Solar Energy Vol. 73, No. 6, pp. 395–401, 2002  2003 Elsevier Science Ltd Pergamon doi:10.1016/S0038–092X(03)00033–1 All rights reserved. Printed in Great Britain 0038-092X/03/$ - see front matter www.elsevier.com/locate/solener

S OLAR ENERGY COLLECTION BY ANTENNAS

R. CORKISH†,1 , M. A. GREEN and T. PUZZER Centre for Advanced Silicon and Photonics, University of New South Wales, Sydney, NSW 2052, Australia

Accepted 29 January 2003

Abstract—The idea of collecting solar electromagnetic radiation with antenna-rectifier () structures was proposed three decades ago but has not yet been achieved. The idea has been promoted as having potential to achieve efficiency approaching 100% but thermodynamic considerations imply a lower limit of 85.4% for a non-frequency-selective rectenna and 86.8% for one with infinite selectivity, assuming maximal concentration in each case. This paper reviews the history and technical context of solar and discusses the major issues: thermodynamic efficiency limits, rectifier operation at optical frequencies, harmonics production and electrical noise.  2003 Elsevier Science Ltd. All rights reserved.

1 . INTRODUCTION solar rectenna ideas, sets them in their technologi- cal and scientific context, discusses efficiency Solar cells, with the exception of their anti- limits and mentions some issues which still need reflection coatings, are quantum devices, only resolution. Some of this work was presented at the able to be understood and designed by application ‘PV in Europe’ conference, 2002 (Corkish and of quantum physics. However, the wave nature of Green, 2002). light is routinely exploited at longer wavelengths in radio and frequency bands. Photon energies are low at radio frequencies and a large 2 . HISTORY OF SOLAR RECTENNAS number is required to give some particular power density. We tend to use wave models in that Bailey proposed the idea of collecting solar regime. At short wavelengths fewer photons are energy with devices based on the wave nature of required for the same power density and we tend light in 1972 (Bailey, 1972; Bailey et al., 1975). to use particle models. In principle, there may be He suggested artificial pyramid or cone structures no reason why the electromagnetic wave tech- analogous to those found in nature and similar to nologies which are so successfully used for radio dielectric rod antennas. His paper describes pairs cannot be scaled to optical frequencies, although of the pyramids as modified dipole antennas, each quantum models may be necessary for at least pair electrically connected to a (half wave some aspects, but there are significant practical rectifier), low-pass filter and load. The antenna issues, especially the sub-mm size scales involved. elements needed to be several wavelengths long A rectenna, or rectifying antenna (Fig. 1), is a to permit easier fabrication. device for the conversion of electromagnetic Marks (1984) patented the use of arrays of energy propagating through space to direct current submicron crossed dipoles on an insulating sheet in a circuit. It has one or more elements, each with fast full-wave rectification. This differed in a consisting of an antenna, filter circuits and a number of ways from Bailey’s proposal, most rectifying diode or bridge rectifier either for each importantly in that Marks’ structure was essential- antenna element or for the power from several ly a conventional broadside array antenna with the elements combined. output signal from several dipoles feeding into a This short paper briefly reviews the history of transmission line to convey their combined power to a rectifier. This design requires the oscillations from each dipole to add in phase. Kraus (1988) (pp. 715–6) proposed two orthoganally-polarised †Author to whom correspondence should be addressed. Tel.: 161-2-9385-4068; fax: 161-2-9662-4240; e-mail: arrays, one above the other with the front one [email protected] supported by a transparent substrate and a reflec- 1ISES member. tor below them (Fig. 2).

395 396 R. Corkish et al.

Fig. 1. Block diagram of rectenna and load.

