  In this paper we revisit the theory of negative capacitance, in a (i)
standalone ferroelectric, (ii) ferroelectric-dielectric, and (iii)
ferroelectric-semiconductor series combination, and show that it is important
to minimize the total Gibbs free energy of the combined system (and not just
the free energy of the ferroelectric) to obtain the correct states. The theory
is explained both analytically and using numerical simulation, for
ferroelectric materials with first order and second order phase transitions.
The exact conditions for different regimes of operation in terms of hysteresis
and gain are derived for ferroelectric-dielectric combination. Finally the
ferroelectric-semiconductor series combination is analyzed to gain insights
into the possibility of realization of steep slope transistors in a hysteresis
free manner.
