Planar Lithographed Superconducting LC Resonators for Frequency-Domain Multiplexed Readout Systems

Abstract

Cosmic microwave background (CMB) polarization experiments are increasing the number of transition edge sensor (TES) bolometers to increase sensitivity. In order to maintain low thermal loading of the sub-Kelvin stage, the frequency-domain multiplexing (FDM) factor has to increase accordingly. FDM is achieved by placing TES bolometers in series with inductor–capacitor (LC) resonators, which select the readout frequency. The multiplexing factor can be raised with a large total readout bandwidth and small frequency spacing between channels. The inductance is kept constant to maintain a uniform readout bandwidth across detectors, while the maximum acceptable value is determined by bolometer stability. Current technology relies on commercially available ceramic chip capacitors. These have high scatter in their capacitance thereby requiring large frequency spacing. Furthermore, they have high equivalent series resistance (ESR) at higher frequencies and are time consuming and tedious to hand assemble via soldering. A solution lies in lithographed, planar spiral inductors (currently in use by some experiments) combined with interdigitated capacitors on a silicon (Si) substrate. To maintain reasonable device dimensions, we have reduced trace and gap widths of the LCs to 4 \(\upmu \)m. We increased the inductance from 16 to 60 \(\upmu \)H to achieve a higher packing density, a requirement for FDM systems with large multiplexing factors. Additionally, the Si substrate yields low ESR values across the entire frequency range and lithography makes mass production of LC pairs possible. We reduced mutual inductance between inductors by placing them in a checkerboard pattern with the capacitors, thereby increasing physical distances between adjacent inductors. We also reduce magnetic coupling of inductors with external sources by evaporating a superconducting ground plane onto the backside of the substrate. We report on the development of lithographed LCs in the 1–5 MHz range for use with FDM systems. These resonators will be used by CMB polarization experiments such as Polarbear-2, Simons Array, and SPT-3G. Existing FDM systems have multiplexing factors up to 16\(\times \). We report the extension to 40\(\times \), i.e., Polarbear-2, and 68\(\times \), i.e., SPT-3G. We present the design criteria of Polarbear-2’s LC circuits, the fabrication techniques, and the testing. Concerns such as yield, accuracy in frequency, loss, and mutual inductance between spatially neighboring channels will be discussed.