# THz Rectennas and Their Design Rules
## 6 Thermal Effect
### Seebeck Effect  
A recent trend in research considers another thermal effect that occurs between two different conductors, whereas the difference can either be in the nature of the conductor or even in their geometric shape as will be shown afterwards. This effect is referred to as the Seebeck effect, which has been stated by [PERSON] [98] as follows: \"It is manifest as an electromotive force (EMF) or voltage \(V\) which appears when the junction between two dissimilar conductors (A and B) is heated.\" In its simplest form, it may be represented by (26) as shown below. \[\
abla V=-S_{AB}\
abla T, \tag{26}\]  
where \(\
abla T\) represents the temperature gradient in the studied conductor, \(S_{AB}\) is the Seebeck coefficient difference between Conductors A and B and \(\
abla V\) is the resulting potential difference gradient. While the Seebeck effect was first introduced for junctions between different conductors, subsequent literature [99] experimentally shows that the Seebeck effect is dimension-dependent even for the same conductor. This fact has been deployed to obtain the Seebeck effect by fabricating thermocouples of the same conductor and introducing a discontinuity in the connection cross-section of the conductor [84]. Figure 11 represents the fabricated thermocouple rectenna with the metal junction discontinuity. However, the results of several experiments that have been conducted to find the Seebeck coefficient value based on measurements have led to contradicting results [27], which is a key challenge to reach an accurate model to calculate the efficiency of this type of thermocouple rectenna. Therefore, it is expected to have the Seebeck effect for junctions between different conductors or even the same conductor. Here, disregarding the thermionic current component, an important question arises. That is: Is the output of the diodes used in rectennas attributed to the thermocouple effect or the charge particle transition mechanics demonstrated in earlier sections? In fact, experiments' output might be considered helpful to answer this question. The output of the experiment conducted by [PERSON] et al. [96] addresses this issue such that the \(I(V)\) characteristics of the fabricated diode could refer to the actual theory of operation. The fabrication process resulted in operating antennas (meaning having the expected output response) and defect antennas. In their experiment, they differentiate between them based on their \(I(V)\) response. Through their work, they found out that the rectenna systems that showed the expected antenna response, where the rectenna output is polarization-dependent as a result of tunneling, had a relatively small resistance value in the order of kilo ohms. On the other hand, the rectennas that did not express a polarization-dependent response had a very high resistance values in the order of mega ohms. According to them, this can be attributed  
Figure 11: Fabricated thermocouple with a metal junction discontinuity (Reproduced with permission from [84], IEEE, 2015). to the \"resistive paths\" formed through the insulator layer instead of having a tunneling behavior. This might suggest that a Seebeck effect is formed through these resistive paths in a similar fashion to that described by [PERSON] et al. [84]. The high resistance property is also supported by the experiment of [PERSON] et al. [100] (This contradicts the low resistance requirement for tunneling-based diodes. For this reason, we have not discussed the dimensioning aspect. Instead, we focused on the ruling theories for these devices, which are critical to be identified before any dimensioning discussion is attempted.). There is a fine line between the polarization-dependent response of the antenna and the theory of operation. In other words, the previous description does not suggest that the Seebeck effect devices are polarization independent. The Seebeck thermal response might be due to the flowing current into the antenna or as a bolometric outcome when the substrate is heated by the incident light.