Metal-ferroelectric-metal structures with Schottky contacts. II. Analysis of the experimental current-voltage and capacitance-voltage characteristics of $Pb(Zr,Ti)O3$ thin films

A modified model of metal-semiconductor contacts is applied to analyze the capacitance-voltage and current-voltage characteristics of metal-ferroelectric-metal structures. The ferroelectric polarization is considered as a sheet of surface charge situated at a fixed distance from the interface. The presumable high concentration of structural defects acting as active electric traps is taken into account by introducing a deep acceptorlike level. The model is applied on a set of metal-$Pb(Zr,Ti)O3$-metal samples with different $Zr∕Ti$ ratios, deposited by different methods, and having different thicknesses, electrode materials, and electrode areas. Values around $1018cm−3$ were estimated for the hole concentration from capacitance-voltage measurements. The space-charge density near the electrode, estimated from current-voltage measurements, is in the $1020–1021cm−3$ range. The total thickness of the interface layer ranges from $3to35nm$⁠, depending on the $Zr∕Ti$ ratio, on the shape of the hysteresis loop, and on the electrode material. The simulated $I-V$ characteristics is fitted to the experimental one using the potential barrier and Richardson’s constant as parameters. The potential barrier is determined to be in the $1.09–1.37eV$ range and Richardson’s constant is $520Acm−2K−2$⁠.