Modeling Resonator Frequency Fluctuations Induced by Adsorbing and Desorbing Surface Molecules

Yook Kong Yong, John R. Vig

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

Resonator frequency fluctuations due to adsorption and desorption of molecules on plate electrodes are studied using the principle of mass-loading effects of adsorbed molecules. The study is based on a 525 MHz, AT-cut quartz resonator enclosed in a small crystal holder. The maximum root mean square of pressure fluctuations at 300 K in a crystal holder with a height and diameter of respectively 1 mm and 2 mm is estimated to be in the order 10−6 torr, and hence would be a factor in frequency fluctuations if the crystal holder pressure is of the same order of magnitude. Equations relating the surface adsorption rates of crystal holder to pressure are derived, and found to be quadratic polynomial functions of the adsorption rates. Calculations based on these equations show that a contaminant gas with a higher desorption energy creates larger changes in pressure when the temperature is varied. The function describing the frequency fluctuations due to any one contaminant site is a continuous-time Markoff chain. Kolmogoroff equations and an autocorrelation function for the Markoff chain are derived. The autocorrelation, and spectral density function of resonator frequency fluctuations are derived. The spectral density of frequency fluctuations at 1 Hz is studied as a function of pressure, temperature, and desorption energy of molecules. The noise levels for a contaminant gas with one type of molecules are found to be lower for lower desorption energies, and higher at lower pressures. Graphs of the power spectral density functions yield power-law noise processes that range from l/f0to l/f2 The noise magnitude is sensitive to the composition of the contaminant gas.

Original languageEnglish (US)
Pages (from-to)543-550
Number of pages8
JournalIEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Volume37
Issue number6
DOIs
StatePublished - Nov 1990

All Science Journal Classification (ASJC) codes

  • Instrumentation
  • Acoustics and Ultrasonics
  • Electrical and Electronic Engineering

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