a) set 1, (b) set 16, and (c) set 18. Delamination can be recognized as the dark region in (a).
material viscous flow and grains sintering (occurs at sintering stage). The compressibility as an output includes an influence of only two mechanisms on to lamination quality: joining of melted resinous constituents, mechanical joining of unevenness in the joint surface. Taking into account the very high impact of variation in sintering conditions, such as uneven temperature inside the furnace on the density (around 48% according to this paper) it is obvious that density analysis is a much better measure of lamination quality. The usefulness of
surface roughness measure as a lamination quality output is not a good solution. It was found that surface roughness depends on the lamination conditions however, this relation is caused by the transfer of steel plate's topology, used during thermocompression, onto laminated structures. Hence, it depends on surface quality of steel plates instead of the lamination process conditions. The initial quality of the process (occurrence of delaminations) between laminates is better to investigate using SAM instead of
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Table 7 Part A of aliasing between second order interactions and main effects. AlCQ AlDl
AlDQ AlEl
AlEQ AlFl
AlFQ BlCl
BlCQ BlDl
BlDQ BlEl
BLEQ BLFl
BlFQ BQCl BQCQ BQDl BQDQ BQEl BQEQ BQFl BQFQ
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1/2 1/2 1/2 1/2 0 0
0 0 0 1/2 1/2 0 0 0 0 1 0
0 0 0 1/2 1/2 0 0 0 0 1/2 1/2
0 0 0 0 0 1 0 1/2 1/2 0 0
0 0 0 0 0 1/4 1/4 1/2 0 3/4 1/4
0 0 0 1/4 1/4 0 0 1/2 1/2 1/2 0
0 0 0 1/2 0 1/2 1/2 0 0 1/4 1/4
0 0 0 3/4 1/4 1/2 0 1/4 1/4 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1/2 1/6 1/2 1/6 0 0
0 0 0 1/2 1/6 0 0 0 0 0 1/3
0 0 0 1/2 1/6 0 0 0 0 1/2 1/6
0 0 0 0 0 0 1/3 1/2 1/6 0 0
0 0 0 0 0 1/4 1/12 0 1/6 1/4 1/4
0 0 0 1/4 1/12 0 0 1/2 1/6 0 1/6
0 0 0 0 1/6 1/2 1/6 0 0 1/4 1/12
0 0 0 1/4 1/4 0 1/6 1/4 1/12 0 0
0 0 0 0 0 1/4 1/4 1/2 0 1/4 1/4
0 0 0 0 0 3/4 1/4 0 1/2 3/4 1/4
0 0 0 1/4 1/4 0 0 1/2 1/2 1/2 0
0 0 0 3/4 1/4 0 0 1 1/2 1/2 0 1/2
0 0 0 1/2 0 1/2 1/2 0 0 1/4 1/4
0 0 0 0 1/2 1 1/2 1/2 0 0 3/4 1/4
0 0 0 1/4 1/4 1/2 0 1/4 1/4 0 0
0 0 0 3/4 1/4 0 1/2 3/4 1/4 0 0
Table 8 Part B of aliasing between second order interactions and main effects.
Al. Bl BQ Cl CQ Dl DQ El EQ Fl FQ
ClDl
ClDQ ClEl
CLEQ CLFl
ClFQ CQDl CQDQ CQEl CQEQ CQFl CQFQ DlEl
1/3 1/4 1/12 0 0 0 0 1/4 1/12 1/4 1/12
1/3 1/4 1/4 0 0 0 0 1/4 1/4 1/4 1/4
1/3 1/2 0 0 0 1/4 1/4 0 0 1/4 1/4
0 3/4 1/4 0 0 1/4 1/4 1/4 1/4 0 0
1/3 0 1/6 0 0 1/4 1/12 0 0 1/4 1/12
0 1/4 1/12 0 0 1/4 1/12 1/4 1/12 0 0
1/3 1/4 1/4 0 0 0 0 1/4 1/4 1/4 1/4
1 3/4 1/4 0 0 0 0 3/4 1/4 3/4 1/4
1/3 1/2 0 0 0 1/4 1/4 0 0 1/4 1/4
1 0 1/2 0 0 3/4 1/4 0 0 3/4 1/4
0 3/4 1/4 0 0 1/4 1/4 1/4 1/4 0 0
0 3/4 1/4 0 0 3/4 1/4 3/4 1/4 0 0
0 1/2 1/6 1/4 1/12 0 0 0 0 1/4 1/12
DLEQ DlFl
DlFQ DQlEl DQEQ
DQFl DQFQ ElFl
0 1/2 1/2 1/4 1/4 0 0 0 0 1/4 1/4
2/3 1/2 0 1/4 1/4 0 0 1/4 1/4 0 0
2/3 1/2 0 1/4 1/4 0 0 1/4 1/4 0 0
0 0 1/6 1/4 1/12 0 0 1/4 1/12 0 0
0 1/2 1/2 1/4 1/4 0 0 0 0 1/4 1/4
0 1 1/2 1/2 3/4 1/4 0 0 0 0 3/4 1/4
0 0 1/2 3/4 1/4 0 0 3/4 1/4 0 0
1/3 1/4 1/12 1/4 1/12 1/4 1/12 0 0 0 0
ElFQ EQFl EQFQ 1/3 1/4 1/4 1/4 1/4 1/4 1/4 0 0 0 0
1/3 1/4 1/4 1/4 1/4 1/4 1/4 0 0 0 0
1 3/4 1/4 3/4 1/4 3/4 1/4 0 0 0 0
D. Jurków et al. / Ceramics International 41 (2015) 7860–7871
Al. Bl BQ Cl CQ Dl DQ El EQ Fl FQ
AlBl AlBQ AlCl
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compression analysis. SAM gives much more precise results which can be easier diagnosed. Meanwhile compression analysis may not detect delamination occurrence. The design of the experiment is a way which can be used for conducting experiments. However, the proper design has to be chosen at initial stage of the experiment – before collecting of results. Otherwise, many useful information can be not achievable in the frame of the investigation, e.g. as in this case due to the lack of interactions analysis or confounding between factors and interactions. Hence, design matrix shall be chosen individually for each experiment taking into account the expected phenomena which can occur during the investigation. Acknowledgment The project was financed by The National Center for Science (Poland) awarded on the basis of Decision number DEC 2011/03/N/ST7/00205. Appendix A. Confounding in Taguchi L18 design matrix The complex aliasing pattern which is present in L18 Taguchi design is presented in Tables 7 and 8. On one hand L18 design enables significant reduction of tests. On the other hand such complex confounding can lead to many uncertainties in results analysis. Moreover, analysis suffers from lack of interaction analysis. The other way of aliasing pattern notation is presented below for factor named Al 1 1 1 1 1 Al ¼ Al0 ClDl ClDQ ClEl ClEQ þ CQDl 3 3 3 3 3 1 CQDQ þ CQEl CQEQ 3 2 2 1 1 1 DlFQ þ DQFl ElFlþ ElFQ EQFl EQFQ 3 3 3 3 3 0 If Al indicates the real (not aliased) influence of linear factor Al, then Al which is entangled factor which presents an influence of real Al0 and several interactions with various weights on to output. Such entangled pattern excludes application of this design in investigation of significance of interaction other than AlBl and AlBQ, because only these two interactions are not entangled with other factors. This limits the use of this design only to verification of simple process without interactions between factors. References [1] K.A. Peterson, K.D. Patel, C.K. Ho, S.B. Rohde, C.D. Nordquist, C.A. Walker, B.D. Wroblewski, M. Okandan, Novel microsystem applications with new techniques in low-temperature co-fired ceramics, Int. J. Appl. Ceram. Technol. 2 (2005) 345–363. [2] L.J. Golonka, Technology and applications of low temperature cofired ceramic (LTCC) based sensors and microsystems, Bull. Pol. Acad. Sci. Tech. Sci. 54 (2006) 2. [3] Y. Imanaka, Multilayered Low Temperature Cofired Ceramics (LTCC) Technology, Springer, New York, 2005.
