Quantitative process–microstructure–rf-conductivity basis for silver thick-film conductors cofired above the melting point in high-Q multilayer ceramic resonators

The 1992 discovery by Shimoda, Ishitobi, Kawamura and Kobayashi that multilayer ceramic triplate resonators cofired above the melting point of their silver thick-film inner conductor gain a sharply higher unloaded Q (141 at 900°C versus 212 at 1000°C at about 1.9 GHz) left a quantitative question that the source letter did not answer: how cofiring temperature, Ag-paste formulation, and stacking pressure control the conductor's cofired microstructure and its effective GHz-frequency conductivity; how the rf-specific losses (skin depth, edge effects, pressure-induced roughness) can be separated so that rf conductivity is predictable from dc measurements; and whether the Q gain translates into bandpass-filter insertion loss as standard theory predicts.

Background

Multilayer ceramic microwave components embed stripline (triplate) transmission lines and resonators — metal patterns sandwiched between ceramic dielectric layers, with the whole stack laminated and sintered in a single cofiring step — to realize miniature filters and front-end parts for mobile radios. A resonator's unloaded Q (its quality factor with no external loading: $2\pi$ times the energy stored divided by the energy dissipated per cycle) sets the insertion loss (the transmission power lost when the filter is inserted in the signal path) and selectivity of bandpass filters built from it. For a maximally-flat (Butterworth) two-pole filter with 3-dB fractional bandwidth $w$ (passband width at the 3-dB response points divided by the center frequency) and resonator unloaded quality factor $Q_0$, the mid-band insertion loss caused by dissipation is approximately

$$\Delta L_A\approx\frac{4.343}{w\,Q_0}\sum_i g_i,$$

where $g_i$ are the low-pass prototype element values — the normalized lumped-element values of the filter's standard low-pass prototype ($g_1=g_2=\sqrt2$ for a two-pole maximally-flat response). At GHz frequencies the conductor loss of embedded resonators usually dominates, and thick-film metallizations (metal-powder pastes screen-printed and fired together with the ceramic) are lossier than bulk metal: inter-particle boundaries, porosity, and surface roughness degrade their effective conductivity, and the radio-frequency (rf) current flows only within a skin depth $\delta=\sqrt{2/(\omega\mu\sigma)}$ of the conductor surface (with $\omega$ the angular frequency, $\mu$ the permeability, and $\sigma$ the conductivity), so the effective rf conductivity can fall well below the dc (direct-current) value — a deficit measured for thick films as early as Patel (1970).

The mainstream low-temperature-cofired-ceramic (LTCC) route keeps the silver thick film solid by using glass-ceramic dielectrics that sinter at about 850–900°C, below the silver melting point (961°C). Shimoda, Ishitobi, Kawamura and Kobayashi (Jpn. J. Appl. Phys. 31, 3160 (1992)) took the opposite route: they cofired the multilayer stack above the silver melting point and found that the molten-then-resolidified inner conductor acquires a coalesced microstructure with markedly higher effective rf conductivity. Quarter-wave (length one quarter of the guided wavelength) triplate resonators in their dielectric (relative permittivity about 10.7) rose in unloaded Q from 141 when cofired at 900°C to 212 at 1000°C, and the effective rf conductivity extracted from measured Q rose from about $0.8\times10^7$ to $2.9\times10^7$ S/m between 900°C and 1080°C (bulk silver: about $6.3\times10^7$ S/m). They attributed the remaining rf-versus-dc conductivity difference to skin-depth and edge effects plus surface roughness introduced by the stacking pressure used in lamination — but without quantifying these contributions, without a systematic map of the process window (firing temperature, paste silver content), without long-term reliability data for the above-melt structure, and with the extraction procedure relating measured Q to effective conductivity left unspecified. The unresolved question is whether the cofire-above-melt route can be placed on a quantitative, predictive basis.

Problem Statement

Problem (from Shimoda, Ishitobi, Kawamura and Kobayashi, Jpn. J. Appl. Phys. 31, 3160 (1992)): for silver thick-film inner conductors cofired within a multilayer ceramic (dielectric of relative permittivity near 10.7), establish the quantitative, mechanism-resolved basis of the cofiring-above-melt process demonstrated in the source, through the following scientifically linked results, all three of which are jointly required to resolve the task.

(1) Process–property map. Establish and quantify how peak cofiring temperature, spanning from below to above the silver melting point (961°C), and Ag-paste formulation (silver content) control the conductor's cofired microstructure, the resonator unloaded Q, and the effective rf conductivity extracted from it, beyond the firing-temperature–Q relationship demonstrated in the source.