Marks also patented devices to collect and (Berland et al., 2001). Berland et al. state that the convert solar energy using solidified sheets con- limiting efficiency is . 85%. ITN have built taining oriented metal dipole particles or mole- model dipole rectenna (rectifying antenna) arrays cules (Marks, 1986) and a later patent (Marks, operating in the microwave range at 10 GHz, 1988) describes antenna-like cylinders, each with achieving . 50% conversion efficiency and have an asymmetrical metal–insulator–metal (MIM) integrated metal–insulator–metal rectifier diode for rectification. Marks also invented a in a mm-scale antenna. Their initial goal was to system (Marks, 1990, 1991) in which a plastic demonstrate the feasibility of high-efficiency opti- film containing parallel chains of iodine mole- cal frequency technology at a single wavelength cules form linear conducting elements for the (Berland et al., 2001). ITN’s collaboration with collection of optical energy. The (theoretical) the US National Institute of Standards and Tech- conversion efficiency was claimed to be 72% nology (NIST, 2002) has made infrared rectenna (Marks, 1990) or, elsewhere, . 80% (Marks, structures with metal–insulator–metal diodes be- 2002). tween dipoles for operation at 30 THz (10 mm Lin et al. (1996) reported the first experimental wavelength) by atomic layer deposition. The evidence for light absorption in a fabricated University of Florida has been investigating the resonant nanostructure and rectification at light application of SiC crystals as antennas for solar frequency in a test structure. The device used energy collection (Goswami, 2001; Mitchell Mar- grooves and deposited metallic elements to form a ket Reports, 1992). parallel dipole antenna array on a silicon substrate and a p–n junction for rectification. They ob- 3 . RELATED TECHNOLOGIES served an output resonant with the dipole length and dependent on light polarization and angle of A solar rectenna is similar to a simple radio the incoming light, indicating that the device telescope or radiometer (Burke and Graham- indeed possessed antenna-like characteristics. Smith, 1997) except that the radio telescope needs ITN Energy Systems Inc. ITN is investigating to measure the radiative power received through optical antennas coupled to fast tunnel diodes the antenna, often with a square-law detector