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[4] W.R. Johnson, J.L. Evans, P. Jacobsen, J.R. Thompson, M. Christopher, The changing automotive environment: high-temperature electronics, IEEE Trans. Electron. Packag. Manuf. 27 (2004) 164–176. [5] F. Bechtold, A Comprehensive Overview on Today's Ceramic Substrate Technologies, in: Proceedings of the European Microelectronics and Packaging Conference, Rimini, Italy, 2009. [6] R.D. Koch, M. Schwab, F.M. Pitschi, J.E. Kiwitt, R. Weigel, Ultra lowprofile self-matched SAW duplexer with a Flip-Chip HTCC package for W-CDMA 2100 mobile applications, in: Proceedings of MTT-S International Microwave Symposium Digest, Boston, USA, 2009, 97–100. [7] G.N. Howatt, R.G. Breckenridge, J.M. Brownlow, Fabrication of thin ceramic sheets for capacitors, J. Am. Ceram. Soc. 30 (1947) 237–242. [8] T. Chartier, A. Bruneau, Aqueous tape casting of alumina substrates, J. Eur. Ceram. Soc. 12 (1993) 243–247. [9] A. Kristoffersson, E. Carlstöm, Tape casting of alumina in water with an acrylic latex binder, J. Eur. Ceram. Soc. 17 (1997) 289–297. [10] J. Stiernstedt, M. Zachrisson, E. Carlström, Environmental and quality analysis of aqueous tape casting, in: H. Kück, H. Reinecke, S.Dimov (Eds.), Proceedings of the 8th International Conference on Multi-Material Micro Manufacture, Stuttgart, Singapore, Research Publishing, 2011, pp. 251-255. [11] L.E. Khoong, Y.M. Tan, Y.C. Lam, Overview on fabrication of threedimensional structures in multi-layer ceramic substrate, J. Eur. Ceram. Soc. 30 (2010) 1973–1987. [12] D. Jurków, L. Golonka, Low pressure thermo-compressive lamination, J. Eur. Ceram. Soc. 32 (2012) 2431–2441. [13] X. Shan, H.P. Maw, C.W. Lu, Solvent-assisted low pressure room temperature lamination of low temperature cofirable ceramic green tapes for formation of embedded micro channels, Microsyst. Technol. 16 (2010) 1501–1506. [14] M.A. Piwonski, A. Roosen, Low pressure lamination of ceramic green tapes by gluing at room temperature, J. Eur. Ceram. Soc. 19 (1999) 263–270. [15] A. Roosen, New lamination technique to join ceramic green tapes for the manufacturing of multilayer devices, J. Eur. Ceram. Soc. 21 (2001) 1993–1996. [16] D. Jurków, K. Malecha, Z. Suszyński, J. Stiernstedt, G. Wetter, L. Golonka, Inspection of multilayer ceramic structure lamination quality— comparison of nondestructive methods, in: Proceedings of the 9th International Conference on Multi-Material Micro Manufacture: 4M, Wien, Austria, 2012 215–218. [17] Z.Q. Yu, Y.C. Chan, D.P. Webb, G.Y. Li, Nondestructive evaluation of ceramic substrate with embedded passive components by SAM, J. Electron. Packag. 122 (2000) 172–177. [18] E. Horváth, G. Harsányi, Optimization of fluidic microchannel manufacturing processes in low temperature co-fired ceramic substrates, Electr. Eng. 54 (2011) 79–86. [19] E. Horvath, G. Henap, G. Harsanyi, Finite element modeling of channel sag in LTCC, Microelectron. Int. 29 (2012) 145–152. [20] D. Jurków, K. Malecha, J. Stiernstedt, L. Golonka, Influence of tapes' properties on the laser cutting process, J. Eur. Ceram. Soc. 31 (2011) 1589–1595. [21] D. Jurków, J. Stiernstedt, Investigation of high temperature co-fired ceramics sintering conditions using Taguchi design of the experiment, Ceram. Int. 40 (2014) 10447–10455. [22] D.J. Weiss, Analysis of Variance and Functional Measurement: A Practical Guide, University Press, Oxford, 2006. [23] R. Ranjit, A Primer on the Taguchi Method, Society of Manufacturing Engineers, Dearborn, 2010. [24] M. Hamada, C.F.J. Wu, Analysis of designed experiments with complex aliasing, J. Qual. Technol. 24 (1992) 130–137. [25] T. Gupta, Handbook of Thick- and Thin-Film Hybrid Microelectronics, John Wiley and Sons, New Jearsy, 2003. [26] J.H. Bray, S.E. Maxwell (Eds.), Multivariate Analysis of Variance, 54, Sage, Newbury, 1985.
