Design and Simulation of an Antenna-Coupled Microbolometer at 30 THz

We propose a model of antenna-coupled microbolometer to be included in an array for receiving and detecting long wave infrared (LWIR) electromagnetic radiation. The antenna is joined to microstrip bandpass filters thus forming a single metal structure to define the operation frequency band. The antenna and microstrip filters are modeled in aluminum thin film. The microbolometer is modeled with superconducting niobium, all together on a silicon nitride membrane. The squared pixel structure is designed on a support frame of 20μm in size. Simulation results for this antenna exhibit a frequency range of operation from 27 to 35 THz and is configured for two arrays, one of 10 × 10 and the other one of 50 × 50 elements. The device has been simulated by means of the commercial electromagnetic software (HFSS), which is based on the finite elements method.The predicted values for the figures of merit of this microbolometer are as follows: τ = 5.8 ns, RV = 5.3 × 10 3 V/W, and D = 2.07 × 10 cm√Hz/W, respectively.


Introduction
Nowadays, the development of planar antennas is growing up fast in large number of imaging applications at different wavelengths, from astrophysics [1][2][3] up to a great variety of civilian markets [4,5], and especially in the terahertz range due to the emerging generation of wireless communication systems [6].In the particular case, the detectors based in antenna-coupled bolometers at wavelengths between 8 and 13 m play an important role because the atmosphere is almost transparent for the incoming electromagnetic radiation and most of the warm objects in the Earth emit radiation in this spectral range.
In general terms, a bolometer is a device for gauging electromagnetic radiation by means of heating of a material with a temperature-dependent electrical resistance.Bolometers are very sensitive to any kind of energy that is deposited in them.They have been used in astronomical instruments with great success in both ground-based and space-borne telescopes [7][8][9] by using complex and expensive cooling systems that can achieve temperatures between 0.1 K and 0.3 K during their operation.Recent studies [10] demonstrate that bolometers can also be performed at higher temperatures, for example, at 39 K, whose application can be focused towards studies of cold planetary objects in the solar system, and up to temperatures of 93 K for detection of microwave radiation [11], whereas most of civilian applications such as security or defense require uncooled bolometers operating at environment temperatures that can be integrated in compact systems since they must be suitable for mobility [12][13][14].
A bolometer can be fabricated up to ten times smaller than the desired radiation wavelength to increase its sensitivity and to reduce its time constant.But, in consequence, less energy will be collected because the collected radiation turns to be proportional to the physical size of such bolometer.To overcome this problem, the coupling of planar antennas resonating at the desired wavelength is a good solution to develop fast bolometers without sacrificing collection area.This was demonstrated with various designs for the detection of infrared radiation [15][16][17][18][19].
In this paper we present a model of an antenna-coupled microbolometer for operation in the 30 THz band.Our model consists in a squared pixel structure designed on a 1 m thick silicon nitride membrane as support frame of 20 m in size.A double dipole antenna is joined to microstrip bandpass filters to define the band frequencies, while a load resistance acts as bolometric sensor, and a passive element works as radiation absorber.The model presented here is aimed at being included in focal plane arrays and is exploratory for the field of imaging in astronomy.The model has been simulated using the commercial electromagnetic software HFSS, which is based on the finite elements method.

Background Theory
Most of the theories and methods reported in the literature [20][21][22][23][24][25] for estimating the figures of merit of a bolometer are consistent with each other for any thermal detector and depend upon the characteristics of each design.In general terms, the theory defines the thermal time constant , of a bolometer detector as the ratio of heat capacity  to thermal conductance  of the device, that is, by The responsivity  V , as the output voltage per unit of input power, is as follows: where   is the intensity of the input power and   is the device active area.The detectivity  * , as the signal to noise ratio with respect to bandwidth Δ and   , is as follows: where NEP =   / V is the noise-equivalent power, that is, the incident radiant power required to generate a signal voltage equal to the noise voltage (obtained by dividing the noise voltage by the responsivity) [21].

Model of a Single Antenna-Coupled Microbolometer
The geometry of the antenna coupled to a microbolometer is depicted in Figure 1.The antenna, the microstrip feed lines, and the microstrip filters were modeled using 100 nm thick aluminum (Al), considered here as perfect conductor material, whose physical properties are included in the system's library of the software, that is,   = 1,  = 38 × 10 6 siemens/m, and so forth.The length of the metal structure is fixed to 16 m, whereas the dimensions of the filters and dipoles are varied in order to achieve the desired frequency band (30 THz), which is equivalent to  = 10 m.
The microstrip feed lines and filters have 0.25 m width.The filters are separated 0.5 m from each other with lengths of 1.75 and 2.5 m, respectively, and they are placed at each side of the feed lines.The dipole dimensions are proportional to /4 to get optimal antenna efficiency.Each dipole is  composed of a rectangular base of 1.5 × 2.25 m 2 with a rectangular extension of 0.5 × 2.75 m 2 thus giving a total length of 5 m (/2).The microbolometer is modeled with niobium (Nb) of 0.5 × 1.0 × 0.1 m 3 , and the ground plane acting as an absorber is modeled with 50 nm thick chromium (Cr).The whole structure is suspended on a silicon nitride membrane of 20 × 20 m 2 and 1 m thickness.In this model, we propose a membrane suspended on a periodically perforated silicon substrate, as is shown in Figure 2. Here, the proposed substrate has 50.8 mm diameter with 196 cavities of 1 × 1 mm 2 each one.This kind of membranes can be easily fabricated using standard microelectronic techniques and can also be characterized for use as frequency selective surfaces in astronomical detectors [26].

