Characterization of Edge Fringing Effect on the $C$ – $V$ Responses From Depletion to Deep D

The edge fringing effect (EFE) on the capacitance-voltage (C -V) responses from depletion to deep depletion (DD) of p-substrate metal-oxide-semiconductor capacitors with ultrathin oxide (2.1-2.9 nm) and high-κ dielectric was examined. It was found that the EFE plays a significant role on the initiation voltage of DD in the C -V curve. The shape of capacitance in DD has been characterized in detail via a modified quantum-mechanical-based EFE model with the consideration of edge direct tunneling current conduction concept. Excellent agreement between the model and the experimental data for gate oxide has been achieved. To elucidate the enhanced fringing effect at edge, the effective surface field ratio between edge and bulk was adopted to clarify the role of injected carriers with the EFE mechanism. It was found that the extracted ratio increases with the oxide thickness and the initiation voltage of DD accordingly.