Sensitivity of SAW devices to Temperature and Mechanical Stresses , application to Physical Sensors

Applications of SAW devices to physical sensors have already reached industrial maturity in the field of passive physical sensors (e.g. wireless torque sensors) the last development being related to the capability of SAW devices to offer remote readout by a radio-frequency link. A review of existing simulation methods is used to derive the sensitivity of SAW devices to temperature or mechanical stress is presented. The emphasis is put on perturbation methods based on Tiersten and Sinha theory. Applications including current commercially available SAW physical sensors will be discussed. Introduction Starting from the very high performance of oscillators based on Bulk Acoustic Wave (BAW) and Surface Acoustic Wave devices (SAW), the idea to apply an external physical parameter to the piezoelectric resonator was investigated first in order to minimise environment effects on high stability clocks ; quartz and now some new piezoelectric materials offer naturally compensated crystalline orientations for which the sensitivity of the device to temperature effects is minimised. Stress sensitivity was also addressed to minimise the sensitivity of high performance quartz oscillators to accelerations in airborne applications. Table 1 shows the present performance of BAW and SAW oscillators as a results of minimising the effects of temperature and mechanical stresses. short term day gstability drift sensitivity BAW 5-10 MHz /d /g SAW 500 MHz /d /g Table 1: State of the art BAW and SAW oscillators It should be noted that such a high level of performance is achieved only when the crystal is perfectly mounted and isolated from the environment and not as a sensing element. However the very high resolution potentially achievable with BAW or SAW-based sensors for which the output parameter is a change in resonant frequency are easily understood. Modeling temperature effects for bulk and surface wave devices The intuitive approach for modeling temperature sensitivity in BAW and SAW devices is explained on fig.1 input output (T0) output (T) L(T) wave velocity V(T0) wave velocity V(T) L(T0) transit time = L(T)/V(T) biased crystal state natural crystal state Figure 1: An intuitive approach for temperature effects If ! "# $ denotes the transit time between input and output for wave propagation, velocity " , propagation length , the Temperature Coefficient of transit Time (TCT) is defined as: $%! $ '& ( $ . If the device is resonant and included in the electronic closed loop of an oscillator, it can be shown that the contribution of environmental effects on the resonator to the oscillator frequency, the Temperature Coefficient of Frequency, TCF, is given by : $%*) &+ ! %! The usual approach to predict these effects and derive temperature-compensated orientations of the crystal is based on the variation of effective elastic constants vs. temperature (hence : V(T)) combined with thermal expansion effects (L(T). This classical approach [1] was very successful to find the so-called AT-cuts for BAWs in quartz and the STcut for SAWs. A polynomial expansion for temperature effects Usually the temperature dependence of frequency in a BAW or SAW device is expressed under a polynomial expansion to the 3-rd order vs. temperature shifts, denoted now as , to avoid possible confusion with stress effects: /. 0 , & , 1 . 0 243 5 , & , 3 1 . 0 2 5 , & , (1) For AT cuts of BAWs in quartz, both coefficients . 0 and .