Dielectric constant reduction using porous substrates in finline millimetre and submillimetre detectors

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1 Dielectric constant reduction using porous substrates in finline millimetre and submillimetre detectors Chris E. North a, Michael D. Audley b, Dorota M. Glowacka b, David Goldie b,paulk.grimes a, Bradley R. Johnson a, Bruno Maffei c, Simon J. Melhuish c, Lucio Piccirillo c, Giampaolo Pisano c, Vassilka N. Tsaneva b, Stafford Withington b, Ghassan Yassin a a University of Oxford, Denys Wilkinson Building, Keble Road, Oxford, UK b Cavendish Laboratory, University of Cambridge, Cambridge, UK c University of Manchester, Manchester, UK ABSTRACT Finlines are planar structures which allow broadband and low loss transition from waveguide to planar circuits. Their planar structure and large substrate makes them ideal for integration with other planar circuits and components, allowing the development of an on chip polarimeter. We have developed a method of extending the employment of finlines to thick substrates with high dielectric constants by drilling or etching small holes into the substrate, lowering the effective dielectric constant. We present the results of scale model measurements at 15 GHz and cryogenic measurements at 9 GHz which illustrate the excellent performance of finline transitions with porous substrates and the suitability of this technique for extending the bandwidth of finline transitions. Keywords: finline, millimetre-wave, substrate, dielectric, porous, bandwidth 1. INTRODUCTION One of the key components in a millimetre or submillimetre astronomical detector is the coupling between the horn and the detector. Modern detectors employ superconducting planar circuits, normally comprising miniature microstrip lines, so an efficient coupling from waveguide to microstrip is required. The next generation of high sensitivity polarimetric instruments also require excellent performance in terms of cross-polarisation over a very wide frequency band. Finline transitions provide a broadband, low cross-polarisation, low-loss transition from waveguide to a number of planar circuit geometries including microstrips. 1 Their performance has previously been proven in SIS (Superconductor-Insulator-Superconductor) mixers at 2 7 GHz. 2 4 Current and future instruments use finlines to couple horns to bolometers such as TES (Transition Edge Sensors) 5 and CEBs (Cold Electron Bolometers). 6, 7 Prime examples are CMB polarisation instruments which are searching for the very faint signature of gravity waves caused by inflation in the early universe. Ground and balloon-borne experiments have limitations on the available frequency bands imposed by the atmosphere, and need to use all available transmissive bands as efficiently as possible. The metal fins are supported on a dielectric substrate, commonly made of quartz or silicon. The supporting substrate, which can be of high dielectric constant, sits in a groove in the waveguide wall. The presence of this thick dielectric can allow the transmission of higher order modes at the high frequency end of the frequency band, limiting the bandwidth of the finline transition and consequently the performance of the entire detector chip. One solution to this problem is to make small ( λ) holes in the substrate. These structures have the effect of lowering the dielectric constant of the substrate and shifting the transmission of higher order modes to higher frequencies. In Section 2 we will describe finlines and the problem of higher order modes. In Section 3 we will discuss the proposed solution, while in Sections 4 and 5 we will detail the results of measurements made at 15 and 9 GHz. Further author information: (Send correspondence to C.E.N.) C.E.N.: c.north1@physics.ox.ac.uk, Telephone: Millimeter and Submillimeter Detectors and Instrumentation for Astronomy IV edited by William D. Duncan, Wayne S. Holland, Stafford Withington, Jonas Zmuidzinas Proc. of SPIE Vol. 72, 722G, (28) X/8/$18 doi: / SPIE Digital Library -- Subscriber Archive Copy Proc. of SPIE Vol G-1

