Diffusion equation-based study of thin film semiconductor gas sensor-response transient

A diffusion-reaction equation has been formulated and solved under non-steady condition in order to simulate how the gas concentration profile develops inside a thin film of semiconducting oxide after its exposure to a target gas. The gas concentration can be expressed by a polynomial function involving diffusion coefficient (D), rate constant (k), film thickness (L), depth from the film surface (x), time (t) and target gas concentration outside (C_s). Remarkably, the gas concentration at a given x exhibits overshooting behavior before reaching a steady value, the magnitude and appearance time of the overshooting being very dependent on x, k and L/D^1/2. The overshooting appears as a result of the competition between diffusion and reaction. Two types of overshooting are recognized, which are ascribable to the gas molecules having entered from the surface and to those having reflected by the wall of substrate, respectively. Reflecting such an overshooting in gas concentration, the response transient also exhibits an overshooting phenomenon.