An analytic model of the dynamic response of mass-sensitive chemical sensors

Mass-sensitive chemical sensors such as quartz crystal microbalances (QMB) or surface acoustic wave (SAW) devices tend to have a slow dynamic response. This is due to the fact that the chemical species to be bound in the selective sensor film diffuses into the film with characteristic diffusion coefficients on the order of only 10−17 m2/s. We derive a closed-form analytic solution to the problem, which involves Jacobian theta functions and is valid for all mass-sensitive sensors the dynamic response of which is dominated by diffusion effects. The model is validated by comparing its predictions to experimental data and to numerical computations. In the end, we deduce a model-based strategy capable of predicting the steady-state response and, thus, of reducing the effective response time of the sensor.