Fig. 2. Kraus’ solar rectenna concept (Kraus, 1988). Solar energy collection by antennas 397 which produces an output voltage proportional to nelling devices are often chosen for such applica- the input power, while the rectenna needs to tions (Wang, 1976; Elchinger et al., 1976). Early convert that power to useful work. There are also MIM devices were ‘cat’s whisker’ diodes but other technologies of relevance. modern diodes of this type are formed from deposited metal films and thin oxides. 3 .1. Microwave rectennas The dream of wireless electrical power trans- 3 .4. Ratchets and brownian motors mission, especially to or from or in space (Hirsh- It is well known that in systems far from man, 2001), has prompted an intense research thermal equilibrium it is possible to rectify un- effort (Brown, 1984), beginning with Tesla in biased noise by breaking spatial inversion symme- 1899. Theoretical and experimental work has been try. The research field of Brownian motors and carried out for wavelengths of 3–122 mm. Re- ratchets is reviewed by Reimann (Reimann, ctenna efficiencies (microwave to DC) have been 2002). The work of Song (Song, 2002) and measured in excess of 80% at a single frequency colleagues has resulted in InGaAs–InP ballistic (Konovaltsev et al., 2001; Brown, 1970). electron devices able to rectify 50 Ghz electro- 3 .2. Radio-powered devices magnetic radiation at room temperature. They are essentially artificial photogalvanic nanocrystals There is a range of low-power electronic de- (Belinicher and Sturman, 1980). Similar struc- vices which derive their operating power from tures may potentially be useful at even higher electromagnetic fields. The earliest radio receiv- frequencies but their upper frequency limit has ers, crystal sets, were self powered by rectification not yet been established. The upper limit may be of the incoming radio frequency signal. Several set by the distance an electron can travel ballisti- inventors have developed devices to monitor cally during a half cycle of the incident field microwave oven leakage or other radiation (assuming a quasi-monochromatic source, for hazards by powering an indicator from the leaking now). Linear polarisation splitting of sunlight radiation via a rectenna. A similar method has would be a necessary prerequisite for solar energy been used to power active biotelemetry devices, conversion. The host material for the ratchet implanted therapeutic devices, radio frequency would need to have bandgap energy exceeding the identification tags and transponders and even the photon energy of the incident radiation to avoid proposed recharging of batteries in microwave the absorption process that is usually encouraged ovens. in solar cells but which would be detrimental here. Such a device would be converting energy 3 .3. Optical and infrared antennas and diodes that is normally lost through free carrier absorp- Optical and infrared antennas and antenna-cou- tion in a . pled detectors are being researched for a range of applications. In the optical spectral range, R.J. Green has developed an optical antenna for 4 . SOLAR RECTENNAS communications (Green, 2002). Others have de- veloped bow-tie antenna structures as probes for 4 .1. Filtering scanning near-field optical microscopy (Oes- Two filters are usually employed in rectennas terschulze et al., 2001). Fumeaux et al. (1999) (McSpadden et al., 1998; Nahas, 1975). An input measured the performance of a lithographic in- filter between the antenna and the rectifier must frared antenna at optical frequencies and observed (a) form an impedance match between the antenna a polarization-dependent response. The response and the subsequent circuitry, (b) ensure a continu- of nanometre-scale metallic antennas have been ous current path for power flow from the antenna simulated and applications proposed in the fields despite the intermittent nature of the rectifier of diagnostic imaging and the detection of chemi- current, and (c) prevent the reradiation by the cal or biological agents (Podolskiy et al., 2002) antenna of harmonic energy produced by the non- and there has been extensive research on infrared linear load presented by the rectifier (Brown, antenna devices intended to enhance the coupling 1970). It was found that power flow continuity into solid state photoconductive or photovoltaic was able to be achieved, even with half-wave detectors (Christodoulou and Wahid, 2001). rectification, by suitable filter design (Raytheon, Extremely fast operation is required for optical- 1975). A choke or L-type output filter following frequency rectification, implying small size (Lin the rectifier should also achieve the desired result. et al., 1996). Metal–insulator–metal (MIM) tun- Harmonic generation is a fundamental result of 398 R. Corkish et al. the rectification process and its re-radiation is a In this case, for maximum concentration, we potential problem because it can result in lost would seek to confine the main beam to the and interference. Several designs are avail- disk, of around 30 arc minutes angular extent. able in the literature for efficient rectifying micro- This would require a square or circular array of wave power converters (Nahas, 1975; McSpadden about 100 wavelengths across (Elliott, 1963). et al., 1996; Razban et al., 1985). Output filtering Metallic structures for this application may need is necessary to smooth the rectified signal to DC. to be limited to a few nm thickness (Podolskiy et In the case of solar energy collection with al., 2002). rectennas, there is an additional problem of the At least partial coherence is needed across an wide bandwidth necessary to encompass the solar array to ensure that the components from the spectrum (wavelength range of 0.2–2 mm corre- antenna elements combine constructively. The sponds to approx. 150–1500 THz). The above transverse coherence distance for the solar disk is requirements will be difficult to satisfy over such around 50 mm(Graham-Smith and King, 2000), a spread of frequencies. In particular, it will be roughly consistent with the array size needed to difficult to deal with harmonics arising from the satisfy the beamwidth requirement, above. How- collection of long-wavelength light since some ever, the issue of temporal coherence along the harmonics will be within the desired bandwidth direction between the sun and the antenna is a for energy acceptance. It will become necessary to more complex issue requiring further examina- split the spectrum and direct different fractions to tion. different rectennas or to frequency-split the output of a broadband antenna. 5 . EFFICIENCY LIMITS 4 .2. Polarisation Bailey (1972) suggested that 100% solar The energy in unpolarised sunlight cannot all energy conversion efficiency may be possible but be collected by a single antenna element, even at he also claimed the same upper limit for photo- a single frequency. At least two orthogonal ele- voltaic converters in general. There was at that ments are required to maximize the power. Prior time considerable confusion in the literature about splitting of sunlight into two orthogonal linear whether the Carnot efficiency limit should apply components, by use of birefringent crystals for to solar energy conversion (Bailey, 1980). Today, example, would be necessary for some possible it is not questioned that it does and, indeed, more converter designs, such as Song’s ratchets (Song, restrictive limits apply for any conceivable con- 2002). verter structure. Kraus (1988) also claimed the possibility of 100% solar conversion efficiency. 