Are ferroelectric multilayers capacitors in series?

We show that ferroelectric multilayers are not simple capacitors in series (CIS) and treating these as CIS may lead to misinterpretation of experimental results and to erroneous conclusions. Here, we present a theoretical model of ferroelectric bilayers using basic thermodynamics taking into account the appropriate electrical boundary conditions and electrostatic fields. The spontaneous polarization mismatch in ferroelectric/ferroelectric (FE/FE), FE/paraelectric (FE/PE), and FE/dielectric (FE/DE) bilayers results in a non-linear electrostatic coupling which produces significant deviations in the overall dielectric response if it is computed using the simple capacitor-in-series (CIS) model. Our results show that the CIS approach is a good approximation only for DE/DE multilayers and for FE heterostructures if the individual layers are electrostatically screened from each other.