2 -1-2 II Frequency 1GHz] Figure 1. Left: measured return loss of a 15 GHz back-to-back antipodal finline chip 1 18 GHz using a VNA. A return loss of below 15 db is seen in the range GHz (35 % bandwidth). Right: photograph of the antipodal finline in the test block, showing the two-step substrate transformer at each end. The metallisation layers are deposited either side of the kapton dielectric. The semicircular features near the centre transform antipodal finline to microstrip. 2. FINLINE TRANSITIONS The synthesis of finline tapers involves tapering some characteristic variable of the finline geometry, such as the characteristic impedance or cutoff frequency. The quantity of choice needs be calculable for any geometry of fin separation or overlap. In the case of unilateral finlines, where the fins are in the same plane, the cutoff frequency is a suitable quantity and can be calculated quickly and easily using Transverse Resonance. 8 The cutoff frequency is then tapered smoothly to synthesise the taper profile, with return losses from the finline taper alone below 3 db. 9 In antipodal finlines, the layers of metallisation are separated by a thin insulating layer (normally SiO or SiO 2 in mm-wave detectors), which allows the fins to overlap. In cases where the fins overlaps or the gap is very small, the cutoff frequency is very hard to calculate due to the complicated geometry. For example, the fin separation or overlap is typically less than a hundredth of the total substrate width, requiring a large number of elements and therefore a correspondingly large amount of memory and CPU time to analyse the system. In these cases, instead of using the cutoff frequency, the characteristic impedance can be calculated from simulations with finite element EM analysis software such as Ansoft HFSS. This impedance is then tapered to produce the finline profile, 1 with similar performance to the unilateral finlines. The performance of finline transitions has been proven in the past, 3 and new synthesis techniques have been proven with measurements at 97 GHz 5 and 15 GHz (see Fig 1). The transition from empty waveguide to a waveguide loaded with dielectric substrate needs to be carefully examined to avoid unnecessary reflections. A two-step transformer, with two reductions in the width of the substrate, can produce a transition with return losses below 2 db over a 3 % bandwidth. The steps are resonant structures, so this transition design is relatively sensitive to manufacturing errors. A photograph of a back-to-back substrate with a two-step transformer and a finline transition is shown in Fig Higher Order Modes The bandwidth of finline transitions is fundamentally limited by the waveguide itself. The cutoff frequency of the waveguide prevents transmission at low frequencies, while the propagation of higher order modes limits the performance at higher frequencies. The dielectric substrate supporting the finline in the E-plane of the waveguide is held in place by a groove in the waveguide wall. Since higher order modes can propagate along this groove, λ/2 serrations are added along the edges of the finline in the groove (see Fig 3). The length of these serrations, and therefore the width of the groove, has been optimised with measurements at 15 GHz. It was found that serration lengths of 1.75 mm produce the best performance, which scales with frequency to 25 µm at 9 GHz and 1µm at 22 GHz. In mm-wave experiments using TES bolometers, the substrate is made of silicon, which has a relatively high dielectric constant of This substrate is also relatively thick to allow the fabrication of the membrane, and Proc. of SPIE Vol G-2

3 Insertion Loss [db] Initial Design Reduced width waveguide 18 µm thick substrate Insertion Loss Higher Order Mode Transmission [db] Initial Design Reduced width waveguide 18 µm thick substrate Higher Order Mode transmission Figure 2. Comparison of effect of three methods of increasing the cut-on frequency of higher order mode, illustrated with the insertion loss of the fundamental mode and higher order mode transmission. Shown are the initial design with WR-4 waveguide and 225 µm thick silicon (solid), the design with reduced waveguide height (dashed), the design with thinner silicon (dotted) and the design with (dot-dashed). its presence lowers the cut-on frequency above which higher order modes are transmitted. The effect is greater at higher frequencies and with higher dielectric constants. For example, a finline transition on a 225 µm thick silicon substrate in WR-1 ( mm) waveguide allows higher-order modes to be transmitted at frequencies above 15 GHz. This limits the maximum frequency at which this substrate can be used, and therefore reduces the potential performance of experiments which require broadband operation. There are three modifications to this design which have been investigated to allow the use of this transition at higher frequencies, described below, with the performance of these modifications shown in Fig 2. The first method is to reduce the height (the short dimension) of the waveguide. This increases the frequency band in which the waveguide operates, and so increases the cut-on frequency of the higher order modes. It has been shown that reducing the waveguide height to 1.1 mm (a 15 % reduction in height) produces a 1% increase in the cut-on frequency. The disadvantage of this method is that the waveguide geometry is non-standard, and requires a waveguide taper to interface with standard components. The second solution is to use a thinner substrate. This solution is also effective at a similar level to waveguide height reduction, with 18 µm thick silicon (2% thinning) producing a 1% increase in the cut-on frequency. Thin substrates make the devices more fragile, and correspondingly yields can be lower due to breakages. The third case, discussed in this paper, is to create small ( λ) holes in the substrate. Small holes in a dielectric substrate to not adversely affect the propagation of electromagnetic radiation. The effect of these structures is simply to reduce the effective dielectric constant of the material. We have considered substrates with a regular grid of holes in them. Holes with a diameter of 125 µm on a 6 µm close-packed grid, removing 2% of the material, increases the cut-on frequency by 1%. 3. POROUS SUBSTRATES To test the performance of these porous substrates, test substrates were designed and measured on VNAs at 15 GHz, and also cryogenically at 9 GHz. The 15 GHz samples are made of duroid RT/61LM, while 9 GHz samples are made of silicon. The effect of the holes can be confirmed with simulations of short lengths of substrate (see Fig 3). The resonant reflections caused can be used to match up the hole size in porous substrates with the effective dielectric constant. Fig 4 shows the comparison between silicon substrates (ε r =11.8) containing 5 and with substrates of dielectric constants of 11.1 and 7.9 respectively, over the frequency range GHz. Fig 5 shows the resonances caused by short lengths of duroid at frequencies of 1 16 GHz, with a range of hole diameters and dielectric constants. The effective dielectric constant scales roughly linearly with the fraction of material remaining, or the effective bulk density of the substrate. The performances of the porous substrates was confirmed with 15 GHz measurements, the results of which are shown in Fig 6, illustrating the good agreement between the HFSS simulations and VNA measurements. Proc. of SPIE Vol G-3

