Characterization of Thermal Gradient Effects on a Quartz Crystal Microbalance

Abstract

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.

Compensation of Thermal Gradients Effects on a Quartz Crystal Microbalance

“…The thermal model of the QCM was developed to compute the temperature field on the crystal with the required accuracy and spatial resolution. The direct measurement of temperature through thermal mapping, in fact, was not accurate enough to derive the temperature gradient [ 17 ] because of the background disturbance, the low emissivity of the deposited electrodes, and the coarse spatial resolution of the infrared camera. As a consequence, the thermal model was implemented and preliminarily validated by correlation with the experimental tests described in [ 17 ].…”

“…The direct measurement of temperature through thermal mapping, in fact, was not accurate enough to derive the temperature gradient [ 17 ] because of the background disturbance, the low emissivity of the deposited electrodes, and the coarse spatial resolution of the infrared camera. As a consequence, the thermal model was implemented and preliminarily validated by correlation with the experimental tests described in [ 17 ]. The validated model has afterward been used to analyze crystals under different thermal conditions.…”

“…The temperatures measured during the test and those predicted by the thermal model are quite close: the maximum error on the electrode temperature is 1 °C, while the one on the heater is 0.34 °C. Considering that the uncertainty in the electrode temperature measurement was 0.85 °C and on the heater 0.42 °C [ 17 ], the contribution of the model uncertainty is of the order of 0.5 °C, a value considered acceptable for this study. The above comparison, therefore, validated the numerical model.…”

“…The system is conceived to remove the effect of the average crystal temperature, assuming that both crystals have the same temperature [ 11 , 12 ], but the effect of temperature gradients is neglected. The uniform temperature condition is hardly achieved when the crystal is actively thermally controlled [ 16 ], and the gradient effect may become dominant when the heat is delivered directly on the crystal through film heaters deposited on it [ 17 ]. This work, starting from the findings reported in [ 17 ], derives the correlation between temperature gradient and frequency change, providing a relationship that can be used to compensate for the effect.…”

“…The uniform temperature condition is hardly achieved when the crystal is actively thermally controlled [ 16 ], and the gradient effect may become dominant when the heat is delivered directly on the crystal through film heaters deposited on it [ 17 ]. This work, starting from the findings reported in [ 17 ], derives the correlation between temperature gradient and frequency change, providing a relationship that can be used to compensate for the effect. An experimental campaign was performed on a QCM, measuring the resonance frequency in different thermal conditions.…”