Full characterisation of a background limited antenna coupled KID over an octave of bandwidth for THz radiation

We present the design, fabrication, and full characterisation (sensitivity, beam pattern, and frequency response) of a background limited broadband antenna coupled kinetic inductance detector covering the frequency range from 1.4 to 2.8 THz. This device shows photon noise limited performance with a noise equivalent power of 2.5 (cid:2) 10 (cid:3) 19 W/Hz 1 = 2 at 1.55 THz and can be easily scaled to a kilo-pixel array. The measured optical efﬁciency, beam pattern, and antenna frequency response match very well the simulations. V C 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/ 4.0/) . [http://dx.doi.org/10.1063/1.4985060]

The next generation of space based imaging spectrometers for sub-millimeter (sub-mm) wave astronomy requires broad band radiation coupling between 1 and 10 THz. 1,2 These spectrometers will allow measurements of a large number of spectroscopic bands over a wide area of the sky in a very limited time. In order to do so, they will require a large number of pixels to cover the telescope field of view or to sample a given frequency band with a high resolution. Kinetic Inductance Detectors (KIDs) are superconducting pair-breaking resonators 3 that are a very attractive choice for these applications since thousands of detectors can be readout with a single coaxial feed line, [3][4][5] enabling simple and cost-effective systems.
Broad band radiation coupling to KIDs can be achieved by using Lumped Element Kinetic Inductance Detectors (LEKIDs), 6 where the radiation is coupled to the inductive section of a resonator, or by coupling planar 7 or horn 8 antennas to the inductive section of the KID. Niobium (Nb) and niobium titanium nitride (NbTiN) technology allows the on-chip fabrication of lossless superconducting striplines and filters between the antenna and the KIDs. At frequencies exceeding the gap frequency (650 GHz for Nb and 1.1 THz for NbTiN), ohmic losses will make this technology impractical. Radiation detection using antennas is still possible, but antenna and KID must be integrated into a single structure to prevent signal loss between them. 9,10 Additionally, these high frequencies are only accessible from space, which results in very high requirements on the detector sensitivity, 12 typically with an noise equivalent power (NEP) of $3 Â 10 À19 W/Hz 1=2 for a non-dispersive spectrometer. Such sensitivities and photon noise performance are achieved with antenna coupled aluminium (Al) KIDs over a broad band 9 around 1.5 THz with poor beam quality and over a narrow band around 850 GHz. 5,11 In this paper, we extend KID technology to higher frequencies and large bandwidths using a leaky lens antenna coupled device.
We intend to make a detector that can be used in an imaging spectrometer, such as the SPICA-SAFARI concept presented by Roelfsma et al. 1 A reasonable set of detector requirements is: (i) Frequency band coverage over an octave at a frequency higher than 1 THz; (ii) radiation detection in 2 polarisations; (iii) antenna scalable between 1 and 10 THz using a reliable fabrication technique over large areas (minimum dimension $100 nm); and (iv) detector aperture efficiency larger than 50%. The aperture efficiency g ap is defined as the ratio between the effective area and the physical area of the lens antenna. For this paper, we have chosen to cover the low frequency band (1.4 -2.8 THz) of the SPICA-SAFARI instrument. 1 We also choose to design a single polarisation prototype, as this allows a more straightforward integration with the KID. Coming to a choice for the antenna, we compare printed antennas that have a broad band coverage: the log spiral antenna, 13 the sinuous antenna, 14 and the leaky lens antenna. 15 A compilation with all the expected performance for these antennas can be found in Yurduseven et al., 16 and it is summarised in Table I. We select the leaky lens antenna because it requires much larger minimum dimensions. At 10 THz, the minimum dimension needed for the spiral and sinuous antennas of k 0 /2000 requires 15 nm features, which are very difficult to fabricate reliably over a large area. The leaky lens antenna 15 is a lens feed consisting of a leaky wave slot kept at an electrically small distance from the dielectric lens in order to obtain a highly directive radiation pattern inside the dielectric. Consequently, it efficiently illuminates the lens. This has been proved experimentally at lower frequencies. 19 Our current design, shown in Fig. 1(a), is optimised to obtain a high, frequency independent, aperture efficiency over the entire bandwidth between 1.4 and 2.8 THz. The optimisation of the slot yields a slot width w s ¼ 173 lm, slot length l s ¼ 602 lm, slot tapering angle c ¼ 15 , and the air-gap between the antenna and the silicon lens h ¼ 3 lm. The lens is optimised obtaining a lens slab l 1 ¼ 737 lm, a lens height l 2 ¼ 442 lm, a subtended angle h 0 ¼ 46.5 , and radius of the lens R ¼ 900 lm. The generic parameter that describes the lens-antenna efficiency is the aperture efficiency g ap ¼ g rad Â g tap . Here, g rad is the radiation efficiency, defined as the fraction of the power absorbed by the central conductor of the coplanar waveguide (CPW) line in the KID, and g tap is the taper efficiency, which relates to the illumination of the lens. A detailed explanation of these efficiencies in antenna coupled KIDs can be found in Ferrari et al. 11 We find g rad ¼ 0.77, g tap ¼ 0.86, and g ap ¼ 0.66 for our design.
