## 2 Experimental Method  
The Cu-solder-resin composite was a paste containing Cu particles, Sn-3 Ag-0.5 Cu (SAC305) solder particles, and polyimide (PI) thermosetting resin. The melting point of the solder was 220 \({}^{\circ}\)C. The cure temperature of the PI resin was 230-240 \({}^{\circ}\)C. The size of the Cu particles and solder particles were approximately 10 and 3 \(\upmu\)m, respectively. The content of the copper in wt.% was approximately three times higher than that of the solder, which facilitated the consumption of the solder through the formation of Cu-Sn IMCs. The PI resin was chosen by considering the curing temperature close to the melting point of the solder and soft mechanical properties, with a yield strength of approximately 1 MPa. This enabled the easy deformation of the resin when it was embedded in the microstructure of Cu and IMCs. The decomposition temperature of the polyimide was greater than 400 \({}^{\circ}\)C. SiC chips were bonded to direct bonded copper (DBC) substrates using the Cu-solder-resin composite. The chips had approximate dimensions of \(8\times 8\times 0.3\) mm and a Ni/Au surface metallization. The DBC substrates were composed of two 0.3-mm-thick copper electrodes bonded to a 0.6-mm-thick silicon nitride (Si\({}_{3}\)N\({}_{4}\)) substrate. The joints were bonded at 250 \({}^{\circ}\)C for 1 min after preheating at 100 \({}^{\circ}\)C for 60 min using the pressureless reflow process in a nitrogen atmosphere. A unique skeleton-shaped Cu-IMC-resin microstructure was generated by heating the resin composite up to the reflow temperature. Further details about the process, materials, and geometries can be found in our previous report [33].  
The SiC-DBC joint was molded by cross-sectioning resin. The serial cross-sectional images of the bonding layer were then obtained by focused-ion-beam scanning electron microscopy (FIB-SEM; NX2000, Hitachi High-Technologies Corporation, Tokyo, Japan) to investigate the three-dimensional (3D) microstructure. The approximate central region of the bonding layer was visualized, where the size of the field of view (FOV) and pitch of the cross-sectional slices were \(50\times 50\)\(\upmu\)m and \(0.5\)\(\upmu\)m, respectively. We obtained 100 cross-sectional images, which were used for 3D reconstruction of the microstructure by FE modeling as described in the next section.  
The SiC-DBC joints were subjected to thermal cycling tests using a thermal cycling chamber (TSA-73 EH, ESPEC Corporation, Osaka, Japan) in the temperature range from -55 to 175 \({}^{\circ}\)C with a dwell time of 15 min at both minimum and maximum temperatures. Similar tests were performed on the SiC-DBC joints bonded by a commercial SAC305 solder paste for comparison. Six joints of each type were tested. Non-destructive observations of the die-attached layers were performed every 300 thermal cycles using scanning acoustic tomography (SAT; FineSAT III, Hitachi Power Solutions Co. Ltd., Ibaraki, Japan). The resolution of the SAT was \(0.1\) mm \(\times\) 0.1 mm. The ratio of unbonded areas was obtained by binarizing the SAT images using an image editing software. After thermal cycling tests, a representative joint was selected from the six joints, and cross-sections along the diagonal axis of the joints were visualized by field-emission scanning electron microscopy (FE-SEM; SU8000, Hitachi High-Technologies Corporation).