Space charge capacitance of ferroelectric memory cells in the nonlinear regime

Recently ferroelectric thin-film capacitors have been modelled using the sub-surface space charge region. The model is similar to the well known abrupt p-n junction theory or semiconductors. This paper describes the sub-surface space charge using the landau free energy within a polarized medium. The capacitance of the ferroelectric storage cell is described from these first principles. The model predicts that the result of the abrupt p-n junction depletion capacitance (linear medium model) is the limit of the ferroelectric p-n junction model (nonlinear medium) when the polarization approaches zero. The results of the model are applied successfully to 60/40 PZT capacitors where the intrinsic heterogeneity (high election concentration in the near surface region) is always present due to high oxygen vacancy concentration. Both the linear and the nonlinear models are reasonable at high Voltages but only the nonlinear model is accurate at lower voltages. The results are also useful to characterize device parasitics and elucidate the effect of the microstructure on device behavior.