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 (φB). 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 ∼330 K. For many defective dielectrics with large barrier heights (φB ≥ ∼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 φB values may not be correct. We provide a quantitative guide to avoid future misapplications of the SE model.