The KID is designed, combining the hybrid NbTiN/Al technology, 20 the all-Al antenna concept, 9 and the leaky lens antenna printed on a thin SiN membrane. 19 The NbTiN-Al hybrid KID, due to the reduction in KID internal two level systems (TLS) noise 21 by the use of NbTiN, 22 allows multiplexing of thousands of KIDs with phase readout. 4 The all-aluminium antenna concept is used because a NbTiN ground plane would result in very significant signal loss in the antenna ground plane at frequencies above the NbTiN superconducting gap ($1.1 THz for a T c of $15 K). The all-Al antenna concept uses a thick 100 nm ground plane and a thin 50 nm central KID strip. 9 The Al has a lower resistivity than the NbTiN. Hence, a thick Al ground plane yields a lower loss above 1.1 THz, resulting in an absorption of the THz radiation to the central strip of the KID of $90%.
A front and back illuminated optical image of the leaky lens coupled KID is shown in Fig. 1(b). The KID is a section of coplanar waveguide (CPW), shorted at its far end and open ended near the feedline. The KID length is $8 mm, corresponding with a resonant frequency of $3.5 GHz. THz radiation is coupled to the slot in the Al ground plane, which launches the radiation into the two, very narrow, Al CPW lines. The length of the Al lines ($1.25 mm) is such that all THz radiation is absorbed before the lines become wide. The narrow linewidth (0.8 lm strip with a 1.2 lm gap) is needed to limit radiation loss. The narrow Al line broadens at either end and connects to a wide NbTiN CPW. The NbTiN central conductor is shorted to the NbTiN ground at the far end of the resonator. At the other end, the NbTiN that remains wide (strip of 12 lm with a gap of 8 lm) is deposited on the bare Si substrate for most of its length. Both strategies reduce the TLS noise 23 so photon noise can be observed using the phase signal readout.
We fabricate a 19 pixel array, hexagonally packed, with a pitch of 1.6 mm. The fabrication process starts with a 375 lm thick high resistivity (>10 kX cm) h100i orientation Si wafer, covered with a low tensile stress ($250 MPa) low pressure chemical vapour deposited (LPCVD) SiN with a thickness of 1 lm on both sides [ Fig. 2(a-1)]. The SiN on the back of the wafer is etched with reactive ion etching (RIE) to define the future location of the SiN frontside membrane. We use RIE using 35% SF 6  all detectors and a large square aperture almost as large as the membrane [ Fig. 2(a-4)]. We use the same reactive ion etching process to create a sloped edge on the NbTiN to allow good step coverage for the Al. Next, we spin coat 1 lm polyimide LTC9505 on the wafer [ Fig. 2(a-5)]. The photosensitive polyimide is patterned and cured into a dielectric stub with sloped edges that will give the support of the superconducting short between the ground planes of the feedline 24 [ Fig. 2(a-6)]. The wafer is then immersed in a 10% diluted solution of HF for 10 s to remove surface oxides and organic contaminations and guarantee a clean NbTiN-Al interface. Immediately afterwards, a film of Al with a thickness of 75 nm is sputtered on the front side of the wafer [ Fig. 2(a-7)], patterned, and wet etched with a commercially available Al etchant 25 [ Fig.  2(a-8)]. The thickness of the Al is chosen such that it is thicker than the penetration depth at 1.4 THz to assure radiation absorption. It is important that the Al thickness is thicker than the penetration depth to assure that all the THz radiation is absorbed. If the antenna was thinner than the penetration depth, less current would be induced with the consequent reduction in the absorbed power and drop in the coupling efficiency. The opening of the membrane is done by submerging the wafer in a KOH bath while protecting the front side of the wafer [ Fig. 2(a-9)]. Afterwards, a SC-2 (Standard Clean 2) cleaning step 26 is introduced in order to eliminate potassium residue on the membrane back side. This additional cleaning has proven to enhance the internal Q factor (Q i ) of the resonators from 40 to 50 thousand (without the SC-2 clean) up to a few millions and reduce the TLS noise.
