An Analysis of the Thermal Behavior and Effects of Circular Quartz Crystal Resonators for Microbalance Applications

Surface Roughness Effects on the Vibration Characteristics of AT-Cut Quartz Crystal Plate

With the miniaturization and high-frequency requirements of quartz crystal sensors, microscopic issues affecting operating performance, e.g., the surface roughness, are receiving more and more attention. In this study, the activity dip caused by surface roughness is revealed, with the physical mechanism clearly demonstrated. Firstly, the surface roughness is considered as a Gaussian distribution, and the mode coupling properties of an AT-cut quartz crystal plate are systematically investigated under different temperature environments with the aid of two-dimensional thermal field equations. The resonant frequency, frequency-temperature curves, and mode shapes of the quartz crystal plate are obtained through the partial differential equation (PDE) module of COMSOL Multiphysics software for free vibration analysis. For forced vibration analysis, the admittance response and phase response curves of quartz crystal plate are calculated via the piezoelectric module. The results from both free and forced vibration analyses demonstrate that surface roughness reduces the resonant frequency of quartz crystal plate. Additionally, mode coupling is more likely to occur in a crystal plate with a surface roughness, leading to activity dip when temperature varies, which decreases the stability of quartz crystal sensors and should be avoided in device fabrication.

Characterization of Thermal Gradient Effects on a Quartz Crystal Microbalance

Quartz crystal microbalances are widely used sensors with applications for the detection of very-low-mass deposition in many different fields, from contamination monitoring in the high vacuum of deep space missions to the monitoring of biological activity or pollution using specifically designed active substrates. These sensors are very stable over time; nevertheless, their sensitivity to the temperature is well known, and different implementations have been devised to correct it, e.g., through compensation with a dual crystal. This paper deals with the effects of temperature on QCM but separates the case of uniform crystal temperature from the case of in-plane temperature gradients considering a QCM based on quartz crystals with deposited film resistors used as both RTDs and heaters. This configuration allows both an accurate temperature measurement and efficient thermal control, allowing the achievement of crystals temperatures in the order of 400 °C higher than the environment with a low power dissipation of the order of 1 W. The film resistors deposited around the electrodes allow directly measuring the average crystal temperature and directly delivering power to the crystal for thermal control. The localized delivery of the heat nevertheless also determines uncommon temperature fields on the crystal, and thus, an analysis of both the effects of temperature on the new microbalance was performed. The temperature gradient has strong effects on the frequency; therefore, along with the temperature, the thermal gradients have tobe compensated. The calibration of the QCM thermometers and the assessment of the achievable measurement accuracy were performed, as well as the determination of the frequency-temperature relationship. The comparison between frequency changes in the case of uniform temperature and those observed while using crystal heaters proved that temperature gradients have a strong effect on the crystal frequency. To identify the temperature field on the crystal surface of a QCM crystal, the gold coating of the deposited films was removed to achieve an emissivity acceptable for thermal imaging with an IR camera. Moreover, image processing for emissivity correction was developed. In order to correlate the temperature gradient with the frequency variation, a test campaign was performed to measure the frequency changes derived from different power levels delivered to the crystal heaters. From this test campaign and thermal analysis, the effect of the thermal gradient was assessed.