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A 3d simulator for nanowire field-effect sensors and transistors including fast varying charge concentrations at an interface is presented. This simulator is based on a system of partial differential equations calculating the electrostatic potential of the whole device and the charge concentrations in the semiconducting nanowire. Therefore, three domains need to be modeled. The nanowire is described by the drift-diffusion-Poisson system, the Poisson-Boltzmann equation is used for the simulation of an aqueous solution, and the Poisson equation holds in the remaining oxide. Such devices can be used as gas sensors, and by functionalization of the nanowire surface, i.e., by attaching probe molecules, they can also be used for the detection of biomolecules in aqueous solutions. Binding of target molecules to the surface induces a field effect due to changes of charges in a small layer around the surface. This effect is responsible for the sensor response and hence is of paramount importance. A homogenization method resulting in two jump conditions is implemented which splits the computation into the charge of the boundary layer and into the remaining device. In order to take into account the geometry of the devices, 3d simulations are necessary and hence a parallelization technique has been developed. To include the jump conditions of the homogenization method, a novel finite-element tearing and interconnecting (feti) method has been developed. With this simulator it is possible to solve the three dimensional and heterogeneous system of partial differential equations with discontinuities in feasible time using realizable computer power. As a result, sensitivity in terms of geometrical and physical properties can be predicted and sensors can be improved. |