4 (c) Figure 3. Photos of samples measured at 15 GHz, showing a short resonant length, a back-to-back porous duroid substrate with two-step transformers, and a back-to-back unilateral finline on a duroid substrate (c). All are sitting in one half of a split-block waveguide. The serrations along the groove of the waveguide can clearly be seen in the right panel. The copper is on the underside of the kapton dielectric to prevent grounding to the top half of the split-block waveguide after assembly. Return Loss [db] -1-2 Return Loss [db] µm holes ε r = µm holes,ε =11.1 ε r = ,ε =7.9 Figure 4. Simulations of short resonant lengths of substrates at GHz. The comparison between substrates containing holes (solid) with those of reduced dielectric constant (dashed) shows good agreement, indicating that the holes are behaving as predicted. Hole sizes of 5 µm and 125 µm were used. Figure 5. The return loss (greyscale) of short resonant lengths of substrate at frequencies of 1 16 GHz (y axes). The x- axes show the variation of effective dielectric constant and varying hole diameter. The holes were regularly spaced on a 4 mm grid. The right panel has an x-axis scaled linearly with the fraction of material remaining. The comparison of this scale with the upper scale of the left panel shows that the effective dielectric constant reduction is closely related to the average density of the dielectric. The results of these simulations can be used to deduce the effective dielectric constant for a given hole size. Proc. of SPIE Vol G-4

5 S11 (HFSS) S11 (VNA) S11 (HFSS) S11 (VNA) Figure 6. The return loss for short resonant lengths of duroid with 1 mm and 2 mm holes drilled in them. The VNA measurements (solid) are consistent with the HFSS simulations (dashed). Return Loss [db] -1-2 No holes.3 mm holes, 4 mm grid 3. mm holes, 4 mm grid Figure 7. Return loss (RL) and insertion loss (IL) of back-to-back porous substrates containing.3 mm (dashed) and 3 mm (dotted) holes, compared to the return loss of a substrate with no holes (solid). All three show good performance at GHz, with minor differences within the band GHZ MEASUREMENTS To demonstrate the applicability of these porous substrates to detectors, we have designed, made and tested substrates at 15 GHz. The substrate used is duroid RT/61LM (ε r =1.2). The effective dielectric constant is derived by comparing the two panels of Fig 5, and two-step notch transformers can be designed for that value. A range of hole diameters, from.3mm (λ/6) to 3mm (λ/6) were made, giving a range of effective dielectric constants as shown below. The results of the measurements, shown in Fig 7, show that the porous substrates do not give worse return losses than the non-porous substrate. The two-step transformers were designed to give < 18 db return loss across a 1 16 GHz band, and the back-to-back nature adds 3 6 db to this figure in measurements. The transformers are relatively sensitive to manufacturing errors, and these errors ( 1 µm) are likely to be responsible for the slightly poorer performance seen with of some of the test substrates. A set of substrates were made with holes on a 2 mm grid instead of a 4 mm grid. With small holes, the effect of a smaller grid was negligible, though with larger holes the effect is more apparent, as seen in Fig 8. There is an apparent shift in dielectric constant seen for the larger holes in the right panel. The holes in these samples are a reasonable fraction of a wavelength, and so it is reasonable to expect the behaviour to change. The manufactured substrates are summarised in Table Measurements of finline transitions The critical factor in the applicability of this technique is the effect on planar structures such as finlines. Measurements at 15 GHz have shown that the finlines have very little effect on the performance of the substrates, apart from the expected loss due to the room temperature copper. The finlines were made using photolithography of Espanex (18 µm thick copper deposited on on a 25 µm thick kapton dielectric) and placed on the duroid substrates. This excellent behaviour has been shown to extend to finlines on porous substrates. Proc. of SPIE Vol G

