Simulation of noise processes in thickness-shear resonators caused by multilayer adsorption and desorption of surface molecules

The effects of multilayer contamination of mean resonant frequency and frequency fluctuations in thickness-shear resonators are studied. A model based on mass-loading of contaminant molecules with adsorption and desorption rates is developed. Equations relating the change in mean frequency and frequency fluctuations to adsorption and desorption rates are derived. Since the adsorption and desorption rates are functions of pressure and temperature, the change in mean frequency and spectral density of frequency fluctuations is studied with respect to pressure and temperature. Calculations are performed for a 10 MHz thickness-shear resonator. Frequency-temperature and frequency-pressure curves are plotted for the 10 MHz resonator. The curves do not follow a cubic polynomial function and have a magnitude in the range of 10 p.p.m. The mean square of frequency fluctuations under multilayer contamination is significantly greater than that under monolayer contamination. The spectral density of frequency fluctuations at 1 Hz is quite constant in a wide range of temperatures (-50 to 100 °C) when the values of heat of absorption for the second and subsequent layers are close to that of the first layer. The magnitude of spectral density of frequency fluctuations is about -120 dBc (Hz²/Hz)