## 3 Simulation Methodology  
Recently, [PERSON] et al. [34] developed a method to \"fabricate\" an IC from its GDSII file in a computer under ANSYS environment. Once the IC is fabricated, the ANSYS high frequency structure simulator (HFSS) is employed to compute the EM field distribution over the surface of the chip. ANSYS HFSS has a limitation that it cannot simulate transistors. To overcome the limitation of ANSYS HFSS, transistors are removed from the layout and respective voltages and currents as obtained from circuit simulator are inputted at respective circuit nodes for the proper functionality of the IC. With such replacements, our circuit can be completed, and the currents thus computed will be accurate. In this work, the values of these voltages and currents are obtained from the advanced design systems (ADSs) file of the circuit during the circuit simulation in the post layout phase. Figure 3 shows the flow chart of the method as also reported in the work of [28] for clarity, and Figure 4 shows the \"fabricated\" IC in the ANSYS environment. With this method, the magnetic field distribution of the IC can be obtained at different frequencies (2, 3, and 4 GHz). The method is verified with experimental results, as shown in the work of [34]. In Figure 4a, black circles represent input ports, while Pin is another input port used in simulation in HFSS. The following equations are used in determining the electromagnetic distribution as given below [35]:  
\[\
abla\times(\frac{1}{\mu_{r}}\
abla\times E(x,y,z))-k_{0}^{2}\varepsilon_{r }E(x,y,z)=0\;, \tag{1}\]  
\[H=\frac{\
abla\times E}{-j\omega\mu}\;, \tag{2}\]  
\[\
abla\times(\frac{1}{\mu_{r}}\
abla\times E(x,y,z))-(k_{0}^{2}\varepsilon_{ r}-jk_{0}Z_{0}\sigma)E(x,y,z)=0, \tag{3}\]  
\[E(x,y,z)=\int\limits_{S}{(j\omega\mu_{0}H_{\text{tan}}G+E_{\text{tan}}\times \
abla G+E_{normal}\
abla G)dS}, \tag{4}\]  
where  
Figure 2: Image of power amplifier IC at 1600\(\times\) magnification captured (using Leica S8 APO equipment). \(E(x,y,z)\) is a phasor representing an oscillating electric field;  
\(k_{0}\) is the free space wave number;  
\(\omega\sqrt{\mu_{0}\varepsilon_{0}}\), where \(\omega\) is the angular frequency, which is \(2\pi f\);  
\(\mu_{r}\) is the complex relative permeability;  
\(\varepsilon_{r}\) is the complex relative permittivity;  
\(S\) represents the radiation boundary surfaces;  
\(j\) is the imaginary unit (\(\sqrt{-1}\));  
\(\varepsilon_{0}\) is the relative permeability of the free space;  
\(H_{tan}\) is the component of the magnetic field that is tangential to the surface;  
\(E_{normal}\) is the component of the electric field that is normal to the surface;  
\(E_{tan}\) is the component of the electric field that is tangential to the surface;  
\(G\) is the free space Green's function;  
\(J\) is the current density. Equations (1)-(3) are employed in the finite element method (FEM). FEM solves for the three-dimensional electromagnetic field, taking \(x\), \(y\), and \(z\) directions in consideration, and solves for the volume distribution using the curl function. As we are dealing with 3D IC, FEM in ANSYS HFSS will be most appropriate for the determination of EM distribution. Figure 3: Flow chart of the methodology followed for simulation [28]. ADS, advanced design system; HFSS, high frequency structure simulator. To perform electromagnetic field calculation, FEM is necessary. This necessity can be seen by comparing the magnetic field simulation using HFSS (which utilizes FEM) and SIwave (which uses method of moments (MOM)). Figure 5a shows the test structure used for magnetic field simulation and Figure 5b shows the results. One can see a significant difference in the amplitude and distribution of the magnetic field. The difference in the amplitude and distribution of the magnetic field is due to the fact that the magnetic field is not uniform in the direction of the magnetic field.