# THz Rectennas and Their Design Rules
## 2 Historical Notes  
### Discovery of the Photovoltaic Effect  
The idea of harvesting sun or light radiation and converting it into electricity is not new, and it may be traced back in time to the nineteenth century in 1839 when [PERSON] [6] noticed the effect of illuminating silver chloride inside an acidic solution, which resulted in the generation voltage and current. From that point on, many contributions took place to optimize the system, paving the way for a more efficient prototype by Bell Labs in 1954 [7].  
The mechanism of the photovoltaic effect is relatively straightforward and has remained the same since the release of the prototype mentioned above [7]. As shown in Figure 1, a solar cell is made from a junction of p- and n-doped semiconductor material, whereas the p-type dopant pushes the Fermi level down closer to the valence band. On the other hand, the n-type dopant pushes the Fermi level closer to the conduction band above which electrons are freed from the hole bound. When a photon hits the semiconductor material and gets absorbed by an electron-hole pair (and has enough energy to free the electron from its hole pair), the electron is freed such that it moves into the conduction band (i.e., above the red line shown in Figure 1), where the electric field of the depletion region sweeps it away into the n-type side cathode. Similarly, the resulting free hole is also swept away by the same field, but into the opposite direction of the p-type side anode. The resulting effect is an electromotive force (EMF) that causes a potential difference between the anode and the cathode, which can also generate a current in a closed circuit and is represented in Figure 1 as V\({}_{\text{OC}}\) by the displacement of the Fermi level upwards in the n-type and downwards in the p-type.  
Although the mechanism is simple, a critical power efficiency limitation is imposed (throughout the rest of this paper, the power efficiency is defined as the ratio of the DC power output yield to the input AC power delivered by the impinging radiation) because the required photon energy should be exactly equal to the energy required just to free the electron-hole pair. Clearly, if less energy is provided by the photon, then the bound will not be broken. Conversely, if the power provided by the photon is more than enough to free the electron, then the excessive energy will be wasted as heat into the semiconductor material. In other words, conversion efficiency can be optimal only for a narrowband radiation whose photon energy is just equal to that required to free the electron. Otherwise, the wideband nature of the solar radiation will yield sub-optimal efficiencies below the 44% Shockley-Queisser limit [9] calculated for a 1.1 eV energy gap. In practical terms, this limitation is considered the major reason [10] as to why single junction solar cells have efficiency figures of around 20%. This frequency-dependent behavior is not only limited to p-n junction solar cells, but also affects the rectennas' behavior in modeled prototypes as will become more evident in Section 5.  
Notwithstanding all of the aforementioned facts, commercial systems are becoming more widespread, and some novel designs have managed to exceed 20% efficiency [11]. Thanks to multijunction solar cells [12], efficiencies up to 40% may be reachable. Although current commercial systems can reach up to 20% power efficiency, which is technically a poor figure, their production costs are still high with the current lowest production cost for a GaAs substrate reaching $150 for a six-inch wafer [13]. It should be pointed out, however, that other alternatives, such as perovskite, may replace the typical solar cells with reported efficiencies in excess of 20% and much less expensive production costs [14]. Nevertheless, their lifetime is much shorter than that of their typical counterparts.  
For all of the above, it might be more favorable to look for structurally different solutions that outperform the typical solar cells, preferably at a lower cost.