**7. Conversion efficiency**

The figure of merit in solar rectennas is the conversion efficiency, which depends on several factors related to both the antenna and the MIM diode. The conversion efficiency, ηt, of a solar rectenna can be described as [27].

$$
\mathfrak{n}\_{\mathsf{f}} = \mathfrak{n}\_{\mathsf{f}} \mathfrak{n}\_{\mathsf{g}} \mathfrak{n}\_{\mathsf{g}} \mathfrak{n}\_{\mathsf{c}} \tag{2}
$$

where ηr is the antenna radiation efficiency, ηs is the efficiency that related to the losses inside the antenna, ηq is the quantum efficiency that is responsible for the rectification of the received power, and ηc is the coupling efficiency between the antenna and the diode. It is worth noting that the term ηrηs in (2) depends on the antenna type and its characteristics and is referred, in this chapter, to as antenna-dependent efficiency of solar rectenna. On the other hand, the term ηqηc relates strongly to the diode parameters and is referred to as the diode-dependent efficiency.

For solar energy conversion, each efficiency factor is required to be optimized and maximized. Recent works have focused on improving only the quantum efficiency [28] or the diode-dependent efficiency by assuming a perfect antenna (i.e., do not include antenna efficiency limits) [4]. The analysis of the complete conversion efficiency in one single work gives the reader a close physical insight on how the IR solar rectenna works, including the parameters that affect its performance. In the following sections, we will investigate each term of (2) individually with a detailed description of its main parameters and how to compute them. After finding the optimum values of each efficiency term in (2), the overall conversion efficiency will then be calculated and plotted.

#### **7.1 Antenna-dependent efficiency**

As mentioned in Section 7, the antenna-dependent efficiency is represented by the term ηrηs. This section demonstrates how to find this efficiency numerically, which depends totally on antenna parameters. The calculation of antenna efficiency should take into account the losses that relates to reflection, conduction, and dielectric inside the antenna. The reflection losses will be represented by the coupling efficiency, ηc, and will be discussed in details in the following section. Thus, this section will be dedicated to the calculation of the conduction and dielectric losses inside the antenna structure. Since it is very difficult to compute and separate these losses individually, they will, therefore, be lumped together to form the conductiondielectric efficiency, cd, which can be defined as [29]. *CD* = \_

$$
\mathfrak{m}\_{CD} = \frac{R\_r}{R\_r + R\_l};
\tag{3}
$$

where *Rr* is the radiation resistance of the antenna and *Rl* represents the conduction-dielectric resistance, which can be written as [29]

$$R\_l = \mathbf{2} \frac{L}{P} \mathbf{R}\_s \text{ ; \tag{4}$$

**189**

*Solar Rectennas: Analysis and Design*

uniform current distribution.

frequencies should be calculated.

**7.2 Diode-dependent efficiency**

efficiency of solar rectennas.

coupling efficiency can be written as [5].

*DOI: http://dx.doi.org/10.5772/intechopen.89216*

*Rs* = √

Before starting the calculation of the conduction-dielectric efficiency, it is important to recall that metals are no longer perfect electric conductors at optical and infrared frequencies [30]. Consequently, the DC bulk conductivity of metal cannot be utilized in (5). Instead, the frequency-dependent conductivity at optical

The two terms of the diode-dependent efficiency are the coupling efficiency, ηc, and quantum efficiency, ηq. In this chapter, we will set *ηq = S hω*/*e*, where *S* is the MIM diode responsivity, which will be explained more explicitly later in this section, *h* is Plank's constant, and *e* is the charge of the electron. In contrast, the

*c* = 4 *Ra RD*/ (*Ra* <sup>+</sup>*RD*)<sup>2</sup> \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

where *R*a is the antenna resistance, ω is the angular frequency, *RD* is the diode resistance, and *CD* is the diode capacitance. For simplicity of analysis, the reactance of the antenna was assumed to be negligible; however, for the antenna in this work, this approximation is more realistic for the wavelength between 8 and 12 μm where a low reactance part of the impedance is noticed. The value of *RD* depends on the I-V

*CD* = \_ 0 *rA*

where *εr* represents the relative permittivity of the insulator layer of the MIM diode, *ε*0 is the free-space permittivity, *A* is the diode junction area (overlapping area), and *s* is the thickness of insulator layer. It is clearly evident that the MIM diode parameters play a significant role in determining the entire conversion

