Quantum-mechanical study of the direct tunneling current in metal-oxide-semiconductor structures

Abstract

A quantum-mechanical model is developed to describe an electron transmission through a metal-oxide-semiconductor (MOS) capacitor with ultrathin dielectric when the inversion regime is realized at the semiconductor/insulator interface. For a particular form of the electrostatic potential in the depletion layer, the Schrödinger equation is solved for metal gate, oxide layer, and semiconductor substrate. An analytical expression for the leakage current is derived, provided that an incident flux flows from an ideal contact attached to the silicon substrate to the metallic gate through the MOS capacitor. The obtained formula for the leakage current reproduces the well-known Wentzel-Kramers-Brillouin approximation for the direct tunneling through a trapezoidal barrier at small gate voltages, and the Fowler-Nordheim quasiclassical expression, which describes an electron tunneling through a triangular barrier at higher voltages. Computation of the leakage current through an ultrathin gate oxide according to the obtained analytical expressions yields good agreement with the experimental data without the use of fitting parameters.