A model for describing current-voltage characteristics of SrTiO₃ capacitors under low electric fields

It is now widely accepted that the well-fabricated SrTiO₃ (STO) thin-film capacitors with high-work-function metallic electrodes show excellent low leakage characteristics. However, the magnitude of the leakage current in the low electric fields shows strong dependences on the measurement conditions, namely the values of voltage-step ΔV and delay-time t_d in the conventional staircase current-voltage ramps. This anomalous effect is attributed to the dielectric relaxation phenomena of the STO capacitor structures. In this paper, we propose a model which describes the relationship between such measurement conditions and observed current-voltage characteristics. The absorption current due to the dielectric relaxation of the Debye-type relaxation species can be formulated as I(V=jxΔV)=ΔV^mΣ_i=1ⁿ Σ_j=1(C_i/τ_i)exp(-jxt _d/τ_i), where C_i and τ_i respectively denote the capacitance and the relaxation time constant of the i-th relaxation species. The unknown parameters in the equation, C_i and τ_i, can be determined by applying a multiple nonlinear least squares method to the current-time measurements. The model was applied to characterize the sputter-deposited STO capacitors which exhibited apparent leakage currents of less than 10 nA/cm² for the electric field strengths of less than 1 MV/cm. We observed three kinds of relaxation species for such capacitors. The current-voltage curves calculated based on these relaxation species fit very well with the measured values obtained under the various measurement conditions