Near-Zero Thermal Expansion Through Hybrid Ceramic Fillers

Thermal expansion of dielectric substrates is a major materials concern in electronic packaging, especially in dense multilayer architectures where thermal cycling can create mismatch stresses between the substrate and silicon chip while dielectric performance must be retained. Bismaleimide–triazine resin is well suited to this setting because the cured network combines attributes associated with cyanate ester and bismaleimide chemistry, including thermal stability, limited water absorption, and useful dielectric properties. When reinforced with glass-fiber cloth, however, the resulting composite still has a coefficient of thermal expansion substantially higher than that of silicon. Reducing this mismatch is not a matter of lowering the expansion coefficient of the polymer phase alone. The composite contains a resin network, woven glass reinforcement, ceramic inclusions, and a set of interfaces whose mechanical and thermal responses are coupled. Silica improves dimensional stability through its low positive thermal expansion coefficient, whereas negative-thermal-expansion ceramics can more directly offset expansion of the polymeric matrix. Negative-thermal-expansion ceramics offer a more direct route to suppressing matrix expansion, but their use introduces another practical consideration: fillers with strong negative thermal expansion may be costly to prepare and difficult to incorporate economically at high loading.

In a recently published research paper in Polymer Composites Dr. Zikang Zhou and Professor Fei Liang from Huazhong University of Science and Technology working together with Dr. Yuyao Zeng, Professor Chuntian Yang and Professor Zhongxin Wu from Wenzhou Institute of Industry & Science developed BT resin/glass-fiber composite substrates modified with mixed silica and zirconium tungsten phosphate ceramic fillers. Their distinct contribution was the use of a 3:7 silica-to-zirconium-tungsten-phosphate ratio to create a hybrid filler with an effective thermal expansion coefficient close to zero. They also developed an improved calculation route that combines the Turner model for the mixed filler with the Schapery model for the final composite. This approach linked hybrid-filler composition, bulk modulus, and composite thermal expansion in a single predictive procedure.

The researchers first optimized the BT resin matrix before they introduce ceramic fillers. They also varied the bismaleimide-to-cyanate-ester ratio which showed that a higher bismaleimide fraction generally increased both dielectric constant and dielectric loss. A balanced resin composition was therefore selected for subsequent modification, while its thermal expansion remained high enough to require filler-based control.

They also examined 2,2′-diallylbisphenol A as a modifier of the BT resin/glass-fiber system. Microscopy showed progressively better encapsulation of the glass-fiber cloth as its content increased. Dielectric performance, however, followed a non-monotonic trend: moderate addition reduced dielectric loss, whereas excessive addition promoted pore formation and stronger interfacial polarization. The selected formulation therefore provided good resin–fiber compatibility without introducing the dielectric penalties associated with excessive modifier content.

The authors subsequently incorporated individually Silica and zirconium tungsten phosphate as mixed fillers and found that each single filler lowered the coefficient of thermal expansion as its content increased, with zirconium tungsten phosphate producing a larger reduction because of its negative thermal expansion behavior. The hybrid fillers followed a different trend. As the silica fraction increased, the composite expansion coefficient first declined and then rose. The lowest value occurred at a silica-to-zirconium tungsten phosphate ratio of 3:7, where the mixed filler approached a near-zero thermal expansion response and reduced the BT resin/glass-fiber composite to 4.3 ppm/°C.

The team performed microscopy and found that the resin, glass fiber, silica, and zirconium tungsten phosphate were closely bonded, while the differing particle sizes of the two ceramic fillers allowed smaller particles to occupy spaces between larger ones. The mixed filler therefore contributed through more than the algebraic combination of positive and negative thermal expansion. Its particle-scale arrangement plausibly reduced voids and microstructural defects that could otherwise contribute to positive expansion. They also conducted thermomechanical modeling to clarify why the 3:7 mixture behaved differently from either single filler and found that for silica-filled composites, the rule of mixtures and Schapery model tracked the experimental values reasonably well, while the Turner model underestimated them. For zirconium tungsten phosphate-filled composites, the Turner model was closest to experiment, reflecting the importance of the negative-expansion filler’s relatively low bulk modulus. Neither the conventional rule of mixtures nor the Turner model adequately described the mixed-filler composites. The researchers therefore calculated the hybrid filler’s effective thermal expansion using the Turner approach and inserted that value into an adapted Schapery calculation for the BT resin/glass-fiber composite. This improved procedure yielded values close to experiment.

The mixed filler approached a near-zero calculated thermal expansion coefficient at a silica-to-zirconium-tungsten-phosphate ratio of 3:7, a condition the authors termed the zero-value effect. Across the filler contents examined, this mixture consistently reduced composite thermal expansion more effectively than either silica or zirconium tungsten phosphate alone. Dielectric measurements added an important second dimension: the mixed-filler composites retained an adjustable dielectric constant and low dielectric loss. For chip-packaging substrates, the significance of the new formulation is not only lowering thermal expansion and shows that a hybrid ceramic filler can be designed to balance the expansion response of the resin-based composite and in the same time preserve dielectric characteristics appropriate for substrate applications. The result is relevant to multilayer structures, where dimensional stability must be considered alongside the compatibility of the resin, glass-fiber reinforcement, and ceramic phases.

The practical value of the silica–zirconium tungsten phosphate combination comes from its ability to reduce thermal expansion without relying entirely on a negative-thermal-expansion ceramic. Zirconium tungsten phosphate contributed the negative expansion needed to counteract the BT resin matrix, while silica adjusted the effective filler response and introduced a lower-cost component into the formulation. The 3:7 silica-to-zirconium tungsten phosphate mixture produced the lowest measured composite CTE because the hybrid filler approached a near-zero expansion condition. This creates a useful formulation principle for substrate engineers: the objective need not be to maximize the negative-expansion filler content, but to select a hybrid composition that balances filler expansion, stiffness, particle packing, and matrix constraint. The measured dielectric behavior also supports use in high-frequency substrate design. The mixed-filler composites retained an adjustable dielectric constant together with low dielectric loss, allowing thermal expansion and dielectric performance to be tuned together rather than treated as separate material targets. Close bonding among the BT resin, glass cloth, and ceramic phases is also relevant to fabrication, since a well-integrated microstructure helps preserve continuity across the composite and avoids obvious interfacial separation. Beyond the particular BT resin system examined, the calculation approach offers a useful engineering method for hybrid-filler composites. By first estimating the thermal expansion of the mixed ceramic phase with the Turner model and then incorporating that effective phase into an improved Schapery calculation, the researchers provided a route for predicting multiphase composite behavior where standard two-phase models are insufficient. This can help guide filler-ratio selection before extensive formulation trials. For electronic substrate development, the study therefore connects thermal-expansion matching, dielectric adjustment, filler economics, and model-based materials design within one experimentally supported composite strategy.