Optical antennas have been proposed as an alternative option for solar energy harvesting. In this work the power conversion efficiency of broadband antennas, log-periodic, square-spiral, and archimedian-spiral antennas, coupled to Metal-Insulator-Metal and Esaki rectifying diodes has been obtained from both theoretical and numerical simulation perspectives. The results show efficiencies in the order of 10−6 to 10−9 for these rectifying mechanisms, which is very low for practical solar energy harvesting applications. This is mainly caused by the poor performance of diodes at the given frequencies and also due to the antenna-diode impedance mismatch. If only losses due to antenna-diode impedance mismatch are considered an efficiency of about 10−3 would be obtained. In order to make optical antennas useful for solar energy harvesting new rectification devices or a different harvesting mechanism should be used.
© 2013 OSA
Solar radiation represents a direct source of energy in which 85% of it consists of radiation in the 0.2-2μm spectral range. Approximately 80% of this energy is absorbed by the Earth’s surface and atmosphere and it is re-emitted as infrared radiation in the 7-17μm spectral range , also some other artificial thermal sources such as engines, furnaces, etc., emit within the same IR band. Photovoltaic technology has been used to retrieve solar energy and convert it into electric energy [2, 3], however the IR part of the optical spectrum has been sub-utilized by current photovoltaic technology which only covers the 0.4μm to 2.5μm spectral range [4, 5]. Although thermodynamic limitations due to the small temperature difference between the source and detector exist, there is some amount of energy that can be harvested with this technology, and can be used for several applications, for example when considering autonomous high-altitude airborne electronics looking down the Earth surface. Therefore harvesting energy in the IR spectrum requires the use of novel techniques, including ultra-low-power electronics , which can complement current photovoltaic technology [7, 8].
One alternative technique that has been explored for solar energy harvesting is based on optical antennas which naturally absorb the propagating optical radiation by inducing an AC current in their resonant elements [9, 10], these technique has been used successfully in the past for sensing  and mixing  of optical radiation. Optical antennas can be designed to absorb at a specific wavelength or at a broad spectral bandwidth. This last option would be a good fit for solar energy harvesting applications .
Although optical antennas capture infrared energy in an efficient manner [11, 14] they need a mechanism, such as a rectifier to recover energy, similar to what electromagnetic receiving devices do in the microwave region of the spectrum , these devices which couple rectifiers to optical antennas are also known as rectennas.
The most mature technologies to rectify infrared wavelengths (without an external voltage bias) are the asymmetric Metal-Insulator-Metal (MIM), Metal-Insulator-Insulator-Metal [12, 16–21] and Esaki diodes [22–25]. These type of diodes incorporate an insulating layer between two electrodes thin enough to allow tunnel conduction [26, 27]; since tunneling is an inherently fast process junctions can show a high switching speed [28, 29].
The rectifying mechanism of diodes is based on the asymmetry of the tunnel transport which causes a net DC current to flow in one direction (square-law rectification [30, 31]). The rectified signal is then proportional to the non-linearity of the current-voltage curve (given by the ratio of the second-to-first derivates) and the amplitude of the excitation :31] (Fig. 1):11], therefore the diodes used should consist of tunnel barriers with high non-linearity to improve its performance . Figure 1 shows the equivalent electrical circuit for a rectifying diode coupled to an antenna [13, 31].
The antenna, when operated at its resonant frequency, behaves as a voltage source with an internal impedance RA whose output voltage is limited by the diode resistance RD, and its speed by the capacitance CD of the junction. The cut-off frequency of the device is evaluated by the relation:
Therefore, in order to achieve a fast switching speed of an antenna-coupled diode its RC constant must be small, which can be obtained with a small junction area .
These rectifying devices with small area junctions have been used to rectify currents from the microwave region of the spectrum up to the visible (λ = 633 nm ). However, the most efficient rectifying barriers introduce a high impedance mismatch to the antennas they are coupled to [31, 33]; this impedance mismatch reduces their efficiency by as much as 90% [34–36]. Recently, some methods to better match diodes to optical antennas have been proposed with good results .
In this work, three broadband antennas tuned to the IR region of the spectrum are coupled to different types of diodes and analyzed as potential systems for harvesting thermal radiation. This analysis is performed through finite element simulations using the commercial software COMSOL Multiphysics.
2. Broad band antennas and rectifying diodes
The goal of this contribution is to obtain the optical conversion efficiency of antennas coupled to rectifying diodes. We analyze three different types of broadband antennas: a log periodic, a square-spiral, and an Archimedean spiral gold antennas (Fig. 2) designed to absorb thermal radiation (from 3μm to 17μm). These antennas are coupled to two different tunnel diodes. The analysis is made using finite element simulations.
The log-periodic antenna considered is a circular-toothed structure with an outer radius of 3.6 μm, a bow angle of β = 60° and a toothed structure repeated three times with a scale factor τ = 2 and an angle of α = 30°. The square-spiral antenna is designed using two symmetrical arms composed by seven elements 200 nm wide and 200 nm thick. The Archimedean spiral is composed by two arms each 12.4 μm long, 200 nm wide and 200 nm thick, with an external radius of 2.4 μm and an approximate spacing between arms of 560nm.
