## 4 Electromagnetic Field Intensity Distribution
Change in 'X' changes the magnitude of the magnetic field distribution significantly, as expected, especially when the distance between them is very small. The distribution pattern remains the same, as all the operational conditions are identical. Figure 11 shows that the maximum magnetic field strength for 2D-3D-IC at the surface is \(7.44\times 10^{5}\) A/m, where the red line represents the maximum magnetic field strength for single IC at the surface, which is \(1.07\times 10^{5}\) A/m. We are seeing more than double in the maximum magnetic field strength with an additional die. This value decreases rapidly as we increase the dies' separation, but it is always more than \(1.07\times 10^{5}\) A/m, showing the significant effect of EMI from one die to another in a stack. The EMI increases up to seven times when two dies stack up. Figure 9: Hypothetical 3D-IC layout in HFSS: (**a**) two layers in stack of 3D-IC (2D-3D-IC) and (**b**) three layers in stack of 3D-IC (3D-3D-IC). Figure 11: Maximum magnetic field strength versus the distance between the layers of 2D-3D-IC at 3 GHz operating frequency. Figure 10: Maximum magnetic field strength at the surface of top IC with different vertical separation between the dies in a stack of 3D-IC with two layers. The vertical separation is as follows: (**a**) 0 \(\upmu\)m, (**b**) 50 \(\upmu\)m, and (**c**) 300 \(\upmu\)m, respectively, and the operating frequency is 3 GHz. Figure 12 shows the difference in the maximum magnetic field for 2D-3D-IC and 3D-3D-IC, where the black line represents the maximum magnetic field strength for single IC at the surface, which is \(1.07\times 10^{5}\) A/m. The maximum magnetic field strength for 3D-3 DIC structure obtained is \(4.28\times 10^{6}\) A/m. Although this maximum value decreases as we increase the dies' separation, it will always be greater than \(7.44\times 10^{5}\) A/m, which is maximum magnetic field strength of the 2D-3D-IC structure. In other words, the more dies are stacked up, the higher will be the maximum magnetic field strength. Hence, it could be possible that each die in a stack may not have high EME, and the stacked structure could have very high EME that renders circuit malfunction. Figure 13 shows the maximum magnetic field strength on the top surface of each die in the 3D-3D-IC stack, and one can see that the maximum field strength occurs at the top surface of the middle die. This is expected as it is placed in the middle of the two dies and it gets the emissions from the top and bottom dies. With the decrease of 'X' in 3D-ICs, an increase in the EMI can be expected. Tradeoff is thus required to keep the emissions and distance in check, and it requires careful evaluation, which is demonstrated in this work. For the example used in this work, the optimum distance between stack of dies should be around 50 \(\upmu\)m for 2D-3D-IC, while this value increases to 105 \(\upmu\)m for 3D-3D-IC, shown by green lines in Figures 11 and 13, respectively. These values are considered because further increase in 'X' does not result in a significant reduction in the magnetic field. If the lowest EMI is needed, then 'X' should be even more, but there is a limit on the minimum magnetic field achievable, which is higher with a higher number of stacked dies. Figure 12: Maximum magnetic field strength versus the distance between the reference plane and topmost layer of 3D-IC at 3 GHz operating frequency. The lowest EMI in 3D-IC structure is always higher than the single IC, as can be seen in Figures 12 and 13, and thus reduction of EMI from a 3D-IC architecture is critical.