Design, fabrication and characterization of wideband terahertz waveguide terminations Master’s thesis in Wireless, Photonics and Space engineering Karl Birkir Flosason Department of Space, Earth and the Environment CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2023 www.chalmers.se www.chalmers.se Master’s thesis 2023 Design, fabrication and characterization of wideband waveguide terminations Karl Birkir Flosason Department of Space, Earth and the Environment Onsala Space Observatory Group for Advanced Receiver Development - GARD Chalmers University of Technology Gothenburg, Sweden 2023 Design, fabrication and characterization of wideband waveguide terminations Karl Birkir Flosason © Karl Birkir Flosason, 2023. Supervisor: Professor Vincent Desmaris, GARD Examiner: Professor Victor Belitsky, GARD Group for Advanced Receiver Development (GARD) Department of Space, Earth and the Environment Division of Onsala Space Observatory Chalmers University of Technology SE-412 96 Gothenburg Telephone +46 31 772 1000 Cover: Microscope pictures and simulated S11 of the waveguide terminations Printed by Kompendiet AB, Göteborg. Gothenburg, Sweden 2023 iv Design, fabrication and characterization of wideband waveguide termina- tions Karl Birkir Flosason GARD Onsala Space Observatory Department of Space, Earth and the Environment Chalmers University of Technology Abstract This thesis reports on two novel designs for high performance, wideband waveguide terminations for terahertz frequencies, demonstrated here in the range 210-370 GHz corresponding to ALMA bands 6-7. With advancing technology in the design and fabrication of high sensitivity radioastronomy receivers, each component and aspect of the system needs to be pushed to the limits when it comes to performance and bandwidth. The highest sensitivity and state-of-the-art receivers today for radioastronomy use 2SB mixer topologies, which require terminations to terminate the fourth port of a waveguide RF hybrid coupler. Reflections from that termination will both increase the level of noise generally but also risk introducing spectral line images or ghosts from the heterodyne downmixing process, which may cause confusion of spectral lines when the tools are used for spectroscopy. Minimizing the reflections from that waveguide termination is a step in improving over-all performance, and taking full advantage of increased performance of the 2SB topology. The goal of the project was to design, fabricate and measure two distinct and novel termination designs, fabricated with well established methods, and materials with known and reliable behaviours in cryogenic operation, and achieve the best possible performance over the widest possible bandwidth. One design based on an E-probe on quartz substrate, showing in simulations S11 < -26 dB over 270-370 GHz, and another design based on a tapered finline structure showing in simulations S11 < -37.5 dB over 220-390 GHz. Both designs use TiN resistive thin-film to dissipate the RF energy in ohmic losses. To validate and verify the design and fabrication process, the performance was then measured using a VNA and the required frequency extensions. Measuring reflection accurately at such low levels and at these frequencies is challenging, and the measurements are likely to underestimate the real performance. Uncertainties in the measurements are described and their scale evaluated both by measurements and simulation. Keywords: Terahertz, waveguide termination, wideband, rf load, waveguide load, VNA, microwave metrology, reflection coefficient. v Acknowledgements First and foremost I would like to extend my gratitude to my examiner Victor Belitsky for attentively overseeing this work, being generous with his time and wealth of knowledge. I would like to thank my supervisor Vincent Desmaris for having me in on this project, and his helpfulness and patience in guiding the process. Huge thanks to Denis Meledin for his incredible patience with extensive staring through the microscope and delicately mounting ludicrously small objects to unbe- lievable precision, and help with the measurements. Thanks to Sven-Erik Ferm for this considerable skill with the machining, and at- tention to detail, which is indispensable in fabricating waveguide blocks to such high quality, as this project shows beyond doubt. Thanks to Leif Helldner for the excellent waveguide block layout and struggling through strange file import/export problems with me, and help with the measurements. Thanks for Alexey Pavolotskiy for saving us with mask printing, and being there for good advice. And last but not least thanks to Cristian Daniel López for his appreciated insights, useful discussions, simulation advice, company and help in the clean room. This project would not have been possible, and not as fun, without the great team at GARD. It has been a pleasure and an honor, and the highlight of my time in Chalmers to take part in this work. In loving memory of my father, dr. Flosi Karlsson TF3FX (1960-2013), whose key is now silent. Karl Birkir Flosason, Gothenburg, June 2023 vii List of Acronyms Below is the list of acronyms that have been used throughout this thesis listed in alphabetical order: 2SB Two-sidebands, sideband separating AC Alternating Current ALMA Atacama Large Millimeter/submillimeter Array CAD Computer-Assisted Drawing DC Direct Current FBW Fractional Bandwidth FIR Far-infrared GHz Gigahertz (109 Hz) IF intermediate frequency IR Infrared LO Local Oscillator MMIC Monolithic Microwave Integrated Circuit RF Radio frequency RFI Radio Frequency Interference SIS Superconductor-Insulator-Superconductor SSR Sideband-Separation Ratio THz Terahertz (1012 Hz) VNA Vector Network Analyzer ix x Physical constants c = 1/ √ µ0ε0 = 299792458 m/s Speed of light in vacuum η = √ µ0/ε0 ≈ 376.73 Ω Wave impedance of free space µ0 = 4π × 10−7 H/m Magnetic permeability of free space ε0 ≈ 8.8541878128 × 10−12 F/m Electric permittivity of free space xi Contents List of Acronyms ix List of Figures xv List of Tables xix 1 Preface 1 2 Introduction 3 2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Prior work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 Theory 7 3.1 Resistivity at high frequencies, and skin depth . . . . . . . . . . . . . 7 3.2 Thin film resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 Transmission lines and waveguides . . . . . . . . . . . . . . . . . . . . 8 3.3.1 General transmission line characteristics . . . . . . . . . . . . 8 3.3.2 Scattering parameters, S-matrix . . . . . . . . . . . . . . . . . 10 3.3.3 Chain scattering parameters, T-matrix . . . . . . . . . . . . . 11 3.3.4 Microstrip line . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3.5 Slotline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3.6 Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3.7 Finlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4 Waveguide-to-substrate transitions . . . . . . . . . . . . . . . . . . . 15 3.5 Impedance matching, multi-section transformers and tapers . . . . . . 15 4 Design 17 4.1 E-probe based design . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.1.1 Initial design constraints . . . . . . . . . . . . . . . . . . . . . 18 4.1.2 Substrate channel in waveguide . . . . . . . . . . . . . . . . . 19 4.1.3 Design of the resistive microstrip load . . . . . . . . . . . . . . 21 4.1.3.1 The width of the load . . . . . . . . . . . . . . . . . 22 4.1.3.2 The length of the load . . . . . . . . . . . . . . . . . 23 4.1.4 Probe design . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.1.5 Probe-to-Load matching . . . . . . . . . . . . . . . . . . . . . 27 4.1.6 Simulated performance of optimized E-probe based waveguide termination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 xiii Contents 4.1.7 Initial investigation of tolerances . . . . . . . . . . . . . . . . 29 4.1.8 Tolerance analysis . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.2 Finline based design . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.2.1 Initial design constraints . . . . . . . . . . . . . . . . . . . . . 34 4.2.2 Impedance and matching . . . . . . . . . . . . . . . . . . . . . 35 4.2.3 Straight narrow finline, or substrateless slotline . . . . . . . . 38 4.2.4 Short circuit termination . . . . . . . . . . . . . . . . . . . . . 38 4.2.5 Simulated performance of finline-based waveguide termination 39 5 Fabrication 41 5.1 Waveguide blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.2 E-probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.2.1 Mounting in waveguide . . . . . . . . . . . . . . . . . . . . . . 46 5.3 Finline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.3.1 Mounting in waveguide . . . . . . . . . . . . . . . . . . . . . . 51 6 Measurement and characterization 55 6.1 Measuring the thin-film resistance . . . . . . . . . . . . . . . . . . . . 55 6.2 VNA measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.2.1 Exploration of sources of error in VNA measurement . . . . . 59 6.2.1.1 Waveguide losses . . . . . . . . . . . . . . . . . . . . 59 6.2.1.2 Waveguide flange misalignment . . . . . . . . . . . . 61 6.2.2 VNA measurements of E-probe waveguide termination . . . . 64 6.2.3 VNA measurements of Finline waveguide termination . . . . . 67 6.3 Measurement conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 69 7 Conclusion 71 Bibliography 73 xiv List of Figures 2.1 A block-schematic view a 2SB mixer setup, showing the placement of the RF load on one port of the 90° RF hybrid . . . . . . . . . . . . . 4 3.1 Incident and reflected waves, a and b, in a 2-port network . . . . . . 11 3.2 Section of microstrip line, with the conductor and ground plane in yellow and dielectric as transparent blue . . . . . . . . . . . . . . . . 12 3.3 Section of slotline on substrate . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Section of rectangular waveguide of width a, and standard propor- tions b = a/2. Also showing in dashed lines, the centerline of dimen- sion a, along which the waveguide can be split. . . . . . . . . . . . . . 13 3.5 Small segment of finline in waveguide. Substrate shown in gray, con- ductor in yellow, surrounding waveguide made transparent . . . . . . 15 4.1 E-probe based design. Gold shown in yellow, crystalline quartz sub- strate in transparent blue, TiN resistive thin film in purple. Splitblock plane on waveguide shown in dashed lines . . . . . . . . . . . . . . . 18 4.2 Finline based design. TiN resistive thin film shown in purple. Split- block plane on waveguide shown in dashed lines . . . . . . . . . . . . 18 4.3 Looking into the input waveguide, showing the placement of the sub- strate channel in the floor, outlines of the substrate in blue, and the plane of the splitblock in dashed lines . . . . . . . . . . . . . . . . . . 20 4.4 Top-down view on split plane of waveguide structure, showing loca- tion and sizes of the substrate slot . . . . . . . . . . . . . . . . . . . . 21 4.5 Dimensions and placement of quartz substrate in channel. Split plane indicated with dashed lines . . . . . . . . . . . . . . . . . . . . . . . . 21 4.6 Real and imaginary microstrip characteristic impedance v.s. width, of the lossy microstrip at 320 GHz . . . . . . . . . . . . . . . . . . . . 23 4.7 The angle of the characteristic impedance normalized over π v.s. width of the lossy microstrip at 320 GHz . . . . . . . . . . . . . . . . 23 4.8 Circuit model of the beginning, end and one ∆z segment of a lossy transmission line, showing the input impedance, the characteristic impedance and the termination load . . . . . . . . . . . . . . . . . . 23 4.9 Plotting tanh(γl) of the telegrapher’s equation, for a γ of the 30 Ω/□, 120 µm wide resistive microstrip line at 320 GHz, over a range of lengths 24 4.10 Chosen shape of E-probe on suspended substrate, after optimization . 25 4.11 Output impedance of E-probe on smith chart, normalized to 50 Ω . . 26 xv List of Figures 4.12 Cross-section of substrate showing overlap between the deposited gold shown in orange, and TiN shown in purple, to ensure low contact resistance and robustness to any lithography mask misalignments . . 27 4.13 Top-down view in split plane, showing linear taper of length 303 µm, matching between probe and resistive microstrip termination . . . . . 