## 6 Simulation and Results  
### On-Chip Antenna Simulation inside a Chip Package  
In the simulation, all the cores (A, B, C, D, E, F, G, H, I) have the same configuration of a zigzag and dipole antenna. However, only cores A, B, C, E, and I were selected because they represent the expected worst-care scenario.  
The zigzag and dipole antenna is optimized to have a reflection coefficient (\(S_{11}\)) of less than 10 dB at 462.5 GHz and 446 GHz, respectively, as illustrated in Figure 5. All the transmissions at the 462.5 GHz (for zigzag antenna) and 446 GHz (for dipole antenna) frequency bands in this paper are measured with respect to Antenna A.  
From Figure 7, we can see that the transmission coefficients in the case of a zigzag antenna at 462.5 GHz, the \(|S_{21}|\) between Antenna A and Antenna I, and that between Antenna A and Antenna C are \(-33\) dB and \(-41\) dB, respectively, which highlight that the transmission gets reflected more from the enclosed surface of the chip in the case of Antenna I.  
A similar case can be observed from Figure 8, from which we can see that the transmission coefficient in the case of a dipole antenna at 446 GHz, the \(|S_{21}|\) between Antenna A and Antenna I, and that between Antenna A and Antenna C are \(-28.26\) dB and \(-28.98\) dB, respectively, which are quite similar. Despite Antenna I being farther away, this indicates that the waves get more reflected from the structure of the chip in the case of Antenna I.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Thickness (mm)** & **Material/Properties** \\ \hline Heat sink & 0.5 & Aluminum \\ \hline Heat spreader & 0.25 & Aluminum nitride (AIN) (\(\epsilon_{r}=8.6\), \(tan\delta=0.0003\)) \\ \hline Polyimide & 0.5 & \(\epsilon_{r}=3.5\), \(tan\delta=0.008\) \\ \hline Silicon & 0.5 & \(\epsilon_{r}=11.9\), \(tan\delta=0.2\) \\ \hline Interconnect & 0.013 & Copper \\ \hline Ceramic carrier & 0.5 & Alumina (\(\epsilon_{r}=9.4\), \(tan\delta=0.006\)) \\ \hline Solder balls & 0.32 & Perfectly electric conductor \\ \hline Dipole and zigzag antenna & - & Copper \\ \hline \hline \end{tabular}
\end{table}
Table 1: Materials and their properties of layers inside a chip package.  
Furthermore, this observation is verified by the electric field distribution across the surface of the chip as shown in Figures 9 and 10 for zigzag and dipole antennas, respectively. The cross-sectional view for both antennas shows that there is a high density of e-field plots on the surface of the chip where the antenna is excited and the low-intensity waves become more important to other cores. In this case of intra-chip communication, the mode of propagation is the surface waves as confirmed in [48]. As can be seen from Figures 9 and 10, the E-field distribution of the dipole antennas is more distorted than that of the zigzag antenna. Therefore, when designing on-chip antennas for the intra-chip communication among the cores in a multi-core processor, it is important to consider the analysis of the field distribution. In addition, if the directional or phased array antenna were used for the communication, there might be diffraction causing beams to distort due to the small components inside a chip that ultimately reduces the gain.  
Figure 8: Transmission coefficient for dipole antennas with Antenna A as the transmitter.  
Figure 7: Transmission coefficient for zigzag antennas with Antenna A as the transmitter.  
Here, the field distribution differs at different frequencies because each antenna resonates at a distinct frequency with a maximum reflection coefficient.