## 2 Materials and Methods  
There have been various methods used to model reactive multilayer foils that have been studied to enhance the understanding of the limits of their usability and functionality, but these are mainly concentrated on their operating states [27; 28; 29] as opposed to their respective performance during manufacture. Therefore, simulations targeting reactive bonding processes in microsystems and microelectronics packaging (such as [30; 31; 32; 33; 34]) are generally at an elementary stage compared to the average simulation methodology in the field. The approach used here is the CFD method, as similarly simulated in [35], where a 3-D shoebox model was created comprising various layers, namely a chip, solder, reactive multilayer, substrate and the surrounding air environment. The extent of the boundaries surrounding the model, where the domain is 20 mm \(\times\) 20 mm \(\times\) 15 mm in size, a volume which was chosen to provide sufficient displacement of the external boundaries from the main region of interest whilst maintaining a reasonably sized mesh. The respective thicknesses of the layers were 400 \(\upmu\)m for the Si chip, solder thickness of 200 \(\upmu\)m, a total reactive foil thickness of 30 \(\upmu\)m and an LTCC thickness of 570 \(\upmu\)m.  
The mesh was subdivided in a manner such that consistent mesh sizing with edge length of 10 \(\upmu\)m could be prescribed in the y direction, with a mesh edge length of 100 \(\upmu\)m in the x and z directions, as shown in Figure 5. The mesh comprised approximately 5,000,000 cells, representing a mesh significantly larger than that used in similar previous work [35]. The fixed mesh lengths of 100 and 10 \(\upmu\)m ensured that the aspect ratio of the cells was within a reasonable range (10:1, for x and z:y), albeit the aspect ratios were slightly larger in the isolation layer, for example, where 4 cells span the 35 \(\upmu\)m gap. Three temperature probes, P1-P3, approximating Pt-100 temperature sensors with silver vias, were integrated into the model inside the LTCC substrate. In Figure 6, the main dimensions of each probe in the x-z plane and the layer thicknesses are shown. Figure 4: Cross section performed with light microscope. Similarly, in Figure 7, the main dimensions in the x-y plane are illustrated for the model and the 3 temperature probes, P1-P3, are also highlighted. The sensing volume, i.e., the part for which volume-averaged temperatures were calculated, was 430 \(\upmu\)m \(\times\) 210 \(\upmu\)m \(\times\) 10 \(\upmu\)m, corresponding to a sensing volume of 0.0009 mm\({}^{3}\). These probes are displaced from the next probe by 1 mm in the x direction, with the front edge of P1 displaced by 0.3 mm from the leading edge of the reactive multilayer. The top surface is 35 \(\upmu\)m displaced below the reactive foil, meaning they are separated by the full thickness of the isolation layer. Note that there was only one element through the thickness of the Pt probes, which is not ideal, but increasing the number of cells through the thickness of the probes would have a highly detrimental effect on the aspect ratio of the cells, and therefore the stability of the model. These probes were included to help in developing the understanding of the requirements for manufacturing similar prototypes, and furthermore, to understand the interference caused by the presence of the probes themselves. Figure 5: Close-up of mesh of solid structures towards leading edge of reactive foil (Yellow = Si, Brown = Solder, Blue = reactive foil, Green = Green tape ceramics, Turquoise = Temperature probe). Figure 6: Dimensions of probes and layer thicknesses in x–z plane. It is considered to be relatively straight-forward to measure the propagation velocity of reactive foils, due to the intense luminescence of the wave front. However, temperature measurements are more complicated owing to the interference caused by the presence of the thermocouples.