To create the 3D structure required for the operation of the leaky lens antenna, we use an assembly of three different chips: the antenna chip, the spacer wafer that assures a 3 lm gap, and the lens array, which is shown in Fig. 2(b). The lens array is made out of a 1 mm thick, >10 kX cm, h100i silicon wafer using laser ablation. 27 The spacer chip is fabricated on a 250 lm thick, >10 kX cm, h100i orientation Si wafer covered with a low tensile stress ($250 MPa) LPCVD SiN with a thickness of 300 nm on both sides. Alignment holes are created with a KOH etch. A 3 lm gap is etched with RIE on the spacer chip at the position where the antennas are placed. A few columns are left on the gap to prevent the membrane of sticking to the spacer chip. A second etch of 25 lm is performed, after covering the 3 lm gap, to increase the distance between the chip with the antenna and KIDs and the spacer wafer. This is done in order to minimise the area in which particles larger than 3 lm can be sandwiched in between the two chips. The alignment accuracy achieved with this method is 15 lm.
We measure the device sensitivity and coupling efficiency mounting the chip on a sample box inside a light-tight box, in a pulse tube pre-cooled Adiabatic Demagnetization Refrigerator (ADR). The sub-mm calibration signal is supplied by a black body radiator whose temperature can be varied from 3 up to 35 K. The radiation is coupled to the detector via a series of 8 metal mesh IR filters, defining an optical bandpass of 0.1 THz centred around 1.55 THz. 9 A 2.65 mm diameter aperture is placed at 20 mm of the lens to limit the throughput. The power absorbed from the black body source by the Al strip equals P abs ¼ 0:5 g opt Ð k 2 F B d, where the factor 0.5 is associated with a single-polarised antenna, g opt is the optical coupling efficiency, k is the wavelength of the incoming radiation, F is the filter frequency response, and B is the mode occupation. The optical coupling efficiency g opt ¼ g rad Â g so describes the fraction of the power emitted from the black body source that is absorbed in the Al strip of the KID, where g so is the spill over efficiency, defined as the ratio of power of the antenna beam that is contained in the solid angle defined by the limiting aperture to the black body source with respect to the total beam power.
We have made some design choices to ease the fabrication and assembly of the device: (i) The lens array does not have an anti-reflective coating to probe the broad band reception, introducing an $30% reflection loss. (ii) The Al section of the KID and the antenna ground plane are made of a single layer, resulting in $30% of the power coupled to the antenna to be absorbed in the ground plane; and (iii) the Al CPW has a total width of 3.2 lm, limited by the resolution of the optical lithography, with an impedance mismatch to the antenna and a radiation loss of $9% and $6%, respectively. The combined effect is a reduction of g rad to 0.37. Additionally, we found that the lens array is misaligned with respect to the antenna position by 15 lm, which reduces the spill over efficiency g so from 0.45 (for a well aligned system) to 0.3. The expected optical coupling efficiency between the KID and the black body radiator g opt ¼ g rad Â g so ¼ 0.11. The effective implementation strategy chosen leads to an aperture efficiency g ap ¼ g rad Â g tap ¼ 0.24.
