Evaluation of the differential capacitance for ferroelectric materials using either charge-based or energy-based expressions

Differential capacitance is derived based upon energy, charge or current considerations, and determined when it may go negative or positive. These alternative views of differential capacitances are analyzed, and the relationships between them are shown. Because of recent interest in obtaining negative capacitance for reducing the subthreshold voltage swing in field effect type of devices, using ferroelectric materials characterized by permittivity, these concepts are now of paramount interest to the research community. For completeness, differential capacitance is related to the static capacitance, and conditions when the differential capacitance may go negative in relation to the static capacitance are shown.