CERAMICS INTERNATIONAL
Ceramics International 41 (2015) 7860–7871 www.elsevier.com/locate/ceramint
Investigation of High Temperature Co-fired Ceramic tapes lamination conditions Dominik Jurkówa,n, Johanna Stiernstedtb, Mateusz Dorczyńskia, Göran Wetterb a
Wroclaw University of Technology, Faculty of Microsystem Electronics and Photonics, 50-372 Wrocław, Poland b Swerea IVF AB, P.O. Box 104, SE-431 22 Mölndal, Sweden Received 30 December 2014; received in revised form 6 February 2015; accepted 23 February 2015 Available online 28 February 2015
Abstract The main goal of this paper was to analyze the influence of lamination process conditions and High Temperature Co-fired Ceramic (HTCC) tape composition on the lamination quality (existence of delaminations). The second aim was to estimate the influence of lamination conditions and HTCC tape composition on three process outputs: compressibility, surface roughness and density of High Temperature Co-fired Ceramics and to recognize if these outputs can be useful from lamination quality investigation point of view. The bonding quality was investigated using scanning acoustic microscopy (SAM). The analyzed ceramics was fabricated using water based slurries in the frame of tape casting process. The paper additionally discusses limitations and drawbacks of the used investigation methods and experiment design. & 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Keywords: Ceramics; Lamination; Water based tape casting; HTCC
1. Introduction Multilayer ceramic technology can be divided into two main parts: Low Temperature Co-fired Ceramics (LTCC) and High Temperature Co-fired Ceramics (HTCC). LTCC contains glass which gives a firing temperature compatible with silver and gold, and LTCC is utilized in the fabrication of wireless components (e.g. antennas), sensors, actuators, chemical reactors and microsystems [1–3]. HTCC is fired at higher temperature (1500–1600 1C) and is used in applications where higher chemical or thermal stability is needed [4], moreover, it can be used as well in RF devices or packages [5,6] and automotive applications [5]. Both LTCC and HTCC are fabricated in the frame of tape casting process from various slurries [7]. The slurry composition decides about mechanical and electrical properties of both green and fired tapes. The trend of toxicity reduction of materials caused the necessity of slurry composition changes. The possibility of utilizing more environmental and user friendly water based solvents instead of high flammable and toxic n
Corresponding author. E-mail address: [email protected] (D. Jurków).
http://dx.doi.org/10.1016/j.ceramint.2015.02.123 0272-8842/& 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
organic solvents was previously reported [8–10]. After tape casting the laser cutting systems, punching units or embossing machines permit the fabrication of structures in each single tape. The structured tapes are aligned and stacked, in order to build up 3D components. Then the lamination is conducted. This process is extremely important due to the fact that it affects the homogeneity of tapes in region of the tapes interface. In other words if the process is carried out improperly, delaminations between tapes on the tapes interfaces will occur. There are two groups of lamination techniques which are worth to be mentioned thermo-compressive lamination [11,12] and chemical laminations [13–15]. The usefulness of the chemical methods is mainly limited to the special complicated 3D structures without electrical components. On the other hand standard thermocompressive methods are widely used but can cause high deformation of 3D structures fabricated using single tapes. After lamination the tapes are co-fired in a furnace. This process drives off all organic materials from the tapes and permits sintering of the ceramic grains together. Hence, the hard dense ceramics is obtained. The quality of sintered ceramics can be investigated from several points of view, e.g. surface roughness, delaminations,
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compressibility or density value. Given the level of surface roughness for ceramics, the most useful method of measuring is mechanical profilometry. The surface roughness depends mainly on the size of the ceramic grains and its optimal level depends on the application. This material property is not correlated with the other ceramic properties mentioned above. Delamination is a frequently investigated output, since it can indicate an insufficient lamination process or variation in the material composition. The quality of sintered ceramics can be examined using several different inspection methods, of which the most promising are non-destructive [16], such as Scanning Acoustic Microscopy (SAM) [16,17]. SAM permits the detection of delaminations in ceramic structures [16,17] and therefore it is also very useful in LTCC and HTCC structures inspection [16,18,19]. SAM is a very sensitive control method of delaminations, since inclusion of air causes a total reflection in the signal. Therefore, SAM inspection was used as a reference investigation method in order to validate the other inspection methods applied in this work. Measurement of density through the Archimedes method permits detection of closed porosity; if any close gas voids exits between layers the measured density will be lower than the expected mean value. However, the limitation is the fact that open delaminations will not be detected by this method. The compressibility is correlated with delaminations through the expectation that some compressibility is needed for proper lamination, hence, if the compressibility is low, this indicates delaminations. The measurement of compressibility is, however, dependent on the tape thickness variation and might be misleading. In the present study delaminations were detected only for samples with low compressibility. Optimization from laser cutting and sintering point of views of the tapes presented in this paper were done before [20,21]. The aim of this paper was to investigate the influence of the lamination process conditions and tape composition on the lamination quality (existence of delaminations). Three measures of quality of lamination were proposed in this paper: compressibility and surface roughness of the green tapes, and density of the fired tapes. The usefulness of these three outputs on the lamination quality analysis was verified in the frame of the experiment. Moreover, the tape compressibility, sintered ceramics surface roughness and density were investigated for different values of a number of process parameters, and the bonding quality was investigated using Scanning Acoustic Microscopy (SAM). The experiment was planned using Design of the Experiment (DoE) [20,21] and the data were analyzed using analysis of variance and orthogonal contrasts methods [20,21]. The paper additionally discusses limitations and drawbacks of the used investigation methods and experiment design.
binder content and binder composition. The investigated inputs are given in Table 1. The preheating means that tapes were left in the laminating machine for a particular period before the lamination pressure was turn on. This solution is used to provide even temperature distribution for all laminated tapes. The value of each of the lamination conditions as well as binder content and tapes composition was chosen based on the expert knowledge. This knowledge was gained in the frame of earlier investigations [20,21]. The samples used in the study were laminates of two HTCC square tapes 20 20 mm2, around 180 mm thick (in green state). The tapes were made by aqueous tape casting using alumina powder (AKP30, Sumitomo Chemical), dispersant (Dolapix PC21, Zschimmer & Schwarz) and latex binder (Resicel E50N, Lamberti Speciality Chemicals, or LDM 7651S, Celanese Emulsions). The compressibility was calculated as the ratio between prelaminated green tape and laminated sample thicknesses multiplied by 100. The density was measured using the Archimedes method in water and its value is given as a relative value of theoretical alumina density given in percent. The average roughness results were calculated based on 10 mm long surfaces scans of the ceramic (Taylor-Hobson mechanical profilometer). The experiment consists of three runs; three samples were measured from up and down sides (total cardinality was equal to 108). The cardinality of each of the runs for compressibility verification was 10 with two replications (total cardinality was equal to 360). The density was measured as average density of 3 samples with three replications (total cardinality was equal to 162). The results are given only as average values of all achieved results to simplify the form of tables. All statistical calculations were conducted according to an analysis of variance method (ANOVA) and the type influence of inputs on outputs was found using an orthogonal contrasts method. The second solution permits to find if the relation between input and output is linear, square or mixed linearsquare [22].
