Magnetic field robust high quality factor NbTiN superconducting microwave resonators

We systematically study the performance of compact lumped element planar microwave $\mathrm{N}{\mathrm{b}}_{70}\mathrm{T}{\mathrm{i}}_{30}\mathrm{N}$ (NbTiN) resonators operating at 5 GHz in external in-plane magnetic fields up to 440 mT, a broad temperature regime from 2.2 K up to 13 K, as well as mK temperatures. For comparison, the resonators have been fabricated on thermally oxidized and pristine, (001) oriented silicon substrates. When operating the resonators in the multi-photon regime at $T=2.2$ K, we find internal quality factors $Q_{\mathrm{i}\mathrm{n}\mathrm{t}}\simeq$ $2\cdot {10}^5$ for NbTiN resonators grown on pristine Si substrates, while resonators grown on thermally oxidized substrates show a reduced value of $Q_{\mathrm{i}\mathrm{n}\mathrm{t}}\simeq$ $1\cdot {10}^4$, providing evidence for additional loss channels for the latter substrate. In addition, we investigate the $Q$-factors of the resonators on pristine Si substrates at millikelvin temperatures to asses their applicability for quantum applications. We find $Q_{\mathrm{i}\mathrm{n}\mathrm{t}}\simeq$ $2\cdot {10}^5$ in the single photon regime and $Q_{\mathrm{i}\mathrm{n}\mathrm{t}}\simeq$ $5\cdot {10}^5$ in the high power regime at $T=7$ mK.