Compensation of Thermal Gradients Effects on a Quartz Crystal Microbalance

Quartz Crystal Microbalances (QCM) are widely used instruments thanks to their stability, low mass, and low cost. Nevertheless, the sensitivity to temperature is their main drawback and is often a driver for their design. Though the crystal average temperature is mostly considered as the only disturbance, temperature affects the QCM measurements also through the in-plane temperature gradients, an effect identified in the past but mostly neglected. Recently, it has been shown that this effect can prevail over that of the average temperature in implementations where the heat for thermal control is released directly on the crystal through deposited film heaters. In this study, the effect of temperature gradients for this kind of crystal is analyzed, the sensitivity of frequency to the average temperature gradient on the electrode border is determined, and a correction is proposed and verified. A numerical thermal model of the QCM has been created to determine the temperature gradients on the electrode borders. The frequency versus temperature-gradient function has been experimentally determined in different thermal conditions. The correction function has been eventually applied to a QCM implementing a crystal of the same manufacturing lot as the one used for the characterization. The residual errors after the implementation of the correction of both average temperature and temperature gradients were always lower than 5% of the initial temperature disturbance. Moreover, using the correlation between the heater power dissipation and the generated temperature gradients, it has been shown that an effective correction strategy can be based on the measurement of the power delivered to the crystal without the determination of the temperature gradient.