Biologically sensitive FETS (BioFETs) are a promising technology for replacing today's analyzing and sensing facilities in bio-chemistry. These devices consist of a semiconductor transducer, a dielectric layer, a functionalized surface with immobilized biomolecule receptors where the analyte binds, and an electrolyte with an electrode instead of the common gate contact (see figure 1). When analyte molecules bind to the receptors, their charges change the potential near the transducer-surface and thus the conductance in the field-effect transistor channel. The change of the potential happens at the Angstrom length-scale while the device dimensions are on the micrometer length-scale. Therefore it is very important to have an appropriate model to describe the transducer solution interface.
There are two established descriptions for the analyte. Firstly, the Poisson-Boltzmann model, which treats the salt concentration as continuous quantity and assumes the salt ions in thermal equilibrium with their environment and secondly the Debye-Hückel model, which can be derived by linearizing the Poisson-Boltzmann model. However, the often used Poisson-Boltzmann model breaks down at high potential values, especially for low salt concentrations. Due to the low number of counter ions at small buffer concentrations, the screening of the proteins/DNA is overestimated by the Poisson-Boltzmann model. Within the analyte, the salt ions are covered in a shell of water molecules. Due to this increased ion radius, there is a region close to the surface where no screening takes place, which is also known as the Stern layer.
We introduced an extended Poisson-Boltzmann model which takes the average closest possible approach of two ions within the liquid into account. This model is able to reproduce the Stern layer and its screening behavior can be adjusted in accordance to the salt concentration (see figure 2). However, the physical behavior is far more complex and requires further investigation.