Ultra-porous alumina for microwave planar antennas

Abstract We report on the experimental study of ultra-porous alumina (UPA) of transition phases γ and θ, which we fabricate by oxidation of laminated metallic aluminum followed by chemical and thermal treatments. Its morphology of a nanostructured monolith with up to 99% porosity brings together several crucial advantages with respect to existing aluminum oxides: an ultra-low density, the potential of refractive index gradients, and a chemically tunable hydrophilic character. Its extremely low permittivity measured here for the first time, εr ≈ 1.2 at 130–165 GHz, makes UPA a promising substrate material for planar electromagnetic components in this microwave spectral range of great interest for the cosmic microwave background observation. The dielectric loss tan δ ≈ 10−3, although being relatively low, can be further reduced after a chemical treatment that conveys hydrophobic character to the UPA constituting nanofibers. Graphical abstract


Introduction
For the last few decades, compact microstrip antennas have drawn a great deal of attention because of miniaturization purposes related to portable communications, going from the market of consumer electronics to applications fields associated to satellite-born antennas. In particular, their use is becoming ubiquitous for the cosmic microwave background (CMB) observation in the 40-600 GHz range, where they are used to illuminate telescope optics, or as waveguide probes in horn structures. Planar antenna-coupled detectors are considered as crucial devices for future space missions, because they are naturally polarization-sensitive, they can feed microstrip filters, they can easily be fabricated with superconducting technologies, and they can be coupled to the most sensitive cryogenic direct detectors in use today. In this context, dielectric materials must be suitable for low-loss cryogenic operation, device miniaturization and frequency-independent beam forming with lenses, polarization diplexing, etc. Moreover, millimeter-wave devices are also relevant for satellite communications, where the Ka-band (26-40 GHz) is already in use for space missions. For such applications there is a demand for innovative low-loss substrates, which should either be micro-machined to reach the required specification of impedance matching with vacuum or have a very low refractive index. Planar antennas are one of the most interesting items that can benefit from this study on ultra-porous alumina (UPA). In fact, a key issue where low refractive index plays a role is the radiation efficiency. This fundamental parameter depends on the ratio P sw /P rad where P rad is the power launched in free space, and P sw is the power leaking into surface waves. Since this ratio must be as small as possible, we have to avoid the onset of surface wave modes, whose cut-off frequency scales as [4 × t × √(ε r − 1)] −1 , t being the substrate thickness. 1 This effect is well known and potentially harmful, but we can see how a low permittivity is decisive to push to higher frequencies all the unwanted modes for a given t, in a given frequency band. Another potentially interesting device for the THz spectral range is the Luneburg lens, a tentative version of which has been fabricated for radio communications from 12 to 16 GHz, by assembling spherical shells of different dielectric constants. 2 The realization of Luneburg lens for the THz spectral range would require advanced low-ε materials with a smooth radial variation of the refractive index.
In this context, the aluminum oxide of transition γ and θ polymorphs is a material of high technological value. The aluminum oxide is presently produced via the Bayer method but also by a sol-gel process developed by Sasol. Massive porous units of typical ~3-5 mm size are commonly prepared by powder compaction, for several applications as adsorbents, catalysts, etc. A direct way to form massive aluminum oxides with an inherent nanofibrous structure, through the oxidation of liquid-metal alloys, was discovered in Al-Hg system over one century ago. 3 Since that time, different fabrication methods of fibrous alumina have been developed and investigated. [4][5][6][7][8][9] The obtained raw material is aluminum oxyhydroxide (Al 2 O 3 ·nH 2 O), which is transformed into the transition phases after thermal annealing at a temperature range between 750 and 1200 °C. This transformation can be delayed via the chemical vapor impregnation of a silica layer 7 reinforcing the mechanical stability of the monoliths. Both chemical and thermal treatments remove the adsorbed and structural water from the fibrous structure. 10 Alumina, which was used for microstrip antenna substrates before being replaced by low-permittivity dielectrics like Duroid®, is also employed as an insulator in microelectronics, and for high-pressure resistant optical windows in the 0.15-5 μm spectral range. Broadband dielectric properties of commercial aluminum oxide have been reported, with a refractive index n ~ 3.1 (for a frequency f < 10 THz) and a dielectric loss 10 −3 < tan δ<10 −2 (0.4 < f < 2 THz), the latter decreasing to 3.1 × 10 −4 (f ~ 0.02 THz) in higher purity 99.6% alumina. 11 Alumina photonic crystals with a photonic band gap between 0.40 and 0.47 THz have been fabricated and their guiding properties studied, 12 in the perspective to control THz waves. Although the principle feasibility of nanofibrous alumina photonic structures has been demonstrated, 9 and the importance of measuring their dielectric and guiding properties in the THz range has been highlighted, 13 no practical realization of such systems has been published to date.
In the present communication, we report on the sample preparation and the measurements of refractive index and dielectric loss in the GHz-THz frequency range in nanofibrous UPA.

