Fluctuations of the number of particles and mass adsorbed on the sensor surface surrounded by a mixture of an arbitrary number of gases

In this paper the theory of the adsorption and desorption process of an arbitrary number of gases on the sensor surface is presented. It is assumed that the sorption follows the Langmuir isotherm. The exact expressions are derived for the power spectral density of the fluctuations of the number of adsorbed particles for each gas from the mixture, as well as for the total adsorbed mass fluctuation, using the analytical Langevin approach. Since these fluctuations cause adsorption–desorption (AD) noise, the presented theory enables determination of the limiting performance of various micro/nanoelectromechanical devices (micro/nanocantilever sensors and oscillators), resistive gas sensors and chemical and biochemical sensors based on surface plasmon resonance effect, and optimization of their parameters. This model is also applicable for the theoretical study of adsorption–desorption processes in general. We used it for investigation of the possibility of identification of gases in the mixture, based on the power spectral density of the adsorbed mass fluctuations. We also considered the possibility of the lowering the adsorbed mass fluctuations (i.e. AD noise level) by adding a certain amount of a gas to the mixture. As an example of the application of the presented theory, we calculate the fluctuations of the mass adsorbed on the surface of the silicon micro/nanocantilever sensor surrounded by the atmosphere of two and three gases.