6 ε eff Hole size (mm) Grid size (mm) Hole size (mm) Grid size (mm) Table 1. Summary of porous substrates manufactured for testing at 15 GHz RL:.3 mm holes, 2 mm grid IL:.3 mm holes, 2 mm grid RL:.5 mm holes, 4 mm grid IL:.5 mm holes, 4 mm grid ,.5 mm holes RL: 1 mm holes, 2 mm grid IL: 1 mm holes, 2 mm grid RL: 2 mm holes, 4 mm grid IL: 2 mm holes, 4 mm grid , 2 mm holes Figure 8. Comparison of porous substrates with identical predicted effective dielectric constants, but different sized holes and grid sizes. Plotted are insertion loss (IL) and return loss (RL). In the left panel, substrates with.3 mm (solid) and.5 mm (dashed) holes, show very similar performance. In the right panel, the peaks from the substrate with 1 mm holes are shifted relative to those for the 2 mm holes, suggesting a different effective dielectric constant. Back-to-back unilateral transitions were designed for the appropriate effective dielectric constants and measured on a VNA. The finlines cause negligible additional return loss when placed on porous substrates, as shown in Fig 9. The performance of the finlines is a good indication that the effective dielectric constants are close to the predictions, as an incorrect dielectric constant would cause the finline to be incorrectly tuned. The lower dielectric constant substrates require a slightly longer (and therefore marginally more lossy) finline to achieve the same theoretical return loss. For example, the substrate with 3 mm holes and ε =7. requires a finline which is 18 % longer than that for a substrate with no holes. 5. MILLIMETRE-WAVE MEASUREMENTS To demonstrate the performance of porous substrates at millimetre wavelengths, substrates were designed at 9 GHz, with two-step transformers tuned to the predicted effective dielectric constant. Holes with diameters of 5, 8, and 125 µm were etched into silicon substrates using Deep Reactive Ion Etching (DRIE), with a mask as shown in Fig 1. The measured insertion loss of the back-to-back substrates is shown in Fig 11. The results show the cut-on frequency of higher order modes to increasing with hole size, as expected. The higher order mode cut-on frequencies are measured as 14 GHz and 17 GHz for samples with no holes and 5 µm holes, and above 11 GHz (above the maximum frequency of the VNA) for the 8 µm and, which is in agreement with the simulations (see Fig 12). The hole diameters, grid sizes, fraction of material removed and effective dielectric constants are shown in Table 2. Hole diameter Grid cell size Amount Removed ε eff (µm) (µm) (%) Table 2. Summary of porous substrates fabricated for testing at 9 GHz Proc. of SPIE Vol G-6

7 RL with finline IL with finline RL substrate only IL substrate only mm holes, 4 mm grid, ε ef f =9.9 RL with finline IL with finline RL substrate only IL substrate only mm holes, 4 mm grid, ε ef f = RL with finline IL with finline RL substrate only IL substrate only (c) 1. mm holes, 2 mm grid, ε ef f =8. RL with finline IL with finline RL substrate only IL substrate only (d) 2. mm holes, 4 mm grid, ε ef f =8. Figure 9. Performance of porous substrates at 15 GHz showing the comparison between substrates alone (dashed) and substrates with finlines on (solid), as measured on a VNA. Plotted are the insertion loss (IL, grey) and return loss (RL, black). The return loss shows that the finlines have negligible effect on the performance, while the insertion loss shows loss due to the copper finlines, as expected at room temperature. s S S Figure 1. : Image of the mask used to make the 9 GHz test substrates. The devices tested were the back-to-back (symmetric) substrates with two-step transformers. The assymetric devices with large square ends were designed to test the rigidity of the porous substrates, and proved to be physically robust. : A photo of a test substrate in the test block. Proc. of SPIE Vol G-7