28 4.14 S11 response of the E-probe based waveguide termination, after opti- mization. 270-370 GHz range delimited on the graph, showing per- formance of under -26 dB across the band. S-parameter normalized to the input impedance of the waveguide. . . . . . . . . . . . . . . . . 29 4.15 E-probe based waveguide termination, mounting assistance cavity on the left side. Seen in top-down view on split-plane . . . . . . . . . . . 30 4.16 +/- 5 µm shifts in the Y-direction . . . . . . . . . . . . . . . . . . . . 31 4.17 +/- 5 µm shifts in the Z-direction . . . . . . . . . . . . . . . . . . . . 32 4.18 +/- 5 µm shifts in the Z- and Y directions . . . . . . . . . . . . . . . 32 4.19 E-probe termination in its final form, showing TiN alignment marks on substrate, mounting assistance cavity to the left . . . . . . . . . . 33 4.20 Plot showing the relation between finline gap widths and impedances, and interpolated with a 5th order polynomial . . . . . . . . . . . . . 36 4.21 The finline structure shown in purple, in top-down view on the split plane. The gap widths indicated with arrows, at 285 µm long inter- vals. Section (a) is the substrateless slotline, and section (b) is the short termination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.22 The finline-based waveguide termination as seen looking into the waveguide input, showing the finline in purple and the waveguide split plane in dashed lines . . . . . . . . . . . . . . . . . . . . . . . . 37 4.23 Comparison of S11 between the Chebyshev taper and after optimizing for lower frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.1 Lower half of splitblock, showing the 3 different variations of each waveguide, for each of the 2 termination designs. Also shown are holes for alignment pins which align the upper and lower block, and holes for screws which tigthen them together. . . . . . . . . . . . . . 42 5.2 Layout of mask on 1x1" quartz, the inset picture showing a higher magnification of several copies of the E-probe, and three sheet resis- tance test strips to measure the sheet resistance of the thin-film . . . 44 5.3 Graphic showing the deposition steps and layers of the lithography, and etching process for the E-probe design. Layer thicknesses only indicative, not to scale. . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.4 Inspection of quartz substrate with E-probe based design under mi- croscope, after TiN sputtering, step 3) . . . . . . . . . . . . . . . . . 46 5.5 Microscope photo of TiN layer, after step 3) in the process. . . . . . . 46 5.6 Part of the lower half of the splitblock waveguide model, showing the substrate channel and alignment cavity . . . . . . . . . . . . . . . . . 47 5.7 Focus-stacked microscope picture of the mounted E-probe waveguide termination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.8 3d model from the same angle as the microscope picture . . . . . . . 48 xvi List of Figures 5.9 Mask layout for finline on 1x1" silicon wafer, showing several copies to be fabricated, along with alignment marks and resistance test strips. 49 5.10 Graphic showing steps of the etching and lithography process for the Finline design. Layer thicknesses only indicative, not to scale. . . . . 50 5.11 Finline structure with triangular back-tab to facilitate mounting and maneuvering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.12 Lower half of splitblock waveguide for finline structure, showing the slot in which the back-tab sits . . . . . . . . . . . . . . . . . . . . . . 51 5.13 Figure showing the finline structure, outlined in pink, mounted in the waveguide, emphasizing the space around the backtab. The finline structure sits on a solid shelf, with some air space above and around it. The split plane is indicated with dashed lines. . . . . . . . . . . . 52 5.14 Microscope picture showing the finline mounted in the waveguide. . . 52 5.15 Focus-stacked microscope picture showing a broken tip of one finline structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.1 Resistive strips on mask, identified by their L/w proportions. Gold pads visible on the ends of each . . . . . . . . . . . . . . . . . . . . . 56 6.2 Resistance measurement setup of test strips . . . . . . . . . . . . . . 56 6.3 Resistance measurement results of resistive thin-film test strips on quartz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6.4 VNA setup. The size transition shim is used for measuring the 760x380 sized waveguides, but is not needed nor used for the standard WR waveguide ports . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 6.5 Photograph showing part of VNA setup: frequency extender (1), the calibration plane (2) marked with green dashed line, waveguide size transition shim (3) and the waveguide block containing the DUT (4). Measuring Finline 760x380 port . . . . . . . . . . . . . . . . . . . . . 58 6.6 Measured S11 from empty waveguide block, through one waveguide size transition, for E-760. Lowpass filtered for clarity of demonstration 60 6.7 VNA setup of 2xThru measurement. Locations of waveguide flanges with potential for misalignment marked in numbers, 1-3, . . . . . . . 61 6.8 A cross-section view of exaggerated waveguide flange misalignment, as seen through the waveguide, showing the axis of the electric field and magnetic field, for a TE10 mode . . . . . . . . . . . . . . . . . . 61 6.9 Measured S11 of the 2xThru setup, with potential for 3 misaligned waveguide flanges. The red dashed line shows where the WR3.4 and WR2.2 are joined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.10 Simulated S11 comparison of the finline termination, with a single 30 µm E-plane misalignment (red) v.s. perfect alignment (blue) . . . . . 63 6.11 Example of a VNA setup, showing WR3.4 extender, and a waveguide size transition A down to 760 µm waveguide containing the E-probe termination. Same transitions are used for E-760 and F-760 . . . . . 64 6.12 Measured S11, compared between E-WR and E-760 . . . . . . . . . . 65 6.13 Comparison between the simulated S11 of the E-probe design, and the measured E-WR . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 xvii List of Figures 6.14 Measured S11 of F-WR v.s. F-760 . . . . . . . . . . . . . . . . . . . . 67 6.15 Simulated S11 comparison of the finline termination, with a single 30 µm E-plane misalignment v.s. simulated perfect alignment . . . . . . 68 xviii List of Tables 4.1 Waveguide and substrate channel dimensions . . . . . . . . . . . . . . 21 4.2 Dimensions of E-probe, after optimization with resistive microstrip termination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.3 Impedance of E-probe . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.4 Dimensions of optimized linear taper . . . . . . . . . . . . . . . . . . 28 4.5 S11 and bandwidth of E-probe based waveguide termination . . . . . 29 4.6 Estimates of potential dimensional errors in fabrication . . . . . . . . 31 4.7 Comparison of finline tapers, Chebyshev matching v.s. after opti- mization. Gap widths measured from the tip, each section is 285 µm long . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.8 S11 and FBW of Finline based waveguide termination . . . . . . . . . 39 5.1 Waveguide sizes and dimensions, and frequency range of the Virginia Diodes VNA extenders used for measuring the WR sizes . . . . . . . 43 xix List of Tables xx 1 Preface In the autumn of 1609 in the town of Padua in Italy, Galileo Galilei pointed his newly built telescope at the moon. Through the magnifying lenses he could clearly see the rough, cratered and uneven surface of the moon, which was in stark contradiction to the dominant cosmology of his time. According to that Aristotelian worldview, the heavens were perfect and immutable, and the moon should be a smooth, ideal sphere. Soon after, with an improved telescope, he turned to the planets and saw that they looked different from the point-like stars, and discovered that Jupiter had moons. He also observed that Venus shows full phases through its orbit, which did not fit with the old Ptolemic, earth-centric model of the solar system, but confirmed the Copernican helio-centric model, which was still a serious debate then. This new instrument shattered the old view of the world, and heralded a new age of observational astronomy. An age of basing our understanding of the cosmos on empirical data acquired by observations through ever improving instruments. Familiarity with the night sky had been useful through human history. The phases of the moon, the equinoxes and solstices, and the rise and fall of star constellations keep track of time and the changing of the seasons. The Pole Star guides travellers by indi- cating cardinal north. But when we started fully applying our advancing tool culture to observing it, fundamental changes to our view of the world and our place in it followed. Johannes Kepler derived the laws of planetary motions, based on detailed observations of their orbits made by Tycho Brahe. This would serve as a foundation and inspiration for Newton’s theory of gravitation. Since then, by more meticulous collection of data with ever improving instruments, much of our fundamental understanding of the universe and our place in it has been revolutionized, and a more accurate one reestablished more firmly Experiments with radio receivers in the early and mid- 20th century revealed that outer space was the source of a great deal of radio signals. Telescopes for radiowaves were developed to explore that, and they revealed that scientific discoveries in space were in no way limited to visible light and optical telescopes, but the whole electromagnetic spectrum conveys to us evidence of a great range of processes and phenomena in space, many of which are otherwise undetectable. Through these tools we have discovered and mapped the Cosmic Microwave Back- ground, and learned from it about the origin, composition and structure of the universe. Deviations from the expected behaviour of gravity on large scales has been found in the rotations of galaxies. We have confirmed the widespread existence of water and even complex organic molecules in distant celestial objects, witnessed the formations of solar systems and the heat glow of accretion discs around swirling black holes. What more is out there yet to be discovered, is unknown. But as we build and deploy even better instruments, we will find out. 1 1. Preface 2 2 Introduction With wavelengths in the range of 1-0.03 mm, the terahertz range of approximately 0.3-10 THz sits between infrared light and microwaves in the electromagnetic spec- trum. It has until recent years been the most underutilized part of the electro- magnetic spectrum. With advances in detector technology and sources suitable for use as oscillators, science has increasingly been taking advantage of this range of frequencies. Photon energies at those frequencies are relatively low so the radia- tion is harmless to humans and other organisms, but with shorter wavelengths than microwaves, the achievable angular resolution is greatly enhanced. Additionally, a wide variety of molecules have uniquely identifiable emission spectra in this fre- quency range, making it very useful for spectroscopic identification and analysis of chemical compositions [1]. In astronomy, THz instruments have proven to be a powerful part of the toolkit, and given us eyes to see parts of our universe that are otherwise invisible to us. Among the largest and most ambitious projects in ground-based astronomy is the radiotelescope ALMA (Atacama Large Millimeter/submillimeter Array) [2]. Located in the high plateau of the Atacama desert in Chile, ALMA consists of 66 individual antennas, operating together as an interferometer with adjustable baselines from 150 meters to 16 kilometers. Each ALMA antenna has 10 different receivers to cover different parts of the frequency range between 35 and 950 GHz, each receiver built by different teams in an international co-operative effort. The research group GARD, Group for Advanced Receiver Development, in Chalmers, has to date contributed to developing and fabricating receivers for two of the bands, band 2 and 5, as a part of the Onsala Space Observatory group, OSO [2]. 