We measure first the device noise at a temperature T ¼ 120 mK and a black body radiator temperature of 3 K. The internal quality factor Q i is $2 Â 10 6 , and the loaded quality factor Q is $50 Â 10 3 . At this temperature, the power emitted by the radiator in the frequency band defined by the filters is negligible. The measured noise under these conditions is shown in Fig. 3(a) as the solid dark blue line. The black line represents an estimation of the TLS-dominated device noise, obtained from two measured reference resonators (wide NbTiN resonator and narrow Al resonator) and the assumption of a jẼj 3 -TLS noise dependence. 23,28 As the black body source temperature increases, the power spectral density also increases, and eventually, the noise level becomes flat and remains constant. Moreover, the roll-off between 0.1 and 1 kHz (due to the quasiparticle lifetime) is reduced by an increasing optical load following a P À1=2 source dependence. We thus conclude that the device is photon noise limited at absorbed powers P abs >1 fW.
To measure the NEP and coupling efficiency of the detector, we use the method developed by Ferrari et al. 11 The measured NEP is given by NEP 2 ðxÞ ¼ S h ðxÞ=ðdh= dP abs Þ 2 , where S h is the power spectral density of the phase signal and dh/dP abs is the phase responsivity. We measure an optical NEP equal to 2.5 Â 10 À19 W/Hz 1=2 at the lowest loading and is shown in Fig. 3(b). The background limited NEP in which h is Planck's constant, is the radiation frequency, (1 þ g opt F B) is the correction to Poissonian statistics due to photon bunching, D is the superconducting energy gap, and g pb is the pair breaking efficiency. We observe a good match between the data (dots) and NEP BLIP (calculated). A more detailed analysis 11 of the data results in g opt,meas ¼ 0.106, which is very close to the calculated value.
To measure the beam pattern and frequency response, we mount the device on the cold stage ($300 mK) of a He7 cooler with optical access from room temperature with several filters, defining a frequency window from 1 to 2.7 THz. A glow bar with 2 mm diameter aperture acts as the source of radiation. The source is placed outside the cryostat and can be moved using motor controlled translational stages in the two directions orthogonal to the optical axis of the detector beam. A polariser is placed in front of the glow bar. A narrow band pass filter centred at around 1.55 THz in front of the glow bar is added for the beam pattern measurement and removed for frequency response measurement. The source is modulated at a few Hz to remove 1/f noise from the system. The measured pattern at around 1.55 THz is shown in Figs. 3(c) and 3(d) together with the simulated one, showing a good agreement. The elliptical shape of the beam pattern is tentatively attributed to the radiation absorbed by the common mode of the KID CPW close to the antenna. The frequency response of the detector, measured using a Fourier Transform Spectrometer (FTS), is shown in the inset of Fig.  3(b). The FTS shows a frequency range larger than an octave of bandwidth, limited by the optical filters in the setup (1 THz and 2.7 THz for the lower and higher frequencies, respectively). In this experiment, we lower the pressure in the entire setup, which reduces but does not eliminate completely the absorption from water. The dip in the frequency response is tentatively attributed to a poor correction for water absorption lines.
We have fabricated and tested a single-pole leaky lens antenna coupled KID operating in a 1.4 -2.8 THz frequency band. The device combines excellent sensitivity with a measured optical NEP ¼ 2.5 Â 10 À19 W/Hz 1=2 and shows a very good match between the measured and calculated optical coupling efficiency, beam pattern, and frequency response. The efficiency of the measured device is limited by the design choices described in this paper for easier fabrication and assembly. It is possible to increase the efficiency of the device by: (i) The utilisation of a non-antireflective coated lens to reduce reflection loss; (ii) the implementation of a dual thick-thin Al layers to confine the quasiparticles to the narrow central line of the KID 9 to reduce the loss in the ground plane; (iii) the use of e-beam lithography to reduce the radiation loss in the CPW KID and the impedance mismatch between the KID and the antenna; and (iv) improve the alignment between the lens and the antenna. We expect to achieve an aperture efficiency g ap ¼ 0.66 for an optimised device. This device and assembly can also be scaled and used for the higher frequency bands (up to 10 THz) of SPICA-SARI. 1 The CPW section of the KID close to the antenna needs to be made with electron beam lithography in order to make $300 nm lines and the gap between the lens and the antenna needs to be reduced down to 1 lm. This is a serious engineering challenge, but there is no physical reason why it should be achieved.