William Carty, who has been my ceramic engineering mentor for the last 3 years and helped mold me into a materials scientist. Effect of TiO2 content added to Ag paste on Ag grain size calcined at 900oC. The sintering potential of Ag (ΣAg) and Ag+3.67 vol% TiO2 calculated using equation 4) is also given for comparison.
The foam development during co-firing of the two-layer Ag/BTZB laminate measured experimentally is in good agreement with that calculated using the linear shrinkage rate difference between Ag+3.67 vol% TiO2 and BTZB laminates.
INTRODUCTION
D IELECTRIC M ATERIALS OF LTCC
The properties of the final composite are determined by the ratio of glass to ceramic filler and the individual properties of the blends. The borosilicate glass + alumina system developed by Fujitsu and the lead borosilicate glass + alumina from DuPont are two of the typical systems [16,17]. The degree of crystallization that occurs during firing is the dominant factor controlling the properties of the final products.
In order to optimize the treatment parameters, a thorough and systematic understanding of the crystallization kinetics and mechanism of glass-ceramic systems is therefore necessary. One of the main advantages of the glass-ceramic approach is to have a low dielectric loss due to a small amount of residual glass remaining.
M ODULES AND MANUFACTURING PROCESS OF LTCC
Due to its processing robustness and simplicity in fine-tuning the physical properties of fired multiphase composites, this approach is preferentially used in the commercially available LTCC systems and also chosen in this study. In the case of glass-ceramic systems, a crystallizable glass is used, e.g. crystallizable cordierite by IBM and crystallizable CaO-B2O3-SiO2 glass by Ferro [18,19]. The concern with this approach is the low densification temperatures, which are too close to what is required for binder burnout.
This can result in poor densification and high dielectric loss due to an excessive amount of residual carbon present in the fired units.
![Table I. Electrical Resistance and Melting Point of Conductor Metals [4]](https://thumb-ap.123doks.com/thumbv2/123dok/10492397.0/13.918.170.823.107.302/table-i-electrical-resistance-melting-point-conductor-metals.webp)
M OTIVATION OF THIS STUDY
LITERATURE REVIEW
C ONSTITUTIVE EQUATIONS FOR A POROUS VISCOUS MATERIAL UNDER SINTERING
The free strain rate (𝜀̇𝑓) is related to the sintering potential or sintering stress (𝛴), which is an obvious driver of densification. The sintering potential is the hydrostatic pressure stress to reduce the volume of the sintered body. If a hydrostatic tensile stress equal to the sintering potential is applied in each direction (𝜎𝑋 = 𝜎𝑌 = 𝜎𝑌 = −𝛴), shrinkage stops during sintering and the linear strain rate becomes zero (𝜀̇𝑋= 𝜀̇𝑌 = 𝜀̇𝑍 = 0).
Therefore, if the misfit tensile stress generated during sintering of mixed materials is greater than the sintering potential of each constituent material, the possibility of forming sintering defects, including cracks or delamination, becomes higher.
I N - PLAIN TENSILE STRESS GENERATED BY DENSIFICATION MISMATCH DURING COFIRING MIXED
The nominal viscous misfit stress in the metal layer (σ̂𝑀𝑒𝑡𝑎𝑙𝛥𝜀̇) can then be calculated by Eq. 7) using the data for the difference in linear shrinkage rate and the porous uniaxial viscosities. With the data for the calculated σ̂𝑀𝑒𝑡𝑎𝑙, m and n, the average sintering mismatch stress in the metal layer (𝜎𝑀𝑒𝑡𝑎𝑙𝐴𝑉𝐺) can be determined by equating the temperature as a function of the temperature. The nominal viscous misfit stress in the metal layer (σ̂𝑀𝑒𝑡𝑎𝑙) can also be calculated by camber rate in the following.
Including the porous uniaxial viscosity data, the normalized camber speed, n and m in Eq. 8), the nominal viscous mismatch stress in the metal layer (σ̂𝑀𝑒𝑡𝑎𝑙𝜅̇̇) can be calculated. By combining the above nominal viscous mismatch stress data (σ̂𝑀𝑒𝑡𝑎𝑙𝜅̇̇) into Eq. 5), the average sintering mismatch voltage in the metal layer (𝜎𝑀𝑒𝑡𝑎𝑙𝐴𝑉𝐺) is determined as a function of temperature. It is interesting to note that the above calculations in Eq. 5) show only the average sintering mismatch voltage across the metal layer.