2.1 Motivation The signals received in most fields of radioastronomy are of extremely low power, so the highest achievable sensitivity in receiver technology is sought after and the tools constantly developed toward that goal. Since they are also intended for high frequency-resolution spectroscopy to identify molecules, it is important that spectral lines are not superimposed such as by image effects in the heterodyne frequency conversion process, which could cause spectral line confusion. One way to achieve both these goals is the 2SB or sideband separating receiver topology, which separates the sidebands using a mixer layout such as shown in Fig. 2.1, or Superconductor- Insulator-Superconductor, mixing technology. This setup also further reduces the effects of atmospheric noise in the reception [3], and the SIS mixer approaches the 3 2. Introduction quantum limit of noise performance. Receivers based on this principle have shown very good performance, such as in the recent SEPIA instrument for the APEX telescope [4] and ALMA band 5 [5]. But this improved performance is dependent on how effective the sideband separation is, as characterized by the figure-of-merit Sideband Separation Ratio (SSR). A system analysis by [6] shows how improving the SSR from its current state-of-the-art value of around 10 dB up to 20 dB would significantly improve over-all performance, reduce integration time and all but eliminate spectral line confusion. That analysis points to three of the main components of current systems that affect this figure: reflections off the SIS mixer itself, isolation between ports of the RF hybrids, and reflections from the RF load. Improved SSR will lower system noise, which reduces required observation time, and will reduce effects of unwanted artefacts such as image superposition on the signal, which may confuse spectral lines in spectroscopy [7]. RF loads with lower reflections will be one of the improvements needed to reduce internal reflections in the receiver assembly and thus improve the SSR of 2SB SIS receivers. Figure 2.1: A block-schematic view a 2SB mixer setup, showing the placement of the RF load on one port of the 90° RF hybrid Matched RF loads have the function of maximally absorbing RF energy with minimal reflections, such as at the termination of transmission lines or waveguides. They are a standard component and various commercially available solutions exist at those frequency ranges which are in common use. Matched loads with very low reflections are used in measurement systems, and terminations with high power dissipation can be used as dummy loads in power measurements or dry-runs of power amplifier setups. They are also necessary parts of system components where one output port needs to be terminated, such as some couplers and RF hybrids, as reflections would otherwise reflect back into the system and cause interference or increase the noise level, or in the characterization and measurements of multi- port devices where the parameters will not be correctly measured unless the unused ports are terminated with a matching load. Imperfect terminations, ones that are not matched or in other ways do not absorb well enough, cause reflections resulting 4 2. Introduction in standing waves and interferences and more noise in the system. In radioastronomy receivers in particular, reflections from imperfect loads increase noise in the system and can introduce false signals such as spectral line confusion. Designing and fabricating a wideband, high performance waveguide termina- tion at millimeter and sub-millimeter wavelengths will require high-precision man- ufacturing methods. But it will be favorable if the fabrication method is kept relatively simple and not with excessively tight manufacturing tolerances or with materials that are hard to work with. Components for such short wavelengths are generally inherently small, so in some cases larger components are well acceptable and may even facilitate an easy installation. 2.2 Prior work A typical way of implementing a matched load as a waveguide termination is by way of a lossy conductor or a lossy dielectric as an absorber, or combining both together. Several RF loads proposed for use in THz radioastronomy receivers and other RF systems utilize a commercially available epoxy-based material loaded with fragments of a lossy conductor [8]. This material has been characterized over a large frequency range at temperatures of both 300 K and 5 K by [9] and by [10]. Generally it is shaped into tapering cones or wedges and placed in the end of a waveguide, see [11] and [12]. Other approaches have been explored as well for these frequency ranges, such as using a linear tapered finline of thick, lossy silicon shaped by etching, inserted in the waveguide [13], or an elliptically-shaped resistive thin-film on substrate [14]. A matched load as a hidden fourth-port in a waveguide power splitter/combiner T-junction designed and demonstrated by Gouda et al. [15] could be implemented for this functionality. At millimeter wave frequencies it becomes more challenging to implement a good RF load. Methods developed for lower frequencies become less effective. Para- sitic inductances and capacitances in conventional resistors present high reactance at those high frequencies, which limits or entirely prevents power transfer and absorp- tion. Methods from higher frequencies, visible light, infrared (IR) or far-infrared (FIR), are not viable either. Since materials that present as opaque to IR and FIR become increasingly transparent at THz frequencies, all known black, matte paints and opaque materials are not effective [16], as their thickness is diminishing compared to the skindepth at the frequencies in question. While some of these approaches have produced useful terminations, different materials and fabrication methods allowing finer control of the shape to achieve a better impedance match and absorption could push the performance into the levels required for the next generation of radioastronomical instruments, where perfor- mance of each system component is crucial. 5 2. Introduction 6 3 Theory This section introduces the theory as it relates to the design process and its results, following established literature in the field, such as Pozar [17] and other textbooks as is relevant, such as [18] [19] [20]. This involves the main building elements such as transmission lines, their most relevant parameters and the formulas to calculate them, as fits within the scope of this work. 3.1 Resistivity at high frequencies, and skin depth Following Ohm’s law, resistance is the ratio between current and the voltage that is required to make it flow, R = V/I, or equivalently, the energy lost by electrons moving through an imperfect conductor. Resistance is a function of the material property bulk resistivity ρ, and the physical dimensions of the conductor, or that is, its cross-sectional area A = w · t and length L. A practical parameter for thin- films is sheet resistance, ρ/t = R□, or resistance-per-square, and R□ L w = R, or more comprehensively: R [Ω] = ρ L w · t = R□ L w (3.1) The resistivity of conductors increases proportionally with frequency, as √ f , if the thickness is greater than the skindepth. This is due to eddy currents inside the bulk of the conductor, caused by the rapidly changing electromagnetic fields, which oppose the flow of current, causing the current density to concentrate by the conductors’ surface rather than having a more even distribution over the conductors cross-section as it does at DC. The current density decays exponentially from the surface and into the conductor. This is called the skin effect, and the skin depth, δs, is defined as the distance at which the fields inside the metal have been reduced to 1/e of their value at the surface. The skin depth for a given conductor and frequency can be calculated as: δs = √ 2 σωµ (3.2) Where ω = 2πf is the angular frequency, µ = µ0µr is magnetic permeability and σ = 1/ρ is the material bulk conductivity. This applies under the approximation that the mean free path of an electron is much shorter than the skindepth, as noticed by Heinz London [21]. It also assumes a smooth conductor surface, which is not necessarily the case, and a rougher surface results in a longer conduction path along 7 3. Theory the surface, which effectively increases the resistance. At cryogenic temperatures, the resistivity of normal conductors increases even more with high frequencies, by the anomalous skin effect [22, 23, 24]. This exponential decay of current density in the bulk metal yields rapidly diminishing returns of increased conductivity from increasing the thickness of a conductor. Skin depths can also be used in plural form, referring to the depth at which current density has been reduced by factor 1/eN , after N skindepths from the conductors’ surface. As a rule of thumb it is sometimes considered enough to use 3 or 4 skin depths of thickness, which reduces the conductivity by only 1/e3 ≈ 0.05 or 1/e4 ≈ 0.02, to maintain conductivity as good as it gets without inefficient use of materials. The lowest sheet resistance achievable for a given frequency and bulk conductivity can be calculated as: R□,RF,min = √ ωµ 2σ (3.3) If the thickness of the conductor is much thinner than the skindepth, i.e. t << δs, its resistance is dominated by its thinness rather than the skin effect, so its sheet resistance at high frequency approaches its sheet resistance at DC. 3.2 Thin film resistors Resistive thin films are used for some applications in microwave circuits, here it is used as a termination to dissipate RF energy. They can be made with various metal alloys such as Tantalum Nitride (TaN) or Nickel-Chromium (NiCr) [25], but here it is implemented with a Titanium-Nitride [26]. The resistivity is controlled by the amount of Nitrogen, and can then be manufactured to the desired sheet resistance by controlling the thickness of the film, although the available range of adjustment there is limited by the manufacturing process. To then achieve a target resistance value, the ratio between width and length is adjusted, following the formulas 3.1. Thin-film resistors at RF have been characterized by [27] and [28] among others. 3.3 Transmission lines and waveguides As frequency increases, the length of conductors risks becoming a significant propor- tion of the length of the wave, λ. The voltage in different locations on a conductor can no longer be assumed to be the same throughout as in classical circuit theory, as it follows the transmitted wave. To handle these cases a new circuit theory needs to be developed, taking the characteristics and dimensions of the transmission lines fully into account as they relate to the propagation of the electric and magnetic fields, and the power they transfer. 