Multiscale Modeling of Planar and Nanowire Field-Effect Biosensors

Field-effect nano-biosensors (or Biofets, biologically sensitive field-effect transistors) have recently been demonstrated experimentally and have thus gained interest as a technology for direct, label-free, real-time, and highly sensitive detection of biomolecules. The experiments have not been accompanied by a quantitative understanding of the underlying detection mechanism. The modeling of field-effect biosensors poses a multi-scale problem due to the different length scales in the sensors: the charge distribution and the electric potential of the biofunctionalized surface layer changes on the Ångström length scale, whereas the exposed sensor area is measured in micrometers squared. Here a multi-scale model for the electrostatics of planar and nanowire field-effect sensors is developed by homogenization of the Poisson equation in the biofunctionalized boundary layer. The resulting interface conditions depend on the surface charge density and dipole moment density of the boundary layer. The multi-scale model can be coupled to any charge transport model and hence makes the self-consistent quantitative investigation of the physics of field-effect sensors possible. Numerical verifications of the multi-scale model are given. Furthermore a silicon nanowire biosensor is simulated to elucidate the influence of the surface charge density and the dipole moment density on the conductance of the semiconductor transducer. The numerical evidence shows the conductance varies exponentially as a function of both charge and dipole moment. Therefore the dipole moment of the surface layer must be included in biosensor models. The conductance variations observed in experiments can be explained by the field effect and they can be caused by a change in dipole moment alone.