2. Experiment
3. Design of the Experiment (DoE)
In the investigation of lamination quality, the compressibility of the tapes, and surface roughness and density of sintered samples were analyzed and the following process conditions were investigated: duration time of tapes preheating at lamination tempera ture, lamination time, lamination temperature, lamination pressure,
Taking account that influence of 6 inputs were investigated at once it was decided to apply Design of the Experiment (DoE) methodology in the analysis [22,23]. This solution permits the reduction of costs and time of the experiment. The most sufficient experiment design would be full factorial design, which enables
Table 1 Investigated process parameters. Factor
Preheating of structure at lamination temperature Lamination time Lamination temperature Lamination pressure Binder content Resicel/LDM ratio
Factor acronym
Factor level 1
0
þ1
A
10 min –
0 min
B C D E F
2 min 26 1C 5 MPa 20% 100/0
20 min 80 1C 20 MPa 30% 0/100
11 min 50 1C 12.5 MPa 25% 50/50
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Table 2 Experiment design and results of compressibility, surface roughness and density analysis. set Preheating Lamination time Lamination temperature Lamination pressure Binder content Binder ratio Compressibility analysis
Surface roughness analysis
Average density analysis
Δz=z0 [%] V [%] Ra [nm] V [%] ρ [%] V [%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
A
B
C
D
E
F
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1
1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1
1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0
1 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1 1
1 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0
to obtain the most correct results and analyze influence of main effects as well as interaction between inputs. It has to be mentioned that it is expected that interactions exist between the analyzed inputs. However, the full factorial design on three levels demands to conduct test for 3n=36=729 combination of inputs values (where: n – number of inputs). This is in practice impossible. Another type of design which could be applied would be one of the fractional (or partial) factorial designs where the number of needed combinations can be reduced meanwhile some interactions still can be investigated [22]. The most reduced experiment designs which enable investigation of only main effects without interactions were proposed mainly by Taguchi [23] and are called screening designs. Using of such designs permits only very rough estimation of results and experiment findings correctness is endangered by existence of aliasing between main effects and interactions. The aim of this experiment was to get basic knowledge about the lamination process and to roughly verify the variability of results and usefulness of outputs from lamination quality point of view, hence it was decided to use fractional factorial design L18 which was proposed by Taguchi. This matrix is presented in Table 2 and is widely used by many authors [23] who indicate that aliasing of main effects and interactions of this design is very efficient from the analysis point of view. However, as it will be discussed further in this paper this aliasing pattern is not always sufficient This problem was reported by other authors who proposed some ways of coping with this using orthogonal contrasts procedure [24], but this procedure was also found incorrect by other statisticians. The confounding of L18 design exclude the possibility of any more precise analysis, which is limiting the usefulness of this design only for very simple verification of processes where no interactions occur. The chosen screening design permits the investigation of the influences of up to 8 inputs on outputs at once and one second level interaction. The aliasing pattern which occurs between main effects
1.774 2.673 4.390 1.410 2.149 2.931 1.992 3.259 4.334 3.757 1.549 2.650 1.672 3.797 1.833 2.971 1.546 2.791
31.89 50 13.11 72 4.53 123 30.01 57 0.52 74 0.48 74 4.26 70 4.89 83 21.46 69 4.73 87 12.35 70 5.99 75 2.07 77 9.10 77 9.89 70 4.53 77 49.09 76 2.10 59
18.03 3.79 18.69 6.39 2.17 2.54 2.87 4.68 3.76 8.80 10.45 5.51 9.96 7.38 4.13 2.38 6.96 1.45
92.32 98.86 96.84 94.54 93.97 95.75 94.38 98.12 94.64 91.23 94.19 93.98 93.80 95.32 96.68 93.78 95.21 95.92
0.97 0.52 2.27 1.21 0.89 1.58 1.19 1.36 0.47 0.30 2.04 2.30 1.06 1.71 0.61 1.29 0.98 0.89
and second order interactions were as well calculated and is presented in the Appendix A to this paper. This appendix explains the limitation of the used design and indicates the risk which is present when researchers are using such design. Moreover, the fact of existence of such complex aliasing pattern can lead to wrong conclusions, hence, the analysis of results has to be conducted very carefully. 4. Analysis of variance (ANOVA) The results of the experiment were analyzed using analysis of variance (ANOVA) [22]. This statistical method permits to find which of the factors is significantly important from results (outputs) point of view. The calculated results of analysis of variance are presented in an ANOVA table, which consists of several columns: f – number of degrees of freedom, SS – Sum of Squares, SM – square mean, F – estimated Fisher coefficient, Fc – critical value of the Fisher test, SS' – pure sum of squares, P – percent contribution, error – influence of not investigated inputs. The meaning of the coefficients which were listed above and are present in Tables 3–5 can be found in [22]. The most important from the analysis understanding point of view are F, Fc and P, hence, these coefficients will be additionally explained. If F is smaller than Fc then the factor is insignificant. This means that its influence on the result shall not be investigated. Otherwise it is significant. The significance of a factor is indicated additionally by asterisk (n) placed after the Fc value in Tables 3–5. For all significant factors it is possible to calculate the percentage influence of this factor on the output, which indicates more visually how important a particular factor is. The significance level, α, for which all statistical tests were conducted was fixed for the whole experiment at α=0.05. The significance level can be defined as likelihood of accepting the result as significant when
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Table 3 Filled ANOVA table (compressibility measurements). The letters L or Q after acronym indicates the type of relation between factor and output [L – linear or Q – quadratic].