3.3.1 General transmission line characteristics Modelling the transmission line as sequence of multiple small segments, where each segment can be modelled as resistors and inductors in series, and resistors and 8 3. Theory capacitors in parallel, its characteristic impedance Zc, can be calculated as: Zc = √ R + jωL G + jωC (3.4) Where the R is the resistance, G is shunt conductance, and L and C are inductance and capacitance, per unit length. The ∆z indicates that all the values are per small segment. The impedance is generally a complex number, a real valued resistance and imaginary reactance, ZL = RL + XL. A transmission line would sometimes be approximated as lossless and with no shunt conductance, setting R = 0 and G = 0, reducing the characteristic impedance to Z = √ L C , which is a pure real number. Another important parameter for transmission lines is the propagation con- stant γ: γ = α + jβ = √ (R + jωL)(G + jωC) (3.5) Where α is its attenuation factor and β the wavenumber. The propagation constant describes how the phase and magnitude of a wave travelling on the trans- mission line get translated forward, or with l as distance or location on the line: V = V +e−γl + V −eγl (3.6) In the exponent, a real-valued α ̸= 0 results in an exponential decay of the voltage in the positive direction, and the imaginary-valued β a periodic voltage wave. For a line with R = 0 and G = 0 and thus no loss, the the attenuation is taken to be 0, or α ≈ 0. The attenuation factor α is the sum of different factors that all contribute to attenuation, i.e. α = αc + αd + αr + . . . , where the subscripts denote conductor, dielectric and radiative and other possible losses. Conductor losses, or ohmic losses are due to current flowing through an imperfect conductor and relate to the resistance and the impedance, and for low losses can be roughly approximated as: αc ≈ 2R Z0 (3.7) Combining the aforementioned elements of transmission lines, the telegrapher’s equation expresses what impedance a transmission line presents at its inputs,Zin, given its own characteristic impedance Zc according to formula 3.4, the terminating impedance ZL, it’s propagation constant γ and its length l. Zin = Z0 ZL + Z0 tanh(γl) Z0 + ZL tanh(γl) (3.8) 9 3. Theory The goal of a transmission line is to deliver power, from a source to a load. How well it does this depends on the match or mismatch of the source, transmission line and load. A well matched sequence delivers power much better, and over a wider frequency range than a badly matched one, as expressed in the following formula. PR = |VL|2 8RL 4RSRL |ZS + ZL|2 = |VL|2 8RL (1 − |Γload|2) (3.9) Where VL is the voltage across the load, and RS and RL is the internal resis- tance to the source, and the load resistance respectively. Maximum power transfer between a source and a load is achieved if their impedances are conjugate matched, Zsource = Z∗ load. But for maximal bandwidth both components should have purely real impedance or as close to purely real as possible, since any imaginary component to the impedances of each will in the general case not stay perfectly conjugate over a wide range of frequencies and would thus limit the bandwidth of this match and thus the power transfer. The implication of this for a waveguide termination is that it needs to present an impedance as close to real as possible. 3.3.2 Scattering parameters, S-matrix A useful way of measuring and describing microwave systems and components is in terms of power of travelling waves, either reflected or incident [20]. When devices have multiple inputs and outputs, the relations are conveniently presented in a so- called scattering parameters, the S matrix, shown for an n-port device: S =  S11 . . . S1n ... . . . ... Sn1 . . . Snn  (3.10) Which translates between incident and reflected voltage waves between the ports in the following way: [V −] = [S][V +] (3.11) And each entry of the S matrix can be expressed as Sij = V − i V + j ∣∣∣∣∣ V + k =0 for k ̸=j (3.12) Or stating the same in plain words, following the theory outlined in Pozar [17]: If you drive port j with an incident wave of voltage V + j , and then measure the amplitude of the reflected wave at port i, V + i , while any other ports are terminated with a matching load, their ratio is the S parameter Sij. Keeping in mind that i = j is allowed, and presents how much is reflected back to the same port. The S-parameters then relate the incident and reflected waves a and b in the following way, as shown in the following figure. 10 3. Theory Figure 3.1: Incident and reflected waves, a and b, in a 2-port network b1 = S11a1 + S12a2 b2 = S21a1 + S22a2 (3.13) The most important S-parameter in this work is the S11, as it relates to the reflection coming back out of port 1 when it is excited with a wave, and is thus the obvious measure of the performance of a waveguide termination. For one-port, S11 is equivalent to its reflection coefficient, Γ, and a lower value means a lower reflection. 3.3.3 Chain scattering parameters, T-matrix Another note-keeping and calculation method for multi-port networks in microwave systems is the T-matrix, or chain scattering matrix. Different from the S-matrix, the T-matrices of cascaded microwave devices can be cascaded themselves, to calculate the total T-matrix of the chain. This can be a useful tool, such as for de-embedding fixtures for VNA measurements. The 2x2 T-matrix is related to the 2x2 S-matrix in the following way: T = T11 T12 T21 T22  =  S−1 21 −S−1 21 S22 S−1 21 S11 S12 − S11S −1 21 S22  (3.14) Since the T-matrices are invertible, if a measured device-under-test (DUT) is embedded in a test fixture with known S- or T-parameters: [Tmeasured] = [TA][TDUT ][TB] (3.15) Its de-embedded T-matrix can be found simply using matrix algebra [TDUT ] = [TA]−1[Tmeasured][TB]−1 (3.16) Which is then trivial to convert back to the S-matrix. 11 3. Theory 3.3.4 Microstrip line Microstrip lines consist of a conductor separated from a conducting ground plane by a dielectric. They have become ubiquitous in electric circuits for several reasons, such as ease of manufacture and system integration, as they make for convenient integration with other circuit elements such as mixers, filters and amplifiers. Since microstrip lines have two conductors, they can support a TEM mode of propagation, but other modes may arise. At the TEM mode, the impedance of an ideal microstrip line is nearly independent of frequency. Figure 3.2: Section of microstrip line, with the conductor and ground plane in yellow and dielectric as transparent blue The impedance of a microstrip line depends on the width of the conductor, w, the separation distance from the ground plane, d, and the permittivity of the dielec- tric ε. Formulas to calculate their impedance have been developed from empirical methods, based on curve-fitting to measurements [17]. Z0 =  60√ εr ln ( 8h W + W 4h ) 120π/ √ εe[W/h + 1.393 + 0.667 ln(W/h + 1.444)] W/h ≤ 1 W/h ≥ 1 (3.17) Where εe is the effective relative permittivity εe = εr + 1 2 + εr − 1 2 1√ 1 + 12h/w (3.18) When designing with microstrip lines, they are often first approximated as lossless, this makes its impedance purely real valued. In the design presented in later chapters the microstrip line is deliberately made of a lossy, resistive material, as it is used as an absorber. This adds series capacitance to its impedance, as char- acterized by [27], and can be seen from formula 3.4 for transmission line impedance. These formulas approximate a microstrip where the electric field only interacts between the microstrip and the ground conductor. Microstrips are often enclosed in conductive boxes, and here in a substrate channel described in 4.1.2, which will affect the distribution of the electric field, and thus the effective permittivity, which affects the characteristic impedance. These formulas may still serve as initial ap- proximations, but more accurate values need to be found as needed using full-wave EM simulators [19]. 12 3. Theory 3.3.5 Slotline The slotline is implemented as two metal strips separated by a gap, on top of a dielectric material substrate. Like the microstrip line, the electric field is partially in air and partially in the dielectric substrate, but for the slotline the electric field concentrates in the gap between the conductors. The slotline has the benefit of not requiring a ground plane under the substrate, but the drawback that it demonstrates high losses. The defining attributes for the impedance are the width of the separating gap, the height of the substrate and its dielectric permittivity. Figure 3.3: Section of slotline on substrate Similarly to the microstrip line, the impedance of slotlines has been explored by measurements and curvefitting, as described in [18], although limited to proportions 0.02 ≤ W/h ≤ 1, or that is, with a gap W not wider than the substrate thickness h. 3.3.6 Waveguide A waveguide consists of a conductive or reflective boundary surrounding a dielec- tric. This is most commonly implemented as an air-filled rectangular metal pipe. Waveguides see widespread use in RF systems for their relative ease of manufacture and low attenuation at high frequencies, and shielding from radio interference. Since high frequency radioastronomy systems generally use a parabolic reflector to collect and focus the incoming radiowaves, the highest coupling factor into a RF front-end system is achieved with a corrugated horn on waveguide. Figure 3.4: Section of rectangular waveguide of width a, and standard proportions b = a/2. Also showing in dashed lines, the centerline of dimension a, along which the waveguide can be split. 13 3. Theory The waveguide only uses a single conductor, therefore it doesn’t support a TEM propagation mode, only TM and TE modes. The impedance of a waveguide is not uniquely defined, but a common definition is the wave impedance of the mode being used, here ZT E : ZT E = kη β , β = √ k2 − k2 c (3.19) k = ω √ µε, kc = √( mπ a )2 + ( nπ b )2 (3.20) Where m and n are integers corresponding to the different modes of field dis- tribution, and a and b are the waveguide dimensions. Inconveniently, the impedance of waveguides is not constant over frequency, but is much higher on the lower end of its band, but for the standard proportions a/b = 2 its ZT E impedance converges to 400 ohms as the frequency increases. The mode waveguides are generally designed to use is the lowest TE mode ofTE10, but for any TEmn mode the cut-off frequency can be found as: fc = c 2π √ εr √( mπ a )2 + ( nπ b )2 (3.21) For waves propagating in the fundamental mode, TE10, virtually no currents flows across the centerline shown in figure 3.4. This enables manufacturing methods such as producing the waveguide in two halves, a splitblock, split along the middle of "a", or using those sides for inputs and outputs into the waveguide, which will be utilized in the designs presented in the upcoming sections. 3.3.7 Finlines The finline was proposed by Meier [29] and found to be very useful at high fre- quencies, several standard components for millimeter frequencies were subsequently developed based on that technique [30], such as matching networks, filters, direc- tional couplers and antennas [31] and waveguide-to-substrate transitions [32]. Sev- eral variations of the finline concept exist, but the one used here consists of a thin, metallized, dielectric slab or substrate, inserted parallel to the E-field, and along the propagation axis of a waveguide. The slabs come out of the wider sidewalls and towards the center, but remain separated by a gap of variable width. The gap width, substrate thickness and permittivity are the defining features of the finline, having the greatest impact on its impedance. Impedance decreases with a narrower gap for a given substrate. 14 3. Theory Figure 3.5: Small segment of finline in waveguide. Substrate shown in gray, con- ductor in yellow, surrounding waveguide made transparent Approximate formulas exist for the impedance and guided wavelengths, but thin and high permittivity dielectric with a separation width large compared to the substrate thickness. The formulas are too elaborate and long to be presented here, but they are described in more detail in [18] among other literature [29], [30], [31]. The substrate is inserted into a waveguide, the electric field concentrates in the gap between the conductors. Various approaches at synthesizing smooth finline tapers have been published, such as [31] and [33]. 3.4 Waveguide-to-substrate transitions Waveguides are commonly used at the front-end of radiosystems at very high fre- quencies, but the components that work with the signal are on substrates, such as mixers and transistors, so the need arises to interface or transition between those two propagating media. It is important that this transition couples effectively with the waveguide and captures as much of the RF energy as possible. Several designs have been proposed to achieve this, two categories of which will be mentioned here. One approach is to use a conductor on a suspended substrate as a probe inserted parallel into the electric field, a so-called E-probe, such as the radial probe by Kooi et. al. [34] in a full-height waveguide, or at higher frequencies by [35], or the one developed by Gouda et. al. [15] for use in a power-divider/combiner. Others have suggested dipoles [36] or butterfly shapes [37]. Another category is to use a finline structure such as proposed by [29], and has been shown by [32] to be very effective and broadband as an interface between waveguide and SIS mixer. 3.5 Impedance matching, multi-section transform- ers and tapers With impedance playing a central role in the design and function of microwave systems, transforming it to achieve a match between different systems or propagating mediums is crucial. 