Sensors and Actuators A, 2527 (1991) 385-393 385 A Differential Resonator Design using a Bossed Structure for Applications in Mechanical Sensors HARRIE A. C. TILMANS, SIEBE BOUWSTRA, DOMINICUS J. IJNTEMA and MIKO ELWENSPOEK MESA, Insfitute for Mirroelectronics, Marerials Engineering, Sensors and Actuators, University zyxwvutsrqponmlkjihgfedcbaZY of Twente, P.O. 7500 AE Enschede (The NetherlandsJ CARL F. KLEIN Johnson Controls Inc., Milwaukee, WI (U.S.A.) Box 217, Abstract Theory and experimental results are pre- sented of a differential resonator design em- ploying a bossed structure for applications in mechanical sensors. The effects of residual strain, temperature and mechanical load on the resonance frequency are investigated. Mis- matches in the resonators are accounted for in the analysis, resulting in a predicted tempera- ture dependence of the offset and of the sensitivity. Experimental data obtained from a macroscopic brass model, mounted on a steel bar and applied as a force sensor, are given. Compared to a design employing a single resonator, the measurements indicate a dou- bling in force sensitivity and a reduction of both the intrinsic temperature dependence and of the differential thermal expansion effects. The results of this research are directly appli- cable to micromachined structures in silicon. Introduction Resonant sensors provide a frequency-shift output and are very attractive in the precision measurement field because of their high sensi- tivity, high accuracy and high stability [ 11. This paper deals with mechanical sensors uti- lizing resonant strain gauges for measuring a variety of loads such as pressure, force or acceleration. In a practical sensor design, the output signal responds to changes of the phys- ical quantity to be measured but at the same time to changes of a number of unwanted 0924-4247/91/$3.50 quantities. The challenge of good sensor design is to maximize the sensitivity to the desired load and to minimize the sensitivity to others. To minimize the effects of environmental pertur- bations such as mass loading, humidity and corrosion, on the resonance frequency, the resonator should be housed in a stable (inert) environment, preferably a vacuum [ 2-41. The use of high-quality construction materials will result in a good long-term stability by reducing effects such as creep and stress relaxation, fatigue and aging of material properties. Tem- perature often remains as the major cause for error readings in the output signal. Tempera- ture can alter the resonance frequency via two major effects. First, the material properties and dimensions, which determine the resonance frequency, are all temperature dependent, causing an intrinsic temperature dependence. Secondly, differential thermal expansion be- tween the different construction materials causes stresses to be established, which inter- fere with the measurement stresses. These include the stresses caused by a thermal mis- match of the different materials used for the sensor itself, but also mounting- or package- induced stresses caused by the differential thermal expansion between the sensor chip and the mount. Various techniques have been applied to minimize the influence of unwanted parame- ters. In piezoresistive devices, where tempera- ture sensitivity is a severe problem, a Wheatstone bridge configuration and a signal- conditioning IC, often including a tempera- ture-sensitive device attached to the sensor, 0 Elsevier Sequoia/Printed in The Netherlands