Optical antennas and resonant structures have been extensively investigated due to its potential for electromagnetic detection and energy harvesting applications. However their integration into large arrays and the role of connection lines between individual antennas has drawn little attention. This is necessary if we want to exploit its potential constructively and to enable economical large-scale fabrication. In this contribution we point out some features that an efficient antenna array should address. Experimental measurements on aluminum microbolometers are compared to electromagnetic simulations, it is shown that the finite size of a real array and the interconnection lines interact and affect the global performance.
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Bolometers are resistive elements constructed from materials with a high temperature coefficient of resistance (TCR) so that absorbed radiation will produce a change in resistance. They are operated by passing a bias current through them and monitoring the output voltage; a change in this voltage will reflect changes in resistance. Small size devices have also the advantage of fast response and less power consumption . Indeed uncooled microbolometer arrays have emerged as a good alternative against photon detectors for IR measurements and in image-forming systems .
On the other hand, antenna elements that capture electromagnetic energy from IR and visible radiation have been demonstrated. Dipoles, spirals and loops have been extensively studied, and they present their own bandwidth and radiation patterns [3, 4]. The element size is typically a fraction of the wavelength’s radiation. When used as detectors these antennas are typically connected to a transducer that is placed at the feed point of the antenna. The transduction mechanism can take the form of a rectifying junction that provides a voltage signal. Some operating antenna-coupled detectors use metal-oxide-metal structures to produce the rectification of the currents built at the antenna structure. In an array, the output of the rectifiers can be connected together, allowing a large number of antennas to be networked to increase output power.
In any case, the building of electrical currents within the metallic structures produces heat dissipation that can be sensed using the bolometric effect. Although microbolometers do not rectify, when coupled to optical antennas their response can be evaluated by measuring voltage changes under different polarization states. In this case a bias voltage is necessary for operation. Micro-antenna coupled IR detectors arranged in large arrays have been demonstrated for imaging applications and laser characterization [5, 6]. They have been also proposed for solar energy harvesting .
When antennas are deployed in large arrays, the role of bond pads, load lines, biasing in-chip circuitry, and connection metal strips between antennas is non-negligible [8, 9]. They become long-wire antennas themselves. Even more, considering a bolometric device, the response of these auxiliary elements compete both as dissipative DC structures, and also as resonant elements that may mask the signal from the individual antennas. Buried load lines and vertical biasing has been proposed and experimentally demonstrated . However, if only a planar fabrication is available, the connection lines should be taken into account to fully understand the performance of the fabricated devices.
In this paper we are not interested in figures of merit such as responsivity or efficiency of the individual resonant elements, but rather in the overall performance of the whole array. We have shaped a bolometer to form an antenna structure sensitive to the polarization of the incoming beam and, using this individual element, two types of arrays were fabricated and tested. Their response illustrate a complicated collective behavior: the connection lines resonate with the incoming irradiance contributing to the signal at different polarization states, shadowing the polarization selectivity of the antenna array. This is also modulated by the distribution of the current bias. The experimental results have been satisfactorily simulated. Finally we address designing issues necessary to produce useful large arrays of electromagnetic collectors.
2. Optical antenna arrays
The array design has been performed by modelling an infinite array of bow-tie antennas. We have used the commercial software CST Microwave Studio (Computer Simulation Technology AG), setting periodic boundary conditions, where the geometry of the simulated unit cell is shown in the inset of Fig. 1(a). The antennas are 30 nm thick Aluminium devices over a 400 nm thick layer of SiO2 and an infinite silicon substrate layer. The antenna array is excited by an incident plane wave with a polarized electric field. The figure of merit that was used in the optimization was the absorption efficiency. This is defined as the percentage of power dissipated in the structure normalized by the power carried by the incoming plane wave. The antennas give a nearly constant wavelength dependency in the region from 9.4 μm to 15 μm. Both vertical (i.e. along the bow-ties) and horizontal polarization were investigated. For vertical polarization, it was found that the infinite array absorbs 19% of the power of a plane wave incident from the air region (and 60% of the power from a plane wave incident from the silicon region). Instead for the horizontal polarization, the array receives 4% and 12% of the power depending if the plane wave comes from the air or the silicon region. The bolometric effect will be distributed along the whole structure and enhanced at the resonant locations.
