Principal Investigator: Prof. Dr. Martin Hoffmann, RUB

Achieved results and methods

Continued work on MEMS reflectarrays; to be continued in S01 in the 3^rd phase

Demonstrators of MEMS reflectarray antennas were designed, fabricated, and characterized. For mechanical beam steering, each actuator needs to perform a defined, individual, and stepwise displacement of the reflector [3]. Additionally to step-by-step actuators [4], a new actuator based on a micromechanical digital-to-analogue converter (M-DAC) [5] has been introduced. Both systems were analytically investigated, simulated, fabricated, and characterized. A detailed description of both systems is presented in [6]. Fig. 1a/b show fabricated 5- and 16-step actuators, Fig. 1c the displacement of a 5-step actuator. The 16-step actuator has a maximum throw of 230.7 ± 0.9 µm at 54 V.

An N step actuator requires at least N+1bondpads (Fig. 1a). As a reflectarray requires 80+ reflectors with 27 positions each [7], reflectarray wiring and control become very complex. Therefore, a micro-mechanical digital-to-analogue converting actuator (M-DAC) was proposed. The M-DAC addresses 3^N equidistant, discrete, and individual positions using 2N actuators with 2N+1 wires, reducing the complexity significantly [3]. Fig. 2a shows a single Bit in its initial position. In Fig. 2b, the Bit i is in position 0-1 with the downward actuator actuated. In Fig. 2c, both actuators are activated, and the Bit is in middle position 1-1. In Fig. 2d, the upwards actuator is actuated, and the Bit is in the upward position 1-0.

By combining N = 3 of these bits with linking springs, the M-DAC addresses 27 (3^N = 3³) discrete positions. The DAC can be combined with a mechanical amplifier converting a small throw into a large displacement of the reflector. Fig. 3a shows a fabricated chip with M-DAC, mechanical amplifier, and reflector. The reflector requires a thickness of (at least) 300 µm and combines a device (50 µm) and a handle (250 µm) layer of the SOI substrate [8]., A DRIE process has been developed allowing to keep the handle and device layer combined with an opened reflector for the feeding THz wave (Fig. 3a). Fig. 3b shows a reflectarray with two sets of four reflectors (3 active reflectors and one passive static reflector) stacked, aligned and with electrical connection.

The displacement achieved so far is 234.5 ± 1.8 µm as shown in Fig 4a for a DAC with 8 logical positions (=2³ DAC) [5]. Here, the total displacement of the reflector including amplifier, the displacement of the DAC (without amplifier) and the amplification ratio are shown. The experimental results are compared with the simulation. Fig. 4b shows the displacement of three stacked active reflectors (Fig. 3b). The integration strategy was successful as the three reflectors displace independently from each other without “mech. crosstalk” while the connecting springs can be improved in linearity.

This work attracted interest in the microactuator community and was invited for an article [9] included in an Actuators Special Issue “Cooperative Microactuator Systems” edited by M. Kohl, S. Seelecke and U. Wallrabe (DFG SPP KOMMMA) and was also highlighted in a review paper [10]. Lisa Schmitt (doctoral researcher from C12) graduated with the doctoral degree in February 2023 [6].

Dielectric all-Si THz waveguides

As the wavelength decreases compared to the dimensions (length) of the waveguides, a time-domain “snapshot” from Finite Difference Time Domain (FDTD) simulations of the field distribution can be misleading. The Beam Propagation Method (BPM) describes the forward distribution at the price of neglected reflective parts. During 2^nd phase of MARIE, C12 successfully qualified the BPM solver BeamPROP^® for simulation of dielectric waveguides in the THz domain. The BPM simulation was implemented by qualifying the software for THz waves (λ ≈ 1.000 µm). To our and the supplier’s knowledge, it is the first use for THz applications.

Starting point for dielectric waveguides in C12 were single-mode slot and ridge silicon waveguides, as shown in Fig. 5 with dimensions to scale and in relation to a WR-3 hollow waveguide.

