Theory of gas-diffusion controlled sensitivity for thin film semiconductor gas sensor

Abstract

Influences of gas transport phenomena on the sensitivity of a thin film semiconductor gas sensor were investigated theoretically. A diffusion equation was formulated by assuming that an inflammable gas (target gas) moves inside the film by Knudsen diffusion, while it reacts with the adsorbed oxygen following a first-order reaction kinetic. By solving this equation under steady-state conditions, the target gas concentration inside the film was derived as a function of depth ( x) from the film surface, Knudsen diffusion coefficient ( D K), rate constant ( k) and film thickness ( L). The gas concentration profile thus obtained allowed to estimate the gas sensitivity ( S) defined as the resistance ratio ( R a/ R g), under the assumption that the sheet conductance of the film at depth x is linear to the gas concentration there with a proportionality constant (sensitivity coefficient), a. The derived equation shows that S decreases sigmoidally down to unity with an increase in L k/D K . Further by assuming that the temperature dependence of rate constant ( k) and sensitivity coefficient ( a) follows Arrenius type ones with respective activation energies, it was possible to derive a general expression of S involving temperature ( T). The expression shows that, when the activation energies are selected properly, the S versus T correlation results in a volcano-shaped one, its height increasing with decreasing L. The dependence of S on L at constant T as well as on T at constant L can thus be simulated fairly well based on the equation.