Quantum Mechanical Connection of Schottky Emission Process and Its implications on Breakdown Methodology and Conduction Modeling for BEOL Low-k Dielectrics

Abstract

Using a full quantum mechanical calculation, we investigate the fundamental validity of the Schottky emission model for its applications to electron injection into dielectrics from a metal or semiconductor electrode. We cover a wide range of electric fields from10kV/cm to 10MV/cm and a temperature span for a large range of barrier heights. We conclude the Schottky emission model is only applicable for a very small class of dielectrics under 0.1MV/cm and at high temperatures over ~330°K. For many defective dielectrics with a barrier height (ΦB ≥ 1eV) in BEOL/MOL/MIMCAP applications, the corresponding electric fields for the measurable currents far exceed 0.1MV/cm and up to 10MV/cm, the application of the Schottky emission model is unequivocally invalid so that the extracted barrier height values are fundamentally incorrect. Several misconceptions and malpractices as widely occurred in the reliability community have been clarified with a guide to avoid future misapplications.