Application of electrode stress for improving frequency-temperature behavior of UHF quartz resonators

We present a new method in which the electrode stress can be used to improve the frequency-temperature (f-T) behavior of ultra-high frequency (UHF) quartz resonators. The electrode films are treated as composite layers of different metals in a plate resonator. A FEM model for the effects of non-homogeneous thermal stress on the f-T behavior of quartz resonators was developed. For our 1 GHz AT-cut resonator, the use of chromium-aluminum electrodes yields improved frequency-temperature behavior compared to the case where aluminum electrodes are used alone. The UHF quartz resonators must be treated as composite plates of quartz and electrode film since the ratio of electrode thickness to quartz plate thickness is significant. The quartz-aluminum composite plate rotates the f-T curve clockwise while the quartz-chromium composite plate rotates the f-T curve counter-clockwise. The titanium was found to be a good electrode metal due to its small effect on the f-T curve.