Optimized tapered dipole nanoantenna as efficient energy harvester

Youssef M. El-Toukhy; Mohamed Hussein; Mohamed Farhat O. Hameed; A. M. Heikal; M. M. Abd-Elrazzak; S. S. A. Obayya

doi:10.1364/OE.24.0A1107

1. Introduction

In early 1970s, Bailey has proposed the concept of rectenna in the field of solar energy harvesting [1] where rectenna stands for a rectifying diode coupled with antenna. Nanoantenna is responsible for transforming solar radiation into an AC electric field across the diode which rectifies the signal to obtain DC power. In recent years, due to the large demand on renewable clean energy, rectennas design and fabrication techniques are getting more mature as this approach promises to offer highly efficient solar energy harvesting systems. Referring to the radiation spectrum of the sun, maximum irradiance occurs at the visible wavelength range from 400 to 700 nm. Nonetheless, extending the utilization of rectenna systems to visible frequencies (PHz) resulted in several challenges. First, the challenge of scaling down antenna dimensions to submicrometer which is becoming more realizable with advanced technologies [2]. However, suitable rectifiers are still not available for this operation criteria. Metal\insulator\metal (MIM) diode topology is gaining interest as a candidate for high frequency operation [3] and an investigation of MIM diode limitations will be illustrated later.

The main factors contributing to the efficiency of nano-rectenna systems are:

(1) Harvesting efficiency of the nanoantenna device.
(2) The cut off frequency of the diode and responsivity at zero voltage bias.
(3) Impedance matching between the nanoantenna and the diode.

Vandenbosch and Ma [4,5] reported an upper bound for total solar harvesting efficiency of 64%, over wavelength range 400-1200 nm, for a silver dipole nanoantenna. This design offers a nominal input impedance of 250 Ω at resonance and harvesting efficiency of 26% at wavelength of 500 nm. Bowtie [6,7] and Vivaldi [8] nanoantennas offered a low input impedance of about 100 Ω at resonance. However, authors study didn’t provide calculations for harvesting efficiency at visible light range. Other design topologies were proposed, such as spiral, log-periodic [9], flower-shaped dipole and elliptic dipole nanoantenna [10]. While some of these designs offer higher efficiencies up to 90% at 500 nm wavelength, they suffer from very high design complexity and the lack of impedance analysis in the literature, especially over the visible light region. A tapered dipole nanoantenna topology was firstly introduced in [11] where two structures were presented, two-arm and cross arm dipole antennas with tapered end. The simulation results for these structures show high field confinement in the antenna gap where the cross dipole antenna exhibits the higher field enhancement. However, this study was not intended for solar harvesting application and thus no further analysis for the harvesting efficiency or input impedance was presented [11]. A study of the field distribution around nanoantenna and current induced on the surface was also carried out for the bowtie and spiral designs [6,9] where simulation and experimental results showed high enhancement over the conventional dipole design [5]. However, these rectenna devices are reported to suffer from low coupling efficiency between nanoantenna and rectifier due to high impedance mismatch.

To ensure highly efficient operation of rectenna system, MIM diode must obtain several characteristics. One of the main characteristics is the high responsivity which is a measure of the DC output with respect to the input power [3]. Another characteristic is the diode impedance (R_D and C_D) which defines the junction cut-off frequency [3] and plays the major role in coupling efficiency with the antenna device. While nanoantennas have a typical impedance of 100-200 Ω, the reported MIM diodes offer as low impedance as 0.5 – 3 kΩ [6,11] with thickness range from 4 nm down to 0.7 nm (MIM thickness is directly proportional to diode resistance [12]). This deviation between MIM diode and nanoantenna impedances reduces the coupling efficiency significantly as reported in [6,9].

It is worth emphasizing that this work doesn’t aim to model a new rectifier topology. This paper introduces a novel nanoantenna design which offers harvesting efficiencies up to 55.3% at wavelength λ of 500 nm with a field confinement 60 times greater than that of the conventional dipole design. This enhancement is attributed to high divergence of surface current over the nanoantenna surface as a result of the multiple thickness-grading introduced to the design. Moreover, the proposed structure can be tuned to perfectly match a wide range of fabricated rectifier impedances based on the multi-resonance characteristic of this novel design. Three design configurations are introduced which have 500Ω, 1kΩ and 2kΩ resonant impedances to match that of MIM diodes reported in [6,11].

Following this introduction, the theory and design consideration will be presented in section II. A description of the simulation environment and optimization technique are considered in section III. In section IV, detailed simulation results are reported which quantify the benefits of the proposed nanoantenna design topology. Finally, conclusion will be drawn in section V.

