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Accurate electrical models are needed to support the design of modern microelectrode arrays. The point-contact model is presented thoroughly, and an area-contact model is analytically derived in order to model the electrical characteristics of the cell-electrode interface at subcellular resolution. An optimum electrode diameter for recording the electrical activity of neurons is analytically determined at 8 um, with a cell diameter of 10 um and a typical load capacitance of 10 pF. Finally, three- dimensional tip electrodes are characterized using the area- contact model. An improvement of the electrical coupling up to 20 dB is observed for small electrodes, in simulation.