Upper bounds for the solar energy harvesting efficiency of nano-antennas

Abstract

The radiation efficiency of nano-antennas is a key parameter in the emerging field of IR and optical energy harvesting. This parameter is the first factor in the total efficiency product by which nano-antennas are able to convert incident light into useful energy. This efficiency is investigated in terms of the metal used as conductor and the dimensions of the nano-antenna. The results set upper bounds for any possible process transforming light into electrical energy. These upper bounds are the equivalent of the theoretical upper bounds for the efficiency of conventional solar cells. Silver shows the highest efficiencies, both in free space and on top of a glass (SiO₂) substrate, with radiation efficiencies near or slightly above 90%, and a total solar power harvesting efficiency of about 60–70%. This is considerably higher than conventional solar cells. It is found that fine-tuning of the dipole dimensions is crucial to optimize the efficiency.

Introduction

Solar energy is expected to deliver a considerable contribution to the solution of human kind's energy problem. At this moment, 90% of the solar cells in the market are based on crystalline silicon wafers. The disadvantage of this technology is the lower efficiency by which the transformation of energy from optical frequencies to low frequencies is performed. Typical efficiencies are in the order of 20–30%. With these efficiencies, if human kind's energy need would be fully satisfied by present day solar cells, the required area would be about 400,000 km². Assuming that only 10% of the energy need would be provided by solar energy harvesting, it is easily seen that doubling the efficiency of solar panels corresponds to an area of 20,000 km². This is more than half the area of a country like Belgium. The efficiency of solar energy harvesting is a matter of high interest.

In recent years, the idea of using nano-rectennas (nano-antenna or nantenna+rectifier) to harvest solar energy has been suggested. It is claimed that the efficiency of this type of topology may be much larger. The figures mentioned go from a staggering 90% [1], to a more “down-to-earth” 30–40% [2]. It is suggested that the circuits themselves can be made of a number of different conducting metals, and the nano-antennas can be printed on thin, flexible materials like polyethylene, a very cheap and common plastic.

In this paper, to the knowledge of the authors for the first time, realistic numbers are presented for the maximum efficiencies that can be reached with nano-antenna technology. These numbers are based on a detailed study of a single antenna topology, the basic dipole, for a range of different metals and different sizes.

The total efficiency of nano-rectennas consists of two parts. The first part is the efficiency by which the light is “captured” by the nano-antenna and brought to its terminals. Due to reciprocity, this efficiency is the same as the efficiency by which the antenna is able to convert input power given at its terminals into radiation. This efficiency is thus the radiation efficiency η^rad of the antenna. Although this efficiency has been very well studied for traditional antennas, the in-depth characterization of this parameter has not yet been addressed in the nano-antenna research community. To start with, in by far most papers on nano-antennas known to the authors, only gold is considered as metal. Concerning topologies, some information can be found [3], [4]. However, Gao [3] considers only two structures of the same length and a very rough Drude model is used in the FDTD solver used, fitting the experimental material parameter data. It can be proven that this affects the efficiencies considerably. Huang [4] uses only a single frequency.

The second part is the efficiency by which the captured light is transformed into low frequency electrical power by the rectifier. At lower frequencies, rectifying circuits are common, but at IR and optical frequencies and in combination with nano-antennas, efficient rectification is a real challenge. A very interesting new technique to realize this transformation has very recently been introduced. M.W. Knight [5] and colleagues have made an optical nano-antenna that also works as a photodetector capable of converting light into either current or voltage. This was done by growing rod-like arrays of gold nano-antennas directly onto a silicon surface—so creating a metal–semiconductor (or Schottky) barrier formed at the antenna–semiconductor interface. The efficiency of the two steps combined was 0.01%. This very low figure is in sharp contrast with the efficiencies mentioned by Kotter [1] and Service [2], and it illustrates the long way still to go before real practical use can be made of solar energy harvesting with nano-antennas.

This paper considers the first step only, the capturing of the IR and optical waves and the transport of the energy embedded in these waves to the terminals of the nano-antenna. It may be clear that the intrinsic radiation efficiency of nano-antennas is a crucial factor in the energy harvesting debate. A three-fold increase in net energy yield would give enormous advantages if applied at a large scale.

It is essential to point out that the interaction between light and nano-antennas in the frequency bands considered can still be analyzed with a high degree of accuracy using classical electromagnetic theory [3], [7], [8]. The fact that at this small scale, no quantum effects have to be taken into account is really a crucial observation. It means that the concept of an “antenna”, a device able to transmit and receive electromagnetic waves rather than particles, still works. Basically, the coupling between an electromagnetic (light-) wave and a nano-antenna (a so-called nantenna) is thus the same as it is at microwave frequencies, and can be studied in the same way.

Although nano-photonics, and especially plasmonics, is a rapidly growing research field [6], the more in depth study of nano-antennas as such has emerged quite recently [9], [10], [11], [12], [13], [14], [15], [16]. Following a quite different path, but also quite promising in the area of photovoltaics is the study of the use of so-called nano-wires and nano-tubes, as investigated for example by the group of Lieber [17], [18], [19]. A recent review article concerning nanostructures for efficient light absorption and photovoltaics is [20].