# THz Rectennas and Their Design Rules
## 5 Power Level
### Signal Amplitude  
Studies that address the efficient operation region of diodes for rectification are not new and may be dated back to the studies of [PERSON] and [PERSON] [80] where it was assumed to use a polynomial equation to describe the \(I(V)\) relationship. The assumption of this nonlinear relationship leads to self-consistent equation forms in the simplest case. The recent development in the studies of rectenna diodes yields much more complicated relationships between voltage and current such as exponential, root power and nonlocal functions, just to name a few. While the nonlinearity behavior is considered of major importance, several recent papers overlook its importance and just focus on proving the nonlinearity under DC conditions. It is, therefore, necessary to deploy nonlinear solution schemes for circuits such as linearization [81] and harmonic balance [82]. An important feature of nonlinear systems is that any slight change in the working conditions can lead to unpredicted output, out of the operating range solution or even instability. Therefore, knowing the type of application the rectenna is assigned to and having a good estimate of the expected input power level are of extreme importance. Based on the field of application and the expected operation power level, rectenna systems where the name rectenna is used interchangeably for both categories may be divided into:  
Figure 9: Available and rectified power levels for an MIM diode and a graphene Schottky junction diode. The colored graphs are for the MIM diode and the grey curves for the graphene Schottky junction case (Reproduced with permission from [79], AIP Publishing, 2016). * **Detectors:** where it is important that the detector behavior is linear at least in the working range. It is worth noting that most of the recent work is dedicated to the use of the diodes as detectors [45; 72; 83; 84]. * **Rectifiers:** where it is of a major importance to express a good level of nonlinearity within the working range to increase the rectification efficiency for the harvested energy. In order to quantitatively characterize the diodes as efficient rectifiers, [PERSON] et al. [19] reinforced what has been set by [50; 85; 86] as the criteria that a diode should satisfy to be considered a rectifier. The rectifier figures of merit are asymmetry \(f_{asym}(V)\), nonlinearity \(f_{NL}(V)\) and responsivity \(f_{RES}(V)\). They can be calculated using (21)-(23), respectively. In these equations, the current is represented as a function of voltage \(I(V)\); forward and reverse current values for the same voltage absolute value are \(I_{F}(V)\) and \(I_{R}(V)\), respectively. The minimum figures of merit values required are shown next to the respective equations. Having said that, it should be noted that these devices are, after all, nonlinear where it is better to be approached subjectively. This means that these ruling figures are just for guidance, and each device design would have its own characteristics. \[f_{asym}(V) =\left|\frac{I_{F}(V)}{I_{R}(V)}\right| f_{asym}(V)>1,\] (21) \[f_{NL}(V) =\frac{dI(V)}{dV}\bigg{/}\frac{I(V)}{V} f_{NL}(V)>3,\] (22) \[f_{RES}(V) =\frac{d^{2}I(V)}{dV^{2}}\bigg{/}\frac{dI(V)}{dV} f_{RES}(V)>7V^{-1},\] (23)  
Having a good estimate of the power level is not only good to predict a stable mathematical solution, but also for physical stability!During the fabrication of the prototype, [PERSON] used in his work the geometric diode [72]; the prototype underwent what is referred to as \"electromigration\", which can tear down the structure under voltages as low as 0.1 V.  
Another important aspect regarding the power level is engineering the rectenna structure physically and geometrically (i.e., in terms of the good choice of material, doping concentration and the dimensions) in order to maximize the efficiency. To achieve this goal, it has been suggested to introduce asymmetry into the diode structure.