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

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 (DK), 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 (Ra/Rg), 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 Lk/DK. 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.