Experimental Study of Mode-Coupling Strength of AT-Cut Quartz Resonators with High Mesa Step Height

Abstract

In this paper, the bi-mesa resonators, which can be fabricated with very high mesa steps, were fabricated, and their frequency-temperature (f-T) characteristics were measured as an index of the mode-coupling strength. Since the mode-coupling affects to the first-order temperature coefficient of the TS-1 mode, the f-T curve of the pure TS-1 mode rotates clockwise depending on the mode-coupling strength. The experimental results showed that the tendency of the first-order coefficients of the measured f-T data were in good agreement with the calculated mode-coupling strength in the mesa height range of 0 to 50%. These results indicate the validity of the calculated mode-coupling strength between TS-1 and TF modes. It is also showed that choosing lower mesa height is desirable because the face-shear modes caused by the X-Z' boundary tend to couple with the TS-1 mode when the mesa step is very high.