  Ferroelectrics subject to suitable electric boundary conditions present a
steady negative capacitance response. When the ferroelectric is in a
heterostructure, this behavior yields a voltage amplification in the other
elements, which experience a potential difference larger than the one applied,
holding promise for low-power electronics. So far research has focused on
verifying this effect and little is known about how to optimize it. Here we
describe an electrostatic theory of ferroelectric/dielectric superlattices,
convenient model systems, and show the relationship between the negative
permittivity of the ferroelectric layers and the voltage amplification in the
dielectric ones. Then, we run simulations of PbTiO3/SrTiO3 superlattices to
reveal the factors most strongly affecting the amplification. In particular, we
find that giant effects (up to 10-fold increases) can be obtained when PbTiO3
is brought close to the so-called "incipient ferroelectric" state.
