Mathematical Models and Characterization of BioFETs

The purpose of this project is to model, simulate, and characterize BioFETs (biologically active field-effect transistors). BioFETs are biosensors whose transducers (signal converters) consist of semiconductors. As target biomolecules bind to a biofunctionalized oxide surface, the charge distribution at the surface is changed and hence the conductance of the semiconducting transducer is modulated as well. The small conductance changes are recorded and enable the detection of the biomolecules by a field effect. BioFETs have been demonstrated based on the conventional MOSFET device structure and more recently based on silicon nanowires. The advantages of BioFETs are direct, label-free, continuous, (near) real-time, highly selective, and highly sensitive sensing. As opposed to optical detection methods, they operate without markers and integrate the transducer into the read-out circuit. Since no labeling of the analyte is necessary, it is expected that faster and cheaper devices will be developed. The BioFET concept is also a very general one, since the sensor can be made selective for an arbitrary class of biomolecules by employing a suitable (monoclonal) antibody. Therefore there is a vast number of applications, e.g., in preemptive medicine. In this project, silicon oxide and germanium oxide surfaces will be biofunctionalized to act as biosensors and characterized by a spectroscopic method. Using FTIR (Fourier transform infrared) spectroscopy, data about the density and the orientation of biomolecules in a surface layer will be collected. The characterization of biofunctionalized surfaces is of great interest by itself and yields the data to check quantitative theories. A theory for the functioning of the devices will be developed based on new multi-scale models, and a quantitative understanding of the biosensors will be achieved by simulation. One challenge stems from the fact that in BioFETs the length scale differs from a few Ångström (the charge distribution in biomolecules at the surface) to several micrometers (the length of the sensor surface). Our models and simulation source code will allow us to gain insight into the physics of the sensors by providing a self-consistent description of all the charges in the system.

There are two important results from this project: First, we have developed mathematical models for the simulation and theoretical understanding of nanowire ?eld-effect biosensors; second, we have characterized and optimized the functionalization of silicon-oxide surfaces with biomolecules for use in such sensors.The devices we have investigated in this project are nanowire ?eld-effect biosensors.These devices had been realized experimentally a few years ago, but their theoretic understanding had been missing. Being based on silicon nanowires, the devices are highly miniaturized and they provide high sensitivity. After suitable functionalization, the sensors can detect DNA oligomers, RNA oligomers, and all kinds of proteins and antigens such as tumor markers. Therefore there is a multitude of applications in biotechnology and in clinical settings whenever biomolecules need to be detected in a liquid.The nanowire sensors are functional devices, and their physics based simulation requires the modeling of various aspects in a self-consistent manner. Another mathematical aspect inherent in these devices is the multiscale problem that stems from the different length scales of the biomolecules and the whole device.For the numerical simulation of nanowire ?eld-effect biosensors, we have developed a model that consists of a system of partial differential equations after homogenization of the fast oscillations at the sensor surface due to the biomolecules. We showed existence, local uniqueness, and smoothness of the solution. We have also developed a Monte-Carlo algorithm for the quanti?cation of the electrostatic screening effect around charged biomolecules, which is crucial for the detection mechanism. Furthermore, we developed and implemented a parallel algorithm for the system of equations. Based on these results, we have implemented a 3D, self-consistent, and parallel simulator for nanowire sensors. Our simulation results show excellent agreement with measurements from literature and those obtained from the leading experimenter in this ?eld. Our models and simulation tools make it possible to understand, to design, and to optimize this new sensor technology.An important experimental question is the functionalization of the sensor surfaces with antibodies for the selective capture of target molecules as close as possible to the transducer. Using Fourier transform infrared spectroscopy utilizing silicon elements, we could for the ?rst time monitor the attachment of linkers and probes to sensor surfaces. In-situ monitoring also enabled us to optimize functionalization protocols and to determine the density of probe molecules at the sensor surface, which is an important design parameter of the devices.