Analytical expression for concentration and sensitivity of a thin film semiconductor gas sensor

In this paper, a mathematical model for gas sensing thin film semiconductor at an internal diffusion limitation for non-steady-state conditions is discussed. The model is based on diffusion equations containing a linear term related to the reaction processes. Analytical expressions for concentrations are derived using Laplace transformation. The gas sensitivity for both actual and equivalent models has been reported for all the values of reaction parameters such as rate constant and film thickness. Furthermore, in this work a complex inversion formula is employed to solve the boundary value problem. An excellent agreement with simulation data is observed. The dependence of sensitivity on temperature, film thickness and time are discussed for both actual and equivalent models.