Arrays of metallic thermocouples in the shape of spiral nanoantennas are proposed as infrared detectors, which use the thermoelectric properties of the metallic interfaces to generate electrical DC signals. The responsivity of these types of antennas is evaluated from both theoretical and numerical perspectives pointing out its potential as infrared sensors. Moreover, the same structures can be used to characterize the state of polarization of the optical near fields with a spatial resolution comparable to the wavelength.
© 2014 Optical Society of America
Nanoantennas are resonant metallic structures that provide a way to confine the optical energy into sub-wavelength volumes with a high level of control [1,2]. These nanostructures take advantage of the wave nature of the radiation in order to induce a resonant current along its structure that confines the optical energy [3–5], opening this manner a new route to sense, manipulate and harvest the infrared and visible wavelengths [6–9].
In the far-infrared regime, the introduction of antennas to sense the thermal wavelengths has led to the development of infrared (IR) image acquisition systems and harvesting devices of novel functionalities [10,11]. First antenna thermal detectors have used coupled niobium micro-bolometers in order to introduce substantially faster detectors than the bulk-bolometers at the time (µs), showing efficiencies around 0.01% [12–14]. Meanwhile, the substitution of micro-bolometers by THz nano-rectifiers (based on metal-insulator-metal or metal-insulator-insulator-metal tunnel barriers [15–19]) had added to the antennas the capability to harvest the optical energy. These so-called rectifying antennas were experimentally realized and employed to detect the infrared and visible wavelengths with success, albeit for harvesting applications was not the case. In spite of its attractive recovering efficiency that is claimed to be 100% [8,9], rectifying antennas present major inconvenient due to its low-performance, which to our acknowledge reach efficiencies values of 10−9 and 10−12 percent for the most explored barrier . The match between diodes and the antennas, and the diode-like behavior of the tunnel barriers are self-dependent key parameters that should be improved to increase the performance of devices [8,9]. By the other hand, the incorporation of nano-rectifiers to the antennas (whose dimensions are demanded to be around 60 nm x 80 nm for THz rectification ) requires the use of multi-level e-beam lithography processes what can conduce to not-reproducible results. In order to incorporate antennas for harvesting applications, different mechanism other than direct rectification should be explored. Geometric rectification has been proposed as an alternative way to overcome these difficulties using graphene-based devices .
In this contribution, we propose a different infrared sensor based on the thermoelectric effect using optical nanoantennas. It permits to overcome, or forget the transfer energy constraint (or mismatch impedance) between the antennas and coupled fast rectifiers, increase the efficiency of devices and reduce the technological problems arising from fabrication. The proposed IR nanoantennas combine the optical properties of antennas to capture radiation with the use of the Seebeck effect as the transduction mechanism. Especially for null or very low bias, the response of thermoelectric IR detectors is potentially very advantageous. The work of Dillner et al  shows that sensor detectivity (D*) can be several orders of magnitude higher in IR detectors based on the Seebeck effect. On the other hand, recent contributions has shown the capabilities of this transduction mechanism [23,24] and even state that Seebeck effect is responsible for the signal in Metal-Oxide-Metal devices failing to tunnel the generated currents .
The proposed IR sensors consist of series arrangements of nano-thermocouples in the shape of antennas sized to absorb the thermal wavelengths around 10.6 µm. When the structures are illuminated, the resonant current causes a thermal gradient inside the structures (by Joule heating) that leads the thermocouples to generate a Seebeck voltage at the open ends [26, 27]. This signal is given by :26].
In this work, we determine the Seebeck voltage and responsivity of a series of infrared devices from both numerical and theoretical perspectives showing its potential for infrared sensing. We choose as proof of concept three types of spiral nanoantennas, currently used to sense and retrieve optical energy at a wavelength of 10.6 μm [13, 28].
2. Numerical simulations
A sketch of the infrared detectors is shown in Fig. 1 (a)-(c). The detector integrates a square spiral (Fig. 1(a)) and a single loop nanoantenna (Fig. 1(c)) that are sensitive to linear polarized radiation, and an array of Archimedean spiral antennas (Fig. 1(b)) that detect right and left-handed circularly polarized radiation.
