Design of antenna-coupled lumped-element titanium nitride KIDs for long-wavelength multi-band continuum imaging

Many applications in cosmology and astrophysics at millimeter wavelengths — CMB polarization, studies of galaxy clusters using the Sunyaev-Zeldovich effect, studies of star formation at high redshift and in our local universe and our galaxy — require large-format arrays of millimeter-wave detectors. Feedhorn, lens-coupled twinslot antenna, and phased-array antenna architectures for receiving mm-wave light present numerous advantages for control of systematics and for simultaneous coverage of both polarizations and/or multiple spectral bands. Simultaneously, kinetic inductance detectors using high-resistivity materials like titanium nitride are an attractive sensor option for large-format arrays because they are highly multiplexable and because their high responsivity can render two-level-system noise subdominant to photon and recombination noise. However, coupling the two is a challenge because of the impedance mismatch between the microstrip exiting these architectures and the high resistivity of titanium nitride. Mitigating direct absorption in the KID is also a challenge. We present a detailed titanium nitride KID design that addresses these challenges. The KID inductor is capacitively coupled to the microstrip in such a way as to form a lossy termination without creating an impedance mismatch. A parallelplate capacitor design mitigates direct absorption, uses hydrogenated amorphous silicon, and yields acceptable two-level-system noise. We show that an optimized design can yield expected sensitivities very close to the fundamental limit from photon and recombination noises for two relevant examples: single spectral band designs appropriate for 90 and 150 GHz for CMB polarization and a multi-spectral-band design that covers 90 GHz to 405 GHz in six bands for SZ effect studies.