**5. Nanodiodes**

The most commonly used nanodiodes in solar rectennas are metal-insulatormetal diodes, which act as a promising rectifying element in solar rectennas. MIM diodes are made of thin insulator layer sandwiched between metal electrodes and depend on the tunneling mechanism. Work functions of metals and the electron affinity of insulators play an important role in MIM diodes by making a barrier at the interface between metal and insulator. **Figure 8** shows a typical MIM diode where a difference between metal work function is clearly indicated to ensure efficient electron transport across the insulator. The quantum-mechanical tunneling of electrons governs the charge transport mechanism through the barrier. Electron tunneling in MIM diodes is ultrafast, and this makes them operate at THz frequencies. A thin insulator layer (few nanometers) is required to ensure the tunneling of electrons through the diode layers.

Recent years have witnessed tremendous lithographical efforts to reduce the size of MIM diodes. To this end, the insulator layer is grown by oxidizing metal films to achieve the desired thickness. The second metal is then deposited, where this method helps to avoid vacuum break at the barrier and reduce the contamination. It is worth mentioning that controlling the roughness of the insulator layer as well as the metal films is very important during the fabrication process.

#### **5.1 MIM diode characterization**

The major obstacle in using MIM at optical frequencies is the high RC time constant. The diode resistance and capacitance must be well controlled through the fabrication techniques and processes in ordered to reduce it. In this section, the most important parameters of the MIM diode will be discussed:

• **Resistance:** The diode resistance (RD) can be obtained directly from the I-V characteristics of the diode. Since the antenna impedance is low (in the order of 100 Ohm), the diode impedance must be low as well to achieve a reasonable impedance matching and hence ensure a maximum power transfer between the antenna and the diode.

**185**

**Figure 9.**

**Figure 8.**

*heights 1 = 0.4 eV and 2 = 1.75 eV [20].*

*Solar Rectennas: Analysis and Design*

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

associated directly with high barrier diodes.

• **Responsivity:** The responsivity of MIM diodes is a measure of the diode rectification efficiency. It is the second derivative of the diode's I-V curve over the first derivative. The responsivity represents the DC power generated by the incident AC power on the diode. The larger I-V curvature, the higher responsivity obtained, and hence the higher DC power generated. High curvature is

• **Asymmetry:** The ratio of the forward current to the reverse current represents the diode asymmetry, which is another measure of the diode's rectification

*Equilibrium band diagram of (a) symmetric Nb/Nb2O5/Nb diode and (b) asymmetric Nb/Nb2O5/Pt diode [20].*

*Current versus biasing voltage for the asymmetric MIM diode with insulator thickness = 5 nm and barrier* 


#### **Figure 8.**

*Recent Wireless Power Transfer Technologies*

**5. Nanodiodes**

**Figure 7.**

electrons through the diode layers.

**5.1 MIM diode characterization**

the antenna and the diode.

The most commonly used nanodiodes in solar rectennas are metal-insulatormetal diodes, which act as a promising rectifying element in solar rectennas. MIM diodes are made of thin insulator layer sandwiched between metal electrodes and depend on the tunneling mechanism. Work functions of metals and the electron affinity of insulators play an important role in MIM diodes by making a barrier at the interface between metal and insulator. **Figure 8** shows a typical MIM diode where a difference between metal work function is clearly indicated to ensure efficient electron transport across the insulator. The quantum-mechanical tunneling of electrons governs the charge transport mechanism through the barrier. Electron tunneling in MIM diodes is ultrafast, and this makes them operate at THz frequencies. A thin insulator layer (few nanometers) is required to ensure the tunneling of

*Electric field variation with wavelength for bowtie nanoarray and single bowtie of the same footprint area [19].*

Recent years have witnessed tremendous lithographical efforts to reduce the size of MIM diodes. To this end, the insulator layer is grown by oxidizing metal films to achieve the desired thickness. The second metal is then deposited, where this method helps to avoid vacuum break at the barrier and reduce the contamination. It is worth mentioning that controlling the roughness of the insulator layer as well as

The major obstacle in using MIM at optical frequencies is the high RC time constant. The diode resistance and capacitance must be well controlled through the fabrication techniques and processes in ordered to reduce it. In this section, the

• **Resistance:** The diode resistance (RD) can be obtained directly from the I-V characteristics of the diode. Since the antenna impedance is low (in the order of 100 Ohm), the diode impedance must be low as well to achieve a reasonable impedance matching and hence ensure a maximum power transfer between

the metal films is very important during the fabrication process.

most important parameters of the MIM diode will be discussed:

**184**

*Equilibrium band diagram of (a) symmetric Nb/Nb2O5/Nb diode and (b) asymmetric Nb/Nb2O5/Pt diode [20].*

**Figure 9.**

*Current versus biasing voltage for the asymmetric MIM diode with insulator thickness = 5 nm and barrier heights 1 = 0.4 eV and 2 = 1.75 eV [20].*

efficiency. High asymmetry can be obtained by employing different metals on both sides of the diode with a difference in their work functions.