15 3. Theory The quality of matching between source impedance Z0 and load impedance ZL can be expressed with the number Γ = Z0−ZL Z0+ZL , which is optimized at Γ = 0 when Z0 = ZL. A multi-section transformer is based on inserting several transmission line sections in a sequence of impedances in the range between Z0 and ZL, where the reflections from each impedance mismatch is small. Keeping each section of an electrical length equivalent to λg/4 additionally creates destructive wave interference of the reflections from neighbouring sections, further reducing their effects at the output and input. The number of sections corresponds to the performance, as measured by Γ and the bandwidth over which it is minimized, but compromises in performance can be made to reduce the number of sections. A common compromise is to accept some level of ripples in Γ over the matched frequency band, and thus reducing the number of transformer sections. By using Chebyshev-polynomials, it is possible to optimally place the zeros of the transfer function in the Gamma-plane to keep the height of in-band ripples equal, and achieve a wider bandwidth under the acceptable level [17]. Another matching method is to use a linear or triangular taper to gradually change from one impedance to another, usually over a length of transmission line of at least one guided wavelength λg, or more. Linear tapers are generally inferior in performance to Chebyshev multisection transformers, having a higher Γ, but they are very simple to implement and optimize, and sometimes the performance is acceptable in that context. The linear taper is defined as a linearly changing impedance. In waveguide that corresponds to a linear change, but in microstrip it deviates slightly from that. It is however a common approximation to implement it as linear change in width of microstrip. 16 4 Design Two waveguide terminations were studied, and will be presented in this chapter. The first design, described in section 4.1 utilizes a waveguide-microstrip transi- tion or an E-field probe, to pick up the incoming waves from the waveguide and lead into a resistive thin-film microstrip deposited on a single 65 µm thick crystalline quartz substrate. This design focused on the frequency range 270-370 GHz, and aimed to achieve a reflection ratio of below -26 dB. The second one, described in section 4.2, consists of bilateral finlines tapering together into a substrateless slotline, then coming together in a short circuited end. It’s a single structure made of 30 µm thick high-resistivity silicon, with one broad- side and all sides of the structure coated in resistive thin-film TiN, leaving the substrate on the other broadside as uncovered silicon. This design focused on and achieved the whole useable waveguide band, 210-370 GHz. Both terminations were designed for waveguide size of 760 × 380 µm, designed for the frequency range of 210 - 370 GHz of ALMA bands 6-7, although only the finline structure covers the whole waveguide band. The cut-off frequencies for modes TE10 and TE20 of this waveguide size are respectively 197.2 GHz and 394 GHz, as calculated by formula 3.21, showing the lower and upper limits of its single mode propagation in the fundamental mode. Both terminations are designed to use a resistive thin-film as the lossy conduc- tor in which the RF energy is dissipated, aiming for a sheet resistance of 30 Ω/□. A range of sheet resistance values can be fabricated, as discussed in 3.2, but this one is chosen based on in-house experience as one that is straight-forward to achieve and can be produced consistently to a good accuracy. To put the resistivity in perspec- tive to known conductors, referring to formulas in 3.1, its bulk resistivity at DC is in the range of 2.5 × 105, compared with Au at 4.1 × 107, making it certainly an unfavorable conductor if low losses are desired, while still not being high resistivity. An indispensable tool to design RF hardware is 3D electromagnetic full-wave simulators, integrated with a 3D CAD software, the one used for this project is Ansys High Frequency Structure Simulator (HFSS). The design process starts with finding reasonable building blocks and elements for the use case, such as transmis- sion lines, material qualities, components and impedance matching methods, then calculating physical dimensions and electrical characteristics according to theory, and then sketching them in the 3D CAD software. The software can then simulate its performance and calculate the relevant performance metrics, such as in this case the reflection coefficient, S11. The user can then define an optimization strategy, choose which parameters such as widths and lengths should be modified and over which range, to achieve a better performance. 17 4. Design Figure 4.1: E-probe based de- sign. Gold shown in yellow, crys- talline quartz substrate in transparent blue, TiN resistive thin film in purple. Splitblock plane on waveguide shown in dashed lines Figure 4.2: Finline based design. TiN resistive thin film shown in pur- ple. Splitblock plane on waveguide shown in dashed lines Figures 4.1 4.2 present both designs in their final form, as seen looking into the waveguide as it is described in section 3.3.6. Since this is a termination, the waveguide is shorted at the back. The end-corners of the backshorted waveguide are rounded, since they are milled with CNC machining. The smallest available tool diameters useful for such milling are on the order of 60 µm, which sets the limit on the radius of the end corner fillet. Above that size range however, the fillet radius can also be a tuning parameter for the electromagnetic behaviour of the backshort. 4.1 E-probe based design The electric-field probe consists of a gold conductor on a dielectric substrate, de- scribed further in section 4.1.4. It couples to the EM fields in the waveguide and leads the RF energy into a resistive termination where it is dissipated, described in section 4.1.3. This structure sits inside a substrate channel, placed in the correct location in the larger waveguide structure, described in section 4.1.2. The whole design has several degrees of freedom, but certain constraints are well defined from the start, described in next section 4.1.1. 4.1.1 Initial design constraints Using the splitblock manufacturing method, based on the ability to split a waveguide along the broad-wall’s centerline as described in 3.3.6, the larger input waveguide leads into a smaller waveguide, here referred to as the substrate channel. The width of the substrate should not be so large that it becomes a waveguide by itself, i.e. supporting propagating substrate modes. For some safety margin, setting the frequency cut-off at 395 GHz, following formula 3.21, the widest allowed substrate is found to be 180 µm. The substrate will need to sit in a substrate channel with some gaps on the sides, so somewhat narrower than 180 µm is preferred. To maximize power transfer from the TE10-moded waveguide to the microstrip termination, an E-probe with a very high S21 or coupling-factor over the desired 18 4. Design bandwidth will be required, and an output impedance adjustable within the range of the resistive microstrip line widths that fit on the substrate. The substrate material for this design is 65 µm thick crystalline quartz. Its relative electrical permittivity is εr = 4.43. It is mechanically strong, and has seen use in many other designs for cryogenic operation and terahertz applications, for its low loss-tangent and reliability through thermal cycling. At millimeter-frequencies, the sizes of many components become very small. The relatively low permittivity of quartz is appealing in this regard, as it keeps the design larger which will make it easier to process and handle. An E-probe designed by [34] uses quartz and achieves an impedance very close to pure real, and presents designs on other higher permit- tivity substrates such as Silicon and Gallium-Arsenide which have some reactive components and approximately 2/3rds of the size of the quartz-based one. From formulas 3.5 and 3.17, a higher relative permittivity would enable a higher R Z ratio, resulting in a theoretically attenuation per unit length. This could potentially result in a physically smaller load, which might be desirable at lower frequencies, but with the already miniature size in question here, a physically larger and more mechanically robust structure makes the manufacturing and mounting more conve- nient. A suitable conductor material is gold, Au, to be deposited by electron beam evaporation to a thickness of 500 nm. It is also a common choice for cryogenic applications and high frequencies. Additionally, experience shows that depositing a thin layer of titanium first improves adhesion between the gold and quartz, here a 10 nm such layer was used. The material for the resistive thin-film is Titanium-Nitrogen, TiN. The nitro- gen acts as a pollutant which reduces the conductivity of the titanium. They are mixed by sputtering titanium in a nitrogen gas rather than a near-vacuum, the ni- trogen enters the titanium crystal as it’s forming, and reduces its conductivity, as described in section 3.2. The goal sheet resistance was 30 Ω/□. 4.1.2 Substrate channel in waveguide The quartz substrate carrying the E-probe and resistive microstrip sits in a substrate channel, which is a waveguide cavity from the input waveguide, perpendicular from its propagation axis and terminated in a short. The substrate itself sticks out of the substrate channel, suspended across the input waveguide. The location of the hole is so that the conductor-side of the substrate, where the E-probe sits, is in the center of the floor, at the peak of the voltage distribution of the TE10 mode. Enclosing a microstrip changes its effective dielectric constant, and so its impedance. Generally it is desirable to have the walls and ceiling far enough away to have minimal coupling with the electric field, to minimize this effect to simplify design. Relative to the substrate thickness, a rule of thumb recommended for mi- crostrip design is that the distance to ceiling should be eight times the thickness, and the distance to walls should be five times the thickness [19]. But in the detailed study on E-probes presented by Kooi et al. [34], they find that best bandwidth is achieved by having the the substrate channel height not more than twice the the thickness of the substrate. The starting value for optimization was with the height 19 4. Design exactly twice the thickness, and exploring values to both sides in the simulation it was found to best at 70 µm, compared to the 65 µm substrate thickness. The distance to the backshort, the bottom end of the terminated waveguide, is another important factor. Here it is measured from the center-line of the sub- strate, as indicated in figure 4.4. Given a centered placement of the substrate in the substrate channel, it determines where the E-probe sits in the standing wave. Following the theory and dimensions presented in [34], the starting value for op- timizations was 190 µm, but values ranging from 140 to 350 were explored, and best simulated performance was at 188 µm. One way to think of the function of the E-probe with regards to its placement against the backshort is that it should be located on the peak of the first standing wave, where the voltage peak is the highest. For the center frequency here, 320 GHz, which in the 760x380 µm waveguide gives a TE10-mode λg/4 = 297.5 µm, which should be the backshort distance according to that understanding. If this distance is shorter than λg/4, it rotates the electrical short around the smith chart and turns it into an inductive shunt tuning element, as explored in Kooi et al. [34]. Figure 4.3: Looking into the input waveguide, showing the placement of the sub- strate channel in the floor, outlines of the substrate in blue, and the plane of the splitblock in dashed lines 20 4. Design Figure 4.4: Top-down view on split plane of waveguide structure, showing location and sizes of the substrate slot Figure 4.5: Dimensions and place- ment of quartz substrate in chan- nel. Split plane indicated with dashed lines Dimensions Initial Values [µm] Optimized Values [µm] Backshort Distance 190 188 Input Waveguide Height 380 - Substrate Channel Width 190 185 Substrate Channel Length 1000 765 Substrate Channel Height 110 135 Substrate Width 180 155 Substrate Thickness 65 - Gap 10 15 Table 4.1: Waveguide and substrate channel dimensions The table lists the sizes and dimensions shown in the previous figures. The dimensions of the input waveguide height, and the substrate thickness, were decided by other factors and not subject to optimization. 