Compact capacitance modeling of a 3-terminal FET at zero drain–source voltage

The accuracy and continuity of the C–V characteristics of a transistor at Vds = 0 is one of the main benchmark tests a good compact model must pass. Singularities (in the form of 0/0 divisions) at Vds = 0 in compact capacitance models developed for several types of undoped 3-terminal devices, such as Double-Gate and Surrounding-Gate MOSFETs, have been corrected by means of techniques based on dealing individually with each of the targeted devices. Due to the lengthy calculations required for each of those particular cases, it will be useful to develop relationships between capacitances, with expressions easy to calculate, that can be applied to any type of undoped 3-terminal FET. We present compact modeling schemes valid for long-channel 3-terminal devices at Vds = 0 and we demonstrate suitable relationships between the different capacitances, deriving general analytic expressions for them in terms of the derivative of the drain charge sheet density with respect to the drain voltage; we also show how they can be calculated using the device charge control model.