Antennas were simulated on a high-resistive (ρ = 3000Ω-cm) semi-infinite Si substrate separated by a 1.3 μm thick insulating SiO2 layer (εr = 4.84 at 10.6μm) and the simulations were performed using the optical parameters of metals reported at THz frequencies .
Esaki and MIM diodes based on semiconductor n-InAs/AlSb/p-GaSb [22–25], and metal Al/Al2O3/Pt hetero-structures [18, 39, 40] with small contact-areas (0.0056μm2) and small capacitances (CEsaki = 70aF and CMIM = 15aF) were selected as high frequency rectifiers with cut-off frequency high enough to rectify a significant portion of the IR incident radiation (fcEsaki~14THz and fcMIM~68THz). The resistance of the rectifiers was obtained from previously reported resistivities (ρS) for these devices [22, 39], values around 300kΩ were obtained for rectifiers with small junction areas and their gamma factors were calculated from experimentally reported J-V curves  obtaining the following sensitivity values of γEsaki = 40V−1 and γMoM = 0.5V−1; which give a big response advantage in the performance of these kind of junctions at the infrared regime, even if the resistance mismatch between antennas and diodes is important [31, 36]. The 300kΩ devices were selected since they provided the best resistance/sensitivity tradeoff for both MIM and Esaki diodes.
Computer simulations were performed using COMSOL Multiphysics by launching an electromagnetic plane wave incident from the air side of the device and normal to the substrate, with a chosen E-field polarization in order to match the polarization of antennas in every case: linearly polarized for the log-periodic antenna, and right-hand circularly polarized for both spiral antennas. The E-field magnitude of the electromagnetic wave was 239 V/m constant over the whole range of frequencies. This value corresponds to an irradiance of 152 W/m2 . This situation is seen at night by a high-altitude balloon looking down the Earth at 289 K in the analyzed frequency range. The current induced on the antennas (IAC) was numerically obtained by using the Ampere’s Law which relates the integrated H-field around a closed loop at terminals to the current passing them.
The induced voltage on the antennas was obtained by using the relation V = RA* IAC (Fig. 3).
The rectified signal produced by diodes coupled to these antennas was estimated by first obtaining the AC voltage vD across to diodes by using Eq. (2) and the reduced resistance x = RD/RA, where RA is the resistance of the antennas at resonance (assumed as a first order approximation to be 188Ω for the three antennas in the range frequency ). This voltage was used to estimate the rectified current by using the square-law rectification relationship (Eq. (1)).
The conversion efficiency of the harvesting devices was estimated as the ratio of the power PDC associated to the rectified current and the power P collected by the antennas using the relationship:11, 13]
In Fig. 4 we have plotted the current rectified by these devices as a function of frequency from 6THz to 100THz (50µm to 3µm). Results show that, for both types of rectifiers the signal from the spirals antenna-coupled diodes shows a FWHM of more than 20 THz in a broad range of frequencies (from 20 to 60THz) whereas log-periodic antennas showed a well-defined multi-band response .
On the other hand, the signals obtained from the antennas when coupled to InAs/AlSb/GaSb backward diodes are around fifteen times greater than that of MIM diodes. This difference results from the difference in their gamma factors (from which its response depends linearly). However, since the capacitance of the backward diodes is not low enough, its response when coupled to antennas is reduced drastically as the frequency of incident radiation increases.
Figure 5 shows the efficiency of both types of tunnel diodes used to convert THz radiation into electrical energy obtained by using Eq. (4) and considering a constant impedance from the antennas .
Numerical results show that, even when infrared antennas couple thermal radiation in an efficient way, their efficiency to obtain electrical energy when coupled to square-law rectifiers is quite poor (η ~10−9–10−12). By estimating the reflection coefficient between antennas and diodes (defined as Γ = (ZD-ZA)/(ZD + ZA)) it can be seen that impedance mismatch reduces the conversion efficiency by a factor of a thousand. But more important, this estimation allows to realizing the poor efficiency of square-law rectifiers (10−6–10−9). Even if the antenna-diode mismatch could be solved, a better rectifier is still necessary. Some advances have been made in the proposal of new rectifying mechanisms that could improve these Figs [42, 43].
A variety of broadband antennas coupled to square-law rectifying diodes were characterized numerically at THz and infrared frequencies. The use of broadband antennas for detection and collection of infrared sun’s energy has a big potential advantage over the traditional solar cells junctions. In contrast with traditional cells that are restricted to narrow spectra, antennas can be tuned at any specific wavelength and respond within a wide range of frequencies by using a single structure.
However, conversion efficiency of MIM and Esaki diodes coupled to these antennas is still low (η ~10−9–10−12) even if antennas captured radiation in an efficient way. This is due to several factors: the impedance mismatch between the antenna and diode, the choice of the antennas’ materials, but most important to the efficiency presented by these types of square-law rectifiers. Square-law rectifiers’ signal depends on its gamma factor and their input current, which for solar applications is of some μ-amperes when using antennas. Summarizing these results, antennas are attractive systems for coupling solar energy, but energy harvesting using optical antennas requires further developments, especially in the rectification mechanism.
Part of this work has been funded by Project ENE2009-13430 from the Ministerio de Ciencia e Innovación of Spain, and by PROMEP.
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