Following the criteria extracted by the electromagnetic simulation a variety of arrays were fabricated. These structures were written by electron beam lithography on a Si wafer coated with 0.4 μm insulating layer of SiO2. For our study, we have fabricated arrays of 10 × 6 and 20 × 12 antennas connected in series. A scanning electro microphotograph (SEM) of a 10 × 6 array of antennas is shown in Fig. 1(a). Another interconnection configuration was fabricated and experimentally investigated. These were 20×12 and 38×24 arrays of antenna devices in a parallel-series arrangement. Figure 1(b) shows a SEM image of a 20 × 12 array. As illustrated in the inset, rows of antennas in series are connected side by side in a parallel configuration. This provides robustness in case of a failure of an individual device. Thus, we have tested arrays based on these two grid configurations.
3. Measuring setup and experimental results
A diagram of the experimental setup is shown in Fig. 2(a). A CO2 laser (LASY-5 Access Laser) at 10.6 μm wavelength and chopped at a frequency of 1 KHz is used as a light source. A polarized beam is focused at the working area using a 25.4 mm focal length lens (ISP optics). The laser beam was characterized using the knife-edge technique and a ∼ 50 μm Gaussian spot diameter was measured at the beam waist . Thus, light is incident perpendicular onto the wafer and excites currents on the antenna bow-tie structure.
The readout lines are eventually connected to a voltage divider composed by two resistances: Ra, the resistance of the antenna array, and Re, the external resistance used to fix the biasing voltage. Using this voltage divider we derive a DC resistance of 874±23 Ω for the 10×6 series arrays and 1941±86 Ω for the 20×12 series arrays. The 20×12 and 38×24 series-to-parallel arrays of antenna devices show the same resistance of 481± 12 Ω. This resistance accounts for all the elements from the array, the lead-line connections and the bond wiring. However, since the cross section of the antenna array device is so small, nearly 50% of this resistance is due to the array alone.
This arrangement produces a voltage signal proportional to the optical irradiance at the antenna plane. Thus, a current I, generated by the bias voltage (set to Vbias = 100mV), flows through the array. The illumination power absorbed by the bolometer will rise its temperature. This causes a change in the resistance of the bolometer (ΔRa) and consequently in the voltage across it. From a simple analysis of the DC voltage divider:
Moreover, considering that the temperature increase (ΔT) is small, so that the resistance change is linear with temperature, then ΔRa = αRaΔT, where α is the TCR constant of the material. Thus, the relative current change when the array is illuminated is
In our experiments, and in order to decouple the resonant behavior from the purely bolometric effect, we monitor the voltage output signal as a function of light polarization. As illustrated in Fig. 2(a) a half-wave plate (Altechna Co.) was employed to rotate the polarization plane in 5° steps. The average laser power reaching the device was 150 mW and a thermopile based detector (Thorlabs S310C) was used to compensate for laser power drift.
The alignment of the laser beam with the array was a critical issue. The optical axis of the beam was found to move as the waveplate rotated. Therefore, to find the center of the array, we performed a two-dimensional scan in an x–y plane recording the response of the device in each position , the device is moved using DC-motor stages (PI M-415.DG). The length of the scan depended on the size of the arrays. When the scan is finished the position for the maximum response is found and the laser beam accordingly located. At this location the voltage reading is stored along with the polarization angle and the power from the monitor detector. Instrument control and data processing was performed by a computer using Matlab.
