Interfacial effects and negative capacitance state in P (VDF-TrFE) films with BaTiO ₃ nanoparticles

We analyze the temperature dependences of the effective dielectric permittivity of P (VDF-TrFE) films with BaTiO₃ nanoparticles (with the average size 24 nm and dispersion 10 nm). We reveal significant deviations from the temperature dependences expected either for P (VDF-TrFE) films or for BaTiO₃ nanoparticles. Such dependences for BaTiO₃ nanoparticles would have a pronounced maxima corresponding to the average Curie temperature of the nanoparticle ensemble (located below 125°C in dependence on the particle average size and size distribution function) and a moderate frequency dispersion in the frequency range 0.1−100 kHz. Instead of these expectations, a transition from a weak to a strong nonlinear temperature dependence of the dielectric permittivity is observed near the freezing temperature (near −50°C) of P (VDF-TrFE). The transition is followed by a diffuse step-like change in the temperature range (0–40)°C, and a subsequent maximum of the dielectric permittivity in the P (VDF-TrFE) films with a lower content (~20–40 vol.%) of BaTiO₃ nanoparticles; or by a quasi-plateau of the dielectric permittivity in the P (VDF-TrFE) films with a higher content (~50–70 vol.%) of BaTiO₃ nanoparticles. The frequency dispersion of the dielectric permittivity is significant in the vicinity of its maxima. The temperature-frequency shift of the permittivity region with a strong temperature dependence is positive. The temperature-frequency shift of the maxima is insignificant (or negative) for the P (VDF-TrFE) films with lower content of BaTiO₃ nanoparticles. Increasing the content of BaTiO₃ nanoparticles leads to a significant increase in the relative dielectric permittivity of the P (VDF-TrFE)-BaTiO₃ films compared to pure P (VDF-TrFE) films (from 8 to 50 at 25°C). At the same time, the voltage response of the studied P (VDF-TrFE) – BaTiO₃ films to the frequency-modulated IR radiation flux has rather photoelectric than pyroelectric nature. A phenomenological model, which considers the screening charges at the interfaces, as well as dipole–dipole cross-interaction effects between the ferroelectric nanoparticles, is proposed to describe the temperature and frequency behavior of the effective dielectric permittivity. The negative capacitance state, which originates due to the interfacial effects, is predicted in the P (VDF-TrFE) films with a high content of BaTiO₃ nanoparticles.