Sample preparation and structural characterization
The nanofibrous UPA monoliths ( Fig. 1) were grown according to our original patented method. 14 Since low-refractive index media are required for applications in THz optics, a compromise has to be found between UPA mass density and mechanical strength. The crystallization of γ, θ, and α phases in UPA takes place, respectively, at 870, 1100, and 1200 °C. Raw UPA has a mass density of 0.03 g/cm 3 , porosity of 99%, specific area of 300 m²/g, and thermal conductivity of 0.01-0.03 W/ mK. The characteristic size of alumina fibrils and specific area of these polymorphs are: 7 nm and 150 m 2 /g (γ), 10 nm and 100 m 2 /g (θ), and 250 nm and 10 m 2 /g (α), respectively. At the same time, the raw alumina mass density augments up to 3 g/cm 3 as the thermal treatment temperature is increased up to 1700 °C. Along with the pure UPA materials, UPA treated with the trimethylethoxysilane (TMES: (CH 3 ) 3 -Si-C 2 H 5 O) vapor at room temperature were used in the present work. The monolayer of grafted TMES molecules on the alumina fibers endows them with a hydrophobic character and gets transformed into a molecular silica layer after the thermal treatment. Moreover, partial hydrophobicity of the formed silica layer can be expected. 15,16 The THz absorption of UPA samples is related to a water content, which is expected to be high in such open structure nanofibrous materials. In fact, the raw UPA is aluminum oxyhydroxide that contains structural and adsorbed water. According to Khodan et al., 10 the adsorbed water amounts to 0.5-0.7 molecules per Al 2 O 3 regardless of heat treatment temperature, while structural water content decreases almost to zero (<0.04 molecules) at temperatures above 700 °C, when the material crystallises to transition γ and θ phases. At the same time, the transition aluminas are most indicated for THz applications because of their low mass density associated with relative mechanical strength. This makes necessary to eliminate a significant fraction (50-70 mol.%) of adsorbed water to attain a high THz transparency for UPA samples.
The transition aluminas were obtained by adequately tuning the treatment temperature: 870 °C (γ) and 1050 °C (θ) in pure UPA and 1100 (γ) in UPA with silica-covered fibers, as indicated in Table 1. The appearance of the crystalline phases was checked by XRD diffraction method. 8 For electromagnetic measurements, the produced UPA were compacted in disks of 32-mm diameter and different thicknesses as indicated in Table 1. Since the applied pressure tends to increase the material mass density and consequently its refractive index, moderate static pressures P ≤ 1000 bar have been used. Two compaction methods (A and B) were applied as indicated in Fig. 2. The simplest one-stage method A, used for samples 2, 4, 8, and 10, consisted in UPA growth followed by a thermal treatment (4 h) and compaction of disks at a static pressure. The mass density of these samples is close to 1 g/cm 3 . A slight modification of method A, consisting in the introduction of chemical impregnation with TMES vapor at room temperature overnight before thermal treatment and compaction, was used for samples 1, 3, 7, and 9. Finally, samples 5 and 6 were prepared according to a two-stage method B, where the intermediate thermal treatment was introduced at temperature T 1 below the crystallization threshold of γ phase (870 °C). Samples prepared according to methods A and B are shown in Fig. 3. UPA samples non-treated with silica can be easily compacted by method A. In contrast, silica-treated UPA disks produced by this method contain shape failures. Method B results in quasi-perfect defect-free disks that conserved high porosity of UPA monoliths. As this can be seen from Table 1, the mass density of disk samples varied between 0.2 and 1.2 g/ cm 3 depending on preparation conditions. The hydrophobic treatment was applied to reduce the significant content of adsorbed atmospheric water in samples (50-70 mol.%). The treatment included immersion of the sample into 2 vol.% solution of -oxy]-propyl}-silane in dehydrated decane for 2 h followed by rinsing with ethanol and drying in the oven at 130 °C for 1 h. After drying the samples, the successful hydrophobization procedure was checked by the measurement of contact and rolling angles formed by 10-μL water droplet according to method described in 17 . Typical values of contact angle for hydrophobically treated samples exceeded 160°, and rolling angles were less than 13°.

