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A design-oriented numerical study of vertical Si-nanowires to be used as sensing elements for the detection of the intracellular electrical activity of neurons. An equivalent lumped-element circuit model is derived and validated by comparison with physics-based numerical simulations. Most of the component values can be identified individually by geometrical and physical considerations. The transfer function and the SNR of the sensor in presence of thermal noise are derived, and the impact of the device geometry is shown.