2. Theory and design consideration

This research work focuses on overcoming the drawbacks of previously studied nanoantenna designs such as: low field confinement at the gap, small nominal input impedance and low harvesting efficiency at visible light frequencies. Moreover, this study introduces a novel design that offers relatively high manufacture feasibility as will be discussed later.

For an efficient operation of rectenna system, high intensity field should exist at the surface of the MIM diode $δ_{s}$ so that sufficient electrons can tunnel through the diode. Therefore, high field confinement at the gap of the nanoantenna represents a major requirement in the nanoantenna design. According to the electromagnetic theory, electric field tends to be accumulated at the metal tips of the antenna structure [6,13]. Based on this phenomenon, the proposed design was constructed by inserting more steps of smaller dimensions into the conventional dipole design, as shown in ‎Fig. 1, which increases the number of tips and consequently the electric field confinement by the nanoantenna. This is directly related to the antenna efficiency where the harvested electric energy is transformed to AC power at the antenna port. Figure 1 demonstrates the design parameters of the conventional dipole and the two proposed nanoantennas topologies, type 1 and type 2. Type 1 nanoantenna is considered a modified version of the conventional dipole where one more step of smaller dimensions is inserted. On the other hand, type 2 nanoantenna represents a 3-steps tapered dipole. Silver material is selected for all the nanoantennas studied in this work as it’s reported to offer higher efficiency when compared to other metals [5]. The proposed design parameters are chosen so that the overall nanoantenna volume is less than that of the conventional dipole reported in [4] to obtain a shorter device length and to have a fair comparison with the conventional dipole as larger material volume will increase the harvested light. Additionally, a minimum feature size of 5 nm is maintained in grading adjacent dipole steps to reduce design complexity.

Fig. 1 (a) Conventional dipole [‎4], (b) Type 1 (2-steps tapered dipole), (c) Type 2 (3-steps tapered dipole).

$P_{r a d} = ∯ S_{s c} d s$	$P_{l o s s} = \underset{a n t e n n a - v o l u m e}{∭} Q d V$
$S_{s c} = \frac{1}{2} R e (E \times H^{*})$	$Q = Q_{r l} + Q_{m l}$
$Q_{r l} = \frac{1}{2} R e (J . E^{*})$	$Q_{m l} = \frac{1}{2} R e (j ω B . H^{*})$

Antenna parameters	conventional dipole [4]	Type 1	Type 2
$T$	40 nm	40 nm	40 nm
$G$	10 nm	41.3 nm	49.8 nm
$L_{1}$	250 nm	97.5 nm	103.5 nm
$W_{1}$	40 nm	31.3 nm	51 nm
$L_{2}$	-	103.4 nm	70 nm
$W_{2}$	-	11.6 nm	19.5 nm
$L_{3}$	-	-	5 nm
$W_{3}$	-	-	13.4 nm
Relative volume	1	0.42	0.67

Antenna parameters	Type 2 design resonance impedance
Antenna parameters	500Ω	1kΩ	2kΩ
$T$	40 nm	40 nm	40 nm
$G$	49.8 nm	47 nm	40.2 nm
$L_{1}$	103.5 nm	99.7 nm	129.9 nm
$W_{1}$	51 nm	49.5 nm	54.6 nm
$L_{2}$	70 nm	73.6 nm	60 nm
$W_{2}$	19.5 nm	17.9 nm	39.8 nm
$L_{3}$	5 nm	9.1 nm	10.5 nm
$W_{3}$	13.4 nm	5.6 nm	8.6 nm
Relative volume	1	0.94	1.4

Parameter	Tolerance	Harvesting efficiency	Impedance
$L_{1}$	103.5 nm ± 5%	Higher than 53.9%	500 Ω ± 54 Ω
$W_{1}$	51 nm ± 5%	Higher than 53.8%	500 Ω ± 58 Ω
$L_{2}$	70 nm ± 5%	Higher than 55.2%	500 Ω ± 35 Ω
$W_{2}$	19.5 nm ± 5%	Higher than 55.25%	500 Ω ± 31 Ω
$L_{3}$	5 nm ± 5%	Higher than 55.45%	500 Ω ± 30 Ω
$W_{3}$	13.4 nm ± 5%	Higher than 55.5%	500 Ω ± 27 Ω

Abstract

1. Introduction

2. Theory and design consideration

3. Simulation environment and numerical methodology

4. Simulation results

4.1 Model validation

4.2 Efficiency and return loss analysis

4.3 Electric field confinement analysis

4.4 Gap study for type 2 nanoantenna

4.5. Configurability of type 2 nanoantenna input impedance

4.6. Fabrication tolerance analysis for type 2 nanoantenna

5. Conclusion

References and links

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Figures (16)

Tables (4)

Equations (7)

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