Most of the MIM diode parameters are extracted directly from the I-V characteristics, which is the key factor in the characterization of MIM diodes. **Figure 9** demonstrates typical MIM diode parameters.

### **6. Semiconductor nanoantennas**

In this section, a comparison between the performance of nanoantennas fabricated by different materials will be presented. The characteristics of the designed dipole nanoantennas have been obtained by solving Hallen's integral equation numerically. Obtained results show that carbon exhibits very low conductivity compared with other types of proposed semiconductors like Si and Ge.

This is because of the fact that carbon has a relatively wide energy gap, which is the main reason to enhance carbon nanoantenna performance. In contrast, creating extra defect states by phosphor or iron doping in the narrow band gap of Si and Ge can increase the conductivity and, thus, the efficiency of the host material.

The calculated efficiencies of these heavily doped semiconductor nanoantennas are unity. This is because of the high conductivity of these materials. Moreover, obtained results show that these materials behave like a perfect electric conductor at the wavelength range of interest. In addition, the performance of these semiconductor nanoantennas is compared with nanoantennas made of gold that showed approximately similar performance.

To investigate the impact of the conductivity () on the antenna parameters, pure and heavily doped semiconductors materials are used instead of metal in designing nanoantennas. Since plasmonic materials like gold are being used to fabricate metallic nanoantenna, a modeling comparison between the metallic and heavily doped semiconductor antenna is proposed to study the impact of the material on the performance of nanoantenna to exploit the mid-IR to generate presentable power.

Furthermore, the mid-IR radiation provides very low penetration depths for the electromagnetic fields. Generally, most studies on this area were focused on operating system with 10 m wavelengths, which may provide a wide range of energies [12].

To solve Hallen's integral equation, which is numerically used to evaluate the input impedance of the cylindrical dipole nanoantennas [21], method of moments (MOM) is generally used for this purpose. A study has been conducted to investigate the effect of replacing gold in plasmonic nanoantennas at mid-IR by heavily phosphorus-doped germanium on the antenna operation [22]. In this study, however, carbon nanotube semiconductor material is extended to heavily doped silicon by iron as common unavoidable contamination in Si. In both cases, the characteristics of the gold center-fed cylindrical dipole antenna that is used in this study include L = 0.47, N = 51, and a = 50 nm for = 10 m, where L is the total length of the dipole, N is the number of segments, and a is the radius of dipole. In addition to that, for the delta-gap source, MoM is used to solve Hallen's integral equation. An approximate kernel can only be utilized since the ratio a/ ⩽ 0.01, and in this example, a ratio of 0.005 is used which gives an acceptable approximation.

One of the methods used to increase the efficiency of nanoantenna is by developing the quality of materials that are used to fabricate the nanoantenna. In this work, heavily doped Ge with phosphorous and heavily doped Si with Fe have been proposed as an alternative to carbon. The value of the

**187**

**Figure 11.**

**Figure 10.**

*Solar Rectennas: Analysis and Design*

centration of 2.23 × 1019 cm<sup>−</sup><sup>3</sup>

lowing equation [26]:

been studied and reported in [25].

conductors behave like perfect electric conductor [22].

*Real and imaginary parts of Ge conductivity versus wavelength [22].*

*Real and imaginary parts of Si conductivity versus wavelength [22].*

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

frequency-dependent dielectric constant of heavily doped Ge with a doping con-

hand, the values of heavily doped Si with a doping concentration of 1 × 1020 cm<sup>−</sup><sup>3</sup> have been obtained by another study [24]. The interaction between Fe and Si has

The dielectric constant (εr) has frequency-dependent real and imaginary parts, in which the metal conductivity () at IR wavelengths can be obtained as the fol-

σ = iω ε0(ε*<sup>r</sup>* − 1) (1)

The complex form of material conductivity at IR wavelengths is illustrated as real and imaginary parts in **Figures 10** and **11**, respectively. Both figures show that heavily doped semiconductors exhibit considerably high conductivity at a range of wavelength between 5 and 15 m. Consequently, both of the heavily doped semi-

It is found that the conduction-dielectric efficiencies at the wavelength 10 μm for both Ge and Si are 100% as what is expected to having the same behavior as the

has been given somewhere else [23]. On the other

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

*Recent Wireless Power Transfer Technologies*

demonstrates typical MIM diode parameters.