The dielectric waveguides are designed and fabricated in High-Resistivity-Si (HR-Si, ρ > 10 kΩ⋅cm) with a refractive index of 3.4 – 3.5 corresponding to ε_r ≈ 12 from 250 GHz up to 270 THz [11]. HR-Si requires a sequential DRIE process to prevent the substrate from overheating while maintaining almost vertical etching by using a silica hardmask. Photoresist-masked DRIE as used for doped Si is not suitable.

Photonic Si-based waveguides are usually fabricated on a low-refractive-index, e.g. a silica cladding, but silica processing is difficult, especially for actuated waveguide components. Polymer claddings as used for THz waveguides exhibit similar difficulties. Therefore, an all-silicon metacarrier with low refractive index was investigated that is much thinner than the common full-waveguide height metamaterial embedding [1], which allows for nearly “unclad” waveguides. The low-index metamaterial based on heavily perforated silicon is combined with both waveguide concepts, see Fig. 6. A mechanically reliable spatial localization was solved by a two-step front/backside etching process on HR-Si realizing a thin membrane with a low Si/air ratio and thus a low effective index. Honey-comb membranes allow for the lowest fill factor (n ≈ 1.6; circular holes: n ≈ 2.6) in combination with high mechanical stability. These structures profit from a high proportion of air and the grids are “small” compared to the wavelength (<λ/20) at 300 GHz to prevent resonant effects and scattering. Fig. 6d shows a realized slot-ridge converter: The waveguide has the height of the substrate (200 µm) while the metamaterial is reduced to 40 µm thickness, only.

Fig. 7a shows the measurement setup (in cooperation with M04, [14]). The waveguides are characterized using a vector network analyzer (VNA). The signals are coupled using two WR-3 hollow waveguide probe antennas (220 GHz to 330 GHz). In order to estimate the insertion and coupling losses, a direct probe to probe measurement in varying distances from (nearly) 0 mm to 40 mm is performed. The transmission curve vs. gap (without waveguide) for 275 GHz is presented in Fig. 7b.

Fig. 8 depicts the measured transmission (S21) of the a) slot and b) rib waveguides, which is referenced to free space transmission. Silicon slot and rib waveguides show excellent functionality as losses <0.15 dB/mm are measured. For bends, rib waveguides show much lower loss than slot waveguides as the mode is confined within the silicon. The coupling factor of hollow waveguides turned out to be better for “large” singlemode rib waveguides as compared to similar slot waveguides. The theoretical coupling (eigenmodes from BeamPROP^®) is 90 % for the rib and 54 % for the slot waveguide. For more precise low-loss measurements, a more accurate referencing and calibration is required (WP2, 3^rd phase).

To successfully create a fully integrated THz circuit (TIC), further building blocks are needed including mode converters between slot and ridge waveguides (Fig. 6d). This allows a low-loss conversion between both types of waveguides and enables MEMS compatibility and new functionalities.

Dielectric waveguides & MEMS

Combining dielectric waveguides and MEMS has been achieved in optical communication almost three decades ago, for a review see e.g. [15], and it is an emerging field for THz systems nowadays [2]. During the 2^nd phase it turned out that slot waveguides are predestined for a true time delay, as a variation of the slot width allows a modulation of the effective index. The required throw of the actuators is strongly reduced compared to reflective approaches, but the co-integration of actuators and waveguides on HR‑Si had to be considered. C12 designed, fabricated, and characterized a transmissive true-time delay based on electrostatic actuation of slot waveguides around 300 GHz. Consequently, suitable MEMS-guiding mechanisms were investigated and presented in [16]. A demonstrator is shown in Fig. 9a, its basic design in Fig. 9b: the slot waveguide is connected to electrostatic comb-drive actuators using a metamaterial “cladding”. The slot width of the waveguided increases or decreases by actuating one of the two counter-directional actuators. The device is fabricated on an SOI substrate with a doped device layer for the actuators and a HR-Si handle layer for the metamaterial and waveguides [17].