4 .3. Combining antenna element outputs Several authors have claimed that 100% collec- Two basic families of designs have been pro- tion efficiency in the transmission of microwave posed for antenna solar energy collectors. Bailey power should, in principle, be possible. Antenna (1972), for example, had individual pairs of texts routinely state that an aperture antenna can antenna elements each supplying its own rectifier theoretically transfer to its load all the electro- and the DC rectifier outputs were combined. magnetic energy that impinges the aperture Kraus (1988), for example, on the other hand, (Kraus, 1988; Balanis, 1997). That conclusion combined the electrical oscillations from many assumes uniform distribution of energy across the antenna elements in a particular phase relationship aperture, a load ideally matched to the antenna and delivered their combined output to a rectifier. and single frequency, coherent operation. How- With the former method there is the immediate ever, a receiving antenna with a resistive load concern that the tiny power expected from one or must also transmit noise power according to the two antenna elements may not be enough to second law of thermodynamics and the principle produce sufficient voltage to allow proper opera- of detailed balance. Under equilibrium conditions tion of any conceivable actual rectifier diode. The an antenna receiving power from a source and latter approach overcomes that problem but at the transferring it to a load must transmit the same expense of the need for spatial coherence across amount of power back to the source in order to all the antenna elements feeding a rectifier. maintain equilibrium (see, for example, Burke and Graham-Smith, 1997; Pawsey and Bracewell, 4 .4. Antenna size and coherence 1955). The origin of the transmitted power is the The beamwidth, or acceptance angle, of an voltage generated in a conductor by thermal array antenna is related to its size in wavelengths. agitation of the charge carriers, known as Johnson Solar energy collection by antennas 399 or Nyquist noise, from the resistive load at the gestion that the presence of rectifying diodes may same effective temperature as the source. At offer that benefit in rectennas. However, even if frequencies below | 1013 Hz a classical approxi- that were so, we must still consider the generation mation suffices and the available white noise of noise by the rectifiers (Ambrozy,´ 1982). Shot power from a resistor at absolute temperature, T, noise is a fundamental consequence of the trans- is kTB Watts, where k is Boltzmann’s constant port of quantised charge carriers across a potential and B is the equivalent noise bandwidth (Hz) barrier and the sharp current pulses due to carriers (Schwartz, 1990, Section 6–14). The noise is either becoming or ceasing to be minority carriers ‘white’, having a frequency-independent power (van der Ziel and Becking, 1958). The noise spectral density of kT/2. At higher frequencies, power is proportional to the DC current through a including the optical range, quantum effects are rectifying barrier. Shot noise is often considered evident and the noise current spectral density is as an independent phenomenon to thermal noise given by (Schwartz, 1990, Section 6–14) but they have been shown to actually be special limits of a more general noise formula (Landauer, 1 hf hf 1993). The shot noise form is evident when the G ( f ) 51] ] ]]]]] i 22FGexp(hf/kT 2 1) mean free path is short compared to the sample size, as in most semiconductor junction devices. where h is Planck’s constant. The first term is due to the quantum mechanical zero point energy. This spectrum is not white, but decreases with 6 . SPECULATION ON POSSIBLE frequency, particularly above kT/h, which is APPLICATIONS 13 l5 m around 10 Hz ( 30 m) at room temperature. 6 .1. Beam steering This re-radiated noise is commonly ignored by antenna engineers and their efficiency estimates It is common at microwave and millimeter are based on the ratio of incoming and reflected wave frequencies to spatially steer the beam of a power at the signal frequency and that, in turn, is phased array antenna without any physical move- based on the analogous ratio in transmission mode ment by controlling the phase of the signal from according to the reciprocity theorem. each element in the array. This suggests the future If power is extracted from the load, reducing its possibility of a concentrating solar energy collec- temperature, a new balance exists between the tor with electronic pointing without moving parts. incoming, extracted and reradiated powers. Hence, the solar energy conversion efficiency 6 .2. Frequency up-conversion limit is expected to be the same as that for a solar The benefits available from up-conversion of thermal collector. That limit is 85.4% for a non- sub-bandgap light passing though a bifacial solar energy-selective collector with maximal concen- cell have been outlined by Trupke et al. (Trupke tration if we assume the Sun to be a 6000 K black et al., 2002). Low energy infrared photons can body and the surroundings to be at 300 K (de Vos, contribute to cell current if the energy of two or 1992, ch. 5), in agreement with that stated by more can be consolidated in the production and Berland et al. (2001). Multicolour thermal con- emission of a super-bandgap photon by an up- verters (de Vos, 1992, ch. 8) use multiple materi- converter. Trupke suggests the use of impurity als with different bandgaps to increase the ef- levels to facilitate up-conversion. ficiency limit, with maximal concentration and an Electromagnetic up-conversion is also possible infinite number of materials, to 86.8%. An infinite through the generation of harmonic frequency series of frequency-selective filters offers the components by non-linear loading, such as in one same advantage and the same limit in the case of style of retail security tag (Crowley, 2000). rectennas. Application of the effect at optical frequencies has There remains an open question about whether previously been proposed (Crowley, 2000). Song 86.8% is the ultimate limit and whether there may (2002) suggests that artificial non-linear nanoma- be scope for rectennas to reach the Landsberg terials have a quadratic response and should limit of 93.3%. Ries (1983) and, independently, therefore generate second harmonics to the exclu- Wright et al. (2000) showed that the ultimate limit sion of higher ones. is theoretically achievable if time-reversal Suppression of the re-radiation of harmonics is asymmetry can be invoked by use of a non- often a problem for the designers of rectennas reciprocal absorber, for example, through the use (McSpadden et al., 1992) but it could be a benefit of optical circulators. There is a tantalising sug- if several diode-loaded optical antennas could be 400 R. Corkish et al. located behind a bifacial solar cell with a reflector C orkish R. and Green M. A. (2002) PV in Europe, WIP, Munich, Rome, 7–11 October (in press). behind the antennas. Frequency-multiplied radia- C rowley R. J. (2000) Optical antenna array for harmonic tion could then radiate energy back to the rear of generation, mixing and signal amplification. USA Patent no. the cell and enhance its output. Sheets of polymer 6,038,060. d e Vos A. (1992). 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