Source of variation
Degrees of freedom Acronyms f
Preheating of structure at lamination Al temperature Lamination time Bl BQ Lamination temperature Cl CQ Lamination pressure Dl DQ Binder content El EQ Resicel/LDM ratio Fl FQ Interaction AB AlBl AlBQ Replications R Error Total
Sum of squares SS
Square mean SM
Empiric Fisher coefficient F
Critical Fisher coefficient Fc
Pure sum of squares SS'
Percent contribution P [%]
1
0.6112
0.6112
3.1370
4.3248
–
–
1 1 1 1 1 1 1 1 1 1 1 1 2 21 35
0.0016 2.0695 4.7762 0.3637 12.4944 1.8033 1.5138 0.5306 0.1847 4.3117 0.3247 1.2726 0.0972 4.0913 34.4465
0.0016 2.0695 4.7762 0.3637 12.4944 1.8033 1.5138 0.5306 0.1847 4.3117 0.3247 1.2726 0.0972 0.1948
0.0083 10.6226 24.5156 1.8668 64.1321 9.2559 7.7701 2.7235 0.9482 22.1312 1.6666 6.5323 0.4988
4.3248 4.3248n 4.3248n 4.3248 4.3248n 4.3248n 4.3248n 4.3248 4.3248 4.3248n 4.3248 4.3248n 4.3248
– 1.8479 4.5546 – 12.2728 1.5817 1.2922 – – 4.0901 – 1.0510 – 7.7562
– 5.36 13.22 – 35.63 4.59 3.75 – – 11.87 – 3.05 – 22.52 100
Table 4 Filled ANOVA table (surface roughness). Source of variation
Acronyms
f
SS
SM
F
Fc
S'
P
Preheating of structure at lamination temperature Lamination time
Al Bl BQ Cl CQ Dl DQ El EQ Fl FQ AB R –
1 1 1 1 1 1 1 1 1 1 1 2 2 38 53
2.60 473.06 243.60 646.01 29.87 4109.88 338.32 2794.88 118.23 592.11 455.92 320.54 223.06 2988.94 13,337.03
2.60 473.06 243.60 646.01 29.87 4109.88 338.32 2794.88 118.23 592.11 455.92 320.54 111.53 78.66
0.0331 6.0143 3.0970 8.2130 0.3798 52.2511 4.3012 35.5329 1.5031 7.5278 5.7964 4.0752 1.4180 –
4.0982 4.0982n 4.0982 4.0982n 4.0982 4.0982n 4.0982n 4.0982 4.0982n 4.0982n 4.0982n 3.2448n 3.2448 –
– 391.10 – 564.05 – 4027.92 256.36 2712.92 – 510.15 373.96 156.61 – 4343.96
– 2.93 – 4.23 – 30.20 1.92 20.34 – 3.83 2.80 1.17 – 32.57 100
Lamination temperature Lamination pressure Binder content Resicel/LDM ratio Interaction AB Replications Error Total
it was insignificant in reality. Exemplary calculations can be found in [22]. One extra factor called replications was investigated for each analysis in this paper. This is a noise factor which indicates if separate runs of measurements for the same process conditions vary significantly between each other. Hence, it indicates if uncontrolled process conditions were constant and were the same for all conducted measurements. In other words, let us assume that three different samples were fabricated at the same process conditions. The expectation is that the properties of all samples will be approximately the same. Unfortunate it can happen that one of the process conditions which was uncontrolled during the process can affect the samples properties significantly e.g. temperature variations. If it will happen then properties of three fabricated samples can very much vary from each other. If e.g. three different samples were fabricated in process conditions
which are expected to be same, experimenter can define one extra input factor in the analysis (replication). This factor has number of levels which is equal to the number of samples in this case 3. In the frame of statistical analysis using ANOVA it is possible to verify if this factor (replication) is significant or not. Thanks to this, it can be estimated if uncontrolled process conditions which were initially recognized as constant are really constant or not. 5. Results and discussion 5.1. Maximal compressibility analysis The aim of the first investigation was to estimate the influence of the lamination process conditions and HTCC composition on compressibility of tapes. It was expected that
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Table 5 Filled ANOVA table (density analysis). Source of variation
Acronyms
f
SS
SM
F
Fc
SS'
P [%]
Preheating of structure at lamination temperature Lamination time
Al Bl BQ Cl CQ Dl DQ El EQ Fl FQ AlBl AlBQ R –
1 1 1 1 1 1 1 1 1 1 1 1 1 2 38 53
15.62 4.16 0.12 47.21 24.13 4.41 0.04 0.43 25.91 0.10 0.00 10.57 17.87 0.99 92.93 244.47
15.6167 4.1558 0.1161 47.2079 24.1288 4.4066 0.0392 0.4268 25.9101 0.1027 0.0003 10.5716 17.8706 0.4927 2.4455
6.3860 1.6994 0.0475 19.3041 9.8667 1.8019 0.0160 0.1745 10.5951 0.0420 0.0001 4.3229 7.3076 0.2015
4.0982n 4.0982 4.0982 4.0982n 4.0982n 4.0982 4.0982 4.0982 4.0982n 4.0982 4.0982 4.0982n 4.0982n 3.2448
13.42 – – 45.01 21.93 – – – 23.72 – – 8.38 15.68 – 116.33
5.49 – – 18.41 8.97 – – – 9.70 – – 3.43 6.41 – 47.59 100
Lamination temperature Lamination pressure Binder content Resicel/LDM ratio Interaction AB Replications Error Total
compressibility can be a good quality measure for lamination analysis. Higher compressibility would in such case indicate better lamination. All verifications were conducted at significance level equal to 0.05. The results of all investigated factors are given as average value and variability coefficient in Table 2. Using analysis of variance (ANOVA) an estimation of the relative importance of the input factors is made, which is presented in Table 3. According to ANOVA all factors are in some way important from the compressibility point of view however, the relation between inputs and outputs and their percentage influence can vary. Most important is lamination pressure, which contributes to compressibility in approximately 41%. It is well related with expectation because the used binders have low Tg (transient glass temperature) so they can in theory be laminated at room temperature. Next significant factors are lamination temperature (around 13%) and Resicel/LDM ratio (around 12%). The lamination temperature affects the rheology of the organic binder, hence the higher temperature the more soft this material is and can be more compressed. The Resicel/LDM binder ratio decides about rheology properties of green tapes because each of these two binders has different properties [20]. The relation which is as well interesting is interaction between preheating of structure at lamination temperature and lamination time. It was found at first that preheating of structure at lamination temperature is insignificant. However, the interaction which contains this factor is significant. This indicates how important interactions are and the fact that analysis of results without investigation of interactions is much less precise. Because of the significance of interaction the factor preheating is significant as well. The reason of this significance from physics point of view is relatively easy to explain. The lamination time is needed for ensuring proper temperature homogeneity of the laminated tapes. If the temperature of lamination is equal to room temperature, the influence of preheating is insignificant but if temperature is much higher, then it takes more time to get uniform temperature distribution and this factor starts to be significant. Hence again investigation of interactions can be essential and gives much more information than analysis without interaction investigation [24]. Therefore, the