Electromagnetic measurements
In order to estimate the complex permittivity of such ad hoc UPA samples, we have resorted to the experimental measurement of their scattering-matrix parameters (Fig. 4). Our setup is based on ABmm® Vector Network Analyser MVNA-8-350, endowed with a set of multipliers that allow to cover W-band (75-110 GHz), D-band (110-170 GHz), and the 170-240 GHz band. For the present work, only the D-band millimetric extension has been used, for which quasi-optical components were readily available in our lab. From an optical point of view, our setup is composed by two identical horn antennas, and by two identical off-axis ellipsoidal mirrors (bulk aluminum, machined in-house). The two horns launch a Gaussian beam (98% of the power in the fundamental mode) with FWHM = 10° and waist radius w 0 ≅ 5.0 mm, located 7.9 mm behind the aperture. Each ellipsoidal mirror bends the beam by 90°, and images the horn waist radius at the common focal point with magnification M = 1 (see Fig. 4). As a result, the waist of the first horn (Port 1) is imaged on the waist of the second horn (Port 2) with overall unitary magnification. In the region between the two mirrors we have a focal point where the beam has a radius comparable with w 0 , so that a sample with a clear aperture of 20 mm collects ~100% of the power launched in the fundamental mode, and it is collimated. Here, we put the sample holder. Material properties are inferred from the measurement of the scattering matrix of our dielectric slab. In particular, the signal launched from Port 1 is received in Port 1 (S 11 scattering matrix element) and Port 2 (S 21 scattering matrix element). The parameter S 11 gives the complex reflected signal, while S 21 provides the transmitted one. Both parameters are available in amplitude and phase vs. frequency. After calibrating the zero optical path length (equal to the path before the insertion of values 1 < n < 2 and 10 −3 < tan δ<10 −2 have been obtained, depending on the preparation method. Hereafter, we discuss the observed correlations between these data. (1) The refractive index is found to correlate with the mass density of the samples, as suggested by Fig. 6. Some deviations are related to small variations of the sample composition due to the chemical treatments. The linear fit of these data results in n = 1 + 0.7ρ, whose extrapolation to the high-density solid Al 2 O 3 is in a good agreement with the direct measurements n ~ 3.1 performed by Rajab et al. 11 (2) The dielectric loss of silica-treated samples is generally found smaller compared to non-treated samples. Moreover, the samples prepared with the two-stage method show smaller losses (~3 × 10 −3 ) as compared the sample, but including the empty framework), the power transmission level sets around ~0.0 dB with −0.01 dB ripples as calibration residuals, while the phase delay is ~0.0°, with peakto-peak residuals typically around 10° (but lower than this, down to 7°-8° in some sub-bands). Deviations from these flat calibration levels, once the sample is introduced in the optical path, provide us with the losses and the refractive index of the material. Usually, Fourier time domain filtering is required to avoid multiple reflections within the optical path (and within the slab itself ). To validate our setup we have used Teflon as a test material, since it is very well known and extensively used at millimeter waves. The measured refractive indices (n) and tangent losses (tan δ) of UPA samples in the frequency range 135-165 GHz are presented in Fig. 5 and Table 2. A quite broad scope of  0.74 cm), we estimate T = 0.025, which is in a good agreement with our THz transmission measurements in untreated UPA sample ( Fig. 9(b)). After the hydrophobic treatment, the transmission of sample ( Fig. 9(a)) considerably improves, corresponding to the removal of about 60 mol.% water and ψ = 0.26. Since γ-UPA contains a very small amount of structural water (~1 mol.%), the main part of the residual water in our sample belongs to the adsorbed water. Its complete removal will decrease the absorbance by a factor of ~26, which would make nanofibrous UPA highly transparent material in the full THz spectral range and suitable for fabrication of refractive THz optics. Our main result here is that we have singled out the fabrication parameters allowing for an ultra-low value of the refractive index results to those presented in other works dedicated to microwave properties of UPA (e.g. 19,20 ), we can see that the refractive index we find in one of our samples (9b) is one of the closest to n = 1 ever reported in literature, nicely scaling to higher values with increasing density. More often, values of n ≥ 2 are presented. On the other side, if we look at dielectric losses, our tan δ is up to two orders of magnitude higher with respect to that found by Penn et al. This effect is likely ascribable to the combined action of humidity and porosity, as described in 21 , who find loss tangent values close to ours, of the order of some 10 −3 , in the range 12-18 GHz and in a moist environment. An improved hydrophobic treatment should allow us to solve this problem.

Conclusion
We have fabricated planar samples of UPA and characterized their morphological and electromagnetic properties while varying the fabrication parameters. The main results of our study, i.e. the extremely low value of the real part of the permittivity and the reasonably low value of its imaginary part, make this material a promising candidate for planar antenna substrates number density of the adsorbed water molecules in the UPA structure (ψ = H 2 O/Al 2 O 3 = 0.6) 10 and the UPA mass density from Table 1 (ρ = 0.234 g/cm 3 , thickness in the 150 GHz range of interest for the CMB. The UPA perfection is under way via the search of an optimal chemical treatment that should turn this material in a hydrophobic one.