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Thin film superconducting microwave resonators have been an area of intense re- search in the past decade for Microwave Kinetic Inductance Detectors (MKIDs) [1] for submillimeter[2], optical/UV [3], and X-ray [4] astrophysics, components in superconduct- ing qubits [5, 6], and fundamental studies in condensed matter physics such as searches for macroscopic quantum states [7] and measurements of the properties of cryogenic liq- uids [8]. These resonators have primarily been coplanar waveguide (CPW) transmission line resonators [9]. A CPW transmission line is a planar structure with a center strip and slots that separate the center strip from ground planes on either side, as shown in the top panel of Figure 1. They are simple to fabricate out of a single superconducting film on a crystalline dielectric. However, in many cases the flexibility of a microstrip resonator, which is a stacked structure with a deposited dielectric separating two conductors, would be advantageous. A microstrip MKID can be deposited on any material, instead of just single crystal silicon or sapphire, and can be made significantly smaller than a CPW MKID. This allows more flexibility in detector design. The low loss deposited dielectrics required for a sensitive microstrip MKID have many other uses, such as in the lumped element capacitors and wiring crossovers in superconducting qubits [10] or the microstrip combiner networks of planar antenna arrays [11]. This work details the first microstrip MKID using a deposited thin film dielectric. 

Microstrip resonators can be made very sensitive by making the dielectric comparable to or thinner than the penetration depth of the superconductor since this causes the device to be dominated by the kinetic inductance of the superconductor, not the magnetic inductance of the transmission line. This leads to a very sensitive detector since MKIDs respond to changes in the kinetic inductance, such as those caused by broken Cooper Pairs from photon absorption. It also makes a compact resonator since the phase velocity on the transmission line can be as low as several percent of the speed of light. Following Swihart [12] and Pond et al. [13], the phase velocity of a superconducting microstrip whose width w is much greater than the dielectric thickness d and at T ≪ T$_{c}$ can be written using the two fluid approximation as 

<img src='content_image/356190.jpg'>

where c is the speed of light in vacuum, ϵ$_{r}$ is the relative dielectric constant of the microstrip dielectric, and λ and t are the penetration depth and the thickness of the top (1) and 