used experiment design might be limited, but on the other hand it permits significant cost reduction of the experiment [23] by the cost of investigation quality [24]. The relation between inputs and outputs can also be investigated using main effects analysis, which is presented in Fig. 1. These graphs permit to have a look at retaliation between process conditions and compressibility value. These graphs can be used to investigate how a value of an input factor affects the value of the output and to present it graphically, but they do not show the relative importance of the factors. It was expected that longer lamination time will make the compressibility higher (see Fig. 1a). Meanwhile the compressibility for the nominal value of lamination time (11 min) gives much lower compressibility than for 2 min lamination. This result can be caused by the drawback of the used design which is related with confounding between main effects and interaction (see Appendix A). On the other hand the variation of green tapes thicknesses could affect this result as well. The second uncertainty relation can be observed in Fig. 1f, there is observed significant decrease of compressibility for nominal lamination time equal to 11 min (Aþ B0). Moreover, the compressibility decreases for longer lamination times if there is no preheating. These relations cannot be logically explained. This can be only assumed that it is related to green tape variation or drawbacks of the used experiment design. All other retaliations are consistent with expectations. The factor which was called replications, which is useful in the indicating if not investigated process conditions were constant, was found insignificant. In other words it means that process conditions from the analysis point of view were constant. This indicates that all measurements were carried out at similar constant conditions. Thanks to ANOVA it was possible to conduct a rough estimation of compressibility at optimal conditions together with results of confirmation test (see Table 6). 5.2. Surface roughness analysis The influence of the investigated lamination and tapes parameters on sintered ceramic average surface roughness was
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Fig. 1. Main effects analysis – maximal compressibility, (a) lamination time, (b) lamination temperature, (c) lamination pressure, (d) binder content, (e) Resicel/LDM ratio, and (f) interaction AB.
analyzed next. The results which are given as an average value and variability coefficient are shown in Table 2. The filled ANOVA table is presented in Table 4 (see description in Section 2). All factors influence the surface roughness in some way according to the conducted analysis of variance. Again, the influence of preheating is significant because of interaction AB significance. The highest impact on surface roughness has lamination pressure (around 30%) and binder content (around 20%). The trends observed in the frame of main effects analysis are shown in Fig. 2. The explanation of the high impact of these two factors is quite easy. The topology of steel plates which are used during the lamination of tapes can be transferred into tapes during thermo-compression of tapes. Furthermore any defects which are presented on these steel plates e.g. scratches can be transferred as well. The higher the lamination pressure and binder content, the softer the tapes are. Hence, this transfer can be conducted easier. The influence of all other factors on output can be explained in the same way. Higher roughness will be achieved for all combination of factors which make the tapes softer and hence make it easier to transfer steel plate's topology into laminated tapes [20]. So obtained results are only true for
the particular steel plates which were used during lamination. The only conclusion which can be done at this stage is that steel plates shall be as smooth as possible. Otherwise the surface roughness of ceramic tapes would be disturbed by unwanted topology transfer from steel plates into green ceramic surface. Hence, this output of lamination quality analysis is useless from the practical point of view. The factor which was called replications was found insignificant. This indicates that all measurements were carried out at similar constant conditions. The comparison of the estimated value of surface roughness and the result of confirmation test is given in Table 6. The correlation can be said to be quite good. 5.3. Density analysis The influence of investigated lamination conditions and tapes parameters on sintered ceramic density was analyzed next. The density is shown as a relative value of theoretical alumina density given in percent. The results are given as average value and variability coefficient in Table 2. The filled ANOVA table is presented in Table 5. In the frame of the analysis it was found that
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Table 6 ANOVA optimization. Significance of factor
Influence on compressibility
Surface roughness Ra [nm]
Density
Preheating Lamination time Lamination temperature Lamination pressure Binder content Resicel/LDM
Yes (10 min) 20 min 80 1C 20 MPa 30% 50/50
Yes (10 min) 11 min 26 1C 5 Mpa 20% 50/50
Yes (10 min) 2 min (according to experiment) (used 10 min)a 50 1C Insignificant 25% Insignificant
Optimization Estimated optimal value Measured optimal value
5.42% 4.12%
43 nm 53 nm
98% 96%
a
a
See explanation in text above.