(2) Mechanism separation and dc-to-rf prediction. Separate and quantify the three rf-specific loss contributions — skin-depth effects in a film whose thickness is comparable to the rf skin depth, edge (current-crowding) effects at the conductor perimeter, and surface roughness introduced by stacking pressure — so that the effective rf conductivity of a cofired conductor can be predicted from dc measurements and microstructural characterization rather than inferred case by case from resonator Q.

(3) Circuit-level validation. Determine whether the conductor improvement is reflected in resonator Q and bandpass-filter insertion loss as the standard dissipation relation predicts (mid-band loss $\approx4.343\,\sum g_i/(w\,Q_0)$ for fractional bandwidth $w$ and prototype element values $g_i$), and quantify any discrepancy.

These results serve one objective: making cofiring above the silver melting point a predictable manufacturing route for low-loss multilayer ceramic microwave resonators and filters, in the system class of the source demonstration (triplate resonators operating near 1.9 GHz, in the band the source letter designates S-band). The source letter reports no long-term reliability data and no full manufacturing-process qualification of the above-melt structure.

References

1. Hideaki Shimoda, Norimasa Ishitobi, Keizou Kawamura, Makoto Kobayashi, Development of a High-Q Multilayer Ceramic Resonator, Japanese Journal of Applied Physics 31 (9S), 3160 (1992). DOI: 10.1143/jjap.31.3160, https://doi.org/10.1143/jjap.31.3160
2. R. N. Patel, Microwave conductivity of thick-film conductors, Electronics Letters 6 (15), 455-456 (1970). DOI: 10.1049/el:19700320, https://doi.org/10.1049/el:19700320
3. S. Vasudevan, A. Shaikh, Microwave characterization of low temperature cofired ceramic system, in Proceedings of the 3rd International Symposium on Advanced Packaging Materials (ISAPM), 152-157 (1997). DOI: 10.1109/isapm.1997.581282, https://doi.org/10.1109/isapm.1997.581282
4. M. Ishitobi, E. Ajioka, T. Abe, H. Ninomiya, The improvement of miniaturized multilayer ceramic band-pass filter, 1999 IEEE MTT-S International Microwave Symposium Digest (Cat. No. 99CH36282), vol. 3, 1343-1346 (1999). DOI: 10.1109/mwsym.1999.779636, https://doi.org/10.1109/mwsym.1999.779636
5. Di Zhou, Hong Wang, Xi Yao, Li-Xia Pang, Microwave Dielectric Properties of Low Temperature Firing Bi2Mo2O9 Ceramic, Journal of the American Ceramic Society 91 (10), 3419-3422 (2008). DOI: 10.1111/j.1551-2916.2008.02596.x, https://doi.org/10.1111/j.1551-2916.2008.02596.x
6. Xiaoming Chen, EM Modeling of Microstrip Conductor Losses Including Surface Roughness Effect, IEEE Microwave and Wireless Components Letters 17 (2), 94-96 (2007). DOI: 10.1109/lmwc.2006.890326, https://doi.org/10.1109/lmwc.2006.890326
7. Xi-Cheng Zhu, Wei Hong, Pan-Pan Zhang, Zhang-Cheng Hao, Hong-Jun Tang, Ke Gong, Ji-Xin Chen, Ke Wu, Extraction of Dielectric and Rough Conductor Loss of Printed Circuit Board Using Differential Method at Microwave Frequencies, IEEE Transactions on Microwave Theory and Techniques 63 (2), 494-503 (2015). DOI: 10.1109/tmtt.2014.2377045, https://doi.org/10.1109/tmtt.2014.2377045
8. Huating Tu, Jiyong Hu, Xin Ding, Measurement of the Conductivity of Screen Printing Films at Microwave Frequency Employing Resonant Method, Journal of Electronic Materials 50, 521-527 (2021; published online 12 November 2020). DOI: 10.1007/s11664-020-08594-w, https://doi.org/10.1007/s11664-020-08594-w
9. Zhuofeng Liu, Wenxue Liang, Wei Li, Yan Xun, Fenglin Wang, Weijun Zhang, Effects of silver paste glass additive composition on co-firing behavior of silver conductor LTCC package, 2023 24th International Conference on Electronic Packaging Technology (ICEPT) (2023). DOI: 10.1109/icept59018.2023.10492305, https://doi.org/10.1109/icept59018.2023.10492305
10. Wen-His Lee, H. Chen, C. W. Tang, C. Y. Su, R. Lei, High performance packaging with multilayer ceramic antenna switch module for wireless communication, Proceedings of the 4th International Symposium on Electronic Materials and Packaging (EMAP 2002), Kaohsiung, Taiwan, 403-408 (2002). DOI: 10.1109/emap.2002.1188873, https://doi.org/10.1109/emap.2002.1188873