**Figure 12** shows the total conversion efficiency (solid line) for an IR solar rectenna versus the wavelength. Moreover, we have added the diode-dependent efficiency (dashed line) to the same graph to show the role that the antenna plays in shaping the conversion efficiency. The total conversion efficiency has been calculated based on the terms of (2), where every single term is calculated individually and all terms are then combined together. The main reason behind this low efficiency is the mismatch between the resistance of the designed MIM diode, *RD*, and the antenna resistance, *Ra*. This mismatch led to a lower coupling efficiency in (6), where one of the conditions to achieve unity efficiency is to have Rd = Ra. Although the diode characteristics have been optimized, the coupling efficiency still needs further improvement. However, this value of efficiency demonstrates an

enhancement to recently reported conversion efficiencies of (ηt ~ 10<sup>−</sup><sup>9</sup>

[31]. It is worth mentioning that the antenna efficiency is very high and the diode responsivity is acceptable; however, the total conversion efficiency is quite low due to the poor coupling efficiency between the antenna and the diode. Recent studies are paying attention and efforts to increase coupling efficiency. Once the coupling is improved, we would expect a high conversion efficiency, which makes solar

\_ *Ra RD Ra* + *RD*

 ) *CD*) 2

1 + ((

characteristics of the MIM diode, whereas the *CD* can be given by

\_ \_ <sup>0</sup>

where ω is the angular frequency, μ0 is the free-space permeability, and σ is the metal conductivity. It is worth mentioning here that Eq. (4) is valid for the case of a

<sup>2</sup> ; (5)

; (6)

*<sup>s</sup>* ; (7)

–ηt ~ 10<sup>−</sup>12)

where *L* is the antenna length, *P* is the cross-section perimeter of the wire antenna of radius a, and Rs is the conductor surface resistance that can be calculated as follows

*Solar Rectennas: Analysis and Design DOI: http://dx.doi.org/10.5772/intechopen.89216*

*Recent Wireless Power Transfer Technologies*

**7. Conversion efficiency**

perfect electric conductor. In contrast, the relatively low conductivity of gold yield

The figure of merit in solar rectennas is the conversion efficiency, which depends on several factors related to both the antenna and the MIM diode. The

where ηr is the antenna radiation efficiency, ηs is the efficiency that related to the losses inside the antenna, ηq is the quantum efficiency that is responsible for the rectification of the received power, and ηc is the coupling efficiency between the antenna and the diode. It is worth noting that the term ηrηs in (2) depends on the antenna type and its characteristics and is referred, in this chapter, to as antenna-dependent efficiency of solar rectenna. On the other hand, the term ηqηc relates strongly to the diode param-

For solar energy conversion, each efficiency factor is required to be optimized and maximized. Recent works have focused on improving only the quantum efficiency [28] or the diode-dependent efficiency by assuming a perfect antenna (i.e., do not include antenna efficiency limits) [4]. The analysis of the complete conversion efficiency in one single work gives the reader a close physical insight on how the IR solar rectenna works, including the parameters that affect its performance. In the following sections, we will investigate each term of (2) individually with a detailed description of its main parameters and how to compute them. After finding the optimum values of each efficiency term in (2), the overall conversion efficiency

As mentioned in Section 7, the antenna-dependent efficiency is represented by the term ηrηs. This section demonstrates how to find this efficiency numerically, which depends totally on antenna parameters. The calculation of antenna efficiency should take into account the losses that relates to reflection, conduction, and dielectric inside the antenna. The reflection losses will be represented by the coupling efficiency, ηc, and will be discussed in details in the following section. Thus, this section will be dedicated to the calculation of the conduction and dielectric losses inside the antenna structure. Since it is very difficult to compute and separate these losses individually, they will, therefore, be lumped together to form the conduction-

*CD* = \_ *Rr Rr* + *Rl*

where *Rr* is the radiation resistance of the antenna and *Rl* represents the

*Rl* = 2 \_ *L*

where *L* is the antenna length, *P* is the cross-section perimeter of the wire antenna of radius a, and Rs is the conductor surface resistance that can be calculated

; (3)

*<sup>P</sup> Rs* ; (4)

ηt = ηr ηs ηq η<sup>c</sup> (2)

decreases in the efficiency to around 90% at wavelengths of interest.

conversion efficiency, ηt, of a solar rectenna can be described as [27].

eters and is referred to as the diode-dependent efficiency.

dielectric efficiency, cd, which can be defined as [29].

conduction-dielectric resistance, which can be written as [29]

will then be calculated and plotted.