Simulation Results
For a single antenna, the return loss is shown in Figure 3.The antenna exhibits a frequency range of operation at −10 dB from 27 to 35 THz, which is equivalent to wavelengths 8 <  < 12 m, with a narrow bandwidth centered at 30 THz and a second resonance around 34 THz.
In Figure 4, the gain patterns are presented for a single antenna, for an array of 10 × 10 elements, and for an array of 50 × 50 elements, respectively.Note that in this simulation for the array of 10 × 10 elements the beam pattern of the main lobe and the side lobes show high degree of symmetry for both the E-H planes.It is also observed that, by increasing the number of antenna elements in an array of  × , the half power beamwidth (HPBW) is reduced down approximately by a factor of , while the gain (G) increases proportionally to .That is easy to observe since for a single antenna we have a HPBW ∼ 25 ∘ with the first side lobes relative to the maximum at  ∼ 0.5 dB; for an array of 10 × 10 elements we have a HPBW ∼ 2.5 ∘ with the first side lobes at  ∼ 0.8 dB; and for an array of 50 × 50 elements we have a HPBW ∼ 0.5 ∘ with the first side lobes at  ∼ 0.85 dB, respectively.A summary of the parameters obtained by simulation for a single antenna is shown in Figure 5.
Each cavity of 1 mm 2 in the proposed substrate can hold an array of 50 × 50 antenna structures that can be connected in a series-parallel combination.For this particular case, each array will provide a single pixel with much higher directivity and a dc resistance approximately the same as that of a single antenna.Hence, we will have a two-dimensional array of 196 pixels in a squared area of 27 × 27 mm 2 .
On the other hand, the analytical predictions for our detector are based on the bolometer's theory, which indicates that one of the most important factors that affect its performance is the thermal conductance , which is essential for determining the time constant.However, it is not easy to predict with accuracy since it involves several factors that can only be determined experimentally; for instance, one way for estimating G is by heating the bolometer by bias current only and measuring the bolometer resistance; then G can be calculated from a relation between the inverse of resistance measured in the bolometer and the square of the applied bias current, whereas the heat capacity can be calculated as  = , where  is the volume of the detector determined from the design and  and  are the density and specific heat, respectively.For different materials,  can be found in tables and in the literature [22]; hence, for our design the heat capacity can be established as  = 11.6 × 10 −14 J/K and  as a typical value of order of  = 2 × 10 −5 W/K.Therefore, the time constant according to (1) provides a value of  = 5.8 ns.
Referring to parameters obtained in Figure 5, the device active area   is related to the maximum directivity of the antenna [27] by   =  2  max /4 = 53.69m 2 .
For estimating the responsivity  V of our bolometer, we know that the resistivity  of niobium at room temperature is 1.44 × 10 −6 Ω⋅m; then by assuming a typical bias current of 1 A, we get an output voltage   = 0.288 V.Therefore, according to (2), we have  V = 5.3 × 10 3 V/W.
Finally, from (3), the NEP can be determined by calculating the Johnson noise whose voltage is given by   = (4    Δ) 1/2 [22], where  is the Boltzmann's constant,   is the absolute temperature of the bolometer, and   is the resistance of the bolometer, thus giving a result of   = 1.95 × 10 −4 V, and NEP = 3.7 × 10 −8 W. Therefore, the estimated detectivity will be of order of  * = 2.07 × 10 10 cm √ Hz/W.It should be pointed out that the simulations and the predicted values shown here were made considering room temperature and vacuum conditions; therefore the heat transfer caused by convection and radiation were not taken into account.It is not surprising to get  * of order of 10 10 ; another model using different software has been reported before with estimated values of order of 10 9 [28].For the case when we considered air atmosphere only, then the detectivity could turn to be of order of  * = 1 × 10 7 cm √ Hz/W.

Conclusions
In this paper, a model of an antenna-coupled microbolometer has been presented.The figures of merit have been predicted analytically.The characteristics and radiation patterns of the antenna were simulated using a commercial electromagnetic package.The results reveal feasibility for integration in focal plane arrays.The presented design is the first step towards the development of multiple arrays to study their feasibility and use in astronomical applications; even for this, the device requires vacuum and cryogenic environments for its operation.This turns to be a challenge for us, since the state of the art of astronomical instruments at LWIR frequencies still is not widely explored.
Future work will consist in building these designs on periodically perforated silicon substrates.The use of new modeling methods for getting accurate characterization [29] will be considered.

Figure 1 :
Figure 1: Antenna geometry (not to scale) coupled to a Nb microbolometer.The squared background corresponds to a pixel area of 20 × 20 m 2 .

Figure 2 :
Figure 2: Schematic arrangement (not to scale) for a silicon substrate periodically perforated, with 196 cavities of 1 × 1 m 2 each one.

Figure 3 :
Figure 3: Simulated return loss for a single antenna.

Figure 4 :
Figure 4: Gain patterns relative to the maximum for a single antenna, for an array of 10 × 10 elements, and for an array of 50 × 50 elements.The squared backgrounds correspond to pixel areas of 20 × 20 m 2 (a), 200 × 200 m 2 (b), and 1000 × 1000 m 2 (c), respectively.