Low-Temperature Properties of Whispering-Gallery Modes in Isotopically Pure Silicon-28

Abstract

Whispering Gallery (WG) mode resonators have been machined from a boule of single-crystal isotopically pure silicon-28. Before machining, the as-grown rod was measured in a cavity, with the best Bragg confined modes exhibiting microwave Q-factors on the order of a million for frequencies between 10 and 15 GHz. After machining the rod into smaller cylindrical WG mode resonators, the frequencies of the fundamental mode families were used to determine the relative permittivity of the material to be 11.488 ± 0.024 near 4 K, with the precision limited only by the dimensional accuracy of the resonator. However, the machining degraded the Q-factors to below 4 × 10 4 . Raman spectroscopy was used to optimize post-machining surface treatments to restore high Q-factors. This is an enabling step for the use of such resonators for hybrid quantum systems and frequency conversion applications, as silicon-28 also has very low phonon losses, can host very narrow linewidth spin ensembles and is a material commonly used in optical applications.

Measurement of the Low-temperature Loss Tangent of High-resistivity Silicon with a High Q-factor Superconducting Resonator

“…At the lowest temperature, 73 mK, the loss tangent is equal to 2.7 • 10 −6 , in agreement with measurements performed on silicon billets in whispering gallery mode configuration [6]. In contrast, our experiment returns higher values compared to indirect estimations based on measurements and simulations of planar devices [5,8,9], that are typically of the order of 10 −7 -one order of magnitude lower than our experimental finding.…”

“…In summary, we described a novel accurate method to directly measure the loss tangent of insulating materials in wafer form by means of high Q-factor superconducting resonators. We reported the first direct measurement of the loss tangent of a high-resistivity silicon wafer in the temperature range ∼ 70 mK -1 K. Furthermore, we showed that loss tangent of high-resistivity Si in the milli-Kelvin range is one order of magnitude higher than what previously indirectly estimated from measurements and simulations of planar devices [5,8,9], although in agreement with values obtained from whispering gallery measurements of Si billets [6]. In addition, we observed an unexpected non-monotonic behavior of the loss tangent dependence on temperature with a minimum around 100 mK, that is currently under investigation.…”

“…However, no direct measurements of Si wafer loss tangent at milli-Kelvin temperature have been presented so far, so a reasonable large degree of uncertainty on the actual Si loss tangent value in the milli-Kelvin range still exists. Loss tangent data of Si at milli-Kelvin temperature exist for silicon billets-not wafers [6], and for high resistivity silicon at higher temperatures [7].…”

Ultrashallow Junction Electrodes in Low-Loss Silicon Microring Resonators

“…This leads to stronger free carrier absorption effects. Concurrently, the anneal may also improve the surface roughness thereby enhancing the Q factors [19,20]. These two values are included in Fig.…”