Predictive Model for Label-free Electrical Detection of Bio-molecules

Biosensors based on MOSFETs, silicon nanowires, and carbon nanotube nanocomposites \textit{promise }highly sensitive, dynamic, label-free, electrical detection of bio-molecules with potential applications in genomics and proteomics. Although tremendous improvements in sensitivity have been reported in electrical detection of bio-molecules, many aspects of experimentally observed sensor response (S) are unexplained within the theoretical frameworks of kinetic response or electrolyte screening. In this paper, we combine analytic solutions of Poisson-Boltzmann and reaction-diffusion equations to show that the electrostatic screening within an ionic environment limits the response of nanobiosensor such that $S\left( t \right)\sim c_1 \left( {\ln \left( {\rho _0 } \right)-\frac{\ln \left( {I_0 } \right)}{2}+\frac{\ln \left( t \right)}{D_F }+\left[ {pH} \right]} \right)+c_2 $ where $c_i $ are geometry-dependent constants, $\rho _0 $ is the concentration of target molecules, $I_0 $ the salt concentration, and $D_F $ the fractal dimension of sensor surface. Our analysis provides a coherent theoretical interpretation of wide variety of puzzling experimental data that have so far defied intuitive explanation and have important implications for the design and optimization of nanoscale biosensors.