A typical response map, obtained from the 10 × 6 series array of aluminum antennas, is shown as an inset in Fig. 2(a). The scan covers an area of 50 × 50 μm2 with a 2.55 μm step size in the x and y-direction. It has been shown that the measured output signal is, in general, the convolution of the arrays’ spatial response and the beam profile . We have plotted the map in a logarithmic scale so that small changes can be seen. A circular pattern is observed, its maximum corresponding to the array center location.
Then the waveplate is rotated 5° and the process starts all over again. A plot of the wave plate rotation angle versus the normalized voltage reading is shown in Fig. 2(b). It is clear that the array shows dependence with polarization, thus confirming the antenna behavior. Note that when the half-wave plate rotates 45° the actual polarization plane rotates by 90°. A visibility ratio was defined to be δ = (Vmax − Vmin)/(Vmax + Vmin). This is a measure of the polarization sensitivity and, for the 10 × 6 array, was evaluated to be 0.19.
The response map obtained from a 20 × 12 series arrangement array is shown in Fig. 3(a). This is a 119 × 119 μm2 scan using a 3.4 μm step. This array also showed polarization dependence, with δ = 0.36. Only double, in spite of an area four times larger than the 10 × 6 array. Moreover, some interesting features were exposed. The probe beam was relatively smaller to the array and the mapping resolved some structures. Two maxima can be seen in the map, and they correspond to the regions of the connection turns between antennas. The inset shows a diagram of the device at the same scale. Clearly, there is a bolometric effect at those locations that is shadowing the induced currents produced at the antennas.
The response map obtained from a 38 × 24 series-parallel array is shown in Fig. 3(b). This is a 765 × 765 μm2 scan using a 17 μm step. It is a large scan since the array itself is quite extensive, and we also wanted to expose readout lines behavior. The inset shows the array at the same scale. Again it can be seen that the maximum response does not correspond to the center of the array, but with some section of the readout connections that feeds the array. In both cases the center of the arrays does not correspond with maximum signal.
As we shall see in next section, a closer look to the read out lines exposed some dependence with polarization. These measurements demonstrate that the arrangement of the grid must be carefully designed in order to interrogate and boost the efficiency of the arrays. These issues will be evaluated using simulations.
Finally, we have preliminary results with bolometric antennas fabricated in titanium. The resistivity and skin depth of Ti is 15 and 3 times larger, respectively, than the one from Al, and the thermal conductivity is 10 times lower . We have measured the polarization sensitivity for a single Ti antenna and δ was found to be 0.46. This is already a factor of 1.3 the δ measured for 20 × 12 Al arrays. Higher polarization dependence is expected for Ti arrays since the bolometric effect will be enhanced. Illuminating from the substrate-side will also improve this figure . Moreover, it has been demonstrated that this sensitivity can be further increased, by improving the thermal isolation of the substrate, at a cost of reducing frequency response .
4. Finite element simulations and discussion
When an electromagnetic wave interacts with resonant metallic structures there are several physical mechanisms that trigger the response of the device. Electromagnetism and heat transfer will play the most significant roles in the description of the element. In some cases an analytical model can be derived that is even expanded to include mechanical vibrations . Typically a multiphysics numerical model approach is necessary to describe this multiple contribution .
To begin with the analysis of the grids, we will focus on a purely DC electrostatic description of the device. At a level of the array connection a simple model can already predict some issues that are of importance to improve the overall performance of the device.
We have used a finite element (FE) method software provided by the Partial Differential Equation Toolbox of Matlab. Thus, in our problem we have a conductive medium, with conductivity σ, and a steady current (bias current). The physical model for this problem consists of the Laplace equation −∇(σ∇V) = 0. The electric potential V is defined at the boundaries that interface the array grid with the readout lines (corresponding to set the Vbias = 100mV). For the rest of the boundaries, we set the normal component of the current density n(σ∇V) to be zero. We also consider variations with z axis negligible.
