## 4 Electromagnetic Field Intensity Distribution  
Figure 7 shows the magnetic field strength of the device under test plotted at various vertical distances and operating frequencies from the surface of the IC. The maximum magnetic field strength of \(1.07\times 10^{5}\) A/m, at 3 GHz operating frequency, is present at the top surface of the IC, and it decreases to \(4.60\times 10^{4}\) A/m drastically within a very small change in distance (around 1 \(\upmu\)m) from the surface of the IC. At 40 \(\upmu\)m vertically from the surface of the IC, the maximum magnetic field strength is reduced to approximately \(10^{3}\) A/m, and it is reduced to around \(10^{2}\) A/m at 140 \(\upmu\)m above the surface. This is expected as the magnetic field is inversely proportional to square of the distance according to inverse square law [27]. Therefore, with the current commercial near field measurement at 200 \(\upmu\)m from the surface, the severity of EMI from an IC can be underestimated, but this can be unimportant as the EMI strength decreases rapidly outside the package. However, such EMI can affect the nearby circuits within a chip and has yet been overlooked. Either these nearby circuits can be on the same die, or they can be on the stacked die, if they are close. If the strong EME source is within the stack dies instead of the topmost die, its identification will not be possible with the current near field measurement. In fact, even if the hot spot for EME is on the topmost die, its identification will be difficult, as illustrated below. Figure 6: Magnetic field distribution obtained through HFSS simulation over the gallium nitride high electron mobility transistor (GaN-HEMT) power amplifier IC at 3 GHz operating frequency. Figure 7: Maximum magnetic field strength versus vertical height of reference plane at different operating frequencies (2, 3, and 4 GHz). Figure 8a shows the magnetic field distribution at the surface of the IC, where the spot for high EME can be identified with high precision. As the observational plane moves away from the surface, the area of the hot spot disperse, and this dispersion renders it difficult to identify the actual source of EME precisely. At 50 \(\upmu\)m, several hot spots of EME appear as a result of the dispersion, and this can result in tackling the wrong parts of a circuit to reduce the EMI. Such a situation will be very likely for stacked dies in 3D. In other words, even if high EME exists on a die, localization of hot spot through electromagnetic field measurement will not be possible. Figure 8: Maximum magnetic field strength for an operating frequency of 3 GHz at different vertical heights: (**a**) 0 \(\upmu\)m (black box represents the maximum emission region), (**b**) 10 \(\upmu\)m, (**c**) 20 \(\upmu\)m, (**d**) 40 \(\upmu\)m, and (**e**) 50 \(\upmu\)m.  
In fact, the above results indicate that the vertical distance for near field (NF) scanning should be in the region from 10 to 40 \(\upmu\)m. However, below 10 \(\upmu\)m, the equipment required to perform NF measurement is not available and, beyond 40 \(\upmu\)m, the precision to find the source of EMI is low. Thus, simulation of EM field strength is necessary. In practical measurement, the probe distance is usually set at 200 \(\upmu\)m to prevent the damage to the probe during scanning. As the electromagnetic field strength decreases significantly over the distance, one can determine the minimum distance between dies separation for 3D-ICs, so that the effect of EMI from a die will have minimum effect on other dies in a stack. To investigate this minimum separation between the dies, simulation is performed on a hypothetical 3D-IC using GaN-HEMT power amplifier IC, as shown in Figure 9, with two dies (2D-3D-IC) and three dies (3D-3D-IC) aligned vertically to each other. The vertical separation between the dies (denoted as 'X') varies from 25 \(\upmu\)m to 300 \(\upmu\)m in this work. Figure 10 shows the magnetic field distributions on the surface of the topmost die as the distance between the two dies vary in 2D-3D-IC.