Improved sapphire dielectric resonators for ultrastable oscillators

It is shown that, in 5 cm Crystal Systems "HEMEX" resonators, unloaded Q values, not limited by wall losses, of 5-8 /spl times/ 10/sup 9/ at 2 K and 3 /spl times/ 10/sup 9/ at 6 K are possible. Frequency-temperature self-compensation, in which the temperature dependence of the real part of the AC susceptibility of paramagnetic impurities balances that due to the dielectric constant of the sapphire, can be achieved in H modes at convenient operating temperatures. Because chromium and iron concentrations are very small, ions with very high frequency ESRs provide essentially frequency-independent self-compensation, allowing freedom of choice of operating frequency. The dominant paramagnetic ion has been identified as Mo/sup 3+/. Since the Mo/sup 3+/ concentration is essentially fixed by the crystal growth process, and one desires the lowest possible frequency-temperature coefficient and dielectric loss, the H/sub m11/ modes are the best candidates for high-stability HEMEX resonators. The observed power dependence of mode frequency, /spl sim/10/sup -8/ W/sup -1/, will require that resonator power fluctuations be maintained at less than 100 nW if a frequency stability of 1 /spl times/ 10/sup -15/ is to be achieved.<
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