Thus, a 2D model of a 3 × 2 array of antennas was simulated and it is shown in Fig. 4(a). Although this is a simplified version of our fabricated designs, it will help to illustrate some issues. In this representation the gray scale is proportional to the modulus of the current density distribution, generated by a voltage difference set between the ends of the array. The connections between antennas show a maximum of current density since the cross section is smaller than at the bow tie locations. In particular, the connection turns, at the beginning and end of each row of antennas, are high current density locations. The square connection, at the left side of the array shows that the kinks are hot spots, and strong Joule heating is expected at those locations, hence a strong bolometric response. In general the electric field, near a sharp point on a conductor, is very high. This can be avoided by using rounded connections. On the right side the connections have been drawn round and the modulus of the associated electric field reduced by nearly 40%. Wide planar structures for read out connections are also preferable to reduce current density.
Other grid arrays have been reported in the literature. Some claimed to meet all the electromagnetic criteria necessary for an efficient energy collector, such as the one illustrated in Fig. 4(b) . It is claimed that this antenna array design enables DC bus lines with minimal coupling, minimized interference between adjacent apertures, and effective coupling to broadband, dual polarization radiation. However, the plot of the current density reveals that in this arrangement there are points of maximum heat dissipation at the junction to the readout lines. More importantly, it does not provide the same bias current to all the elements, the larger this grid; the less bias current is reaching the central antennas. Therefore, this grid arrangement is not adequate for a microbolometer array.
4.1. Polarization sensitivity of connection lines
A full description of the array behavior necessarily includes the effect of the incoming radiation and the power dissipated at each location of the device. As we mention in section 3, it was observed that the response maps obtained from large arrays were sensitive to the incoming light polarization. We have been able to explain and simulate the experimental results in two steps. First, using COMSOL (v. 4.2a) we have modeled a three layer structure: an Al array that forms the antenna’s grid, over an infinite Si substrate, and in between a 0.4 μm thick layer of SiO2 that works as a thermal and electrical insulating layer. Due to limitations in the available computational power, this simulated test array is smaller than our fabricated devices. However it will serve as an approximation. Thus, we have produced maps of a test array where the distribution of power dissipated is represented. This power is produced by the induced currents generated by an incoming polarized plane wave. This multiphysics simulation couples the results of the electromagnetic module with the thermal module that accounts for heat transfer in a stationary regime.
And secondly, this map is convoluted with a Gaussian distribution. This convolution simulates the measurements obtained by scanning the laser beam across the array of antennas. In section 3 we have shown that, when the size of the array is small compared to the beam size, then no structures can be observed, but a circular pattern. In our simulations, and since we cannot increase the size of the arrays, we have chosen to reduce the laser spot in the convolution process. However we keep the relative size constant compared with our experiments. Figures 5 and 7 illustrate the whole process for different grid arrangements and compare the results to the maps experimentally obtained.
In Fig. 5 the test array is a 6 × 3 array of antennas connected in series. Using COMSOL, the distribution of power dissipated in this structure under an incoming polarized plane wave is calculated and plotted in the first column. They are normalized to the maximum value. When polarization is vertical the antennas are aligned and in resonance with the field, particularly the central ones of the array. These sections have strong induced currents; hence power dissipation will be relatively high. A very different map is produced when the incoming polarization is horizontal: Other regions of the array became more active, and more power is dissipated at the connection turns than in the antennas. Those locations dissipating more power are heated producing an increase in the temperature and a change in the signal according to Eq. (1). It is important to note that the maps generated are modulated by the bias current which, for a serial device such as this one, is the same in all the structure. The convolution of these maps with a ∼ 4 μm diameter Gaussian spot produces the images of the second column. These simulated response maps can be directly compared to the experimental measurements plotted in the third column. The measurements were obtained from a 20×12 array of antennas connected in series. Similarities between our simulated and measured maps are apparent. In particular, for the vertical polarization the convoluted map is expected to look more round as the number of central antennas increases, as in our experimental conditions.