8 Insertion Loss [db] No holes 5 µm holes 8 µm holes Figure 11. The Insertion Loss of substrates designed for 9 GHz, measured at 4 K and plotted relative to the insertion loss of the sample carrier alone. Samples with no holes (solid), 5 µm holes (dashed), 8 µm holes (dotted) and 125 µm (dot-dashed) holes were tested over the frequency range GHz. The increasing frequency of the drop in transmission for samples with no holes and 5 µm holes is consistent with simulations of higher order modes. Both the 8 µm and 125 µm hole samples show good performance to at least 11 GHz, which is again consistent with simulations. Insertion Loss [db] No holes 5 µm holes 8 µm holes Higher Order Mode Transmission [db] No holes 5 µm holes 8 µm holes Figure 12. HFSS Simulations results for 9 GHz porous substrates, showing insertion loss of the fundamental mode, and higher order mode transmission. Simulations were for substrates with no holes (solid), 5µm holes (dashed), 8 µm holes (dotted), 1 µm holes (dot-dashed), and (dot-dot-dashed). The holes were arranged in a closepacked grid, as shown in Fig 1. The cut-on frequency of the higher order modes is higher for larger holes (and therefore lower effective dielectric constants), and is consistent with measurements (see Fig 11). A feature noted during fabrication of these samples was the over-etching during DRIE. This has the effect of increasing the hole size, and therefore slightly affects the effective dielectric constant. The effect is small, at the few percent level (though the impact is larger for larger diameter holes), and can easily be accounted for if such accuracy is required. The devices were demonstrated to be physically robust. Simulations of two-step transformers of 225 µm thick silicon in WR-6 ( mm) waveguide at GHz are shown in Fig 13. The insertion loss shows that band can be extended up to 18 GHz by using an effective dielectric constant of 8., which corresponds to hole diameters of roughly 8 µm at this frequency (scaled from 9 GHz). Proc. of SPIE Vol G-8

9 Insertion Loss [db] ε r =11.8 ε r =1. ε r =9. ε r = Higher Order Mode Transmission [db] ε r =11.8 ε r =1. ε r =9. ε r = Figure 13. HFSS simulation results for 15 GHz porous substrates, showing insertion loss of the fundamental mode and higher order mode transmission. Simulations are for substrates with reduced dielectric constants, and show that a dielectric constant of 8. is sufficient to reach 18 GHz, corresponding to a hole diameter of roughly 8 mum on a 2 µm grid. 6. CONCLUSIONS We have demonstrated that the effect of small holes drilled or etched into a dielectric substrate is to decrease the effective dielectric constant. This is particularly useful when the native dielectric constant of the substrate is high and when it is relatively thick compared to the waveguide size, which encourages higher order modes to be transmitted. When combined with finline transitions this allows for excellent performance over a wide bandwidth. Such wide band transitions are needed by current and future astronomical instruments searching for extremely faint signals. The performance of these porous substrates has been demonstrated at 15 GHz and 9 GHz. The combination with finline transitions has been demonstrated at 15 GHz. CEN acknowledges an STFC studentship. ACKNOWLEDGMENTS REFERENCES [1] Yassin, G., Grimes, P. K., King, O. G., and North, C. E., Waveguide-to-planar circuit transition for millimetre-wave detectors, Accepted for publication in Electron. Lett. (28). [2] Yassin, G., Padman, R., Withington, S., Jacobs, K., and Wulff, S., A broad band antipodal finline mixer for astronomical imaging arrays, Electron. Lett. 33, 498 (1997). [3] Yassin, G., Withington, S., Jacobs, K., and Wulff, S., A 35 GHz antipoidal finline mixer, IEEE Trans. on Microwave Th. and Tech. 48, 662 (2). [4] Kittara, P., Yassin, G., Withington, S., Jacobs, K., and Wulff, S., A 7 GHz antipodal finline mixer fed by a Pickett-Potter horn-reflector antenna, IEEE Trans. on Microwave Th. and Tech. 52, 2352 (24). [5] Audley, M. D., Glowacka, D. M., Tsaneva, V. N., Withington, S., Grimes, P. K., North, C. E., Yassin, G., Piccirillo, L., Ade, P. A. R., and Sudiwala, R. V., Performance of microstrip-coupled TES bolometers with finline transitions, Proceedings of the SPIE 72, in press (28). [6] Kuzmin, L., Ultimate Cold-Electron Bolometer with strong electrothermal feedback, Proceedings of the SPIE 5498, 349 (June 24). [7] Kuzmin, L., Yassin, G., Withington, S., and Grimes, P., An antenna coupled Cold-Electron Bolometer for high performance cosmology instruments, Proceedings of the 18th Int. Symp. on Space THz Tech., 93 (Mar. 27). [8] Schieblich, C., Piotrowski, J. K., and Hinken, J. H., Synthesis of optimum finline tapers using dispersion formulas for arbitrary slot widths and locations, IEEE Trans. on Microwave Th. and Tech. 32, (Dec. 1984). [9] North, C. E., Yassin, G., and Grimes, P., Rigorous analysis and design of finline tapers for high performance millimetre and submillimetre detectors, Proceedings of the 17th Int. Symp. on Space THz Tech., 284 (May 26). [1] Pramanick, P. and Bhartia, P., Design tapered finlines using a calculator, in [Microwaves and RF], 111 (June 1987). Proc. of SPIE Vol G-9