Resonator surface contamination-a cause of frequency fluctuations?

The mass loading effects of adsorbing and desorbing contaminant molecules on the magnitude and characteristics of frequency fluctuations are studied in a thickness shear resonator. An equation was derived relating the spectral density of frequency fluctuations to: rates of adsorption and desorption of one species of contaminant molecules; mass per unit area of a monolayer of molecules; frequency constant; thickness of resonator; and number of molecular sites on one resonator surface. The induced phase noises were found to be significant in very high frequency resonators and are not simple functions of the percent area contaminated. The spectral density of frequency fluctuations was inversely proportional to the fourth power of the thickness if other parameters were held constant. Since the resonator frequency is inversely proportional to the thickness, the spectral density is, in effect, proportional to the fourth power of resonator frequency