# Silver Sintering for Silicon Carbide Die Attach: Process Optimization and Structural Modeling
## 2 Materials and Methods
### Elastoplastic Characterization of Silver Sintering  
In order to evaluate the temperature softening effect on nominally bulk sintering material, tests on dogbone samples are carried out at five different temperature: \(-\)65, 25, 100, 150 and 200 \({}^{\circ}\)C. The considered specimen is shown in Figure 2a. The sample width is 2 mm while the length of the narrow part is 8 mm. Sample thickness is 0.5 mm. Specimens are formed sintering silver foils applying a pressure of 20 MPa and a temperature of 250 \({}^{\circ}\)C for 90 s. Then, dogbone samples are cut by die pressing. Sample porosity is quantified by the software recognition method mentioned in Section 2.2. The void measurement result is reported in Figure 2b, resulting in a porosity of 3% that is reasonably close to a sample free of voids. For each thermal condition, four identical samples are tested and the average behavior is reported. Stress and strain data are obtained in displacement control, with a strain rate of 0.00151/s.  
Loads and length are transformed in engineering and true strain/stress values by Equations (1) and (2):  
\[\varepsilon_{true} =\ln\left(1+\varepsilon_{eng}\right) \tag{1}\] \[\sigma_{true} =\sigma_{eng}(1+\varepsilon_{eng}) \tag{2}\]  
in which \(F(t)\) is the measured force by the load cell at time \(t\), \(A_{0}\) and \(l_{0}\) are, respectively, the cross-section and the gauge length of the unloaded sample and \(l(t)\) is the gauge length. True stress and strain consider the real cross-section reduction that occurs during the tensile test, while engineering values do not consider this. Moreover, the Young modulus is measured at a different temperature using the classic method based on strain gauge [22]. For each temperature, five samples are characterized.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Task** & **Equipment** & **Supplier** \\ \hline Sintering & Sinterstar Innovate & Boschmann \\ SAM & Echo LS & Sonix \\ SEM & Neon 40 & Zeiss \\ Electric measurement & 4324-KT & Tesec \\ \hline \hline \end{tabular}
\end{table}
Table 1: Considered equipment for experimentsThere is the need to implement a numerical methodology to extract silver sintering mechanical properties related to sintered layer porosity. Silver unit cells are generated by computer-aided design (CAD) software to reproduce the different arrangements of micrometric Ag-spheres according to the SEM morphological analysis depicted in Figure 3 that refers to package cross-section with a sintering layer and interface. The created silver cells with different a void fraction (8 and 20%) are reported in Figure 4.  
The elastic-plastic properties are from finite element analysis (FEA) considering these cell models. The silver material is assumed to behave as the experimentally characterized  
Figure 4: Cell models of sintering grain reproducing the micro-mechanical structure for two porosity values: 8% (a) and 20% (b).  
Figure 3: SEM picture of an FIB cut showing the morphological details of the sintering layer’s microstructural texture.  
Figure 2: Utilized sample for the tensile test: (a) and void measurement in section A–A (b).  
elastoplastic curve, then a kind of tensile test is simulated to fix the bottom side of the cell and moving upward the top side. The elastoplastic curve is obtained, subdividing the reaction force on the fixed constraint with the imposed displacement on the cell top side.