**7.1 Antenna-dependent efficiency**

**188**

as follows

$$
\hat{\bf \S} \mathfrak{P} \mathfrak{L} \mathfrak{G}
$$

$$
\hat{\bf \S} \mathfrak{R}\_{\mathfrak{s}} = \sqrt{\frac{\mathfrak{a} \mathfrak{f} \mathfrak{a}\_{0}}{2 \sigma}} ; \tag{5}
$$

where ω is the angular frequency, μ0 is the free-space permeability, and σ is the metal conductivity. It is worth mentioning here that Eq. (4) is valid for the case of a uniform current distribution.

Before starting the calculation of the conduction-dielectric efficiency, it is important to recall that metals are no longer perfect electric conductors at optical and infrared frequencies [30]. Consequently, the DC bulk conductivity of metal cannot be utilized in (5). Instead, the frequency-dependent conductivity at optical frequencies should be calculated.

#### **7.2 Diode-dependent efficiency**

The two terms of the diode-dependent efficiency are the coupling efficiency, ηc, and quantum efficiency, ηq. In this chapter, we will set *ηq = S hω*/*e*, where *S* is the MIM diode responsivity, which will be explained more explicitly later in this section, *h* is Plank's constant, and *e* is the charge of the electron. In contrast, the coupling efficiency can be written as [5].

$$\begin{aligned} \text{Item as [5]}. \end{aligned}$$

$$\begin{aligned} \mathfrak{N}\_c &= \frac{4 \, R\_a \, R\_D / \left( R\_d + R\_D \right)^2}{\mathbf{1} + \left( \mathfrak{o} \left( \frac{R\_a \, R\_D}{R\_d + R\_D} \right) C\_D \right)^2}; \\ \end{aligned} \tag{6}$$

where *R*a is the antenna resistance, ω is the angular frequency, *RD* is the diode resistance, and *CD* is the diode capacitance. For simplicity of analysis, the reactance of the antenna was assumed to be negligible; however, for the antenna in this work, this approximation is more realistic for the wavelength between 8 and 12 μm where a low reactance part of the impedance is noticed. The value of *RD* depends on the I-V characteristics of the MIM diode, whereas the *CD* can be given by *CD* = \_

$$\mathbf{C}\_{D} = \frac{\mathbf{e}\_{0}\mathbf{e}\_{\prime\prime A}}{s};$$

where *εr* represents the relative permittivity of the insulator layer of the MIM diode, *ε*0 is the free-space permittivity, *A* is the diode junction area (overlapping area), and *s* is the thickness of insulator layer. It is clearly evident that the MIM diode parameters play a significant role in determining the entire conversion efficiency of solar rectennas.

**Figure 12** shows the total conversion efficiency (solid line) for an IR solar rectenna versus the wavelength. Moreover, we have added the diode-dependent efficiency (dashed line) to the same graph to show the role that the antenna plays in shaping the conversion efficiency. The total conversion efficiency has been calculated based on the terms of (2), where every single term is calculated individually and all terms are then combined together. The main reason behind this low efficiency is the mismatch between the resistance of the designed MIM diode, *RD*, and the antenna resistance, *Ra*. This mismatch led to a lower coupling efficiency in (6), where one of the conditions to achieve unity efficiency is to have Rd = Ra. Although the diode characteristics have been optimized, the coupling efficiency still needs further improvement. However, this value of efficiency demonstrates an enhancement to recently reported conversion efficiencies of (ηt ~ 10<sup>−</sup><sup>9</sup> –ηt ~ 10<sup>−</sup>12) [31]. It is worth mentioning that the antenna efficiency is very high and the diode responsivity is acceptable; however, the total conversion efficiency is quite low due to the poor coupling efficiency between the antenna and the diode. Recent studies are paying attention and efforts to increase coupling efficiency. Once the coupling is improved, we would expect a high conversion efficiency, which makes solar

#### **Figure 12.**

*Total conversion efficiency and the diode-dependent efficiency of a typical IR solar rectenna [8].*

antennas a promising alternative to conventional solar cells and a great addition to the renewable energy sector.

The promising features of solar rectennas have motivated the researcher recently to come up with new approaches and ideas in order to improve the total conversion efficiency. Examples of these approaches include improving the impedance matching and the coupling between the antenna and rectifier [32, 33]. Another approach is to use metasurface absorbers to enhance the performance of solar rectenna [34]. In addition, light concentrators represented by adding a layer of micro lenses lead to increase the captured electric field as demonstrated in [35] or design dual-polarized nanoantennas [36] and/or multiband nanoantennas [37] to get benefits of all received spectrum. The approach was even extended to include harvesting thermal energy at infrared wavelengths from hot bodies [38], which sometimes focuses on preselected narrow frequencies in the infrared region [39].