The square spiral (Fig. 1(a)) is composed by two symmetrical arms 2.4 μm long (200 nm x 100 nm cross section), which are made out of seven linear elements Ln, whose length is given by:
The Archimedean array (Fig. 1(b)) is composed of a left-handed and a right-handed spiral connected by the extremes and separated from centers by a distance of 4 μm. The arms of the spirals are described by the following linearly proportional relationships:29]. The arms of both spirals are fabricated with two types of metals in order to form the arrangement shown in Fig. 1(b). Finally, Fig. 1(c) shows a single square closed-loop composed by four linear elements of 2.8 μm long  and a cross section of 200 nm x 100 nm.
The considered materials are titanium and nickel (colors yellow and orange, respectively) metals that show an appropriate difference in the values of their Seebeck coefficient, property that determines the performance of materials to generate voltage from heat. By the other hand, metals show a low thermal conductivity , allowing the thermocouples to reach a substantial temperature increase and so, to enhance the response of thermocouple given by the relationship (1). The structures were placed on a semi-infinite SiO2 substrate and a 10.6 μm wavelength plane-wave was used for far-field illumination (with an irradiance of 117 W/cm2).
The modeling of the structures was performed by using the software package COMSOL Multi-physics (ver3.5a) which provides a good multi-physics platform where both electromagnetic and thermal domains are fully integrated. The numerical model was built using all the optical, thermal and thermo-electrical properties of materials reported at a 10.6 μm wavelength .
As a first step we evaluated the thermal behavior of the devices by considering the antennas as heat sources when illuminated. For this purpose we determined the increase in temperature by Joule heating due to the optically induced currents. The heat-power density (q(r) [W/m3]) was evaluated inside the volume of the nanoantennas by using :
The power density was then used as a source of heat into the solver in order to determine the steady-state temperature distribution, T(r), inside and outside the resonant metallic structures. The temperature changes were calculated by solving the heat transfer equation:
The temperature increase of the junction ∆T is found from the thermal simulations and used to evaluate the voltage response of the antenna by using Eq. (1), as well as the Seebeck coefficient values of 7.2 μV/K and −19.5 μV/K, for nickel and titanium, respectively. Finally, the responsivity exhibited by the thermo-electric nano-antennas was evaluated by:33]. A conservative value of this parameter is around λ2, although smaller values (≈0.1 x λ2) have been reported .
Even though the thermal-optical analysis is performed by a classical treatment (neither the thermal nor the electric contribution arising from the interfaces are taken into account), this method has shown to give accurate results for thermal-optical analysis of nanoantenna-coupled-bolometers [34, 35].
The three arrangements of Seebeck nanoantennas presented in this paper (see Fig. 1) are illuminated for several polarization states, as it was mentioned in section II.
The first element to consider is the square spiral antenna shown in Fig. 1.(a). It has been tested for three different polarizations: circular polarization (right-handed, RCP), and linear polarization along the X (horizontal, LP 0°) and Y (vertical, LP 90°) axis of the square. This square contains 13 Ni-Ti junctions. In order to have it operational and provide an open circuit voltage we have to choose pairs of these junctions. As expected, the hot and cold character of the junctions changes with polarization. Figure 2 shows the temperature map for three polarization states. We have also represented the profile of temperature along the structure. The locations of the junctions are marked with vertical lines. The locations #1 and #15 are the terminal points and are not considered. There are two possible choices, A and B, for the pairs of junctions used to deliver a given voltage from the spiral. Choice A begins with pair 2-3 and choice B begins with pair 3-4. The difference in temperature for these two possible choices is plotted in the bottom of Fig. 2 for the three states of polarization simulated here. This difference in temperature is the responsible for the Seebeck voltage obtained from the successive contribution of thermopairs connected in series.
From the previous figure we can see that the system can be tailored to have all the temperature differences having the same sign for the same polarization, for example by eliminating some of the junctions at the center of the structure. Both choices of the junctions contain temperature differences, located at the central region of the antenna which diminishes the magnitude of the Seebeck voltages. If this system is used to provide a signal sensitive to the linear polarization we have to calculate the voltages provided by this arrangement. The results are summarized in Table 1.