4.1.3 Design of the resistive microstrip load The load is a length of resistive thin-film conductor, where the RF energy gets dissipated by ohmic losses. While at lower frequencies such a load can be essentially a resistor connected to ground, at the frequencies used here this would be impractical. The quartz substrate does not yield itself well to drilling via-holes for grounding, due to being brittle and hard to drill such small holes in at this scale. Bonding wires to circuit ground add a bandwidth limiting inductance, and it complicates the design, fabrication and mounting unnecessarily if it is at all avoidable, by adding more steps that involve manipulating microscopic elements with high precision. So 21 4. Design a floating load is better suited, i.e. one that is not physically connected to the circuit ground since can be manufactured to a high degree of accuracy and precision using lithographic methods, and integrates well with the E-probe itself and the suitable substrate. By depositing a thin layer of Titanium mixed with Nitrogen, it is possible to control the conductivity and thickness of the metal within a certain range, and in turn its sheet resistance, as explain in section 3.2. With the fabrication method and equipment used, it has been found that a sheet resistance of 30 Ω/□ can be reliably manufactured with high repeatability, so it is chosen as the sheet resistance value of the load. This sheet resistance value results in an approximately 140 nm thick film. 4.1.3.1 The width of the load From the theory explained in 3.7 (γ = α + jβ, with α = 2R/Z0) it is seen that a narrower load would have higher resistance and thus higher attenuation. Another thing to consider however is the bandwidth of the matching and power transfer, as described in section 3.9. As the load becomes wider its impedance becomes closer to being pure real. A narrow, resistive microstrip has a significant series capacitive reactance which will limit the bandwidth of the matching and thus the power transfer between probe and load. Optimizing the performance of this design becomes about finding the balance between attenuation per length unit on one hand and impedance matching over a broad band against the reactive part of the load, on the other. With the small physical dimensions inherent with those frequencies, the slight increase in length that results from the greater width is not of great consequence for this use case and might even benefit fabrication and mounting in the waveguide. To map how the width of the load affects its characteristic impedance, with the previously described substrate and resistive thin film, it is plotted here based on the calculations of microstrip characteristic impedance and transmission line characteristics described in 3.17 and 3.4, for the range of widths that are considered. The plots show first the real and imaginary parts of the characteristic impedance, and then the argument of the complex number, normalized over π, for 30 Ω/□ sheet resistance microstrip, at the center frequency 320 GHz, on 65 µm thick εr = 4.43 quartz substrate. The real part of the characteristic impedance closely follows a lossless microstrip, but the resistivity adds a series capacitance seen as a negative imaginary component. 22 4. Design 0 20 40 60 80 100 120 140 -100 -75 -50 -25 0 25 50 75 100 125 150 Figure 4.6: Real and imaginary mi- crostrip characteristic impedance v.s. width, of the lossy microstrip at 320 GHz 0 20 40 60 80 100 120 140 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 Figure 4.7: The angle of the charac- teristic impedance normalized over π v.s. width of the lossy microstrip at 320 GHz This makes it clear, following equation 3.9 and the surrounding theory, that a wider load with the cost of added length is a worthwhile tradeoff. Setting the width at 120 µm gives a characteristic impedance Zc = 51.6− j9.9Ω, for a lossy microstrip if it were not enclosed in a substrate channel. As mentioned in section 3.3.4, a narrow enclosure will affect the impedance in ways that no closed-form formulas exist to calculate, and the established method is to use numerical computation such as with 3D fullwave simulators to approximate its value. But the change of the real and imaginary components of the impedance with the width of the resistive microstrip can be reasonably assumed to be similar, whether enclosed or not. 4.1.3.2 The length of the load Figure 4.8: Circuit model of the beginning, end and one ∆z segment of a lossy transmission line, showing the input impedance, the characteristic impedance and the termination load The impedance Zin seen looking into a ter- minated transmission line can be calcu- lated with the telegrapher’s equation, 3.8. It can be seen from there that as the prod- uct of loss and length of the transmission line increases, the impedance looking into it converges to its characteristic impedance following tanh(γl), if Real{γ} ≠ 0. So even if the the microstrip line is termi- nated in an open circuit, or that is, a load impedance ZLoad → ∞, at the right length l for a given loss, this becomes irrelevant and Zin → Z0 anyway. Plotting tanh(γl) for a 120 µm wide microstrip line at 320 GHz, and a range of lengths demonstrates this clearly: 23 4. Design 0 200 400 600 800 1000 -2 -1 0 1 2 3 4 Figure 4.9: Plotting tanh(γl) of the telegrapher’s equation, for a γ of the 30 Ω/□, 120 µm wide resistive microstrip line at 320 GHz, over a range of lengths Where tanh(γl) is from the telegrapher’s equation: Zin = Z0 ZL + Z0 tanh(γl) Z0 + ZL tanh(γl) Where Z0 and γ are the transmission line’s characteristic impedance and prop- agation constant respectively, and l is its length or more generally position along its length. This shows that for a lossy transmission line, i.e. Real{γ} = α ̸= 0, yields the convergence tanh γl → 1 with increased l, leading to Z0+ZL tanh γl ZL+Z0 tanh γl → 1 which ul- timately leads to Zin → Z0, or the input impedance converging to the characteristic impedance regardless of the termination. From this, the initial length of the load is chosen to be 800 µm, but the optimization will explore values down to 630 µm. Higher sheet resistance or narrower microstrip would achieve a tanh(γl) ≈ 1 + j0 at lower lengths due to having higher Real{γ}, but would suffer from the problems described in the previous section. 4.1.4 Probe design One of the probe designs presented by Kooi et. al [34] shows nearly pure-real impedance, on quartz substrate and for a similar range of frequencies as in this application. This is very promising, as explained in section 3.3.1 on power transfer. The load impedance is however not pure real, so some modifications are required for a good match. A variation of that probe, presented by [15] has more degrees of freedom in extra width for optimizing the performance against the impedance of the resistive and slightly series-capacitive microstrip load. 24 4. Design It was found through simulation experimentation that low probe impedances, in the range of 25 to 30 Ω resulted in great variations in the argument of the impedance over the frequency, while for higher impedances around 50 to 60 Ω or higher, similar magnitude variations of the imaginary part of the impedance had much smaller effects, as to be expected. As expressed in equation 3.7, a lower impedance would give higher attenuation, but that needs to be balanced out against the bandwidth of the impedance matching, for which variations in the imaginary part of the impedance are detrimental. Figure 4.10: Chosen shape of E-probe on suspended substrate, after optimization The following table shows the dimensions of the probe on the picture, after op- timization with the resistive microstrip line including the matching taper described in the next section, 4.1.5. Since the probe is made on the substrate using lithography, it can be manufactured to a high spatial precision and accuracy. 25 4. Design Parameter Value Unit Belly 22 µm Top Width 124.6 µm Mid Width 137 µm Bottom Width 43.5 µm Length 101 µm Table 4.2: Dimensions of E-probe, after optimization with resistive microstrip termination Figure 4.11: Output impedance of E-probe on smith chart, normalized to 50 Ω The figure above shows how the impedance of this probe structure appears on the smith chart, it is seen that its impedance is close to being a conjugate of the calculated first approximation of the characteristic impedance of the load, at ZC,Load = 51.6 − j9.9Ω, as described previously in section 4.1.3.1. Minor variations through the frequency range remain however. Output Impedance [Ω] 270 GHz 320 GHz 370 GHz Real{Z}: 47.4 56.17 58 Imaginary{Z}: 9.5 6.47 14.81 Table 4.3: Impedance of E-probe 26 4. Design The length and width of the E-probe are important features, but a very im- portant factor in its output impedance turned out to be the width at the base, or the bottom width. Other methods of tuning the impedance E-probe as it appears from the input of the waveguide, include shifting it against the backshort, adding a floating conductive counter-element elsewhere on the substrate, a deeper air-filled channel under the substrate to reduce the effective dielectric constant of the substrate and thus modify the impedance. These methods were explored preliminarily but eventually turned out to not be necessary. 4.1.5 Probe-to-Load matching Direct connection between the probe and taper did not exhibit very good perfor- mance in simulations. The next step was to define a linear taper of Au between them, and also define a 5 µm overlap of the TiN and Au along its contact circum- ference, to both establish adequately low electrical contact resistance, and to ensure that it would be maintained through any minor misalignments in the lithography process. Figure 4.12: Cross-section of substrate showing overlap between the deposited gold shown in orange, and TiN shown in purple, to ensure low contact resistance and robustness to any lithography mask misalignments Since the resistive microstrip load and the E-probe by itself present slightly different input and output impedances respectively, which also change through the optimization process, a convenient way to match them together is to use a simple triangular matching taper. The impedances of both the load and the termination are difficult to evaluate precisely, whether analytically or numerically, and thus need to be optimized together as one structure after the initial and approximate sizes are decided. 27 4. Design Figure 4.13: Top-down view in split plane, showing linear taper of length 303 µm, matching between probe and resistive microstrip termination The linear taper is generally not the most effective impedance matching taper, having a greater length than the other approaches, and higher reflection coefficient than the Chebyshev multi-section transformer. It is however very simple, its ge- ometric structure being defined only by base-width and length, so for very small mismatches between impedance values that are hard to pin down exactly, like in this case, and for optimization purposes, it can serve very well. Lengths of the taper were explored in optimizations from 150 µm to 600 µm, but the best performance found there. The base-width was likewise explored from being more narrow than the probe lead which is 43.5 µm, to being wider up to 100 µm, but 53.5 µm showed the best performance. Taper Width [µm] Taper Length [µm] Taper electrical length at fc [βl] 53.5 303 ∼ π Table 4.4: Dimensions of optimized linear taper The table lists the width of the base of the taper, and its length. It also lists its electrical lengt at the center frequency, 320 GHz. The best performance was found experimentally with a taper length of 303 µm, and width 53.5µm, against the probe base width of 43 µm. This is somewhat surprising. As described in Pozar [17], the lowest reflection coefficient |Γ| from such a taper is achieved at electrical length βl = n2π for n = 1, 2..., but 303 µm here corresponds to approximately βl ≈ π, or half a wavelength at center frequency. It is therefore uncertain whether this taper is performing as an impedance match, or increased contact surface between Au and TiN, or a wave-launcher into the resistive film. 28 4. Design 4.1.6 Simulated performance of optimized E-probe based waveguide termination After optimization of the probe dimensions and its placement within the input waveguide, the performance shown below was achieved. The performance metric for a waveguide termination is its S11, or reflection coefficient, how much of the input power gets reflected back. The design goal was to achieve -26 dB over the frequency band of 270-370 GHz. At the band edges, the S11 is 270 GHz 370 GHz FBW < -26 dB -27 dB -28.8 dB 0.33 Table 4.5: S11 and bandwidth of E-probe based waveguide termination 250 270 290 310 330 350 370 390 -55 -50 -45 -40 -35 -30 -25 -20 -15 Figure 4.14: S11 response of the E-probe based waveguide termination, after op- timization. 