Quartz microresonator temperature sensors using Lame-mode

Lame-mode is very suitable for realization of a miniaturized quartz crystal resonator because its resonant frequency is principally dependent upon the contour dimensions. Since heat capacity for the quartz crystal resonator is small, and frequency response versus temperature is very fast, it is useful for use in temperature sensors. In addition, because a Lame-mode quartz crystal resonator has zero temperature coefficients, designated LQ/sub 1/ cut and LQ/sub 2/ cut, and particularly, the resonator for LQ/sub 1/ cut has a comparatively large value of the second order temperature coefficient /spl beta/, a Lame mode quartz crystal resonator can be obtained with the large first order temperature coefficient /spl alpha/ when /spl beta/=0. In this paper, when cut angles /spl phi/=45/spl deg/ and /spl theta/=45/spl deg/, /spl alpha/ has a value of 44.6/spl times/10/sup -6///spl deg/C in the calculation and 39.9/spl times/10/sup -6///spl deg/C in the experiments with /spl beta/=0 approximately, while when /spl phi/=51.5/spl deg/ and /spl theta/=45/spl deg/, /spl alpha/=68.1/spl times/10/sup -6///spl deg/C in the calculation and 62.0/spl times/10/sup -6///spl deg/C in the experiments with a value of /spl beta/ large than that of /spl phi/=45/spl deg/ and /spl theta/=45/spl deg/. For both cut angles, frequency change versus temperature is found to be sufficiently large, and also the measured data is found to be slightly smaller than the calculated data.