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In principle, it is possible that the enhanced Q for TiN arises due to the larger kinetic inductance of TiN as compared with Al and Re due to an increased electric field for a given power. However, from our measurements of the frequency shift of our TiN resonator with respect to that of our Al resonator of identical geometry and substrate (which we conservatively assume has a much lower kinetic inductance fraction), we extract the TiN kinetic inductance fraction of ∼50 and find that the corresponding electric field intensity increases by 3 dB. Because the TiN and Al curves in Fig. are flat over more than 10 dB at lowest power, the difference in Q value between the TiN and Al resonators arising from this effect would be negligible.
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In principle, it is possible that the enhanced Q for TiN arises due to the larger kinetic inductance of TiN as compared with Al and Re due to an increased electric field for a given power. However, from our measurements of the frequency shift of our TiN resonator with respect to that of our Al resonator of identical geometry and substrate (which we conservatively assume has a much lower kinetic inductance fraction), we extract the TiN kinetic inductance fraction of ∼50 and find that the corresponding electric field intensity increases by 3 dB. Because the TiN and Al curves in Fig. are flat over more than 10 dB at lowest power, the difference in Q value between the TiN and Al resonators arising from this effect would be negligible.
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We note that the high-power Q saturates at a higher power for the Al on sapphire device as compared with the Al on silicon device. This could be due to a differing thermal link between each device and its package through its substrate. This difference could cause the number of quasiparticles generated by heat arising from the high power in the resonator to vary between the two devices and thus could lead to a different saturation value. However, we do not have a definitive explanation and further investigation would be required to understand this effect.
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We note that the high-power Q saturates at a higher power for the Al on sapphire device as compared with the Al on silicon device. This could be due to a differing thermal link between each device and its package through its substrate. This difference could cause the number of quasiparticles generated by heat arising from the high power in the resonator to vary between the two devices and thus could lead to a different saturation value. However, we do not have a definitive explanation and further investigation would be required to understand this effect.
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