270-370 GHz range delimited on the graph, showing performance of under -26 dB across the band. S-parameter normalized to the input impedance of the waveguide. 4.1.7 Initial investigation of tolerances Simulated performance of this waveguide termination exceeded the performance specifications. Preliminary assessments of mounting and fabrication tolerances how- ever showed that it was sensitive to a placement of the substrate within the substrate 29 4. Design channel up to a very high degree of precision, which would pose challenges in mount- ing the cip. In particular, shifts along the length of the substrate channel, in the Y-direction. Figure 4.15: E-probe based waveguide termination, mounting assistance cavity on the left side. Seen in top-down view on split-plane Attempts to mitigate this focused on reducing discontinuities in the microstrip line directly on top of the edge between the input waveguide and the substrate channel, by letting some of the resistive material stick out into the input waveguide, and stretching the lead from the probe further into the substrate channel. This reduced the sensitivity somewhat, but performance is still highly dependent on the mounting accuracy. 4.1.8 Tolerance analysis Precision fabrication is generally needed to fabricate components at such high fre- quencies. The fabrication steps involved, described in more detail in chapter 5, are: depositing the metal on the conductor using lithographic methods, dicing the sub- strate with a saw into rectangles of the right length and width, milling the waveguide out of a solid block of aluminum, and then mounting the substrate chip in the right place in the substrate channel. Each of those steps introduces dimensional errors to the structure to different degrees, no matter how carefully performed. An accurate assessment of the potential inaccuracies is hard to state with absolute confidence, but rough estimates to guide tolerance analysis can be made based on experience, shown in the following table. With the relatively high accuracy of the lithography compared to other sources of inaccuracy, analysing the tolerance of the performance to the other sources will be prioritized. Since the installation is done by hand under a microscope, it has a lot of potential as a source of error in the YZ plane as shown in figure 4.15. With the mounting method, initially using wax to fix it in place, it can however be re-aligned. 30 4. Design Fabrication step Potential error [±µm] Lithography (Au and TiN) <0.1 Substrate dicing 5 Waveguide CNC milling 5 Chip mounting 5 Table 4.6: Estimates of potential dimensional errors in fabrication 250 270 290 310 330 350 370 390 -55 -50 -45 -40 -35 -30 -25 -20 -15 Figure 4.16: +/- 5 µm shifts in the Y-direction Figure 4.16 above shows how the S11 is affected by shifting the substrate chip ±5µm along the Y-direction. Some performance is retained, but decreases significantly to barely -24 dB, and for the -5 µm shift, the bandwidth is reduced. 31 4. Design 250 270 290 310 330 350 370 390 -55 -50 -45 -40 -35 -30 -25 -20 -15 Figure 4.17: +/- 5 µm shifts in the Z-direction Shifting the substrate chip in the Z-direction within the substrate channel makes the gaps asymmetric. As understood from previous sections about microstrip impedance 3.3.4, if conductive sidewalls are close enough to significantly interfere with the electric field, then they affect the impedance. As the simulation show, this affects the performance, but not as much as the Y-shift. Performance remains below -26 dB across the band. 250 270 290 310 330 350 370 390 -60 -50 -40 -30 -20 -10 Figure 4.18: +/- 5 µm shifts in the Z- and Y directions 32 4. Design The worst result would then be to combine both shifts, +5 µm in both Y and Z on one hand, and -5 µm in both Y and Z on the other, as shown on figure 4.18 These results show that adding some features to the design to facilitate accurate mounting in the waveguide would be highly benficial, and also demonstrates some of the difficulties of manufacturing instrumentation for such high frequency ranges. The added features to the design were small 10 × 10 µm wide squares as alignment marks. They should be equally far away from the edges between the input waveguid and the substrate channel. This will be mounted in a microscope, and the substrate is transparent, so it is important that the squares be large enough to be seen clearly through the microscope. Another feature to help with mounting is the alignment cavity on the left hand side of the figure below, to more easily fit narrow-tipped tools to shift the substrate around. The floor of the cavity is also 10 µm lower than the floor of the substrate channel, to add another sharp edge that can be used for alignment. Figure 4.19: E-probe termination in its final form, showing TiN alignment marks on substrate, mounting assistance cavity to the left 33 4. Design 4.2 Finline based design The finline-based waveguide termination consists of a slab of 30 µm thick high- resistivity silicon dielectric, of relative permittivity ε = 11.7, inserted parallel to the electric field in the waveguide and along the propagation direction. The finline transmission line is known to be inherently broadband, but lossy, demonstrating both conductor and potentially radiative losses. It can form a physically large structure relative to wavelengths, which makes it convenient for fabrication and mounting into a sub-millimeter sized waveguide. At the beginning of this project it was uncertain what bandwidth and performance might be achieved in a reliably way, but the goal was to cover the whole frequency range of the waveguide’s fundamental mode, which corresponds to ALMA bands 6-7, 210-370 GHz, and achieve as low Γ as possible. As described in section 3.3.7, the characteristic impedance of a finline depends on the separation gap and the thickness of the substrate. The lowest impedance and highest loss is achieved with the smallest separation distance. To achieve impedance matching the separation distance must be decreased slowly from the waveguide’s full height of 380 µm using a smooth impedance matching taper, and then lead it in a straight 20 µm gap far enough to achieve a similar Zin → Z0 transmission line effect as was discussed in 4.1.3, so it can be terminated in a short circuit. The short circuit also acts as mechanical support, so the structure can be manufactured and mounted in the waveguide as one solid piece The dissipation of the energy is achieved by using a resistive thin-film con- ductor, of sheet resistance R□ = 30 Ω/□, which is sputtered on to the top layer and edges of the finline, leaving one side as exposed silicon. Additionally the finline structure is separated from the waveguide ceiling and floor by a small gap, 5 µm, to make facilitate mounting and to not rely on physical contact for electrical grounding. 4.2.1 Initial design constraints The substrate is shaped using plasma etching. This puts a constraint on how nar- row the narrowest gap in the slotline can be, as the plasma etching effect is nearly line-of-sight, so the walls that make up the slotline gap on finline chips off-center on the wafer might get unevenly etched. For this fabrication the lower width limit was set at 20 µm. Although during the processing it was found it could potentially be narrower, but the impedance and attenuation achieved at 20 µm was sufficient. A 30 µm thick silicon substrate was selected for this, as it is relatively easy to shape in this way to a good precision, but should prove to be mechanically strong enough for mounting, according to in-house fabrication experience. Since this design is intended for operation at cryogenic temperatures it is not feasible to rely on the lossy properties of silicon as a dielectric like was done in a waveguide termination by Beuerle et al. [13], since the dielectric loss tangent of silicon is not reliably high at cryogenic temperatures, as characterized in [38]. Instead, this termination will utilize resistive thin-film, which is known to have a 34 4. Design nearly constant level of ohmic losses, through the temperature range from room temperature to cryogenic. The sheet resistance 30 Ω/□ is chosen for the same reasons as in the E-probe based design, something which is possible to consistently reproduce to a good pre- cision with standard clean room methods. 4.2.2 Impedance and matching The most critical aspect with regards to minimizing the reflection coefficient is the impedance match between the input and the termination. The finline structure with its lossy conductor must closely match the impedance of the waveguide itself. The attenuation is greater at low impedance, since more current flows through the lossy conductor, but the transformation between the impedances needs to be highly effective. This suggests to use a long, smooth tapering of the gap width, from a width close to the full waveguide height and down to the narrowest gap that is practical to produce. The resistive conductor in the taper is likely to achieve some attenuation, but the narrow straight finline at the end achieves the most per length unit, since it has the lowest impedance. The impedance of a full-height waveguide is taken to be approximately 400 Ω, but it is higher at the lower frequency limit. The impedance of a finline varies with the separation between the fins, becoming lower with a narrower gap, and empirically derived formulas exist to approximate it, as referred to in section 3.3.7. It is however unusual to implement it with a deliberately resistive conductor, and the design formulas which assume negligible losses are thus not directly applicable in this context. To acquire starting values on which to base the the taper, a straight finline structure as pictured in figure 3.3.7 with the resistive thin film was simulated in HFSS for the dimensions and specifications of the design constraints, and over a range of widths from the most wide of 370 µm to the most narrow, 20 µm. From the results of those simulated impedance values at the center frequency were chosen for each width, and a polynomial function curve-fitted to the data. From the inverse function, it is straight forward to calculate the physical dimensions of a taper from desired impedance values. 