A  methodology to build multi-compartment lumped elements equivalent circuits for the neuron/electrode systems is proposed. The equivalent circuit topology is derived by careful scrutiny of accurate multiphysics finite-elements method (FEM) simulations that couple ion transport in the intra- and extracellular fluids, activation of ion channels in the cellular membrane, and signal collection by the electronic readout, thus improving upon most common area contact models. We show that the equivalent circuits derived with our method match with good accuracy the reference FEM simulations over a wide range of geometrical/physical parameters such as the neuron and electrode size, the thickness of the electrolytic cleft, the input impedance of the readout amplifier, even in presence of nonuniform ion channel distributions. The impact of the number of compartments on the model accuracy is also analyzed in detail. We finally illustrate by FEM simulations the effect of extracellular ion transport on the reversal potentials of the Hodgkin-Huxley neuron model and how it can affect the recorded signal for very thin electrolyte clefts between the neuron and the electrode, in a way not yet captured by equivalent circuits of the neuron/electrode system.

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.

We derive an analytical model for 1/f noise in MOSFETs, highlighting a term that is often neglected in literature but becomes important for ultra-thin oxides. Furthermore, we identify an interesting relationship between the thermal noise of the gate impedance and the gate noise due to trapping/detrapping between the free carriers in the channel and the oxide traps, as well as the 1/f noise cross-correlation between drain and gate, showing that a single voltage noise generator is not enough to describe completely the 1/f noise. TCAD simulations are used to verify the model predictive capabilities.