**6. Semiconductor nanoantennas**

approximately similar performance.

able power.

energies [12].

efficiency. High asymmetry can be obtained by employing different metals on

Most of the MIM diode parameters are extracted directly from the I-V characteristics, which is the key factor in the characterization of MIM diodes. **Figure 9**

In this section, a comparison between the performance of nanoantennas fabricated by different materials will be presented. The characteristics of the designed dipole nanoantennas have been obtained by solving Hallen's integral equation numerically. Obtained results show that carbon exhibits very low conductivity

This is because of the fact that carbon has a relatively wide energy gap, which is the main reason to enhance carbon nanoantenna performance. In contrast, creating extra defect states by phosphor or iron doping in the narrow band gap of Si and Ge

The calculated efficiencies of these heavily doped semiconductor nanoantennas are unity. This is because of the high conductivity of these materials. Moreover, obtained results show that these materials behave like a perfect electric conductor at the wavelength range of interest. In addition, the performance of these semiconductor nanoantennas is compared with nanoantennas made of gold that showed

To investigate the impact of the conductivity () on the antenna parameters, pure and heavily doped semiconductors materials are used instead of metal in designing nanoantennas. Since plasmonic materials like gold are being used to fabricate metallic nanoantenna, a modeling comparison between the metallic and heavily doped semiconductor antenna is proposed to study the impact of the material on the performance of nanoantenna to exploit the mid-IR to generate present-

Furthermore, the mid-IR radiation provides very low penetration depths for the electromagnetic fields. Generally, most studies on this area were focused on operating system with 10 m wavelengths, which may provide a wide range of

To solve Hallen's integral equation, which is numerically used to evaluate the input impedance of the cylindrical dipole nanoantennas [21], method of moments (MOM) is generally used for this purpose. A study has been conducted to investigate the effect of replacing gold in plasmonic nanoantennas at mid-IR by heavily phosphorus-doped germanium on the antenna operation [22]. In this study, however, carbon nanotube semiconductor material is extended to heavily doped silicon by iron as common unavoidable contamination in Si. In both cases, the characteristics of the gold center-fed cylindrical dipole antenna that is used in this study include L = 0.47, N = 51, and a = 50 nm for = 10 m, where L is the total length of the dipole, N is the number of segments, and a is the radius of dipole. In addition to that, for the delta-gap source, MoM is used to solve Hallen's integral equation. An approximate kernel can only be utilized since the ratio a/ ⩽ 0.01, and in this example, a ratio of 0.005 is used which gives an acceptable approximation. One of the methods used to increase the efficiency of nanoantenna is by developing the quality of materials that are used to fabricate the nanoantenna. In this work, heavily doped Ge with phosphorous and heavily doped Si with Fe have been proposed as an alternative to carbon. The value of the

both sides of the diode with a difference in their work functions.

compared with other types of proposed semiconductors like Si and Ge.

can increase the conductivity and, thus, the efficiency of the host material.

**186**

frequency-dependent dielectric constant of heavily doped Ge with a doping concentration of 2.23 × 1019 cm<sup>−</sup><sup>3</sup> has been given somewhere else [23]. On the other hand, the values of heavily doped Si with a doping concentration of 1 × 1020 cm<sup>−</sup><sup>3</sup> have been obtained by another study [24]. The interaction between Fe and Si has been studied and reported in [25].

The dielectric constant (εr) has frequency-dependent real and imaginary parts, in which the metal conductivity () at IR wavelengths can be obtained as the following equation [26]:

$$
\sigma = \text{io} \,\text{e}\_0 \{ \mathbf{e}\_r - \mathbf{1} \} \tag{1}
$$

The complex form of material conductivity at IR wavelengths is illustrated as real and imaginary parts in **Figures 10** and **11**, respectively. Both figures show that heavily doped semiconductors exhibit considerably high conductivity at a range of wavelength between 5 and 15 m. Consequently, both of the heavily doped semiconductors behave like perfect electric conductor [22].

It is found that the conduction-dielectric efficiencies at the wavelength 10 μm for both Ge and Si are 100% as what is expected to having the same behavior as the

#### **Figure 10.**

*Real and imaginary parts of Ge conductivity versus wavelength [22].*

**Figure 11.** *Real and imaginary parts of Si conductivity versus wavelength [22].*

perfect electric conductor. In contrast, the relatively low conductivity of gold yield decreases in the efficiency to around 90% at wavelengths of interest.