35 4. Design 100 150 200 250 300 350 0 50 100 150 200 250 300 350 400 Figure 4.20: Plot showing the relation between finline gap widths and impedances, and interpolated with a 5th order polynomial It is noteworthy on Fig. 4.20 that at the largest gap width simulated, 370 µm, the characteristic impedance was just over 300 Ω, still not close to the approximately 400 Ω impedance of the full height waveguide. At this gap width, and given the 5 µm space to the sides of the waveguide, the tips of finline structure are merely 5 µm thick, but made of a resistive conductor located in the peak of waveguide’s electric field distribution. Additionally, with the conductivity of the TiN thin-film, its skindepth at the frequency range here as discussed in 3.2 is δs ≈ 10t or almost ten times its thickness, so it is nearly transparent. The permittivity of the substrate is however very high compared to air, so the air-substrate interface has the potential to cause reflections. Figure 4.21: The finline structure shown in purple, in top-down view on the split plane. The gap widths indicated with arrows, at 285 µm long intervals. Section (a) is the substrateless slotline, and section (b) is the short termination 36 4. Design Figure 4.22: The finline-based waveguide termination as seen looking into the waveguide input, showing the finline in purple and the waveguide split plane in dashed lines A Chebyshev matching taper of 7 sections was synthesized to match between the impedances at the largest gap and the narrowest gap, and translated into widths. To reduce discontinuities in an attempt to reduce reflections, the matching taper sections were smoothed out by using cubic spline. The sections of a Chebyshev taper are designed to be λg/4 long at the center frequency, where λg is the guided wavelength in the finline. An initial value for the guided wavelength λg was found by measuring the distance between peaks of current density in the simulated structure at the center frequency 290 GHz, and the mean finline gap width of 200 µm, and it was found to be λg/4 = 250 µm. Early attempts to increase low-frequency performance however showed that section lengths of λg/4 = 285 µm had a marked improvement. Taper Gap widths of each section [µm] Chebyshev 354.5 300 217 103.5 33 22.3 20 Optimized 336.0 300 234.0 149.40 73.60 33.80 20 Table 4.7: Comparison of finline tapers, Chebyshev matching v.s. after optimiza- tion. Gap widths measured from the tip, each section is 285 µm long Table 4.7 lists the widths of the initial Chebyshev matching taper, at λg/4 = 285 µm section lengths, measured as shown on figure 4.21. The initial taper showed promising results, but further optimizations on the taper widths revealed that per- formance could be improved further, especially at the lower end of the band. The optimized taper starts somewhat more narrow, but narrows more slowly. The Cheby- shev taper starts wider, and narrows rather fast around the mid-sections. 37 4. Design 4.2.3 Straight narrow finline, or substrateless slotline After the matching taper, the next part of the structure is the 20 µm wide gap finline, or substrateless slotline, marked as a) on figure 4.21. For this design, the optimal length was found to be 541 µm. The width was chosen based on experience of fabricating such a gap using available plasma etching methods. Narrower gaps might be difficult to etch with plasma, with the substrate thickness being 30 µm. A narrower gap would have lower impedance and higher attenuation, so it potentially could be shorter for the same effect. This transmission line has a similar effect as detailed in section 4.1.3 about the length of the resistive microstrip termination, in this case enabling a short-circuit termination, but making its input impedance look like its characteristic impedance despite that. 4.2.4 Short circuit termination The finline structure is then terminated in a short-circuit, marked with b) on figure 4.21. In this design, the optimal length of this part was found to be 124 µm. Following the discussion of resistance 3.1, the length of this part determines the width of the terminating resistor, and thereby its resistance value. This makes the total length of the finline-based waveguide termination as shown on Fig. 4.21, 2660 µm long. 38 4. Design 4.2.5 Simulated performance of finline-based waveguide ter- mination The performance of the finline-based waveguide termination was shown to be ex- cellent across the whole waveguide band, with S11 < -37.5 dB above 215 GHz, and -26 dB at the intended lower frequency end of 210 GHz. Other aspects of it that are favorable are simple fabrication methods, and a relatively large structure which facilitates mounting in the waveguide. 200 220 240 260 280 300 320 340 360 380 -60 -50 -40 -30 -20 -10 0 Figure 4.23: Comparison of S11 between the Chebyshev taper and after optimizing for lower frequency The performance shown in the figure is very good, and covers the entire ALMA Bands 6-7, with S11 = -26 dB at 210 GHz, and then stays below -37.5 dB from 218 GHz and throughout. It is noteworthy that the initial attempt at the Chebyshev matching taper immediately showed very good performance, but a slightly less steep tapering extended the performance for a lower frequency. 210 GHz 218 GHz 380 GHz FBW < -37.5 dB -26 dB -37.5 dB < -40 dB 0.54 Table 4.8: S11 and FBW of Finline based waveguide termination 39 4. Design 40 5 Fabrication This chapter describes the fabrication process of both designs, and the waveguide blocks they will be mounted in for measurement and characterization. Section 5.1 discusses the waveguide fabrication in more detail. With the small size of components and waveguides, it was convenient to make the waveguides for both components out of a single block. Since this design was made for 760×380 µm, which isn’t one of the standard waveguide sizes, the measurements will require adap- tation to the standard waveguide sizes on the VNA frequency extenders. Additional waveguides with built-in waveguide size transitions were milled into the block so that each design could also be measured natively at each of the neighbouring standard waveguides sizes, WR2.2 and WR3.4. Section 5.2 deals with the fabrication of the E-probe and resistive termination is described in more detail. It was fabricated using standard clean room methods, on a quartz substrate, using TiN for the resistive microstrip termination and Au as the conductor for the E-probe itself. It was then diced by a dicing saw, using a 20 µm thick diamond blade, to shape the substrate into the right widths and lengths of individual chips. Section 5.3 describes the fabrication of the finline based waveguide termina- tion. It was fabricated by etching the shape out of a 30 µm thick high-resistivity silicon substrate. The silicon is provided from the manufactorer on a 300 µm thick backing structure also made of silicon, and they are separated by a 2 µm thick layer of SiOx insulator. After etching the shape, the backing structure is released into individual pieces and then covered with resistive thin-film TiN. Both design take advantage of lithographic methods to place conductors on their substrates. It is an advantage that the fabrication uses well established and standard clean room methods. 41 5. Fabrication 5.1 Waveguide blocks The waveguide blocks are fabricated in a split-block fashion. Following the theory outlined in section 3.3.6, it is possible to split a waveguide along the centerline of its E-plane, since no RF currents flow across the centerline and perfect electrical contact between the blocks is thus not critical for the travelling wave. Taking advantage of this makes the fabrication and mounting easier. Figure 5.1: Lower half of splitblock, showing the 3 different variations of each waveguide, for each of the 2 termination designs. Also shown are holes for alignment pins which align the upper and lower block, and holes for screws which tigthen them together. To make measurements possible, each of the two termination designs denoted by the prefix "E-" and "F-" on the figure, will be mounted in three different waveguide structures, for a total of six chips in a single block. First in the ALMA standard, denoted on figure 5.1 with suffix "-760", secondly in each of the WR2.2 and then in the WR3.4 sizes, using a built-in 2.5mm long linear-taper size transitions between 42 5. Fabrication the standard sizes to the 760 µm wide size the terminations were designed for. With the ALMA Bands 6-7 being the frequency range of 210-370 GHz, the waveguide size chosen for it falls in between the ranges of standard waveguides such as are found in the VNA frequency extenders used for the measurements [39, 40]. Waveguide names, dimensions, and the frequency range of the VNA extenders is listed in table 5.1. Waveguide standard Width [µm] Height [µm] Frequency range [GHz] ALMA Band 6-7 760 380 210 - 370 WR2.2 559 279 330 - 500 WR3.4 864 432 220 - 330 Table 5.1: Waveguide sizes and dimensions, and frequency range of the Virginia Diodes VNA extenders used for measuring the WR sizes The waveguide blocks were milled in-house, out of solid block of aluminum alloy, using a precision CNC. 5.2 E-probe The first step towards the lithographic process is to make the photomasks which control the layers and locations of the to-be-deposited metals, one layer for Au and another layer for TiN. Alignment between layers is critical, so alignment marks are on both layers, and made in a way so they line up but the first doesn’t block the second. Since the width and length of the substrate is another important factor, the size of each chip is delimited at the corners with marks to guide the dicing process. Also included on the mask are thin-film resistors of different L/w aspect ratios of TiN resistive thin-film, to verify the sheet resistance by measuring their resistance, shown in figure 6.3. The dimensions selected were, as indicated on the mask, L/W = [3, 5, 8], and for a sheet resistance of 30 Ω/□ should correspond to resistance values of 90, 150 and 240 Ω, following the theory outlined in 3.1. The test structures also include contact pads of Au, and the length is measured as only the length of TiN between them. The thickness of TiN deposition by sputtering, and so its sheet resistance, may vary slightly with radius from the center, so structures are located at different radii. 43 5. Fabrication Figure 5.2: Layout of mask on 1x1" quartz, the inset picture showing a higher magnification of several copies of the E-probe, and three sheet resistance test strips to measure the sheet resistance of the thin-film The fabrication process is described in Fig. 5.3. For simplicity, cleaning steps are mostly left out, and the 10 nm titanium adhesion layer between Au and quartz is only described in the text. 44 5. Fabrication Figure 5.3: Graphic showing the deposition steps and layers of the lithography, and etching process for the E-probe design. Layer thicknesses only indicative, not to scale. The steps to fabricate the E-probe based design are as follows, leaving out washing and cleaning as needed between stages: 1. Sputter TiN over the whole quartz chip. Measure sheet resistance at this point, to verify correct TiN process. Sheet resistance may increase by 2-4% over the course of a few days due to oxidization. 2. First layer of the photomask, for the TiN layer. This layer is positive-mask, which means that it exposes the areas where sputtered TiN should be removed, leaving only the areas where TiN should remain, covered with resist after development. 3. This leaves the resistive microstrip termination, ready for the next stage. 4. Apply resist with mask. The second mask exposes the areas where Au should remain, so those areas get covered by resist. The mask covers the areas where Au should no remain. 5. Electron beam evaporation of Au on quartz substrate. First step is a 10 nm thick layer of titanium, to improve adhesion between Au and quartz. Electron- beam evaporated gold, to 500 nm thickness. 6. Wash in organic solvent and ultrasonic cleaner, which dissolves the polymer resist mask, releasing the gold from where it should not remain. Rinse off solvent with distilled water, and clean with pressurized air. 45 5. Fabrication Figure 5.4: Inspection of quartz substrate with E-probe based design under mi- croscope, after TiN sputtering, step 3) Figure 5.5: Microscope photo of TiN layer, after step 3) in the process. After the lithography, the chip is ready for dicing. The dicing marks are a part of the TiN layer. It is diced by a very fine 50 µm thick diamond circular sawblade. After dicing, the chips are ready to be released from the glass backing structure, cleaned more, and mounted in the waveguide block. 5.2.1 Mounting in waveguide To align the E-probe correctly in the substrate channel, alignment marks made of 5x5 µm TiN squares placed on opposite sides of the edges between the substrate channel and the input waveguide. To facilitate mounting and alignment in the substrate channel, a second cavity on the far-side of the probe was added, far left on the pictures. It has the same height above substrate, but extends 10 µm below it, deliberately a short distance so that the edge can be made very sharp and straight, to assist with alignment. Space around the substrate on that also helps getting tools near it to place