### **8. Conclusions**

Researchers worldwide pay attention and effort to reduce the cost of conventional solar cells and increase their efficiency by using new materials and different approaches. However, there is no significant improvement in their conversion efficiency, which is still quite low. Breakthroughs in designing efficient nanoantennas led to rapid development in solar rectenna for harvesting solar radiation. Efficient nanoantennas were designed for receiving the solar energy as an AC signal and coupling it to a nanodiode to convert it to DC power.

The focus of this chapter was to highlight different types of nanoantennas that are commonly used in this application. The design and simulation results of four types of nanoantennas have been presented, and a comparison is made to find the best candidate. The figure of merit in the selection process was the captured electric field at the feed gap of the antenna, which is a key factor in calculating the harvested energy. As a result of the comparison, it was found that the spiral nanoantenna exhibited better performance at resonance. Furthermore, it was found that the captured electric field at the feed gap could be increased by coupling many elements in one structure.

Finally, this chapter highlighted the most important factors that influence the conversion efficiency of solar rectennas with the aim to improve and optimize it.

**191**

**Author details**

Baghdad, Iraq

Ahmed M.A. Sabaawi1

\* and Oras Ahmed Al-Ani<sup>2</sup>

1 College of Electronics Engineering, Ninevah University, Mosul, Iraq

\*Address all correspondence to: ahmed.sabaawi@uoninevah.edu.iq

provided the original work is properly cited.

2 College of Electrical Engineering Techniques, Middle Technical University,

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

*Solar Rectennas: Analysis and Design*

the rectification process.

*DOI: http://dx.doi.org/10.5772/intechopen.89216*

It was shown that even when optical antennas couple thermal radiation efficiently, the total conversion efficiency is still low. This is due to the poor matching between the diode and the antenna, where a very high diode resistance is obtained compared to the low antenna resistance, albeit the diode characteristics have been optimized. As a summary, solar rectennas are an attractive option to replace PV cells in harvesting solar energy; however, this technique requires further developments in

### *Solar Rectennas: Analysis and Design DOI: http://dx.doi.org/10.5772/intechopen.89216*

*Recent Wireless Power Transfer Technologies*

the renewable energy sector.

**Figure 12.**

**8. Conclusions**

antennas a promising alternative to conventional solar cells and a great addition to

*Total conversion efficiency and the diode-dependent efficiency of a typical IR solar rectenna [8].*

Researchers worldwide pay attention and effort to reduce the cost of conventional solar cells and increase their efficiency by using new materials and different approaches. However, there is no significant improvement in their conversion efficiency, which is still quite low. Breakthroughs in designing efficient nanoantennas led to rapid development in solar rectenna for harvesting solar radiation. Efficient nanoantennas were designed for receiving the solar energy as an AC signal

The focus of this chapter was to highlight different types of nanoantennas that are commonly used in this application. The design and simulation results of four types of nanoantennas have been presented, and a comparison is made to find the best candidate. The figure of merit in the selection process was the captured electric field at the feed gap of the antenna, which is a key factor in calculating the harvested energy. As a result of the comparison, it was found that the spiral nanoantenna exhibited better performance at resonance. Furthermore, it was found that the captured electric field at the feed gap could be increased by coupling many elements in one structure.

Finally, this chapter highlighted the most important factors that influence the conversion efficiency of solar rectennas with the aim to improve and optimize it.

preselected narrow frequencies in the infrared region [39].

and coupling it to a nanodiode to convert it to DC power.

The promising features of solar rectennas have motivated the researcher recently to come up with new approaches and ideas in order to improve the total conversion efficiency. Examples of these approaches include improving the impedance matching and the coupling between the antenna and rectifier [32, 33]. Another approach is to use metasurface absorbers to enhance the performance of solar rectenna [34]. In addition, light concentrators represented by adding a layer of micro lenses lead to increase the captured electric field as demonstrated in [35] or design dual-polarized nanoantennas [36] and/or multiband nanoantennas [37] to get benefits of all received spectrum. The approach was even extended to include harvesting thermal energy at infrared wavelengths from hot bodies [38], which sometimes focuses on

**190**

It was shown that even when optical antennas couple thermal radiation efficiently, the total conversion efficiency is still low. This is due to the poor matching between the diode and the antenna, where a very high diode resistance is obtained compared to the low antenna resistance, albeit the diode characteristics have been optimized.

As a summary, solar rectennas are an attractive option to replace PV cells in harvesting solar energy; however, this technique requires further developments in the rectification process.