Within ~270 to 350 GHz, the tuned slot achieves a linear phase difference as required for a true time delay, Fig. 10a. At 300 GHz, a phase shift of >360° is achievable. The actuators allow a wide, voltage-controlled displacement, see Fig. 10b, c [17].

Overall, significant advances in reflective beam steering using innovative MEMS actuator arrays have been achieved while novel concepts for transmissive beam steering group antennas based on actuated dielectric THz waveguides have been investigated. The results lay the foundation for complex THz integrated circuits (TIC, analogue to Photonic ICs - PIC) for compact mobile localization and imaging.

Selected project-related publications

1. Schmitt, X. Liu, Ph. Schmitt, A. Czylwik, M. Hoffmann: “Large Displacement Actuators With Multi-Point Stability for a MEMS-Driven THz Beam Steering Concept,” IEEE Journal of Microelectromechanical Systems, 2023, [DOI: 10.1109/JMEMS.2023.3236145]
2. Schmitt, M. Hoffmann: “Large Stepwise Discrete Microsystem Displacements Based on Electrostatic Bending Plate Actuation,” Actuators MDPI, 10(10), 272, 2021, [DOI: 10.3390/act10100272]
3. Schmitt, Ph. Schmitt, M. Hoffmann: “3-Bit Digital-to-Analog Converter with Mechanical Amplifier for Binary Encoded Large Displacements,” Actuators MDPI, 10, 182, 2021, [DOI: 10.3390/act10080182]
4. Liu, L. Schmitt, B. Sievert, J. Lipka, C. Geng, K. Kolpatzeck, D. Erni, A. Rennings, J. C. Balzer, M. Hoffmann, A. Czylwik: “Terahertz Beam Steering Using a MEMS-based Reflectarray Configured by a Genetic Algorithm,” IEEE Access, vol. 10, 2022, [DOI: 10.1109/ACCESS.2022.3197202]
5. Schmitt, X. Liu, A. Czylwik, M. Hoffmann: “Design and Fabrication of MEMS Reflectors for THz Reflect-Arrays,” 2021 Fourth International Workshop on Mobile Terahertz Systems (IWMTS), pp. 1-5, 2021, [DOI: 10.1109/IWMTS51331.2021.9486804]
6. Schmitt, P. Conrad, A. Kopp, C. Ament, M. Hoffmann: Non-Inchworm Electrostatic Cooperative Micro-Stepper-Actuator Systems with Long Stroke, Actuators, MDPI, 2023, 12(4), 150, [DOI: 10.3390/act12040150]
7. Barowski, L. Schmitt, K. Kother, M. Hoffmann: “Design, Simulation, and Characterization of MEMS-Based Slot Waveguides,” IEEE Transactions on Microwave Theory and Techniques, 2023, [DOI: 10.1109/TMTT.2023.3255589]
8. Schmitt, Ph. Schmitt, M. Hoffmann: Highly Selective Tilted Triangular Springs with Constant Force Reaction, Sensors 2024, 24(5), 1677, [DOI: 10.3390/s24051677]
9. Kadera, J. Sánchez-Pastor, L. Schmitt, M. Schüßler, R. Jakoby, M. Hoffmann, A. Jiménez-Sáez, J. Lacik: Sub-THz Luneburg lens enabled wide-angle frequency-coded identification tag for passive indoor self-localization, In: Int. J. Microwave and Wireless Techn. 1 – 15, 2022, [DOI: 10.1017/S175907872200054X]
10. Schenkel, I. Barengolts, L. Schmitt, I. Rolfes, M. Hoffmann, J. Barowski: Silicon based Metamaterials for Dielectric Waveguides in the THz Range“, 21st Mediterranean Microwave Symposium (MMS) 2022, May 9-13, [DOI: 10.1109/MMS55062.2022.9825523]