The Schottky emission effect: A critical examination of a century-old model

Using a quantum mechanical calculation, we investigate the fundamental limitations of the Schottky emission (SE) model for its applications to electron injection into dielectrics from a metal or semiconductor electrode. This work covers a wide range of electric fields from 0.01 to 10 MV/cm and a large temperature span with many barrier height values (Phi(B)). We conclude that the SE model is only applicable for a very small class of dielectrics under 0.1 MV/cm and at high temperatures over similar to 330 K. For many defective dielectrics with large barrier heights (Phi(B) >= similar to 1.5 eV) in back-of-line/middle-of-line/metal-insulator-metal capacitor applications, the corresponding electric fields for the measurable currents far exceed 0.1 MV/cm, and up to 10 MV/cm, the application of the SE model is likely invalid so that the extracted Phi(B) values may not be correct. We provide a quantitative guide to avoid future misapplications of the SE model. Published under an exclusive license by AIP Publishing.

Automated summary

Using quantum mechanical calculations, this study explores the limitations of the Schottky emission model for electron injection into dielectrics. The researchers found that the model is only applicable for a small group of dielectrics under specific electric field and temperature conditions. For defective dielectrics with large barrier heights, the electric fields necessary for measurable currents exceed the range of validity for the Schottky emission model. The study provides a quantitative guide to prevent misapplications of the model.