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 LQ₁ cut and LQ₂ cut, and particularly, the resonator for LQ₁ cut has a comparatively large value of the second order temperature coefficient β, a Lame mode quartz crystal resonator can be obtained with the large first order temperature coefficient α when β=0. In this paper, when cut angles φ=45° and θ=45°, α has a value of 44.6×10^-6/°C in the calculation and 39.9×10^-6/°C in the experiments with β=0 approximately, while when φ=51.5° and θ=45°, α=68.1×10^-6/°C in the calculation and 62.0×10^-6/°C in the experiments with a value of β large than that of φ=45° and θ=45°. 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