Model for the field effect from layers of biological macromolecules on the gates of metal-oxide-semiconductor transistors

The potential diagram for field-effect transistors used to detect charged biological macromolecules in an electrolyte is presented for the case where an insulating cover layer is used over a conventional eletrolyte-insulator metal-oxide-semiconductor (EIMOS) structure to tether or bind the biological molecules to a floating gate. The layer of macromolecules is modeled using the Poisson-Boltzmann equation for an ion-permeable membrane. Expressions are derived for the charges and potentials in the EIMOS and electrolyte-insulator-semiconductor structures, including the membrane and electrolyte. Exact solutions for the potentials and charges are calculated using numerical algorithms. Simple expressions for the response are presented for low solution potentials when the Donnan potential is approached in the bulk of the membrane. The implications of the model for the small-signal equivalent circuit and the noise analysis of these structures are discussed.