Finite element analysis [45] shows that the sintering mismatch stress increases from the top surface of the metal. The largest sintering mismatch stress (𝜎𝑀𝑒𝑡𝑎𝑙𝑀𝑎𝑥 ), which is located at the metal/ceramic lamination interface, can be calculated by [26,27]. Results on aluminum/zirconia hybrid laminates show that joint defects, including cracks and debonding, form if the densification rate mismatch between layers is significant [26,27].
The extent of co-firing defects can be reduced by reducing the mismatch stress during sintering. This can be achieved by using a slower heating rate to relax the mismatch stress or by mixing alumina in the zirconia to reduce the densification rate mismatch between the layers.
E FFECTS OF DENSIFICATION MISMATCH ON CAMBER DEVELOPMENT
EXPERIMENTAL PROCEDURE
S AMPLE P REPERATION
L INEAR S HRINKAGE AND U NIAXIAL V ISCOSITY M EASUREMENTS
C AMBER M EASUREMENTS
RESULTS
L INEAR S TRAIN M EASUREMENTS
3(A) and 3(B) show insignificant difference in shrinkage behavior for the Ag pastes with 1.22-3.67 vol% TiO2, the following analyzes will focus on the Ag pastes with and without 3.67 vol% TiO2. It is found that for pure Ag, the linear strain rate difference between BTZB and Ag exhibits two peaks, the first one with positive values located at 300-600oC and the second one with negative values at temperature above 700oC. However, for the Ag sample with 3.67 vol% TiO2, the first one with positive values shifts to 650-850oC, and the second one with negative values shifts to temperatures above 850oC.
An insignificant shrinkage rate difference is observed after firing at 900oC for 60-120min, where densification of BTZB apparently stops. The results in fig. 4 further shows that the temperature range for observing significant shrinkage rate difference between BTZB and Ag is 300-900oC, which is much wider than Ag with 3.67 vol%. Effect of TiO2 content added in Ag paste on linear shrinkage rate difference between Ag and BTZB (𝛥𝜀̇𝐵𝑇𝑍𝐵−𝐴𝑔).
8 show that the addition of TiO2 slows down not only the densification (Fig. 3 and 4), but also the growth of Ag grains during annealing at 900oC. It is believed that the added TiO2 particles act as restricted sites for densification and grain boundary migration of Ag during annealing, because mutual dissolution between TiO2 and Ag has not been previously observed and reported.
C AMBER M EASUREMENTS
Moreover, the positive curvature implies that the Ag layer is under in-plane compressive stress and the BTZB layer is under in-plane tensile stress during baking. For all examined Ag samples with different amounts of TiO2, a similar trend of curvature development is observed, i.e. a positive camber observed at 750-900oC, which reaches a maximum at 900oC for 10-20 minutes, and then decreases with increasing soaking period at 900oC. However, a larger negative curvature is observed for the Ag samples with less TiO2 during isothermal firing at 900oC.
Figure 10(B) shows the normalized camber rate (𝑘̇) as a function of temperature, which is obtained by taking the derivative of the curves in Figs. For all investigated Ag compositions, the rate of positive camber increases first, reaches a maximum at 800-825oC, and then decreases with increasing temperature. As firing continues, the cam rate is negligible at 860-875oC, and then becomes negative as firing continues.
Both Ag and BTZB layers adhere strongly, with no attachment defects such as cracks and distortion formed at the interface. SEM micrograph for the interfacial area between Ag and BTZB in Ag+3.67 vol% TiO2/BTZB bilayer laminate fired at 900oC for 120 min.
