Formulation of gas diffusion dynamics for thin film semiconductor gas sensor based on simple reaction-diffusion equation

摘要

In response and recovery steps of a thin film semiconductor gas sensor, target gas molecules diffuse in and out of the thin film. The gas diffusion dynamics taking place in these steps have been formulated based on a simple reaction-diffusion equation assuming a first-order reaction of target gas. In order to facilitate mathematical treatments, the actual thin film device was replaced by an equivalent model, for which boundary conditions could be set properly. With this model, the reaction-diffusion equation could be solved by using the methods of Fourier expansion and separation of variables. The solutions given as a function of diffusion coefficient D, rate constant k, film thickness L, depth x and time t, are shown to express well how target gas concentration profile in the thin film develops or vanishes in the response or recovery step, respectively.