Figure 6 shows the effect of an increasing number of parallel lines in a test array with a series-to- parallel grid configuration. To produce these maps an extra consideration is taken into account: According to Kirchhoff law if I is the bias current that flows through the readout lines, then the current flowing through N identical parallel lines is I/N. Increasing N will decrease the bias current in all the antennas and, as described in Eq. (2) it will reduce their efficiency as bolometers.
Analogously as in Fig. 5, a 6 × 3 test array of antennas connected in a series-to-parallel arrangement is illustrated in Fig. 7. The distribution of power dissipated in this structure is also modulated by the bias current. However this time, to resemble our experimental arrays, the current is divided by twenty (N=20) when it flows through the antennas. That explains the relatively high dissipation power observed at the connection in relation with the array. Again, the convolution of these maps with the Gaussian spot produces the images of the second column. They can be compared with the measurements obtained from a 20 × 12 series-to-parallel array of antenas, shown in the third column.
Finally, Fig. 8 shows the polarization sensitivity for the two different grid arrangements analyzed in this paper. In these simulations all the antennas are replaced by a shorted line. The maps in the left column were normalized to a common value, and show the polarization sensitivity of the series arrangement. It can be seen that this grid have a higher response to vertical polarization, however this resonance is shadowed when antennas are present, as illustrated in Fig. 5. On the contrary, for horizontal polarization, even though the response is relatively lower, it is still significant when antennas are placed. In the case of the series-to-parallel arrangement, plotted in the second column, the small amount of current flowing through the lines reduces their efficiency, as it happened when antennas were present (Fig. 7). Nevertheless, the polarization sensitivity is apparent. In general the situation is equivalent to a wire-grid polarizer.
The results clearly show the parasitic resonances and the polarization sensitivity of the readout lines. Also, and in order to have a constant bias, it is clear that an array with a number of parallel connections have to be carefully considered if we want to exploit the whole array efficiently. Finally, and taking into account that the actual devices and the simulated ones have not the same geometric proportions, we consider that our simulated results are in good agreement with the experimental measurements.
Microbolometers working as antenna detectors have been used for sensing optical radiation in the IR. When used as arrays they benefit from the collective behavior of the elements. Besides, the signal produced by these arrangements is larger and therefore better processed by the readout electronics. This situation requires the use of connection lines to bias, and means to collect the signal from the resonant structures.
We have analyzed the role of the connection lines from two points of view: the distribution of the polarizing bias, and the influence of their parasitic resonances. The distribution of current density due to the DC biasing is non-homogeneous along the connection lines, especially at the locations of kinks and straight lines intersections. This is important when considering the bolometric effect as the transduction mechanism. The results show that the geometry of the connection lines influences the bias seen by antennas placed at different locations. It is also expected a better behavior of rounded connection lines that preclude the existence of regions where the electric field (DC and high-frequency AC) is enhanced and may dissipate power.
Moreover, the contribution of the connection lines when the arrangement is illuminated has been also analyzed by using an EM simulator showing the resonances of these auxiliary structures. These results have been positively compared with experimental measurements of bow-tie antennas arranged as rectangular arrays and connected in two different ways: in series, and in combination of serial-parallel distribution. The results show excellent agrement with the simulated patterns.
To summarize, we conclude that the optimization of antenna-coupled detectors requires a detailed analysis of the inner connection lines between resonant elements. When possible they have to be wide to carry low current density and avoid sharp corners or turns that may enhance parasitic resonances. Therefore it is clear that design optimization, at the level of grid arrangement, is required to reach the ultimate efficiency goals.
This research has been partially supported by project ENE2009-14340 from the Spanish Ministry of Science an Education. The authors would like to acknowledge the Instituto de Sistemas Optoelectrónicos y Microtecnología, from Universidad Politécnica de Madrid for the fabrication of the devices and Dr. Jose Antonio Gómez Pedrero for his kind suggestions.
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