# Radiofrequency Performance Analysis of Metal-Insulator-Graphene Diodes
## 3 Model-Based Performance Projection of MIG Rectifiers
### Power Detection
For high power levels, the RF tangential responsivity \(\beta_{\text{v}}\) of the power detector at the determined operation frequency was derived from the linear region of the output voltage as a function of the input power [24] as  
\[\beta_{\text{v}}=\frac{V_{\text{out}}}{P_{\text{in}}} \tag{4}\]  
To calculate the RF responsivity of the power detector, the power range from 0 mW to 4 mW was considered for several frequencies, as shown in Figure 7b. Figure 8 shows the tangential responsivity obtained in the range from 1 GHz to 6 GHz. The highest responsivity was achieved at the lowest evaluated value, i.e., 1 GHz, and then it followed a decreasing trend for higher frequencies. For frequencies above 4 GHz, \(\beta_{\text{v}}\) declined below 2.9 V/W, indicating the detector's reduced response capability beyond this frequency. The MIG-based power detector was simulated at frequencies from 1 GHz to 8 GHz for powers of \(-15\) dBm, \(-5\) dBm, and 5 dBm, as shown in Figure 9. It can be observed that the power detector showed an almost linear response from 2 to 4 GHz. The detector indeed maintained a stable dynamic range up to 4 GHz, with an approximate increase by a factor of 10 in the output voltage for every 10 dB increase in input power. The change with frequency of \(V_{\text{out}}\) beyond this value was, however, power-dependent. While the highest and lowest power values considered followed very similar trends, an abrupt drop was observed for the \(-5\) dBm curve at \(\sim\)5.5 GHz, in contrast to an apparent plateau appearing for the \(-15\) dBm and 5 dBm curves. As a consequence, the results obtained here suggest  
Figure 7: Output voltage versus input RF power at different frequencies. Plots in (**a**) semilogarithmic and (**b**) linear scale. Symbols represent experimental data [13], dashed lines are simulation results presented in [16], and solid lines are simulation results obtained in this work. that between 7 GHz and 8 GHz, similar values of \(V_{\rm out}\) were achieved for a 10 dB range of the input signal below \(-5\) dBm. To evaluate the ideal behavior of the power detector, the circuit in Figure 5 was simulated without considering the parasitic elements, and hence, only the intrinsic MIG diode was considered. The circuit was analyzed over an input power range of 0 to 20 dBm, as shown in Figure 10. The results indicate that, by removing the parasitic elements of the MIG diode, the detected output voltage increased, especially for the operation frequency at which the circuit was designed (i.e., 2.45 GHz). The RF tangential responsivities obtained without parasitic elements were 47.3 V/W and 38.7 V/W for 2.45 GHz and 1.225 GHz, respectively. Table 1 presents a comparison of the FoMs from various works reporting the performance of fabricated MIG diodes, in both DC and RF modes, and the simulation results obtained here. The highest reported tangential responsivities are 168 V/W at 2.5 GHz [25] and 43.6 V/W at 2.45 GHz [16]. Notice that, in [25], the input power was not directly measured but evaluated from \(S_{11}\), which might have led to an overestimation of \(\beta_{\rm v}\). As for DC, the highest recorded responsivity is 71 V\({}^{-1}\)[15], while the nonlinearity reaches its maximum value of 11 at 0.7 V [4]. Finally, the technology addressed in this work showed a remarkable value for asymmetry of 806.6 at 1 V.  
Figure 8: Variation in the device responsivity (markers) with frequency in the range from 1 GHz to 6 GHz. A line has been added as a guide for the eye to show the tendency, which follows an exponential fit. Figure 9: Output voltage versus frequency at different input RF power values. The asymmetry value obtained in this work for the MIG diode demonstrated in [13] is among the highest reported in the literature, reflecting the excellent rectification ability of the diode. Additionally, the nonlinearity value is among the highest documented, highlighting the device's efficiency in applications such as harmonic generators, signal mixers, and frequency multipliers.