Resicel/LDM ratio and lamination pressure are insignificant from the density point of view. The factor which was called replications was found insignificant. This indicates that all measurements were carried out at similar constant conditions. The lamination time is significant because of significance of interaction AB. Unexpectedly it was found that the higher impact on density has lamination temperature (totally around 27%), next is interaction AB (around 10%) and binder content (around 10%). This indicates that the best proportion of LDM to Resiscel is 50/50%. Moreover, thanks to interaction AB investigation as well as to main effects analysis of (Fig. 3) preheating, it also can be said that higher density can be achieved if preheating is used. It was expected that lamination temperature does not play significant role because of low Tg of used binders [20]. However, even if a low Tg means that complete lamination is possible at room temperature, the binder becomes softer at higher temperatures; its rheology [25] decreases, the bonding becomes stronger and the space between ceramic grains decreases. This closer distance between ceramic grains make it easier to sinter grains together after debinding. Lamination time was found insignificant. However, due to the fact that interaction between preheating and lamination time was found significant also lamination time plays a role in the density analysis. The explanation of lamination time vs. density is more complicated. It was found that higher density is achieved for shorter lamination times. This result was probably obtained due to confounding which exists between main effects and interactions in Taguchi design [24] or by measuring errors and this result is not logic. The influence of instability of sintering conditions is visible through error factor. This value is very high for density analysis (around 48%). 5.4. Scanning Acoustic Microscopy (SAM) analysis Beside of compressibility analysis as an initial verification, the lamination quality can be as well investigated through the SAM (Scanning Acoustic Microscope) analysis. This method provides vital information about a missing part of the investigation – delamination. The lamination quality was tested for all samples (all combinations are given in Table 2) using SAM in three modes: backecho, topecho and midecho. The most useful mode from the analysis point of view was backecho which permits to have a look through the whole substrate. The SAM analysis
showed that delaminations occur only for one set of process conditions (set 1 in Table 2). An example of a delamination is presented in Fig. 4a, where the delamination can be recognized as a dark region. Hence, it can be said that from this initial analysis point of view all combinations of process conditions, except set 1, are sufficient for laminating the investigated HTCC green tapes. Hence, it is obvious that density analysis can give more precise information than that and its usefulness is clearer at this point. 5.5. Optimization The findings which of the factors are significant and how much is surly important but it is not all information which can be expected from the analysis point of view. The experiment is conducted to get some estimation how the combination of particular factors values will contribute to the output. Three outputs were investigated in the frame of this investigation. The aim of dividing this work into three parts was to find if these outputs are or are not useful in the lamination quality investigation. The results of compressibility were expected to be similar to the density investigation results at the beginning of the experiment. However, density analysis results vary from compressibility one. This is an effect of additional process occurrence – sintering. The final bonding strength between green ceramic tapes depends on three mechanisms [3]: joining of softened resinous constituents (occurs at lamination stage), mechanical joining of unevenness in the joint surface (occurs at lamination stage), and grains sintering (occurs at sintering stage). This variation is also affected by the relation of compressibility from amount of binder content, more binder higher compressibility. An effect of high binder content is that averagely the ceramic grains are far from each other and it can cause formation of more porosity after sintering, hence, lower density ceramics. In the previous work it was found that the deviation of sintering process conditions has very high impact on the density [21].This impact is also visible in this paper through the error input contribution (see Table 5, row called Error). This factor is relatively high and is approximately 48%. Due to this fact the correlation between density and compressibility analysis is not so obvious. Based on this result it has to be said that it is useless to conduct compressibility analysis if someone wants to verify lamination quality through density
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Fig. 2. Main effects analysis – minimal surface roughness, (a) lamination time, (b) lamination temperature, (c) lamination pressure, (d) binder content, (e) Resicel/LDM ratio, and (f) interaction AB.
analysis. The compressibility test can be used as initial verification, which can be used for initial excluding bad laminating conditions. At this stage it can be said that density analysis make the biggest sense from practical point of view,
because only this analysis gives information which can be useful – higher density is a result of better process conditions. In case of surface roughness analysis the noise which was introduced by topology of steel pates was too high to obtain
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Fig. 3. Main effects analysis – maximal density, (a) preheating, (b) lamination temperature, (c) binder content, and (d) interaction AB.
any useful information beside of conclusion that plates have to be as smooth as possible. As it was earlier written in this paper during density analysis it was unexpectedly found that higher density is achieved for shorter lamination times. This result was probably obtained due to confounding which exists between main effects and interactions in Taguchi design [24] or by measuring errors and this result is not logic. Therefore, the value of this factor in the confirmation test (see Table 6) was set to 10 min which is more logical. If at least two outputs would be recognized as valuable from the lamination quality point of view it would be as well worth to conduct multivariate analysis of variance (MANOVA) [26] which permits to find overall optimal process conditions from the all outputs point of view. However, in this case this solution is not needed because only one output is useful. The optimal process condition which was found for each process output is presented in Table 6. Moreover, this table consists of information about expected value of output for optimal process conditions (estimated optimal value) and real value of this output measured using samples fabricated at optimal process conditions (measured optimal value). The correlation between estimation and real value is not so bad. However, it can be
observed that real values are lower, what indicates imperfection of experiment design which was used in the frame of analysis. This effect is probably caused by complex aliasing structure of the design and extremely limited analysis of interactions which were conducted in this verification. Moreover, word “optimal” has to be used here very carefully. Because this optimal conditions were found for this particular analysis and if another, more precisely design of the experiment was used then other optimal conditions could be found. As it was previously said from the practical point of view only column density is worth to be recognized as valuable information from the lamination quality point of view. 6. Conclusions The most useful measure of the lamination quality is density of sintered ceramic tapes, according to the conducted analysis. This output is much more sufficient because it includes influence of all three ceramic tapes boning mechanics on the bonding strength: joining of melted resinous constituents (occurs at lamination stage), mechanical joining of unevenn ess in the joint surface (occurs at lamination stage), the glass
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Fig. 4. SAM pictures in backecho mode for two samples per set of lamination conditions for (a) set 1, (b) set 16, and (c) set 18. Delamination can be recognized as the dark region in (a).
material viscous flow and grains sintering (occurs at sintering stage). The compressibility as an output includes an influence of only two mechanisms on to lamination quality: joining of melted resinous constituents, mechanical joining of unevenness in the joint surface. Taking into account the very high impact of variation in sintering conditions, such as uneven temperature inside the furnace on the density (around 48% according to this paper) it is obvious that density analysis is a much better measure of lamination quality. The usefulness of
surface roughness measure as a lamination quality output is not a good solution. It was found that surface roughness depends on the lamination conditions however, this relation is caused by the transfer of steel plate's topology, used during thermocompression, onto laminated structures. Hence, it depends on surface quality of steel plates instead of the lamination process conditions. The initial quality of the process (occurrence of delaminations) between laminates is better to investigate using SAM instead of
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Table 7 Part A of aliasing between second order interactions and main effects. AlCQ AlDl
AlDQ AlEl
AlEQ AlFl
AlFQ BlCl
BlCQ BlDl
BlDQ BlEl
BLEQ BLFl
BlFQ BQCl BQCQ BQDl BQDQ BQEl BQEQ BQFl BQFQ
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1/2 1/2 1/2 1/2 0 0
0 0 0 1/2 1/2 0 0 0 0 1 0
0 0 0 1/2 1/2 0 0 0 0 1/2 1/2
0 0 0 0 0 1 0 1/2 1/2 0 0
0 0 0 0 0 1/4 1/4 1/2 0 3/4 1/4
0 0 0 1/4 1/4 0 0 1/2 1/2 1/2 0
0 0 0 1/2 0 1/2 1/2 0 0 1/4 1/4
0 0 0 3/4 1/4 1/2 0 1/4 1/4 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1/2 1/6 1/2 1/6 0 0
0 0 0 1/2 1/6 0 0 0 0 0 1/3
0 0 0 1/2 1/6 0 0 0 0 1/2 1/6
0 0 0 0 0 0 1/3 1/2 1/6 0 0
0 0 0 0 0 1/4 1/12 0 1/6 1/4 1/4
0 0 0 1/4 1/12 0 0 1/2 1/6 0 1/6
0 0 0 0 1/6 1/2 1/6 0 0 1/4 1/12
0 0 0 1/4 1/4 0 1/6 1/4 1/12 0 0
0 0 0 0 0 1/4 1/4 1/2 0 1/4 1/4
0 0 0 0 0 3/4 1/4 0 1/2 3/4 1/4
0 0 0 1/4 1/4 0 0 1/2 1/2 1/2 0
0 0 0 3/4 1/4 0 0 1 1/2 1/2 0 1/2
0 0 0 1/2 0 1/2 1/2 0 0 1/4 1/4
0 0 0 0 1/2 1 1/2 1/2 0 0 3/4 1/4
0 0 0 1/4 1/4 1/2 0 1/4 1/4 0 0
0 0 0 3/4 1/4 0 1/2 3/4 1/4 0 0
Table 8 Part B of aliasing between second order interactions and main effects.
