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.

(Invited) Metal Oxide Decorated Porous Silicon Interfaces for Sensor Applications: The Question of Water Interaction, Stability, Platform Diversity, Sensitivity, and Selectivity

“…An inspection of the log-log and derivative of the response demonstrates that the Langmuir adsorption isotherm struggles to fit the experimentally collected data. However, a developed Fermi distribution function (FDF) 7,9 provides a considerably improved fit. This diffusion-FDF interaction model suggests that electrical effects dominate adsorption effects 7,9 over the concentration ranges that have been considered.…”

“…However, a developed Fermi distribution function (FDF) 7,9 provides a considerably improved fit. This diffusion-FDF interaction model suggests that electrical effects dominate adsorption effects 7,9 over the concentration ranges that have been considered. In a more extended approach, the Inverse Hard/Soft acid /base (IHSAB) concept was used to assess a diversity of conductometric responses for mixed gas interactions, and this framework has been used, in part, to evaluate nonlinear interactions of the analyte gases.…”

“…Linearity 5 , a problem with many semiconductor-based devices, is compensated by evaluating the first and second derivative of the sensor response. At this time it is possible to monitor two and sometimes three gases simultaneously with potential extension to additional gases with an array-based format relying on the combination of p and n-type silicon doping in concert with metal oxide nanostructure modified sensor interfaces [6][7][8][9] .…”

How to Improve the Performance of Porous Silicon‐Based Gas and Vapor Sensors? Approaches and Achievements

“…Another approach was proposed by Laminack and Gole . They have shown that for conductometric gas sensors tested in the pulse mode the derivative of the sensor signal is linear despite direct signal quenching at higher analyte concentrations.…”

“…They have shown that for conductometric gas sensors tested in the pulse mode the derivative of the sensor signal is linear despite direct signal quenching at higher analyte concentrations. Laminack and Gole believe that this mode of measurement which focuses on the onset of sensor response can at least enhance the range of linearity.…”