Analysis and mitigation of interface losses in trenched superconducting coplanar waveguide resonators

Improving the performance of superconducting qubits and resonators generally results from a combination of materials and fabrication process improvements and design modifications that reduce device sensitivity to residual losses. One instance of this approach is to use trenching into the device substrate in combination with superconductors and dielectrics with low intrinsic losses to improve quality factors and coherence times. Here we demonstrate titanium nitride coplanar waveguide resonators with mean quality factors exceeding two million and controlled trenching reaching 2.2 $mu$m into the silicon substrate. Additionally, we measure sets of resonators with a range of sizes and trench depths and compare these results with finite-element simulations to demonstrate quantitative agreement with a model of interface dielectric loss. We then apply this analysis to determine the extent to which trenching can improve resonator performance.