Development of a Fermi Energy Distribution Based Adsorption Isotherm for Response Simulation of Nanostructure Decorated Porous Silicon Substrates

Abstract

A simple MEMS/NEMS platform facilitates the modeling of the interaction of nanostructure directing metal oxide island sites with several gas phase analytes. A “response matrix” created for the nanostructured metal oxides facilitates the modeling process. Sensitive conductometric sensors operating at room temperature and atmospheric pressure, are forgiving, and do not require film based technology or lithography for their construction. Their responses are simulated using a combination diffusion/adsorption–based model where a new adsorption isotherm is derived on the basis of the Fermi distribution function. We show that diffusion dominates the conductometric response and model this process with the aid of the relative sensitivities determined previously for the metal oxides. Not only the direct response but also the derivatives of this response are used to evaluate the modeling of Fickian diffusion. The first derivative, as it is found to be linear in concentration, allows a quick evaluation of a rapid sensor response. The spectral simulations are refined to include the adsorption effects of the analyte gas and evaluate subsequent non-linear interface sensitivities. A new Fermi energy distribution –based response isotherm, based on first principles, is compared to a diversity of well-known empirical isotherms and found to be superior for the modeling of the sensor response. A comprehensive model including not only this response but also its derivative and its log-log plot are demonstrated. This modeling is exemplified for the analytes NH3 and NO.