U NIAXIAL V ISCOSITY M EASUREMENTS
DISCUSSION
Average (𝜎𝐴𝑔𝐴𝑉𝐺) and maximum (𝜎𝐴𝑔𝑀𝑎𝑥) bilayers of (A) pure Ag/BTZB and (B) Ag+3.67 volT under a low temperature TiO2/ 𝛥𝜀̇𝐵𝑇𝑍𝐵 −𝐴𝑔) data from TMA in Fig. Average (𝜎𝐵𝑇𝑍𝐵𝐴𝑉𝐺 ) and maximum ( +3.67 vol% TiO2/BTZB laminate as a function of temperature calculated from the linear strain rate difference ( calculated from Eq. 5 ) where n is the viscosity ratio between Ag and BTZB calculated from Eq. .6) and σ̂𝐴𝑔 is the nominal viscous mismatch stress from Eqs.
The nominal viscous mismatch stress in the Ag layer (σ̂𝐴𝑔𝛥𝜀̇) in Eq. 7) is related to the difference between linear strain rates between BTZB and Ag (𝛥𝜀̇𝐵𝑇𝑍𝐵−𝐴𝑔) (Fig. 4), uniaxial viscosity of Ag (𝐸𝑝𝑝𝑔) of the ̃𝔐 calculated data for Fig. 𝜀̇, m and n, the average sintering mismatch stress in the Ag layer with different TiO2 content (𝜎𝐴𝑔𝐴𝑉𝐺) can be determined as a function of temperature by Eq. The average sintering mismatch stress in the Ag layer (𝜎𝐴𝑔𝐴𝑉𝐺) varies in the range 0.1 MPa for Ag/BTZB (Fig.
10 can also be used to calculate the nominal viscous mismatch stress in the Ag layer (σ̂𝐴𝑔𝜅̇̇ ) from Eq. Including the uniaxial viscosity data (𝐸𝑝𝐴𝑔) in Fig. 13, one can calculate the normalized rate of the camera in Fig. 8), the nominal viscous mismatch stress in the Ag layer (σ̂𝐴𝑔𝜅̇̇ ). Combining the above nominal viscous mismatch stress data (σ̂𝐴𝑔𝜅̇̇ ) in Eq. 5), the average sintering mismatch stress in the Ag layer (𝜎𝐴𝑔𝐴𝑉𝐺) as a function of temperature is calculated, as shown in Fig.
For all investigated compositions and temperatures, the average sinter mismatch stress in the Ag layer (𝜎𝐴𝑔𝐴𝑉𝐺) varies in the range of 0.05 MPa for Ag/BTZB (Fig. The largest sinter mismatch stress (𝜎𝐴𝑔𝑀𝑎𝑥), which is located at interface of Ag/BTZB laminate can be calculated using Eq. Similar calculations are also performed for the BTZB layer, with a small change in the largest sintering mismatch stress (𝜎𝐵𝑇𝑍𝐵𝑀𝑎𝑥) calculated by [26,27].
15 shows that the mismatch stresses of BTZB calculated by the linear shrinkage-strain rate difference are larger than those calculated by the warping results, especially for the pure Ag sample.
SUMMARY AND CONCLUSIONS
Kim, "Low-temperature sintering and microwave dielectric properties of zinc metatitanate-rutile blends using boron". Du, “Densification and characterization of SiO2-B2O3-CaO-MgO glass/Al2O3 composites for LTCC applications,” Ceram. Kamehara, “Effect of Copper-Ceramic Shrinkage Mismatch on Dimensional Control of Multilayer Ceramic Circuit,” J.
Tummala, "Glass-ceramic structures and sintered multilayer substrates thereof with circuit patterns of gold, silver or copper." Chen, "Effect of Compaction Mismatch on Camber Development during Cofiring of Nickel-Based Multilayer Ceramic Capacitors," J. Jean, "Key Factors Controlling Camber Behavior during the Cofiring of Bi-layer Ceramic Dielectric Laminate, J.
![Table II. Dielectric Constant (k) and Quality Factor (Q) of Commercially Available LTCC Systems [15]](https://thumb-ap.123doks.com/thumbv2/123dok/10492397.0/13.918.163.823.386.1026/table-dielectric-constant-quality-factor-commercially-available-systems.webp)
![Figure 2. Typical manufacturing process of LTCC devices [21].](https://thumb-ap.123doks.com/thumbv2/123dok/10492397.0/14.918.200.747.591.1007/figure-2-typical-manufacturing-process-ltcc-devices-21.webp)
