Thin film dielectrics have broad applications, and the performance degradation due to charge trapping in these thin films is an important and pervasive reliability concern. It has been presumed since the 1960s that current transport in intermediate-thickness (IT) oxides ($10-100 nm) can be described by Frenkel-Poole (FP) conduction (originally developed for $mm-thick films) and algorithms based on the FP theory can be used to extract defect energy levels and charging-limited lifetime. In this paper, we review the published results to show that the presumption of FP-dominated current in IT oxides is incorrect, and therefore, the methods to extract trap-depths to predict lifetime should be revised. We generalize/adapt the bulk FP current conduction model by including additional tunneling-based current injection. Steady state characteristics are obtained by a flux balance between contacts and the IT oxide. An analytical approximation of the generalized FP model yields a steady state leakage current J ! exp(ÀBHE)(1 À CHE À D/E), where B, C, and D are material-specific constants. This reformulation provides a new algorithm for extracting defect levels to predict the corresponding charging limited device lifetime. The validity and robustness of the new algorithm are confirmed by simulations and published experimental data. V
We present a dielectric charging model that combines ab initio calculations of trap levels with a continuum-level transport model and apply it to interpret charging currents in amorphous silicon nitride. Density functional theory calculations on an ensemble of structures predict a distribution of electron trap levels up to 1.8 eV below the conduction band edge and provide insight into the physical trapping mechanisms. Incorporating this information in the continuum model, as opposed to the standard approach of a single adjustable trap level, not only leads to a more accurate description of experimental current transients in metal-insulator-metal capacitors, but also to a more precise and physical determination of associated material properties such as metal-dielectric barrier height.
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