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We describe a gas-density gauge based on the analysis of the thermally-driven fluctuations of an atomic force microscope (AFM) cantilever. The fluctuations are modeled as a ring-down of a simple harmonic oscillator, which allows fitting of the resonance frequency and damping of the cantilever, which in turn yields the gas density. The pressure is obtained from the density using the known equation of state. In the range 10-220 kPa, the pressure readings from the cantilever gauge deviate by an average of only about 5% from pressure readings on a commercial gauge. The theoretical description we use to determine the pressure from the cantilever motion is based upon the continuum hypothesis, which sets a minimum pressure for our analysis. It is anticipated that the cantilever gauge could be extended to measure lower pressures given a molecular theoretical description. Alternatively, the gauge could be calibrated for use in the non-continuum range. Our measurement technique is similar to previous AFM cantilever measurements, but the analysis produces improved accuracy.

A pressure gauge based on gas density measurement from analysis of the thermal noise of an atomic force microscope cantilever