Al. Bl BQ Cl CQ Dl DQ El EQ Fl FQ
ClDl
ClDQ ClEl
CLEQ CLFl
ClFQ CQDl CQDQ CQEl CQEQ CQFl CQFQ DlEl
1/3 1/4 1/12 0 0 0 0 1/4 1/12 1/4 1/12
1/3 1/4 1/4 0 0 0 0 1/4 1/4 1/4 1/4
1/3 1/2 0 0 0 1/4 1/4 0 0 1/4 1/4
0 3/4 1/4 0 0 1/4 1/4 1/4 1/4 0 0
1/3 0 1/6 0 0 1/4 1/12 0 0 1/4 1/12
0 1/4 1/12 0 0 1/4 1/12 1/4 1/12 0 0
1/3 1/4 1/4 0 0 0 0 1/4 1/4 1/4 1/4
1 3/4 1/4 0 0 0 0 3/4 1/4 3/4 1/4
1/3 1/2 0 0 0 1/4 1/4 0 0 1/4 1/4
1 0 1/2 0 0 3/4 1/4 0 0 3/4 1/4
0 3/4 1/4 0 0 1/4 1/4 1/4 1/4 0 0
0 3/4 1/4 0 0 3/4 1/4 3/4 1/4 0 0
0 1/2 1/6 1/4 1/12 0 0 0 0 1/4 1/12
DLEQ DlFl
DlFQ DQlEl DQEQ
DQFl DQFQ ElFl
0 1/2 1/2 1/4 1/4 0 0 0 0 1/4 1/4
2/3 1/2 0 1/4 1/4 0 0 1/4 1/4 0 0
2/3 1/2 0 1/4 1/4 0 0 1/4 1/4 0 0
0 0 1/6 1/4 1/12 0 0 1/4 1/12 0 0
0 1/2 1/2 1/4 1/4 0 0 0 0 1/4 1/4
0 1 1/2 1/2 3/4 1/4 0 0 0 0 3/4 1/4
0 0 1/2 3/4 1/4 0 0 3/4 1/4 0 0
1/3 1/4 1/12 1/4 1/12 1/4 1/12 0 0 0 0
ElFQ EQFl EQFQ 1/3 1/4 1/4 1/4 1/4 1/4 1/4 0 0 0 0
1/3 1/4 1/4 1/4 1/4 1/4 1/4 0 0 0 0
1 3/4 1/4 3/4 1/4 3/4 1/4 0 0 0 0
D. Jurków et al. / Ceramics International 41 (2015) 7860–7871
Al. Bl BQ Cl CQ Dl DQ El EQ Fl FQ
AlBl AlBQ AlCl
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compression analysis. SAM gives much more precise results which can be easier diagnosed. Meanwhile compression analysis may not detect delamination occurrence. The design of the experiment is a way which can be used for conducting experiments. However, the proper design has to be chosen at initial stage of the experiment – before collecting of results. Otherwise, many useful information can be not achievable in the frame of the investigation, e.g. as in this case due to the lack of interactions analysis or confounding between factors and interactions. Hence, design matrix shall be chosen individually for each experiment taking into account the expected phenomena which can occur during the investigation. Acknowledgment The project was financed by The National Center for Science (Poland) awarded on the basis of Decision number DEC 2011/03/N/ST7/00205. Appendix A. Confounding in Taguchi L18 design matrix The complex aliasing pattern which is present in L18 Taguchi design is presented in Tables 7 and 8. On one hand L18 design enables significant reduction of tests. On the other hand such complex confounding can lead to many uncertainties in results analysis. Moreover, analysis suffers from lack of interaction analysis. The other way of aliasing pattern notation is presented below for factor named Al 1 1 1 1 1 Al ¼ Al0 ClDl ClDQ ClEl ClEQ þ CQDl 3 3 3 3 3 1 CQDQ þ CQEl CQEQ 3 2 2 1 1 1 DlFQ þ DQFl ElFlþ ElFQ EQFl EQFQ 3 3 3 3 3 0 If Al indicates the real (not aliased) influence of linear factor Al, then Al which is entangled factor which presents an influence of real Al0 and several interactions with various weights on to output. Such entangled pattern excludes application of this design in investigation of significance of interaction other than AlBl and AlBQ, because only these two interactions are not entangled with other factors. This limits the use of this design only to verification of simple process without interactions between factors. References [1] K.A. Peterson, K.D. Patel, C.K. Ho, S.B. Rohde, C.D. Nordquist, C.A. Walker, B.D. Wroblewski, M. Okandan, Novel microsystem applications with new techniques in low-temperature co-fired ceramics, Int. J. Appl. Ceram. Technol. 2 (2005) 345–363. [2] L.J. Golonka, Technology and applications of low temperature cofired ceramic (LTCC) based sensors and microsystems, Bull. Pol. Acad. Sci. Tech. Sci. 54 (2006) 2. [3] Y. Imanaka, Multilayered Low Temperature Cofired Ceramics (LTCC) Technology, Springer, New York, 2005.
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