Calculation of the Response of Field-Effect Transistors to Charged Biological Molecules

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Robust approximations are presented that allow for the simple calculation of the total charge and potential drop <formula formulatype="inline"><tex>$\psi_{0}$</tex> </formula> across the region of electrolyte containing charged biological macromolecules that are attached to the gate area of a field-effect transistor (FET). The attached macromolecules are modeled as an ion-permeable membrane in contact with the insulator surface, exchanging protons with the electrolyte as described by the site-binding model. The approximations are based on a new screening length involving the Donnan potential in the membrane and are validated by comparison to the results obtained by numerical solution of the one-dimensional Poisson–Boltzmann equation in the electrolyte and membrane. For gates covered with amphoteric materials such as SiO<formula formulatype="inline"> <tex>$_{2}$</tex></formula>, the high surface charge density <formula formulatype="inline"> <tex>$\sigma_{0}$</tex></formula> due to proton exchange at values of <emphasis emphasistype="boldital">p</emphasis>H far from the point-of-zero charge is a nonlinear function of <formula formulatype="inline"><tex>$\psi_{0}$</tex> </formula>, but <formula formulatype="inline"><tex>$\psi_{0}$</tex></formula> and <formula formulatype="inline"><tex>$\sigma_{0}$</tex></formula> are still linear functions of the semiconductor surface potential between the source and drain. Nonlinear expressions for the amphoteric site charge at the contacts can thus be applied effectively with the new approximations to calculate the current-voltage characteristics of the FETs using the strong inversion and charge-sheet models. </para>