A model for describing current-voltage characteristics of SrTiO/sub 3/ capacitors under low electric fields

It is now widely accepted that the well-fabricated SrTiO/sub 3/ (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 /spl Delta/V and delay-time t/sub 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=jx/spl Delta/V)=/spl Delta/V/sup m//spl Sigma//sub i=1//sup n//spl Sigma//sub j=1/(C/sub i///spl tau//sub i/)exp(-jxt/sub d///spl tau//sub i/), where C/sub i/ and /spl tau//sub i/ respectively denote the capacitance and the relaxation time constant of the i-th relaxation species. The unknown parameters in the equation, C/sub i/ and /spl tau//sub 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/cm/sup 2/ 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.