Figure 3 shows the temperature profile for both elements of the Archimedean spiral nano antenna array which is sensitive to circular polarization. The thermoelectric junctions are localized at the center of the spirals. The hot junction corresponds to the spiral having the helix orientation in the same direction as the incoming polarization. The difference in temperature is 172.3 mK which provides a Seebeck voltage of 3.82 μV. Assuming an irradiance of 117 W/cm2 and an effective area of approximately 25 μm2 calculated as twice the effective area of a single nanoantenna , the responsivity of a single element would be 112 mV/W.
The square closed-loop geometry (Fig. 1(c)) shows a distinctive behavior when impinged with different linear polarization orientations. Figure 4 shows the temperature map (right) and profile along the loop (left). Temperature profile generates a voltage difference between the metal junctions that is polarization dependent. From the results, we can see that horizontal and vertical polarizations produce positive and negative alternating voltages respectively. This is caused by the interchanged role of the hot and cold junctions when changing the orientation of the incoming electric field. The case of horizontal (0°) and vertical polarization (90°) provides a voltage almost three orders of magnitude larger than for the 45° and 135° degree orientations. This is due to the symmetry of the arrangement and the location of the junctions. The Seebeck voltage should be extracted by opening the loop at some given location.
The responsivity of nanoantennas at 10.6 µm thermal wavelengths was evaluated by considering them as isolated systems. Albeit, in order to integrate them into signal acquisition systems, as the IR imagining device presented in ref. 11, some considerations must be taken into account. First, the thermal impedance of the electric contacts must be higher than that of the antennas in order to prevent the heat exchange between both elements. Second, the electric impedance of the acquisition system should be tuned in order to match the internal impedance Ri of the antennas. When these conditions met, the sensed DC power reach a maximum value given by PDC = V/4Ri , where Ri is usually considered as the mean ohmic resistance of the nano-thermocouples ; here evaluated with the dimensions of the structures and the values 420 nΩ•m and 69.3 nΩ•m for the DC titanium and nickel resistivity, respectively.
An estimation of the efficiency ηe, exhibited by the IR detectors can then be performed by evaluating the ratio of the power that antennas generates PDC to the power by heating they absorb QV (obtained by integrating the heat-power density over the volume of the antennas). The internal resistance, DC power, resistive heating and conversion efficiency were evaluated for some specific cases and presented in Table 2.
The efficiencies values that Seebeck nanoantennas reach range from 10−9 to 10-5%. These values are 1 to 103 greater than the efficiency of the reported rectifying nanoantennas counterpart [20,22]. The efficiency of the rectifying antennas is drastically decreased because two mechanisms of losses are conjugated, the impedance matching between the tunnel barrier and the antenna, and the poor diode-like performance of the tunnel barriers. By using Seeebek nanoantennas not impedance losses are seen, increasing this manner the nanoantennas overall performance. However, the efficiencies of the proposed IR detectors remain low because of the heat losses through the substrate. These losses could be reduced by using air-bridge technologies.
The response of a series of Seebeck nanoantennas to convert the optical power of radiation at λ = 10.6µm into DC power was evaluated by using thermal numerical simulations, showing that devices represent an alternative for infrared sensing (exploiting the optical energy naturally dissipated as heat). Numerical simulations show a voltage responsivity of 112 mV/W for these Seebeck nanoantennas, this value can be increased by reducing the effective thermal conductivity of the substrate. This can be achieved by suspending the device on air above its substrate. Moreover, engineering of large phase-arrays of nano-antennas acting as series thermocouples arrays can also be implemented to increase the voltage output and the capture area of the devices.
When considering Seebeck nanoantennas for the characterization of the state of polarization, the use of the Seebeck effect is well suited to provide a signal that can be related with the difference in power of two orthogonal components of the electric field. This has been demonstrated numerically for an arrangement of two Archimedean Seebeck nanoantennas. This element is sensitive to levo and dextro polarization states and produces a signal proportional to the fourth Stokes parameter. Also the square closed-loop antenna is sensitive to linear polarization when placing the thermocouple junctions at the appropriate place.
This work was supported by the project “Centro Mexicano de Innovación en Energía Solar” from Fondo Sectorial CONACYT-Secretaría de Energía-Sustentabilidad Energética”, by CONACYT through postdoctoral grant CV-45809, by FONDECYT under project 3120059, by La Region Lorraine; and by Project ENE2009-013430 from the Spanish Ministerio de Innovación.
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